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the kantian explanation for ` the unreasonable effectiveness of mathematics in the natural sciences' is that the patterns which we seek out in nature are those patterns with which we are already familiar as innate categories of perception @xcite . when we encounter a new phenomenon , perhaps we first seek to describe this phenomenon in the category of perception most familiar to us . taken one step further , perhaps human choice of research topics is itself influenced by the scientific language of the day . the conventional graphical language in computer science is the language of flowcharts ( _ e.g. _ @xcite ) . a flowchart is a labeled directed graph in which edges represent transitions that can be concatenated . thus , an ordered sequence of edges @xmath0 in which the head of @xmath1 is the tail of @xmath2 for all @xmath3 represents a transition from the tail of @xmath4 to the head of @xmath5 . edges can be prepended or appended to such sequences , and the transition represented by prepending @xmath4 to @xmath6 is guaranteed to coincide with the transition represented by appending @xmath5 to @xmath7 . this property is called _ associativity_. thus , the language of flowcharts natively describes _ sequential _ processes , although this paradigm may be expanded via a _ concurrency symbol_. in previous work we proposed a different diagrammatic formalism called _ tangle machines_. a tangle machine looks visually similar to a coloured tangle diagram in low dimensional topology @xcite . it consists of arcs which we think of as analogous to computer registers and of crossings that we call _ interactions _ which we think of as analogous to logic gates . the interaction below involves three arcs called an _ agent _ , an _ input patient _ , and an _ output patient_. the interaction is labeled by a binary operation @xmath8 , and for labels @xmath9 for the input patient and @xmath10 for the agent , the label of the output patient is @xmath11 . @xmath12{\small $ x$ } \psfrag{y}[c]{\small $ y$ } \psfrag{x}[l]{\small $ x { \triangleright}y$ } \includegraphics[width=0.1\textwidth]{cross.eps}\ ] ] we call operation @xmath8 a _ fusion _ if it satisfies three properties : 1 . @xmath13 for all @xmath9 . thus , fusing information with itself should be the identity operation . an input label can uniquely be recovered from its corresponding output label together with the agent label . thus , fusion should ` not forget ' . 3 . fusing @xmath14 with @xmath15 should equal @xmath16 . thus , fusion should count the redundant appearance of @xmath17 only once towards the final result . the language of tangle machines natively describes networks of fusions ( strengthening the requirement that the fusion ` not forget ' strengthened to @xmath18 being a bijection ) . there is nothing inherently sequential about fusions , so tangle machines and flowcharts are quite different . what is the expressive power of tangle machines ? more prosaically , what tales can a tangle machine tell ? let us adopt an abstract view of a computation as a scheme to apply the information content of a computer program to the information content of input data in order to generate output data . some computations ( in this generalized sense ) are fusions . it turns out that we can describe any turing machine by a tangle machine under this paradigm . if we limit the number of interactions then we can describe any computation in the complexity class @xmath19 @xcite . parenthetically , we do nt know how much more we can describe by tangle machines for example , can tangle machines with bounded interactions describe any computation in complexity class @xmath20 ? what more can be described by tangle machines ? archetypal mathematical examples of fusions are convex combinations and group conjugations , but we suggest that an archetypal real - world example of a fusion operation is fusion of estimates of a random variable . if the random variable follows a bernoulli distribution then estimator fusion and convex combination essentially coincide ( an example of this is in @xcite ) . we consider fusion of normally distributed estimates . the kalman filter is a linear optimal measure to fuse gaussian estimates , but it requires knowledge of how the estimate errors depend on one another . this information is not contained in the estimates themselves and may sometimes be entirely unknown . _ covariance intersection _ is a method to fuse gaussian estimates whose error cross - correlations are unknown . section [ s : ci ] introduces tangle machines as a diagrammatic language for information flow in networks in which information is fused by covariance intersection . it contains a geometric interpretation of covariance intersection as a choice of a point on a geodesic on a _ statistical manifold _ whose points parameterize normal distributions . section [ s : ldt ] explains the connection of tangle machines to low dimensional topology . section [ ss : knots ] recalls a diagrammatic algebra from low dimensional topology . section [ ss : generalize ] generalizes and discusses quandles , after which section [ ss : info ] defined tangle machines and shows how they may describe information fusion networks . the above sections represent an expository account of previous published work of the authors . as discussed in @xcite , tangle machines ( with colours suppressed ) topologically arise as diagrams of embedded networks of intervals and spheres in standard euclidean @xmath21space . section [ s : quantum ] takes tangle machines into the realm of quantum information , presenting several adiabatic quantum computations ( aqc s ) with different performance features . section [ ss : timeentanglement ] presents a computation in which a product state evolves into an entangles state , and section [ ss:2sat ] presents a boolean @xmath22sat problem over four qubits . a further example may be found in ( * ? ? ? * section 5 ) . section [ s : utility ] discusses potential utility of the tangle machine description . inherited from low dimensional topology , tangle machines have topological invariants that are characteristic quantities giving high - level information about what is happening in the machine @xcite . in particular , there are meaningful notions of _ capacity _ and of _ complexity _ for tangle machines . in addition , tangle machines provide a flexible description , and this flexibility may perhaps be useful for fault tolerance @xcite . section [ s : learn ] concludes by discussing the problem of adapting existing causality - detection algorithms to detect tangle machines . we illustrate with an example in which we detect a single crossing in real - world google search data . [ r]covariance intersection [ r]coloured tangle diagrams [ r ] ' '' '' [ c]tangle machines [ l]tms for qi [ l]quantum info fusion a coloured tangle representing this paper . at each crossing , the output topic is an application of the input topic to the agent ( overcrossing ) topic , perhaps in a different sense for each crossing . this figure suggests how a coloured tangle can tell a tale and has no rigourous mathematical meaning.,title="fig:",scaledwidth=60.0% ] the father of the use of tangle diagrams as a diagrammatic language for computation is louis kauffman , who represented automata , nonstandard set theory , and lambda calculus with tangle diagrams @xcite . buliga has suggested to represent computations using a different calculus of coloured tangles @xcite . in another direction , a different diagrammatic calculus , originating in higher category theory , has been used in the theory of quantum information see _ e.g. _ @xcite . in all of these approaches an element in a topologically inspired diagrammatic algebra represents a computation and equivalent diagrams represent bisimilar computations . tangle machines are distinguished by the role of colours , by locality of orientations , and by binding together of operations in ` interactions ' , as discussed in @xcite . was partially supported by the helmsley charitable trust through the agricultural , biological and cognitive robotics initiative of ben - gurion university of the negev .

tangle machines are a topologically inspired diagrammatic formalism to describe information flow in networks . this paper begins with an expository account of tangle machines motivated by the problem of describing ` covariance intersection ' fusion of gaussian estimators in networks . it then gives two examples in which tangle machines tell stories of adiabatic quantum computations , and discusses learning tangle machines from data .

tangle machines are a topologically inspired diagrammatic formalism to describe information flow in networks . this paper begins with an expository account of tangle machines motivated by the problem of describing ` covariance intersection ' fusion of gaussian estimators in networks . it then gives two examples in which tangle machines tell stories of adiabatic quantum computations , and discusses learning tangle machines from data .

1303.0993

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einstein proposed the idea of teleparallelism , or _ fernparallelismus _ ( aka _ absolute parallelism _ , _ distant parallelism _ ) , in order to unify gravity and electromagnetism @xcite . unlike general relativity , spacetime in teleparallelism is equipped with a connection with zero curvature , but non - vanishing torsion . since the spacetime is _ flat _ , the parallel transport of a vector is independent of path , and hence the name _ _ tele__parallel , meaning `` parallel at a distance '' . einstein s quest for unification via teleparallel theory can be found in the interesting account of @xcite . despite einstein s failure to formulate a unified theory , teleparallelism was later revived and studied as a pure theory of gravity . the main motivations were ( 1 ) that the teleparallel formulation was considered to have advantages with regard to the identification of the energy - momentum of gravitating systems , and ( 2 ) teleparallel theory can be regarded as a gauge theory of local translations ( see , e.g. , @xcite ) . in fact einstein s general theory of relativity ( gr ) can be rewritten in teleparallel language ( see , e.g. , @xcite ) . the result is a theory equivalent to gr known variously as the _ teleparallel equivalent of general relativity _ ( tegr ) or gr@xmath0 . recently tegr has been generalized to @xmath1 theory , a theory of modified gravity formed in the same spirit as generalizing general relativity to @xmath2 gravity @xcite . it seems however that observational data puts rather tight constraints on @xmath1 gravity , effectively reducing the theory ( at least for some choices of @xmath1 ) back to tegr ( however , see also @xcite and @xcite ) . this includes constraints from considering a varying fine structure constant @xcite , the formation of large - scale structures @xcite and a varying gravitational constant @xcite , as well as solar system constraints @xcite . this could hint at problems with @xmath1 gravity at the theoretical level . in this paper we will briefly review tegr and more general theories of teleparallel gravity , including @xmath1 gravity , in section [ review ] . in section [ degree ] , we discuss the degrees of freedom for @xmath1 theory . we know that there are extra degrees of freedom in the theory beyond those of gr ; that the number of extra degrees of freedom is generically 3 was clearly revealed by the dirac constraint analysis carried out by li et al . despite this , in a careful linear perturbative analysis up to second order on flat friendmann - lematre - robertson - walker ( flrw ) background , no extra mode appears @xcite . in the case of minkowski background , this had already been pointed out in @xcite . disappearance of extra degrees of freedom is known to happen in some gravity theories ( e.g. , in massive gravity , see @xcite ) ; this can be caused by the accidental disappearance of kinetic terms at the linear level . if so , as we shall argue , it is likely to be a signal of superluminal propagation . we will also discuss the related danger of the _ nonlinear constraint effect _ , which plagued some other theories of gravity in the past . our conclusion is that @xmath1 theory is very _ likely _ to give rise to unwanted problems due to the effects of nonlinear constraints , in addition to propagation outside of the null cone . as a consequence , the number and type of degrees of freedom could vary as a physical system evolves . this is further explored via the method of characteristics in section [ method ] . the method of characteristics is properly introduced in section [ method ] , where we also provide an illuminating example in an application to the nonlinear proca field . the same example is given a hamiltonian analysis that clearly shows the close connection of superluminal propagating modes and nonlinear constraints . although the characteristic equations allow one to obtain superluminal propagating degrees of freedom , one must be careful to distinguish between _ physical _ degrees of freedom and _ gauge _ degrees of freedom , as the example of the maxwell field illustrates . in section [ f(t ) ] , we investigate the dynamical equations in @xmath1 theory and derive a system of partial differential equations that describe the characteristics of the theory . this calculation reveals nonlinear features that are very prone to allow superluminal propagation outside of the metric null cone .. ] furthermore , we also show that the constant - time hypersurface in flrw spacetime , and as a special case minkowski spacetime , can be a cauchy _ horizon _ , which means that even the infinitesimal future time evolution from it is not unique . we conclude with some discussion in section [ discuss ] .

teleparallel theories of gravity have a long history . they include a special case referred to as the _ teleparallel equivalent of general relativity _ ( tegr , aka gr ) . recently this theory has been generalized to gravity . this might hint at hitherto undiscovered problems at the theoretical level . in this work , we also point out problems with the cauchy development of a constant time hypersurface in flrw spacetime in gravity . the time evolution from a flrw ( and as a special case , minkowski spacetime ) initial condition is not unique .

teleparallel theories of gravity have a long history . they include a special case referred to as the _ teleparallel equivalent of general relativity _ ( tegr , aka gr ) . recently this theory has been generalized to gravity . tight constraints from observations suggest that gravity is not as robust as initially hoped . this might hint at hitherto undiscovered problems at the theoretical level . in this work , we point out that a generic theory can be expected to have certain problems including superluminal propagating modes , the presence of which can be revealed by using the characteristic equations that govern the dynamics in gravity and/or the hamiltonian structure of the theory via dirac constraint analysis . we use several examples from simpler gauge field theories to explain how such superluminal modes could arise . we also point out problems with the cauchy development of a constant time hypersurface in flrw spacetime in gravity . the time evolution from a flrw ( and as a special case , minkowski spacetime ) initial condition is not unique .

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a viable theory of gravity should satisfy certain theoretical criteria , including the lack of tachyonic modes , or modes that carry negative kinetic energy ( i.e. , ghosts ) .. ] the theory should also support a well - posed initial value problem , that is , satisfy the cauchy - kowalevski theorem @xcite . moreover any propagation mode in the theory should also be described by hyperbolic quasi - linear partial differential equations with well - behaved characteristics , i.e. , the characteristic surfaces should be non - spacelike . one should also consider a theory with a `` good '' minkowski limit as preferable to a theory that does not have such behavior . the method for studying characteristics is well - known ; see for example the detailed classical work of courant and hilbert @xcite , or chapter 8 of the more recent text of @xcite . a discussion of the method of characteristics in the case of general relativity can be found in lecture 14 of @xcite . for more rigorous treatment see @xcite , as well as in @xcite . see also @xcite for some useful discussions in the context of external fields in gauge theories . here we only give a brief summary . recall that if @xmath58 is a linear differential operator of order @xmath59 , then we can consider @xmath58 as a polynomial in the derivative @xmath60 . in multi - index notation we can write this as @xmath61 we may ask in what directions it is really of order @xmath59 . for an ode @xmath62 for example , it is obvious that @xmath63 is the condition required for the equation to be of order @xmath59 everywhere . for pdes with multiple variables , we need to be careful . consider for example the laplacian @xmath64 in @xmath65 . this is clearly of order 2 in both the @xmath66- and @xmath67-direction , however for an operator which is mixed , e.g. , @xmath68 , it is _ not _ of order 2 in either the @xmath66- or @xmath67-direction . nevertheless , it _ is _ a second - order operator , which can be revealed by introducing new variables , @xmath69 , which renders @xmath70 . that is , this operator is of order 2 in the @xmath71 and @xmath72 directions . in general then , given any operator @xmath58 at @xmath66 , and a direction @xmath73 , we can make an orthogonal change of variable so that @xmath73 points along one of the new coordinate axes , say the @xmath74-axis . now , if the coefficient of the partial derivative @xmath75 ( in the new coordinate system ) is nonzero at @xmath66 , then we can say that @xmath58 is of order @xmath59 at @xmath66 in the direction @xmath73 . we refer to such situation as _ noncharacteristic_. that is , _ characteristic _ refers to the case in which the coefficient of @xmath75 vanishes at @xmath66 . the _ total symbol _ or _ top - order symbol _ of @xmath58 is simply a polynomial obtained by replacing the derivative @xmath60 with a variable , say @xmath76 . the _ principal symbol _ , denoted @xmath77 , is the highest degree component of the total symbol . that is , @xmath78 the principal symbol almost completely determines the qualitative behavior of the solutions of the system . furthermore , it is well known that for hyperbolic ( as well as parabolic ) partial differential equations , the zeros of the principal symbol describe the characteristics of the system . that is to say , _ the characteristic directions are exactly those for which the principal symbol vanishes_. indeed the `` standard procedure '' is to begin with the equation of motion or the field equation , keep only the highest derivative terms , and then replace the said derivatives @xmath79 with components of the normal vector to the characteristics @xmath80 and set the equation to zero . this is called the _ characteristic equation_. we can study how the characteristics propagate by looking for what sorts of vectors are allowed as solutions to the characteristic equation . note that for a characteristic equation that is a _ matrix _ equation , called the _ characteristic matrix _ , it suffices to consider the vanishing of the determinant of the characteristic equation ( known as the _ characteristic determinant _ ) instead of the vanishing of the equation itself ( the latter is of course a stronger statement ) . in this paper , we are interested in one ( or a few ) special characteristic direction that gives the signal of a superluminal mode . by analyzing the characteristic determinant , we can examine all directions at once . the _ characteristic surface _ which is orthogonal to the characteristic direction coincides with the edge of cauchy development , i.e. , the cauchy horizon . this is because the higher order derivative term with respect to the characteristic direction disappears . the disappearance of the higher order derivative term causes the evolution to be singular . thus , the cauchy development of the characteristic surface is only the characteristic surface itself and the evolution from it is meaningless even if it is spacelike . note that for application in theories of gravity , we would like our characteristic directions to be null or spacelike , as a timelike characteristic direction is the signal of superluminal propagation ( and could violate causality , although this is not necessarily so even in theories with local lorentz invariance @xcite ) . correspondingly , there should _ not _ be any non - trivial solution that corresponds to any _ timelike _ vector . the characteristic method is best illustrated via an example or two . consider the lagrangian of the proca field with a nonlinear term @xcite : @xmath81 where @xmath82 and @xmath83 the signature is @xmath4 . the field equations are @xmath84 upon taking the divergence of this equation , because the first term vanishes by the antisymmetry of @xmath85 , we obtain an implicit constraint satisfied by the system : @xmath86 for @xmath87 , this gives @xmath88 , which upon substituting back into the field equation ( [ nlprocaeq ] ) gives @xmath89 which is the klein - gordon equation . the characteristic equation for this case is just @xmath90 , i.e. , the characteristic is null . to find the characteristics in the general @xmath91 case , replace the highest derivative terms @xmath92 by @xmath93 . here @xmath94 means it is not the value of the vector @xmath95 , but represents the change of the vector in a certain direction . we then get the relations @xmath96 a linear combination of these gives @xmath97k\cdot \tilde a=0.\label{anomolous}\ ] ] now from eq . ( [ procafechar ] ) one can see that modes with @xmath98 propagate with null characteristics , but from eq . ( [ anomolous ] ) one can see that modes with @xmath99 generally have non - null characteristics . the normal to the characteristic surface could be timelike , indicating a superluminal characteristic . in that case there is a lorentz frame in which @xmath100 . in such a frame the condition is @xmath101 we want to emphasize that this tachyonic mode of the nonlinear proca field can be detected using the hamiltonian formulation , as we now explain . from the lagrangian , the canonical momenta are @xmath102 that is , explicitly , @xmath103 and @xmath104 ; the latter is a _ primary constraint_. the hamiltonian density , constructed according to the dirac - bergmann constraint procedure @xcite , is @xcite & ^i_i + f^ijf_ij - a_0 _ c ^c + m^2(a^ia_i - a_0 ^ 2 ) + & + ( a^ia_i - a_0 ^ 2)^2+u^0 , where the primary constraint @xmath105 '' denotes dirac s weak equality , i.e. , it only holds on the constraint surface within the phase space . ] has been included with an unknown lagrange multiplier @xmath106 . from the hamiltonian evolution equation @xmath107one finds the meaning of the multiplier , it is the missing `` velocity '' . preserving the primary constraint leads to the secondary constraint : @xmath108 the poisson bracket of the two constraints is @xmath109\delta^3(x - y).\ ] ] generically this is non - vanishing , so they make up a 2nd class pair . however , there is an important exception when the rhs vanishes , _ this is exactly the same as the anomalous characteristic condition _ ( [ procachar ] ) . the dynamical consequence shows up when we require preservation of the @xmath110 constraint , which is the relation that determines the `` unknown multiplier '' @xmath106 : @xmath111 + \mathcal{g},\ ] ] where @xmath112 denotes a collection of field dependent terms which , generically , are non - vanishing . consequently , the field `` velocity '' @xmath113 , given by the lagrange multiplier , @xmath106 , becomes unbounded at any point(s ) where @xmath114 approaches 0 . that is , @xmath115 this is an indication that , with respect to this constant time spacelike hypersurface , there is instantaneous propagation of the @xmath116 mode . the nonlinear constraint has led to a field - dependent constraint poisson bracket value , a signal for the occurrence of superluminal propagation , in complete agreement with the previous analysis obtained from the characteristic equation . one issue that we have to be careful with is the possible presence of gauge degrees of freedom in a theory ( which was _ not _ present in the previous nonlinear proca field example ) . in order to appreciate the issue , first we shall look at the simple example of scalar fields . we consider the lagrangian for the single scalar field defined by @xmath117 we know that the scalar field @xmath118 propagates in the null direction . in terms of characteristics , we can understand it as follows . the equation of motion is @xmath119 so the characteristic equation for @xmath118 is @xmath120 , which means the characteristic is null . let us introduce another scalar field @xmath121 which does not appear in the lagrangian . trivially , the lagrangian does not change under the transformation @xmath122 . this property is a certain kind of gauge transformation . the equation of motion which comes from the variation of the lagrangian ( [ lags ] ) with respect to @xmath121 is trivial , i.e. , @xmath123 . thus the characteristic equation for @xmath118 and @xmath121 becomes @xmath124 , which is trivially satisfied for any @xmath125 . the triviality comes from the gauge mode @xmath121 . since @xmath121 does not appear in the lagrangian , we should not include it in the discussion of characteristics . the situation for any gauge field theory is similar . for simplicity , we consider the maxwell theory of the electromagnetic field ; the lagrangian is @xmath126 where @xmath127 . the equation of motion is obtained to be @xmath128 the principal symbol yields the characteristic equation @xmath129 where we want to seek some nontrivial @xmath130 . if @xmath131 is null then @xmath132 gives a propagating mode on the null cone . however , if @xmath131 is not null , then the characteristic equation can be satisfied by _ any _ @xmath133 for arbitrary constant @xmath134 . in particular @xmath131 can be chosen to be timelike , which means that the characteristic direction will become timelike . this superluminal mode however , as we shall see , actually corresponds to gauge mode and so it is not physical . alternatively we can consider the determinant method . if we write down the characteristic equation without removing the gauge degree of freedom , we will obtain characteristic matrix that satisfies @xmath135 = 0 . \label{eommax}\end{aligned}\ ] ] the left - hand side of this equation is @xmath136 for any @xmath137 , and so this equation becomes trivial . the origin of the triviality is the gauge degree of freedom . if we operate @xmath138 to the left - hand of eq . ( [ eommax2 ] ) , it becomes algebraically @xmath136 . therefore , eq . ( [ eommax2 ] ) has the information of only three independent equations . we know the maxwell field has @xmath139-gauge , i.e. , the lagrangian is invariant under the @xmath139-gauge transformation @xmath140 . since the gauge degree of freedom @xmath141 does not appear in the lagrangian , the variation of the lagrangian with respect to the gauge degree of freedom @xmath141 must be trivial , which is the origin of the above trivial equation . according to the above simple example of scalar fields , we should eliminate the contribution from gauge degrees of freedom in the discussion of characteristics . subtracting the contribution from the gauge degree of freedom , i.e. , considering the @xmath142 matrix whose basis can be anything independentof @xmath137 , we can obtain the exact characteristic equation , which is satisfied only when @xmath125 is null . a more rigorous treatment of the removal of gauge degrees of freedom and the characteristics of maxwell equations can be found in @xcite .

tight constraints from observations suggest that gravity is not as robust as initially hoped . we point out that a generic theory can be expected to have certain problems including superluminal propagating modes , the presence of which can be revealed by using the characteristic equations that govern the dynamics in gravity and/or the hamiltonian structure of the theory via dirac constraint analysis . we use several examples from simpler gauge field theories to explain how such superluminal modes could arise .

teleparallel theories of gravity have a long history . they include a special case referred to as the _ teleparallel equivalent of general relativity _ ( tegr , aka gr ) . recently this theory has been generalized to gravity . tight constraints from observations suggest that gravity is not as robust as initially hoped . this might hint at hitherto undiscovered problems at the theoretical level . in this work , we point out that a generic theory can be expected to have certain problems including superluminal propagating modes , the presence of which can be revealed by using the characteristic equations that govern the dynamics in gravity and/or the hamiltonian structure of the theory via dirac constraint analysis . we use several examples from simpler gauge field theories to explain how such superluminal modes could arise . we also point out problems with the cauchy development of a constant time hypersurface in flrw spacetime in gravity . the time evolution from a flrw ( and as a special case , minkowski spacetime ) initial condition is not unique .

1212.4067

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the gerda experiment ( germanium detector array @xcite ) is a search for the neutrinoless double beta ( @xmath1 ) decay of @xmath0ge . the observation of such a decay would prove that lepton number is not conserved , and that the neutrino has a majorana component @xcite . a discovery of @xmath1 decay would have significant implications on particle physics and other fields , including cosmology @xcite . the importance of the topic has stimulated the development of several experimental approaches to the search for @xmath1 decay on a number of isotopes which undergo double beta decay . for recent reviews on the state of knowledge concerning double beta decay and on running or planned experiments , see refs . @xcite . the experimental signature for @xmath1 decay is a line in the summed electron energy spectrum appearing at the @xmath2-value for the reaction , @xmath3 . the experimental result is a measurement of , or a limit on , the half life , @xmath4 , for the process . within the three neutrino model and assuming the existence of a significant majorana component a positive observation of @xmath1 decay would possibly give access to the neutrino mass hierarchy as well as information on the absolute values of the neutrino masses . the latter is only possible with knowledge of the nuclear matrix elements , @xmath5 , as discussed in ref . the statements on the mass also require an understanding of whether the @xmath1 process is solely due to the majorana nature of the neutrino , or whether additional new physics processes beyond the standard model contribute . a recent review of the particle physics implications of a discovery of @xmath1 decay was given in ref . @xcite . nuclides that are potentially @xmath1 emitters will decay via the standard model allowed @xmath6 decay . both reactions are second order weak interactions , and therefore have extremely long half lives . values have been directly measured for @xmath6 decay in about ten cases and these are in the range 10@xmath710@xmath8 yr @xcite . the half lives for @xmath1 decay , assuming the process exists , are expected to be substantially longer . consequently , @xmath1 decay experiments must be sensitive to just a few events per year for a source with a mass of tens to hundreds of kilograms . backgrounds must typically be reduced to the level of one event per year in the region of interest ( roi ) , an energy interval of the order of the energy resolution around @xmath3 . experiments looking for @xmath1 decay of @xmath0ge operate germanium diodes normally made from enriched material , i.e. the number of @xmath0ge nuclei , the isotopic fraction @xmath9 , is enlarged from 7.8 % to 86 % or higher . in these type of experiments , the source is equal to the detector which yields high detection efficiency . additional advantages of this technique are the superior energy resolution of 0.2 % at @xmath3=2039 kev compared to other searches with different isotopes and the high radiopurity of the crystal growing procedure . disadvantages are the relatively low @xmath3 value since backgrounds typically fall with energy and the relative difficulty to scale to larger mass compared to e.g. experiments using liquids and gases . there is a considerable history to the use of @xmath0ge for the search for @xmath1 decay . after initial experiments @xcite , the heidelberg - moscow ( hdm ) collaboration @xcite and igex @xcite were the driving forces in this field setting the most stringent limits . in 2004 a subgroup of the hdm collaboration @xcite claimed a 4@xmath10 significance for the observation of @xmath1 decay with a best value of @xmath4=1.19@xmath11 yr ; the quoted 3@xmath10 range is @xmath12 yr . to scrutinize this result , and to push the sensitivity to much higher levels , two new @xmath0ge experiments have been initiated : majorana @xcite and gerda @xcite . the latter has been built in the infn laboratori nazionali del gran sasso ( lngs ) at a depth of 3500mw.e . ( water equivalent ) . whereas majorana further refines the background reduction techniques in the traditional approach of operating germanium detectors in vacuum , gerda submerses bare high - purity germanium detectors enriched in @xmath0ge into liquid argon ( lar ) following a suggestion by ref . @xcite ; lar serves simultaneously as a shield against external radioactivity and as cooling medium . phase i of the experiment is currently taking data and will continue until a sensitivity is reached which corresponds to an exposure of 15 kg@xmath13yr with a background index ( bi ) of 10@xmath14 cts/(kev@xmath13kg@xmath13yr ) @xcite ) . this will be sufficient to make a strong statement on the existence of @xmath1 decay in @xmath0ge for the best value given in ref . @xcite . phase ii of gerda is planned to acquire an exposure of 100 kg@xmath13yr at a bi of 10@xmath15 cts/(kev@xmath13kg@xmath13yr ) . for pure majorana exchange and the case that no signal is seen , this will constrain the effective neutrino mass @xmath16 to less than about @xmath17 mev with the precise value depending on the choice of matrix elements @xcite . the gerda experiment is described in detail in the following sections . an overview of experimental constraints and the design is presented first . this is followed by a description of the ge detectors . then , the experimental setup , electronic readout , data acquisition ( daq ) and data processing are described . as gerda phase i has been fully commissioned and has started data production , the main characteristics of its performance are given in the final section .

the collaboration is performing a search for neutrinoless double beta decay ofge with the eponymous detector . the experiment has been installed and commissioned at the laboratori nazionali del gran sasso and has started operation in november 2011 . the design , construction and first operational results are described , along with detailed information from the r&d phase .

the collaboration is performing a search for neutrinoless double beta decay ofge with the eponymous detector . the experiment has been installed and commissioned at the laboratori nazionali del gran sasso and has started operation in november 2011 . the design , construction and first operational results are described , along with detailed information from the r&d phase . example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore

cs0112012

i

traces are used to model the occurrence of events in concurrent systems @xcite . roughly speaking , a letter corresponds to an event and two letters commute when the corresponding events can occur simultaneously . in this context , the two basic performance measures associated with a trace @xmath2 are its _ length _ @xmath1 ( the ` sequential ' execution time ) and its _ height _ @xmath0 ( the ` parallel ' execution time ) . the ratio @xmath4 captures in some sense the _ amount of parallelism _ ( the _ speedup _ in @xcite ) . let @xmath5 be a trace monoid . define the generating series @xmath6 it is well known that @xmath7 is a rational series @xcite . we prove that @xmath8 and @xmath9 are also rational and we provide finite representations for the series . exploiting the symmetries of the trace monoid enables to obtain representations of reduced dimensions . we use the rationality to obtain precise information on the asymptotics of the number of traces of a given height or length . then , given a trace monoid and a measure on the traces , we study the _ average parallelism _ in the trace monoid . one notion of average parallelism is obtained by considering the measure over traces induced by the uniform distribution over words of the same length in the free monoid . in other terms , the probability of a trace is proportional to the number of its representatives in the free monoid . this quantity was introduced in @xcite and later studied in @xcite . here we define alternative notions of average parallelism by considering successively the uniform distribution over traces of the same length , the uniform distribution over traces of the same height , and the uniform distribution over cartier - foata normal forms . we prove in particular that there exists @xmath10 and @xmath11 in @xmath12 such that @xmath13 furthermore , the numbers @xmath10 and @xmath11 are algebraic . explicit formulas involving the series @xmath7 and @xmath9 are given for @xmath10 and @xmath11 . the present paper is an extended version with proofs of @xcite .

we use the rationality to obtain precise information on the asymptotics of the number of traces of a given height or length . then , we study the average height of a trace for various probability distributions on traces . for the uniform probability distribution on traces of the same length ( resp . of the same height ) , the asymptotic average height ( resp . length ) exists and is an algebraic number . to illustrate our results and methods keywords : * automata and formal languages , trace monoids , cartier - foata normal form , height function , generating series , speedup , performance evaluation .

the _ height _ of a trace is the height of the corresponding heap of pieces in viennot s representation , or equivalently the number of factors in its cartier - foata decomposition . let and stand respectively for the height and the length of a trace . we prove that the bivariate commutative series is rational , and we give a finite representation of it . we use the rationality to obtain precise information on the asymptotics of the number of traces of a given height or length . then , we study the average height of a trace for various probability distributions on traces . for the uniform probability distribution on traces of the same length ( resp . of the same height ) , the asymptotic average height ( resp . length ) exists and is an algebraic number . to illustrate our results and methods , we consider a couple of examples : the free commutative monoid and the trace monoid whose independence graph is the ladder graph . * keywords : * automata and formal languages , trace monoids , cartier - foata normal form , height function , generating series , speedup , performance evaluation .

hep-ex0408114

r

the muon fluxes , @xmath78 , conventionally multiplied by the third power of the momentum , and the charge ratios , @xmath79 , are listed for each zenith angle bin in tables [ tab : flux10]@xmath4[tab : flux03 ] with their statistical and systematic uncertainties . the statistical correlation coefficients , @xmath80 , between neighboring momentum bins , as derived from equation ( [ eq : vm ] ) , are also given . due to the limited detector resolution these correlations are inevitable . however , the momentum binning is chosen such that only neighboring bins have a significant correlation . the average momenta , @xmath81 , within a momentum range @xmath82 $ ] are calculated @xcite by fitting the phenomenological muon flux function from reference @xcite to our data and solving @xmath83 it should be noted that the fluxes are neither corrected for the altitude of l3+c nor for the atmospheric profile ( bottom ) to 58@xmath84 ( top ) . the inner bars denote the statistical uncertainty , the full bars show the total uncertainty . for better visibility , an offset of 0.05 @xmath2@xmath11s@xmath66sr@xmath66 was added consecutively and lines are shown to guide the eye . ] to avoid additional theoretical uncertainties . instead , we quote the average atmospheric mass overburden @xmath10 above l3+c , which was continuously measured with balloon flights from close to the experiment to altitudes of over 30 km @xcite . the parameterization of reference @xcite is used to describe the mass profile @xmath10 in g@xmath11 as a function of the altitude @xmath85 in km above sea level : @xmath86 a fit to the live - time weighted balloon data yields @xmath87 , @xmath88 , @xmath89 , @xmath90 and @xmath91 . the measured muon fluxes at the l3+c altitude are shown in figure [ fig : spectrum ] for each zenith angle bin . as no previous continuous zenith angle measurements exist in the large energy range examined here , only the vertical flux can be compared to other experiments , as shown in figure [ fig : vertflux ] . only measurements providing an absolute normalization @xcite are taken into account . the data are extrapolated to sea level using the muon flux predictions of the ` target ` @xcite program . the comparison to low energy experiments @xcite gives a good overall agreement with this analysis above about 40 . at lower momenta , a systematic slope difference seems to be present , which corresponds to about three standard deviations of the systematic molasse uncertainty estimated above . only three previous experiments measured a normalized spectrum at high energies . the shape of the kiel measurements @xcite agree with this result over the full momentum range , but a lower flux normalization is determined by l3+c . + the data obtained with the mars apparatus @xcite significantly disagree with this result , both in shape and normalization . + above momenta of 50 , the recent muon flux measurement from bess - tev @xcite is in very good agreement with this result . the measured charge ratios at the l3+c altitude are shown in figure [ fig : crat ] for each zenith angle bin up to momenta of 500 . in the considered momentum range , the charge ratio is independent of the momentum within the experimental uncertainties . the mean value in the vertical direction is found to be 1.285 @xmath3 0.003 ( stat . ) @xmath3 0.019 ( sys . ) with a @xmath929.5/11 . this is in good agreement with the average of all previous measurements , 1.270 @xmath3 0.003 ( stat . ) @xmath3 0.015 ( sys . ) it is worth noting , that the precision of the data of a single l3+c zenith angle bin is comparable to the combined uncertainty of all data collected in the past . ( bottom ) to 58@xmath84 ( top ) . the inner bars denote the statistical uncertainty , the full bars show the total uncertainty . for better visibility , an offset of 0.5 was added consecutively and lines are shown to guide the eye . ]

the ratio of positive to negative muons is studied between 20 and 500 , and the average vertical muon charge ratio is found to be 1.285 0.003 ( stat . ) 0.019 ( syst . ) . _ the l3+c group dedicates this publication to the late bianca monteleoni . _

the absolute muon flux between 20 and 3000 is measured with the l3 magnetic muon spectrometer for zenith angles ranging from to . due to the large exposure of about 150 msrd , and the excellent momentum resolution of the l3 muon chambers , a precision of 2.3% at 150 in the vertical direction is achieved . the ratio of positive to negative muons is studied between 20 and 500 , and the average vertical muon charge ratio is found to be 1.285 0.003 ( stat . ) 0.019 ( syst . ) . _ the l3+c group dedicates this publication to the late bianca monteleoni . _

cond-mat9702036

i

the interest of the last decade in dynamical and rheological properties of complex fluids has seen the introduction of several new numerical methods for carrying out computer simulations on hydrodynamic time scales , the simulation of which using molecular dynamics often results in intensive computational demands . these new techniques include : ( i ) lattice gas cellular automata ( lgca ) ; ( ii ) lattice boltzmann equation ( lbe ) and ( iii ) dissipative particle dynamics ( dpd ) . the last method was introduced by hoogerbrugge and koelman , and was modified by espaol and warren to ensure a proper thermal equilibrium state . the primary goal of this paper is a theoretical analysis and explicit calculation of transport and thermodynamic properties in terms of model parameters . this is highly relevant in view of the current interest in applications of dpd to systems such as flows past complex objects , concentrated colloidal suspensions , dilute polymer solutions and phase separation . the dpd algorithm models a fluid of @xmath0 interacting particles out of equilibrium and conserves mass and momentum . position and velocity variables are _ continuous _ , as in molecular dynamics ( md ) , but time is updated in _ steps @xmath2 , as in lgca and lbe . the algorithm is a mixture of molecular dynamics , brownian and stokesian dynamics and lgca s , with a _ collision _ and a _ propagation _ step . in the collision step each particle interacts with all the particles inside an action sphere of radius @xmath3 through _ conservative _ forces @xmath4 , _ dissipative _ forces @xmath5 , which are proportional to both the stepsize @xmath2 and a friction constant @xmath6 , and _ random _ forces @xmath7 , which supply the energy lost by the damping . here @xmath8 label the particles . in numerical simulations , this is implemented by simultaneously updating the velocities from their precollision value @xmath9 to their postcollision value @xmath10 according to the instantaneous forces exerted by all particles inside the action sphere . in the subsequent _ propagation _ step of fixed length @xmath2 all particles move freely to their new positions @xmath11 . usual forms of the conservative force mean that the particles may be considered as completely interpenetrable . these softer interactions have the computational advantage of allowing particle motion on the order of a mean free path @xmath12 during each time step of fixed length @xmath2 . this represents a substantial advantage over event driven md algorithms for hard sphere fluids , where the length @xmath2 of the free propagation interval is on average much shorter , especially at fluid densities . by ignoring some of the microscopic details of the interactions , which are presumably irrelevant for fluid dynamics , dpd has the advantages of lgcas , but avoids the disadvantages of lacking galilean invariance and of introducing spurious conservation laws . in fact , the `` point particles '' should not be considered as molecules in a fluid , but rather as clusters of particles that interact dissipatively . the introduction of noise and dissipation represents a coarse - grained mesoscopic level of description and hydrodynamic behaviour is expected at much smaller particle numbers than in conventional md . if @xmath13 denotes the characteristic kinetic timescale in dpd , with @xmath14 the number density , @xmath15 the number of dimensions and @xmath6 the friction constant , then @xmath16 is considered to be large compared to any molecular time scale . in this coarse - grained description the dominant interactions are the dissipative and random forces , whereas the conservative forces can be interpreted as weak forces of relatively long range and may be taken into account as a vlasov mean field term in the kinetic equations . in addition , they can have the spurious effect of tending to force the dpd particles into `` colloidal crystal '' configurations , unless friction and noise are sufficiently large to prevent cooling into a lattice configuration . in the second half of the paper , where we derive a kinetic equation for the single particle distribution function , the conservative force will be neglected . this corresponds to the strong damping limit ( @xmath6 large ) . the random forces act effectively as repulsive forces to prevent collapse of dpd particles . a substantial contribution towards the understanding of the dpd fluid was given by espaol and warren , who derived a fokker - planck equation for the @xmath0-particle distribution function in the limit of continuous time ( @xmath17 ) . these authors also modified the original algorithm by imposing the detailed balance conditions , which guarantee the existence of the proper thermal gibbs equilibrium , described by @xmath18 $ ] where @xmath1 is the hamiltonian of the corresponding conservative system and @xmath19 is the global equilibrium temperature . these results are briefly reviewed in section [ section2 ] to establish the notation . concerning the macroscopic evolution equations , espaol formally established the linearized navier - stokes equations and derived green - kubo formulae for the dpd transport coefficients using a mori - zwanzig projection operator technique . however , to date no quantitative evaluation of these formulae for dpd seems to exist . hence , little is known explicitly about the approach to equilibrium , the validity of standard hydrodynamics ( system size dependence , effects of generalised hydrodynamics ) or about transport coefficients . for the transport coefficients , hoogerbrugge and koelman have estimated the kinematic viscosity @xmath20 , where @xmath21 is the shear viscosity and @xmath22 is the mass density , as @xmath23 with @xmath24 . this result has recently been extended in to include the bulk viscosity by applying the `` continuum approximation '' to the discrete equations of motion for the dpd particles , following suggestions of hoogerbrugge and koelman . in section [ section3 ] we show how the free energy of the dpd fluid _ monotonically _ approaches its equilibrium value by proving an @xmath1-theorem for the fokker - planck equation of espaol and warren , and we make the connection with the detailed balance conditions derived in . as a first step towards establishing the full nonlinear hydrodynamic equations we derive in section [ section4 ] the full macroscopic conservation laws for mass and momentum density , as well as the energy balance equation ( details are given in appendix a ) . the conceptual basis for the existence of hydrodynamic equations is the _ local equilibrium _ state , which in dpd is very different from that in a molecular fluid , because of the unusual role of the temperature . in section [ section5 ] we study in a quantitative fashion the decay of the energy density @xmath25 and `` kinetic '' temperature @xmath26 towards thermal equilibrium with global temperature @xmath27 , and we assess in what sense and on what timescale the dpd fluid describes an _ isothermal _ fluid out of equilibrium . this is done on the basis of a nonlinear kinetic equation -referred to as fokker - planck - boltzmann ( fpb ) equation- for the single particle distribution function @xmath28 . it will be obtained from the first equation of the bbgky hierarchy for the dpd fluid in combination with the molecular chaos assumption . by solving in section [ section6 ] the fpb equation in the hydrodynamic stage , using the chapman - enskog method , we derive the constitutive relations and the navier - stokes equation . this enables us to calculate in section [ section7 ] the transport coefficients of shear and bulk viscosity , as well as the self - diffusion coefficient . so far , we have not discussed the _ discrete time version _ of dpd , as implemented in actual simulations . they show a sensitive dependence of thermodynamic and transport properties on time step @xmath2 . a promising step towards understanding the @xmath2-dependence was recently taken by marsh and yeomans , who calculated the equilibrium temperature as a function of the step size , determined stability criteria for the step size , and validated their result by extensive numerical simulations . we shall not attempt to present here a systematic study of the different @xmath29-corrections to equilibrium distributions and transport properties , but postpone this to a later publication . the paper ends in section [ section8 ] with comments on the most important results and future prospects for dpd .

the algorithm for the dpd fluid , the dynamics of which is conceptually a combination of molecular dynamics , brownian dynamics and lattice gas automata , is designed for simulating rheological properties of complex fluids on hydrodynamic time scales . starting from the-particle fokker - planck , or kramers equation , we prove an-theorem for the free energy , obtain hydrodynamic equations , and derive a nonlinear kinetic equation ( the fokker - planck - boltzmann equation ) for the single particle distribution function . keywords : dissipative dynamics , fokker - planck equation , transport coefficients , kinetic theory , computer simulation techniques .

the algorithm for the dpd fluid , the dynamics of which is conceptually a combination of molecular dynamics , brownian dynamics and lattice gas automata , is designed for simulating rheological properties of complex fluids on hydrodynamic time scales . this paper calculates the equilibrium and transport properties ( viscosity , self - diffusion ) of the thermostated dpd fluid explicitly in terms of the system parameters . it is demonstrated that temperature gradients can not exist , and that there is therefore no heat conductivity . starting from the-particle fokker - planck , or kramers equation , we prove an-theorem for the free energy , obtain hydrodynamic equations , and derive a nonlinear kinetic equation ( the fokker - planck - boltzmann equation ) for the single particle distribution function . this kinetic equation is solved by the chapman - enskog method . the analytic results are compared with numerical simulations . keywords : dissipative dynamics , fokker - planck equation , transport coefficients , kinetic theory , computer simulation techniques .

1701.00591

i

the andreev reflection ( ar ) is an electron - hole conversion process taking place between a normal metal and a superconductor with the excitation energy of the incident electrons is lower than the superconducting gap energy , which was originally proposed by a. f. andreev in 1964 [ ] . this conventional andreev reflection is also called the andreev retro - reflection since the reflected holes will retrace the path of the incident electrons . a recent theoretical observation on the andreev reflection at the interface between a sheet of pure graphene and a sheet of thin film graphene s - wave superconductor induced by proximity effect unvieled another andreev reflection process , known as the specular andreev reflection [ , ] . this process takes place when an incident electron with its excitation energy greater than the fermi energy but lower than the superconducting gap in the conduction band is converted into a hole in the valence band associated with a reverse on the velocity parallel to the n / sc interface . moreover , at the energy higher than the fermi energy the andreev conductance is dominated by the andreev specular reflection . after the discovery of the andreev specular reflection in graphene superconductor junction [ , ] , the andreev specular reflection is also predicted to happen in a 2@xmath6 semiconductor - superconductor junction with finite rashba spin - orbit ( so ) coupling [ ] . in addition , various theoretical works concerning the andreev reflection have been done on a variety of n / sc junctions with underlying honeycomb lattice structure such as graphene/@xmath7-wave superconductor [ ] , bilayer - graphene / s - wave superconductor [ ] and the topological materials [ , ] . these works all relies on the assumption of a clean and smooth n / sc interface . recently , the ar on a graphene - based superconducting junction has been experimentally realized in ref . and , the andreev conductance across a low disorder van der waals interface formed between bilayer graphene and superconducting nbse@xmath8 has been measured . they found the conductance across the n / sc junction was suppressed when the fermi level across the junction was tuned to lie within the superconducting gap , which gave a solid evidence on the transition between andreev retro - reflection ( intra - band process ) to andreev specular reflection ( inter - band process ) on a graphene honeycomb lattice . moreover , due to the limitation on the fabrication technology of transparent n / sc junctions , a finite tunneling transparency on the n / sc junction has been also measured . the above limitations strongly suggest that the previous theoretical calculations on the andreev conductance under the assumption of a transparent n / sc junction are not sufficient to account for the most recent experimental observations . in this paper , we try to simulate realistic n / sc junction with different degree of tunneling transparency . to do so , we first realize that for relatisvistic materials , the impurity potentials in the junction do not suppress the current . instead , due to the phenomena associated with the klein paradox , the impurity potentials tend to enhance the tunneling current [ ] . therefore , unlike the conventional blonder-tinkham-klapwijk ( btk ) formalism [ ] in which the transparency of the tunneling is simulated by the impurity potential across the junction , it is not feasible to control the transparency for the n / sc junctions made by relativistic materials via impurity potentials . in this work , we show that the local strain in the junction is the key factor that determines the transparency of the junction made by relativistic materials . in particular , we describe how to impose different degrees of transparency by adding a narrow homogeneous local strain parallel to the n / sc interface [ , ] for a system with underlying honeycomb lattice . it is shown that a @xmath1-gauge field on the n / sc interface arises and can be used to investitage the andreev reflection in various degrees of tunneling transparency . we choose the graphene normal metal/@xmath5-wave superconductor n / sc junction as an example and compute the andreev conductance via the btk formalism [ ] in the presence of a @xmath1-gauge potential . as the strength of the @xmath1-barrier is varied , the behaviors of andreev conductance obtained via our approach are in good agreement with the results obtained in the case of 1d normal metal/@xmath9-wave n / sc junction in ref . . next , we apply our theory to the case of a @xmath0 topological quantum spin hall insulator . due to the broken valley - degeneracy [ , ] , the andreev conductance from the incident electrons near the two dirac points exhibits entirely different behaviors . we provide experimental profiles of the andreev conductance within certain parameter regimes for future experiments .

it is shown that for relativistic materials , due to the klein tunneling instead of impurity potentials , the local strain in the junction is the key factor that determines the transparency of the junction . are observed as the strength of the gauge field increases . the behaviors of the conductance are in well agreement with the results obtained in the case of n / sc junction .

the andreev conductance across normal metal ( n)/superconductor ( sc ) junctions with relativistic dirac spectrum is investigated theoretically in the blonder-tinkham-klapwijk formalism . it is shown that for relativistic materials , due to the klein tunneling instead of impurity potentials , the local strain in the junction is the key factor that determines the transparency of the junction . the local strain is shown to generate an effective dirac-gauge field . a remarkable suppression of the conductance are observed as the strength of the gauge field increases . the behaviors of the conductance are in well agreement with the results obtained in the case of n / sc junction . we also study the andreev reflection in a topological material near the chiral-to - helical phase transition in the presence of a local strain . the n side of the n / sc junction is modeled by the doped kane-mele ( km ) model . the sc region is a doped correlated km- ( kmtj ) model , which has been shown to feature-wave spin - singlet pairing . with increasing intrinsic spin-orbit ( so ) coupling , the doped kmtj system undergoes a topological phase transition from the chiral-wave superconductivity to the spin-chern superconducting phase with helical majorana fermions at edges . we explore the andreev conductance at the two inequivalent dirac points , respectively and predict the distinctive behaviors for the andreev conductance across the topological phase transition . relevance of our results for the adatom-doped graphene is discussed .

1112.1430

i

understanding how and when supermassive black holes ( smbhs ) grow is currently of central importance in extragalactic astronomy . a significant amount of empirical work has established correlations between smbh mass and host galaxy spheroidal properties , such as luminosity @xcite , stellar velocity dispersion ( the @xmath0@xmath1 relationship , e.g. , @xcite ) , concentration or sersic index @xcite , bulge mass @xcite , and binding energy @xcite . these scaling relationships imply that the evolution of spheroidal galaxies and the growth of smbhs are intricately tied together . the currently favored mechanism for linking the growth of smbhs and their hosts is black hole feedback , whereby black holes grow by accreting gas in so - called `` active '' phases , possibly fueled by a major merger of two gas - rich galaxies , until feedback energy from the smbh expels gas and shuts off the accretion process @xcite . alternatively , it has been suggested that the origin of the scaling relationships does not necessarily require smbh feedback , but emerges from the stochastic nature of the hierarchical assembly of black hole and stellar mass through galaxy mergers . @xcite . feedback - driven ` self - regulated ' growth of black holes has been able to reproduce the local @xmath0@xmath1 relationship in smoothed particle hydrodynamics simulations @xcite . moreover , agn feedback has also been invoked as a means of quenching the growth of the most massive galaxies @xcite . there have been numerous models linking smbh growth , the quasar phase , and galaxy evolution @xcite . while feedback is likely important for regulating the growth of smbhs and galaxies , the fueling mechanisms that contribute to growing the smbh are likely diverse . major - mergers of gas - rich galaxies may fuel quasars at high redshift , and grow the most massive smbhs . however , major - mergers alone do not appear to be sufficient to reproduce the number of x - ray faint agn @xcite , and accretion of ambient gas via internal galactic processes @xcite , may fuel these fainter , lower @xmath0 agn at lower @xmath2 . this is supported by the fact that many agn are observed to live in late - type galaxies out to @xmath3 @xcite , and the x - ray luminosity function of agn hosted by late - type galaxies suggests that fueling by minor interactions or internal instabilities represents a non - negligible contribution to the accretion history of the universe @xcite . the black hole mass function ( bhmf ) provides a complete census of the mass of smbhs and their evolution . because of this , the bhmf is one of the primary empirical tools available for investigating the growth of smbhs , and for constraining theoretical models for the growth of the smbh population . because smbhs and galaxies are thought to be linked in their evolution , the bhmf provides insight into the fueling mechanisms that dominate black hole growth , and therefore into the role of feedback in the evolution of the host galaxy . the bhmf is also an important tool in planning future surveys , as it provides an estimate of the distribution of smbh mass expected for the survey . this in turn is important because mass is a fundamental quantity of the black hole , and therefore is an important observational quantity for empirical studies of black hole accretion physics @xcite . of course , further improvement to our understanding of black hole accretion physics will further improve our modeling and understanding of black hole accretion and feedback , which in turn will improve our understanding of black hole - galaxy coevolution . therefore , the bhmf is an important empirical quantity for smbh studies . in this review we discuss the current status of bhmf estimation and theoretical modeling . in [ s - est ] we discuss the non - trivial task of estimating the bhmf . in [ s - local ] we discuss current estimates of the local smbh bhmf . in [ s - continuity ] we discuss bhmf estimates derived by combining the local bhmf with the agn luminosity function via a continuity equation . in [ s - agn ] we discuss bhmfs estimated for agn only . in [ s - theory ] we review theoretical models for smbh growth that predict the smbh bhmf . finally , in [ s - future ] we discuss directions for future improvements to the empirical and theoretical studies of the bhmf . we note that unlike , say , the luminosity function , the division between ` observational ' and ` theoretical ' studies is not as clear for the bhmf , as some amount of modeling is necessary in order to estimate the bhmf from strictly observational quantities . we have attempted to divide the studies according to whether the bhmf is constrained empirically , as in , say , a formal statistical fitting procedure , or if it is predicted from a theoretical model for smbh growth . in reality , the line between theoretical and empirical studies is blurry , and some procedures which we have considered to be empirical may be thought of as theoretical .

it is one of the primary empirical tools available for mapping the growth of supermassive black holes and for constraining theoretical models of their evolution . in this review we conclude with a discussion of directions for future research which will lead to improvement in both empirical and theoretical determinations of the mass function of supermassive black holes .

the black hole mass function of supermassive black holes describes the evolution of the distribution of black hole mass . it is one of the primary empirical tools available for mapping the growth of supermassive black holes and for constraining theoretical models of their evolution . in this review we discuss methods for estimating the black hole mass function , including their advantages and disadvantages . we also review the results of using these methods for estimating the mass function of both active and inactive black holes . in addition , we review current theoretical models for the growth of supermassive black holes that predict the black hole mass function . we conclude with a discussion of directions for future research which will lead to improvement in both empirical and theoretical determinations of the mass function of supermassive black holes .

1007.0727

i

the chromosphere of the quiet sun is one of the most complex stellar atmospheric regions ( e.g. , harvey 2006 , 2009 ; judge 2006 , 2009 ) . lying between the thin photosphere and the extended @xmath5 k corona , it is here where the magnetic field becomes the globally dominating factor ruling the outer solar atmosphere . measuring the magnetic field vector in the solar chromospheric plasma is , however , notoriously difficult , especially outside sunspots and related active regions . quantitative information can be obtained through spectropolarimetry , but the measurement and physical interpretation of the weak polarization signatures that the hanle and zeeman effects produce in the few chromospheric lines that can be observed from ground - based telescopes is not an easy task ( see trujillo bueno 2010 , for a recent review ) . it is thus important to develop novel methods of measuring " the chromospheric magnetic field , ideally based on the action of the hanle and zeeman effects in spectral lines whose line - center intensity images reveal the fine - scale thermodynamic structuring of the solar chromosphere . here we show that the scattering polarization observed in the ir triplet of ca ii contains valuable information on the thermal and magnetic structure of the quiet " chromosphere , from the shock dominated region of the lower chromosphere " to the upper chromosphere " below the interface region to the @xmath5 k solar corona . the only way to obtain direct empirical information on the intensity and topology of the magnetic fields of the solar chromosphere is via the measurement and interpretation of polarization signals in chromospheric spectral lines . in regions with high concentrations of magnetic flux , such as in sunspots and plages , the polarization patterns are dominated by the zeeman effect . hence , diagnostic techniques based on this effect are quite useful ( e.g. , socas - navarro , trujillo bueno & ruiz cobo 2000 ; socas - navarro 2005 ) . however , in the quiet sun , which covers most of the solar disk at any given time during the solar magnetic activity cycle , the zeeman splitting between the @xmath6 ( @xmath7 ) and @xmath8 ( @xmath9 ) components ( @xmath10 being the magnetic quantum number ) is only a small fraction of the width of the spectral lines formed in the chromosphere . as a result , the transverse zeeman effect makes a very small or insignificant contribution to the emergent linear polarization amplitudes . on the other hand , the circular polarization of the zeeman effect as a diagnostic tool is of limited practical interest for the exploration of the magnetism of the upper chromosphere because the response function of the emergent stokes @xmath11 profiles of strong lines like h@xmath12 and ca ii 8542 is significant only in the photosphere and/or lower chromosphere ( socas - navarro & uitenbroek 2004 ; uitenbroek 2006 ) . there is yet another mechanism producing linear polarization in the spectral lines that can be exploited to diagnose the solar chromosphere . atoms align due to the optical pumping caused by the incident anisotropic radiation field ; i.e. , the individual magnetic @xmath10 sublevels of energy levels with total angular momentum @xmath13 are unevenly populated ( in such a way that the populations of substates with different values of @xmath14 are unequal ) and coherences between them may appear . this , in turn , gives rise to a sizable amount of linear polarization in chromospheric spectral lines , either by selective emission or absorption of polarization components in the spectral line . a remarkable example is provided by the ir triplet of ca ii . its linear polarization pattern was considered `` enigmatic '' for a while ( stenflo , keller & gandorfer 2000 ) because it was impossible to achieve even a qualitative fit to the observed relative polarization amplitudes considering that scattering line polarization results only from selective emission processes caused by the population imbalances of the line s upper level . it was later realized that selective absorption of polarization components caused by the presence of populations imbalances in the line s lower level is a very efficient mechanism for producing linear polarization in the spectral lines of a stellar atmosphere ( trujillo bueno & landi deglinnocenti 1997 ; trujillo bueno 1999 ; trujillo bueno et al . in fact , manso sainz & trujillo bueno ( 2003 ) demonstrated quantitatively that the physical origin of the linear polarization pattern observed in the ca ii lines at 8542 and 8662 is indeed zero - field " dichroism , i.e. , selective absorption of polarization components caused by the presence of atomic alignment in the metastable lower levels @xmath15 and @xmath16 ( see fig . 1 ) , while that observed in the 8498 line is controled by both dichroism and by the selective emission of polarization components that result from the population imbalances between the sublevels of its upper level @xmath17 . the alignment of the atomic @xmath18-levels and the ensuing emergent linear polarization is modified by the presence of a magnetic field through the hanle effect , even if the magnetic field turns out to have a complex , tangled topology , with mixed polarities at subresolution scales ( e.g. , landi deglinnocenti & landolfi 2004 ) . in the absence of collisional depolarization the magnetic field strength @xmath19 ( in g ) that is sufficient to produce a significant change is @xmath20 where @xmath21 and @xmath22 are , respectively , the lifetime ( in seconds ) and the land factor of the @xmath18 level under consideration . interestingly enough , since the lifetimes of the metastable lower levels of the ca ii ir triplet are about two orders of magnitude larger than the upper level lifetimes and levels with @xmath23 or @xmath24 can not carry atomic alignment , the linear polarization of the ca ii line at 8662 ( whose upper level has @xmath25 ) is expected to be sensitive to mg fields only , while the scattering polarization of the 8498 and 8542 lines ( which share the same upper level whose @xmath26 ) can in principle be sensitive also to magnetic fields in the gauss range . in the quiet solar chromosphere depolarization of the ca ii atomic levels by elastic collisions with neutral hydrogen atoms is insignificant for the upper levels of the h and k lines , while such collisions have a rather small impact on the atomic polarization of the metastable lower levels ( manso sainz & trujillo bueno 2003 ; derouich , trujillo bueno & manso sainz 2007 ) . actually , the mere fact that the ca ii 8662 line shows a clear @xmath3 polarization signal ( see stenflo et al . 2000 ) implies that its lower level ( whose @xmath27 ) is significantly polarized in the quiet solar chromosphere ( manso sainz & trujillo bueno 2003 ) . the aim of this paper is to investigate the thermal and magnetic sensitivity of the scattering polarization @xmath3 and @xmath4 profiles of the ca ii ir triplet . after formulating in 2 the multilevel problem of scattering polarization and the hanle effect , 4 discusses the unmagnetized case in the hot " and cool " chromospheric models described in 3 . the impact of the hanle effect on the linear polarization profiles of the ca ii ir triplet is discussed in 5 , showing for each solar atmospheric model detailed results for the cases of disk center ( 5.1 ) and close to the limb observations ( 5.2 ) . the ensuing information is summarized in 5.3 in the form of hanle effect diagrams for each of the spectral lines of the ir triplet . finally , 6 summarizes our main conclusions with an outlook to future research .

the chromosphere of the quiet sun is a very important stellar atmospheric region whose thermal and magnetic structure we need to decipher for unlocking new discoveries in solar and stellar physics . to this end , we need to identify and exploit observables sensitive to weak magnetic fields ( g ) and to the presence of cool and hot gas in the bulk of the solar chromosphere . here

the chromosphere of the quiet sun is a very important stellar atmospheric region whose thermal and magnetic structure we need to decipher for unlocking new discoveries in solar and stellar physics . to this end , we need to identify and exploit observables sensitive to weak magnetic fields ( g ) and to the presence of cool and hot gas in the bulk of the solar chromosphere . here we report on an investigation of the hanle effect in two semi - empirical models of the quiet solar atmosphere with different chromospheric thermal structures . our study reveals that the linear polarization profiles produced by scattering in the ca ii ir triplet have thermal and magnetic sensitivities potentially of great diagnostic value . the linear polarization in the 8498 line shows a strong sensitivity to inclined magnetic fields with strengths between 0.001 and 10 g , while the emergent linear polarization in the 8542 and 8662 lines is mainly sensitive to magnetic fields with strengths between 0.001 and 0.1 g. the reason for this is that the scattering polarization of the 8542 and 8662 lines , unlike the 8498 line , is controlled mainly by the hanle effect in their ( metastable ) lower levels . therefore , in regions with magnetic strengths sensibly larger than 1 g , their stokes and profiles are sensitive only to the orientation of the magnetic field vector . we also find that for given magnetic field configurations the sign of the and profiles of the 8542 and 8662 lines is the same in both atmospheric models , while the sign of the linear polarization profile of the 8498 line turns out to be very sensitive to the thermal structure of the lower chromosphere . we suggest that spectropolarimetric observations providing information on the relative scattering polarization amplitudes of the ca ii ir triplet will be very useful to improve our empirical understanding of the thermal and magnetic structure of the quiet chromosphere .

1007.0727

c

we have investigated theoretically the sensitivity of the scattering polarization @xmath3 and @xmath4 profiles of the ca ii ir triplet to the presence of magnetic fields through the hanle effect . to this end , we have applied a multilevel radiative transfer code ( see appendix a ) for treating the transfer of spectral line polarization due to scattering in weakly magnetized stellar atmospheres . we find that the ca ii 8542 and 8662 lines are mostly sensitive to fields between 0.001 and 0.1 g , the former being also weakly sensitive to fields between 1 and 10 g. otherwise the linear polarization signals are dependent only on the magnetic field geometry , but not to its intensity . the 8498 line is highly sensitive in the whole regime 0.00110 g , but its scattering polarization amplitude is significantly lower in the absence of magnetic fields . probably , the most interesting line of the ca ii ir triplet because of its diagnostic potential is the strongest one : @xmath192 . its linear polarization is sensitive to the orientation of the magnetic field in the chromosphere of the quiet sun , though not too much to its strength unless @xmath193 g there . although its scattering polarization amplitude depends on the thermal structure of the solar chromosphere , the emergent @xmath3 and @xmath4 profiles do not change sign between the ( hot " ) fal - c model and the ( cool " ) m - co model , unlike @xmath194 , which is very sensitive to the physical conditions of the lower chromosphere . the thermal sensitivity of the @xmath195 line ( which is sensitive only to milligauss field strengths ) is similar to that of the 8542 line . therefore , spatial fluctuations in the sign of the emergent @xmath4 profiles of the ca ii 8542 and 8662 lines may be ascribed more safely to spatial variations in the azimuth of the chromospheric magnetic field than is the case for @xmath194 . more generally , the emergent @xmath3 and @xmath4 profiles are produced by the joint action of atomic level polarization , and the hanle and transverse zeeman effects . in this paper we have considered only the action of atomic level polarization and the hanle effect . these effects dominate the emergent linear polarization profiles for inclined magnetic fields with strengths weaker than @xmath196 , where the @xmath196 value depends on the scattering geometry . in the forward scattering geometry of a disk center observation ( @xmath179 ) the linear polarization of the ca ii ir triplet is dominated by the hanle effect if the magnetic field is weaker than about 10 g. in fact , while the contribution of the transverse zeeman effect is negligible for @xmath197 g the hanle effect creates fractional linear polarization signals of the order of @xmath180 already for horizontal magnetic fields as weak as 0.1 g ( see figs . 6 and 7 ) . for magnetic strengths @xmath198 g the contribution of the transverse zeeman effect to the linear polarization observed at the solar disk center should not be neglected . detection of @xmath3 and @xmath4 disk center signals caused either by the hanle effect alone ( if @xmath199 g ) or by the joint action of the hanle and transverse zeeman effects ( if @xmath198 g ) would require very high polarimetric sensitivity together with a spatial and temporal resolution sufficient to at least resolve partially the magnetic field azimuth . given the weakness of the theoretical scattering polarization signals ( @xmath200 at @xmath179 ; @xmath201 at @xmath172 ) , the most favourable geometry for observing them is in quiet regions close to the limb . in this geometry the emergent linear polarization of the ca ii ir triplet is non - zero even if the magnetic field has a random azimuth within the spatio - temporal resolution element of the observation ( see figs . 8 and 9 ) . moreover , for magnetic strengths sensibly weaker than 100 g the contribution of the transverse zeeman effect to the emergent linear polarization is expected to be smaller than that caused by atomic level polarization . for stronger fields ( e.g. , @xmath202 g ) the wings of the emergent @xmath3 and @xmath4 profiles may show sizable features produced by the transverse zeeman effect , but the line - center amplitudes would still be dominated by atomic level polarization . finally , we point out that information on the relative amplitudes and signs of the scattering polarization profiles of the ca ii ir triplet would be very useful to help constrain the thermal and magnetic structure of the quiet solar chromosphere . in principle , to determine the structure of the magnetic field via stokes inversion techniques is possible , although it would be easier if one is able to infer first the atmospheric thermal structure from the observed intensity spectrum . the @xmath3 and @xmath4 signals we have studied here should also be exploited to investigate the reliability of three - dimensional models of the solar chromosphere resulting from holistic magnetohydrodynamic ( mhd ) simulations of the solar atmosphere . to this end , it suffices with confronting spectropolarimetric observations of the ca ii ir triplet with synthetic stokes profiles obtained by solving the non - lte problem of the 2nd kind in 3d snaphot models resulting from such mhd simulations . modeling the spectral line polarization produced by atomic level polarization and its modification by the hanle effect requires calculating , for multilevel systems , the excitation and ionization state of chemical species of given abundance that is consistent with both the intensity and polarization of the radiation field generated within the ( generally magnetized ) plasma under consideration . this so - called non - lte problem of the 2nd kind ( cf . , landi deglinnocenti & landolfi 2004 ) is a very involved non - local and non - linear radiative transfer problem which requires solving the statistical equilibrium equations for the elements of the atomic density matrix and the stokes - vector transfer equation for each of the allowed transitions in the multilevel model . once such a self - consistent excitation state is known throughout the medium , it is then straightforward to solve the transfer equation for any desired line of sight in order to obtain the emergent stokes profiles to be compared with spectropolarimetric observations . to this end , we developed a general computer program , which we will describe in greater detail in a future publication along with the efficient and accurate radiative transfer methods on which it is based ( for a first advance see the workshop contribution by manso sainz & trujillo bueno 2003 ; see also manso sainz 2002 ) . in this appendix we present only a brief summary of the code with emphasis on its application to solve the problem of scattering polarization and the hanle effect in the ir triplet of ionized calcium . 1 . the equations are formulated within the spherical tensors representation of the density matrix and radiation field tensor . there are @xmath203 unknowns @xmath74 with @xmath42 even , for each level with integer angular momentum @xmath18 , and @xmath204 unknowns for each level with semi - integer angular momentum @xmath18 . 2 . the radiative transfer equations for the stokes parameters are integrated along short characteristics using the quasi - parabolic delo method ( delopar ; trujillo bueno 2003 ) . the iterative corrections for the unknowns ( the statistical tensors @xmath74 ) are calculated applying a suitable generalization to the multilevel atom case of the fast iterative methods described in trujillo bueno & manso sainz ( 1999 ) . this implies writing down the statistical equilibrium equations taking explicitly into account the contribution of the diagonal components of the @xmath205 operator and linearizing according to eqs . ( 53 ) and ( 54 ) of trujillo bueno ( 2003 ) . the iterative scheme can speeded up further through polynomial ng - acceleration ( e.g. , auer 1987 ) . the number density of the ion under consideration is computed in non - lte . at each point in the atmosphere we solve the statistical equilibrium equations for the multipolar components of the atomic density matrix plus the conservation of particles equation to calculate the excitation state of the atomic system . we calculate the radiation field at each point in the model atmosphere for each of the allowed radiative transitions in the model atom by formal integration of the radiative transfer equations for the stokes parameters applying the delopar method . then , radiation field tensors @xmath131 are calculated and used to work out the new excitation state of the atomic system and so on , iteratively . figure 16 shows the convergence behavior of the above - mentioned iterative method for the numerical solution of the ( ca ii ) non - lte problem of the second kind .

our study reveals that the linear polarization profiles produced by scattering in the ca ii ir triplet have thermal and magnetic sensitivities potentially of great diagnostic value . we also find that for given magnetic field configurations the sign of the and profiles of the 8542 and 8662 lines is the same in both atmospheric models , while the sign of the linear polarization profile of the 8498 line turns out to be very sensitive to the thermal structure of the lower chromosphere . we suggest that spectropolarimetric observations providing information on the relative scattering polarization amplitudes of the ca ii ir triplet will be very useful to improve our empirical understanding of the thermal and magnetic structure of the quiet chromosphere .

the chromosphere of the quiet sun is a very important stellar atmospheric region whose thermal and magnetic structure we need to decipher for unlocking new discoveries in solar and stellar physics . to this end , we need to identify and exploit observables sensitive to weak magnetic fields ( g ) and to the presence of cool and hot gas in the bulk of the solar chromosphere . here we report on an investigation of the hanle effect in two semi - empirical models of the quiet solar atmosphere with different chromospheric thermal structures . our study reveals that the linear polarization profiles produced by scattering in the ca ii ir triplet have thermal and magnetic sensitivities potentially of great diagnostic value . the linear polarization in the 8498 line shows a strong sensitivity to inclined magnetic fields with strengths between 0.001 and 10 g , while the emergent linear polarization in the 8542 and 8662 lines is mainly sensitive to magnetic fields with strengths between 0.001 and 0.1 g. the reason for this is that the scattering polarization of the 8542 and 8662 lines , unlike the 8498 line , is controlled mainly by the hanle effect in their ( metastable ) lower levels . therefore , in regions with magnetic strengths sensibly larger than 1 g , their stokes and profiles are sensitive only to the orientation of the magnetic field vector . we also find that for given magnetic field configurations the sign of the and profiles of the 8542 and 8662 lines is the same in both atmospheric models , while the sign of the linear polarization profile of the 8498 line turns out to be very sensitive to the thermal structure of the lower chromosphere . we suggest that spectropolarimetric observations providing information on the relative scattering polarization amplitudes of the ca ii ir triplet will be very useful to improve our empirical understanding of the thermal and magnetic structure of the quiet chromosphere .

1011.6289

i

the experimental realization of bose - einstein condensation ( bec ) in dilute atomic gases @xcite has lead to a resurgence of interest in the theory of weakly interacting bose gases @xcite . theories of weakly - interacting bec were initially developed @xcite in the hope of obtaining insight into the physics of the strongly interacting superfluid helium , and can only give a qualitative account of the physics of the liquid superfluid phase @xcite . by contrast , the advent of dilute , weakly interacting bose gases in the laboratory provides for the direct comparison of theories of weakly interacting bec with experiments ( for a review see ref . @xcite ) . more generally , these systems offer an unprecedented opportunity for the quantitative experimental evaluation of quantum - field models at finite temperatures , and away from equilibrium , as noted by other authors @xcite . the analysis of the weakly interacting bose gas at finite temperature is significantly complicated by the necessity of considering interactions between excitations of the condensate . a self - consistent mean - field approach , based on approximate factorizations of field - operator products @xcite leads to the so - called hartree - fock - bogoliubov ( hfb ) formalism for the finite - temperature field , which is also obtained in a variational approach to the problem @xcite . this description , however , violates known exact constraints on the excitation spectrum @xcite , due to the inconsistent introduction of ( leading - order ) many - body effects @xcite into the description of atomic interactions . the simplest resolution of this problem is provided by the so - called popov approximation @xcite to the hfb theory ( hfb - popov ) , in which interactions between excitations at the hartree - fock level are retained @xcite , while many - body corrections are neglected in the treatment of all interatomic interactions . a systematic perturbative treatment of the beyond - quadratic terms of the bose - field hamiltonian @xcite ( see also refs . @xcite ) demonstrates that the failure of the hfb method results from an inconsistent treatment of hamiltonian terms cubic in the bose field operator in the mean - field factorization approximation . this provides support for an extension of the conventional hfb approach @xcite in which the popov theory is augmented by spatially dependent _ effective _ interaction strengths , which serve to upgrade the hartree - fock interactions between atoms to interactions mediated by a many - body @xmath1 matrix , which accounts for all ladder - diagram processes contributing to interactions in the finite - temperature medium @xcite . however , in this theory the zero - energy limit of the @xmath1 matrix is substituted for the interaction strength in all condensate - excitation interactions , neglecting the dependence of the @xmath1 matrix on the collision energies . more complicated ( bubble - diagram @xcite ) effects which appear at the same order of perturbation theory @xcite as the ladder - diagram corrections are also neglected . kinetic theories which include processes beyond those contained in the hfb theories , such as the exchange of atoms between the condensate and thermal cloud , have been considered by several authors @xcite . an alternative approach to modeling the finite - temperature bose gas is provided by the so - called classical - field ( or c - field ) formalism @xcite . in this approach , one considers the dynamics of a classical dynamical system corresponding to the high mode - occupation limit of the formal second - quantized field theory @xcite for the dilute bose gas . the classical - field model provides a leading - order description of the long - wavelength physics which dominate the critical behavior associated with the bose - condensation phase transition @xcite . more generally , the _ dynamical _ classical - field equations of motion arise as the `` classical '' component of the atomic - field evolution in the wigner representation of the second - quantized field @xcite . the classical - field model is thus expected to give a good description of the most highly occupied modes of the system , including the condensate and its low - lying excitations , for which quantum fluctuations can be safely neglected . the introduction of an explicit single - particle energy cutoff restricts the system to these low - energy modes @xcite . in closely related stochastic - field methods @xcite , the description of the low - energy modes includes explicit damping and noise terms arising from the coupling of these modes to the eliminated high - energy component of the bose field . the classical wave - mixing dynamics of the resulting ( hamiltonian or stochastic ) field equation of motion then provide an intrinsic nonperturbative description of all interaction processes in the low - energy field , neglecting only the quantal nature of excitations , which is essentially irrelevant in the high - temperature regime . the inclusion of many - body effects beyond bogoliubov theory in the hamiltonian classical - field theory , and agreement of this theory with the second - order perturbative treatment of ref . @xcite was demonstrated for a homogeneous field in refs . @xcite . in this article , we present a comprehensive , explicit demonstration that the equilibrium classical - field dynamics provide an intrinsic description of many - body interactions in the finite - temperature , harmonically confined bose field . introducing appropriate @xmath0-symmetric field variables , analogous to the modified ladder operators of number - conserving bogoliubov theories @xcite , we quantify the anomalous and non - gaussian nature of the field fluctuations . these correlations reveal signatures of many - body processes neglected in ( e.g. ) the hfb theories . we discuss the importance of these processes in shaping the condensate orbital , and demonstrate the consistency of the penrose - onsager definition of condensation in the classical - field equilibrium . in particular , we show that the penrose - onsager condensate appears as an effective eigenfunction of the total mean - field potential it experiences , provided that the contributions of anomalous averages ( both pair and triplet ) to the latter are taken into account . we also consider the temperature dependence of the many - body effects , and discuss the relation between condensation and the overall suppression of density fluctuations in the system . our results reveal that the partially condensed bose gas exhibits non - trivial correlations as a result of purely thermal ( classical ) fluctuations of the atomic field , which dominate over the quantum fluctuations of the field in realistic experimental systems @xcite . this article is organized as follows : in sec . [ sec : formalism ] we briefly review the derivation of the projected gross - pitaevskii equation ( pgpe ) formalism , and give the parameters of the system we investigate . in sec . [ sec : correlation_functions ] we describe the microcanonical interpretation of the pgpe , and define @xmath0-symmetric classical - field variables appropriate for the evaluation of anomalous correlation functions of the classical field . in sec . [ sec : correlations ] we discuss the local correlation functions of the noncondensed component of the field and their relation to many - body interaction effects described by the classical - field model . in sec . [ sec : e_dependence ] we consider the dependence of the noncondensate correlations and interaction effects on the energy ( and thus temperature ) of the classical - field equilibrium . in sec . [ sec : suppression ] we consider the various contributions to the suppression of density fluctuations in the field which are neglected in mean - field theories . in sec . [ sec : conclusions ] we summarize and present our conclusions .

we discuss the extension of this method to the calculation of more general correlations , including the so - called anomalous correlations of the field , without recourse to symmetry - breaking assumptions . our method is based on the introduction of-symmetric classical - field variables analogous to the modified quantum ladder operators of number - conserving approaches to the degenerate bose gas , and allows us to rigorously quantify the anomalous and non - gaussian character of the field fluctuations .

the classical - field formalism has been widely applied in the calculation of normal correlation functions , and the characterization of condensation , in finite - temperature bose gases . here we discuss the extension of this method to the calculation of more general correlations , including the so - called anomalous correlations of the field , without recourse to symmetry - breaking assumptions . our method is based on the introduction of-symmetric classical - field variables analogous to the modified quantum ladder operators of number - conserving approaches to the degenerate bose gas , and allows us to rigorously quantify the anomalous and non - gaussian character of the field fluctuations . we compare our results for anomalous correlation functions with the predictions of mean - field theories , and demonstrate that the nonlinear classical - field dynamics incorporate a full description of many - body processes which modify the effective mean - field potentials experienced by condensate and noncondensate atoms . we discuss the role of these processes in shaping the condensate mode , and thereby demonstrate the consistency of the penrose - onsager definition of the condensate orbital in the classical - field equilibrium . we consider the contribution of various noncondensate - field correlations to the overall suppression of density fluctuations and interactions in the field , and demonstrate the distinct roles of phase and density fluctuations in the transition of the field to the normal phase .

1011.6289

c

we have presented a methodology for the calculation of general spatial correlations of the finite - temperature bose gas , including anomalous correlations , in a classical - field approach . we introduced @xmath0-symmetric classical - field variables , analogous to number - conserving quantum ladder operators considered by other authors @xcite , in order to rigorously quantify the anomalous correlations in the microcanonical pgpe ensemble . we have demonstrated that the finite - temperature bose field exhibits non - gaussian correlations which are classical in origin , and by relating these correlations to many - body corrections to the mean - field interaction potentials @xcite , we have explicitly demonstrated that the classical - field theory provides an intrinsic nonperturbative description of many - body processes in the field . we discussed the role of these processes in determining the condensate mode , and demonstrated the consistency of the penrose - onsager @xcite definition of condensation in the classical - field equilibrium . finally , we elucidated the contribution of the anomalous and non - gaussian correlations of the noncondensate to the overall suppression of density fluctuations in the field , and discussed the distinction between the quasicondensate defined by the suppression of density fluctuations , and the true condensate defined by the suppression of phase fluctuations . our demonstration of the intrinsic description of many - body interaction effects provided by the classical - field method underlines the utility of these techniques in describing low - dimensional systems @xcite , in which such effects can have profound consequences for the structure of the field equilibrium @xcite . indeed our results illustrate the complexities introduced by the independence of phase and density fluctuations @xcite in the inhomogeneous finite - temperature bose gas even in the comparatively straightforward three - dimensional case . moreover , although we have only considered systems at equilibrium , our results demonstrate that the classical - field model of the low - energy coherent region does describe the higher - order processes associated with quasiparticle damping , and the exchange of atoms between the condensate and its excitations , which are essential for the description of nonequilibrium dynamics of the finite - temperature bose field @xcite . while making revisions to this article , the authors were saddened to learn of the passing of professor allan griffin , and would like to acknowledge discussions and correspondence with him that have helped to shape the ideas presented here . n.p.p . would like to thank the university of queensland node of the arc centre of excellence for quantum - atom optics for hospitality during his visit , and the uk epsrc for financial support . this work was supported by the australian research council through the arc centre of excellence for quantum - atom optics ( ce0348178 ) . m.j.d . is the recipient of an arc qeii fellowship ( project dp1094025 ) .

the classical - field formalism has been widely applied in the calculation of normal correlation functions , and the characterization of condensation , in finite - temperature bose gases . here we compare our results for anomalous correlation functions with the predictions of mean - field theories , and demonstrate that the nonlinear classical - field dynamics incorporate a full description of many - body processes which modify the effective mean - field potentials experienced by condensate and noncondensate atoms . we discuss the role of these processes in shaping the condensate mode , and thereby demonstrate the consistency of the penrose - onsager definition of the condensate orbital in the classical - field equilibrium . we consider the contribution of various noncondensate - field correlations to the overall suppression of density fluctuations and interactions in the field , and demonstrate the distinct roles of phase and density fluctuations in the transition of the field to the normal phase .

the classical - field formalism has been widely applied in the calculation of normal correlation functions , and the characterization of condensation , in finite - temperature bose gases . here we discuss the extension of this method to the calculation of more general correlations , including the so - called anomalous correlations of the field , without recourse to symmetry - breaking assumptions . our method is based on the introduction of-symmetric classical - field variables analogous to the modified quantum ladder operators of number - conserving approaches to the degenerate bose gas , and allows us to rigorously quantify the anomalous and non - gaussian character of the field fluctuations . we compare our results for anomalous correlation functions with the predictions of mean - field theories , and demonstrate that the nonlinear classical - field dynamics incorporate a full description of many - body processes which modify the effective mean - field potentials experienced by condensate and noncondensate atoms . we discuss the role of these processes in shaping the condensate mode , and thereby demonstrate the consistency of the penrose - onsager definition of the condensate orbital in the classical - field equilibrium . we consider the contribution of various noncondensate - field correlations to the overall suppression of density fluctuations and interactions in the field , and demonstrate the distinct roles of phase and density fluctuations in the transition of the field to the normal phase .

1305.0386

i

since the theory of nucleation phenomena was introduced a long time ago @xcite , the question under which conditions the `` conventional theory '' of nucleation is accurate has been debated ( see e.g. @xcite ) and this debate continues until today . for the simplest case of homogeneous nucleation ( by statistical fluctuations in the bulk ) of a one - component liquid droplet from the vapor , the basic statement of the theory is that under typical conditions nucleation processes are rare events , where a free energy barrier @xmath0 very much larger than the thermal energy @xmath4 is overcome , and hence the nucleation rate is given by an arrhenius law , @xmath5 here @xmath6 is the number of nuclei , i.e. droplets that have much larger radii @xmath7 than the critical radius @xmath1 associated with the free energy barrier @xmath0 of the saddle point in configuration space , that are formed per unit volume and unit time ; @xmath8 is a kinetic prefactor . now @xmath0 is estimated from the standard assumption that the formation free energy of a droplet of radius @xmath7 can be written as a sum of a volume term @xmath9 , and a surface term @xmath10 , i.e. @xmath11 since the liquid droplet can freely exchange particles with the surrounding vapor , it is natural to describe its thermodynamic potential choosing the chemical potential @xmath12 and temperature @xmath13 as variables , and expand the difference in thermodynamic potentials of liquid and vapor at the coexistence curve , @xmath14 , @xmath15 and @xmath16 denoting the densities of the coexisting vapor ( @xmath17 ) and liquid ( @xmath18 ) phases . according to the capillarity approximation , the curvature dependence of the interfacial tension @xmath19 is neglected , @xmath19 is taken for a macroscopic and flat vapor - liquid interface . then the critical radius @xmath1 follows from @xmath20 and the associated free energy barrier is @xmath21 however , since typically @xmath22 is less than 100 @xmath4 , the critical droplet is a nanoscale object , and thus the treatment eqs . - is questionable . experiments ( e.g. @xcite ) were not able to yield clear - cut results on the validity of eqs . - , and how to improve this simple approach : critical droplets are rare phenomena , typically one observes only the combined effect of nucleation and growth ; also the results are often `` contaminated '' by heterogeneous nucleation events due to ions , dust , etc . @xcite , and since @xmath6 varies rapidly with the supersaturation , only a small window of parameters is suitable for investigation . therefore this problem has been very attractive , in principle , for the study via computer simulation . however , despite numerous attempts ( e.g. @xcite ) , this approach is also hampered by two principal difficulties : * computer simulations can often only study a small number of decades in time , @xcite , which in typical cases correspond to small barriers @xmath23 rather than the larger ones which are of more interest in the context of experiments . * on the atomistic scale , it is a difficult and not generally solved problem to decide which particles belong to a droplet and which particles belong to its environment ; the vapor - liquid interface is diffuse and fluctuating @xcite . for these reasons , many of the available simulation studies have addressed nucleation in the simplistic ising ( lattice gas ) model , @xcite , first of all since it can be very efficiently simulated , and secondly because one can define more precisely what is meant by a `` cluster '' . associating ising spins @xmath24 at a lattice site @xmath25 with a particle , @xmath26 with a hole , originally `` clusters '' were defined as groups of up - spins such that each up - spin in a cluster has at least one up - spin as nearest neighbor belonging to the same cluster @xcite . however , now it is well understood that these `` geometrical clusters '' in general do not have much physical significance @xcite : e.g. , it is known that there exists a line of percolation transitions , where a geometrical cluster of infinite size appears , in the phase diagram @xcite . this percolation transition is irrelevant for statistical thermodynamics of the model @xcite . based on the work of fortuin and kasteleyn @xcite on a correlated bond - percolation model , it is now understood that physically relevant clusters in the ising model should not simply be defined in terms of spins having the same orientation and are connected by nearest neighbor bonds , as is the case in the `` geometrical clusters '' , but in addition one has to require the bonds to be `` active '' : bonds are `` active '' with probability @xmath27 @xmath28 @xmath29 being the ising model exchange constant . due to eq . , the `` physical clusters '' defined in this way are typically smaller than the geometrical clusters , and their percolation point can be shown to coincide with the critical point @xcite . a geometrical cluster hence can contain several physical clusters . note that to apply eq . , random numbers are used , and hence physical clusters are not deterministically defined from the spin configuration , but rather have some stochastic character . this presents a slight difficulty in using physical clusters in the study of cluster dynamics . while eq . has been used in the context of simulations of critical phenomena in the ising model , applying very efficient swendsen - wang @xcite and wolff @xcite simulation algorithms , this result has almost always been ignored in the context of simulations of nucleation phenomena @xcite . while it is allright to ignore the difference between geometrical and physical clusters in the limit @xmath30 ( obviously @xmath31 then , all bonds becoming active ) , this is completely inappropriate at higher temperatures . the present work hence reconsiders this problem , studying both dynamical aspects of nucleation in the framework of the kinetic ising model @xcite ( without conservation laws ) , and the static properties of large droplets , applying the definition of `` physical clusters '' based on eq . throughout . for comparison , we shall also occasionally use the `` geometrical '' cluster definition , to demonstrate that misleading conclusions would actually result in practice , for the temperatures that are commonly studied . the study will be generalized to ising systems with free surfaces , where a boundary field @xmath32 acts @xcite . first of all , in this way also a systematic investigation of heterogeneous nucleation at planar walls becomes feasible ; secondly , due to the reduction of the barrier @xmath33 in comparison to @xmath34 ; nucleation for reasonably large values of @xmath1 becomes accessible to study . in sec . [ sec2 ] , we consider the equilibrium of the lattice gas model for @xmath35 in systems in a @xmath36 geometry with periodic boundary conditions , to show that physical clusters do occupy precisely the volume predicted by the lever rule analysis , @xcite as they should when the thermodynamic limit is approached . we present evidence that physical clusters are correctly identified by both the lever rule method and the approach based on the `` atomistic '' identification of clusters based on eq . at all temperatures , from zero temperature up to the critical temperature @xmath37 . in contrast , eq . , which implies a spherical droplet shape , is found to work only at temperatures distinctly above the interface roughening transition temperature @xmath38 @xcite , even for very large radii @xmath7 . we attribute these discrepancies to the fact that due to the anisotropy of the interface tension for our lattice model pronounced deviations of the average droplet shape from a sphere occur @xcite , presenting data on the shape of large droplets . in sec . [ sec3 ] , we describe our results on the dynamics of the droplet size distribution and on the attempt to find @xmath1 from the size where growth and shrinking processes of clusters are balanced . this study is also carried out for systems with a free surface , for which the contact angles for various values of the surface field have been estimated previously @xcite , since in this case much lower barriers ( for large clusters ) result , which is crucial for making this study feasible with manageable effort . however , the radii @xmath1 predicted from this analysis of kinetics show slight deviations from the radii @xmath1 predicted from @xmath33 . possible reasons for this discrepancy will be discussed . finally , sec . [ sec4 ] summarizes our conclusions .

the theory considers the nucleation process as a slow ( quasi - static ) cluster ( droplet ) growth over a free energy barrier , constructed in terms of a balance of surface and bulk term of a `` critical droplet '' of radius , implying that the rates of droplet growth and shrinking essentially balance each other for droplet radius . for heterogeneous nucleation at surfaces , `` geometrical clusters '' ( defined such that each site belonging to the cluster is occupied and has at least one occupied neighbor site ) yield valid results only for temperatures less than 60% of the critical temperature , where the cluster shape is non - spherical .

the conventional theory of homogeneous and heterogeneous nucleation in a supersaturated vapor is tested by monte carlo simulations of the lattice gas ( ising ) model with nearest - neighbor attractive interactions on the simple cubic lattice . the theory considers the nucleation process as a slow ( quasi - static ) cluster ( droplet ) growth over a free energy barrier , constructed in terms of a balance of surface and bulk term of a `` critical droplet '' of radius , implying that the rates of droplet growth and shrinking essentially balance each other for droplet radius . for heterogeneous nucleation at surfaces , the barrier is reduced by a factor depending on the contact angle . using the definition of `` physical '' clusters based on the fortuin - kasteleyn mapping , the time - dependence of the cluster size distribution is studied for `` quenching experiments '' in the kinetic ising model , and the cluster size where the cluster growth rate changes sign is estimated . these studies of nucleation kinetics are compared to studies where the relation between cluster size and supersaturation is estimated from equilibrium simulations of phase coexistence between droplet and vapor in the canonical ensemble . the chemical potential is estimated from a lattice version of the widom particle insertion method . for large droplets it is shown that the `` physical clusters '' have a volume consistent with the estimates from the lever rule . `` geometrical clusters '' ( defined such that each site belonging to the cluster is occupied and has at least one occupied neighbor site ) yield valid results only for temperatures less than 60% of the critical temperature , where the cluster shape is non - spherical . we show how the chemical potential can be used to numerically estimate also for non - spherical cluster shapes .

1305.0386

c

in the present work , we have studied aspects of nucleation theory by simulation of clusters and their dynamics , using the ising ( lattice gas ) model on the simple cubic lattice . both homogeneous nucleation and heterogeneous nucleation at planar walls ( where a `` surface field '' acts ) have been considered . although many aspects of this problem have been studied before in works of various groups extending over several decades , most of the previous work is inconclusive since it relied on the use of the `` geometric '' cluster definition . we have given evidence that this geometric cluster definition does not yield correct results for large clusters at the temperatures far above the roughening transition temperature where the clusters have spherical shape ; at temperatures below the roughening transition temperature the geometric clusters and the `` physical clusters '' are basically indistinguishable , but due to the pronounced anisotropy effects a simple analysis of nucleation phenomena is not possible . however , in the limit of large droplet volumes @xmath274 , where one can neglect any corrections to the decomposition of the droplet formation free energy into the bulk term plus a surface correction , one can compute the nucleation free energy barrier @xmath0 from measuring the excess chemical potential @xmath98 that is in equilibrium with a given @xmath192 . fig . [ fig : vcntvsvlr ] shows the enhancement of @xmath0 with respect to the standard result for spherical droplets ( using eqs . , ) . we thus show that in the ising ( lattice gas ) model this enhancement gradually rises from unity as the temperature is lowered from the critical temperature , reaches almost 10% at @xmath275 , and rises steeply below the roughening temperature towards the low temperature limit @xmath276 ( fig . [ fig : vcntvsvlr ] ) . this enhancement reflects the consequences of the anisotropy of the interfacial free energy , such as the gradual crossover of the droplet shape from a sphere to a cube ( fig . [ fig6 ] ) . on the other hand , we demonstrate that physical clusters do give consistent results , at least in the bulk when one is concerned with homogeneous nucleation . we show that in the limit where the droplets get macroscopically large , they converge against the simple lever rule predictions . however , we do find an ( unexpected ) surface excess in the particle number of such clusters also in this case . we also demonstrate the validity of the relation between chemical potential ( of the supersaturated vapor ) and the droplet radius that classical nucleation theory predicts for large droplets near the critical temperature . we also give evidence that the droplet - vapor interface is broadened due to capillary waves ; we remind the reader that mean - field type theories and density functional theories @xcite can not include such capillary wave effects ( which also should give rise to a correction term on the droplet formation free energy , not yet included in eq . ) . we would also like to stress that many of our considerations can be carried over to a study of clusters in @xmath277 dimensions , where a construction as in fig . [ fig1 ] also holds . however , we expect two distinctions : ( i ) the roughening transition temperature @xmath38 is zero , so the crossover of droplet shape from the circle to the square occurs without any singularity even for arbitrarily large droplets . ( ii ) percolation coincides with the critical point , but geometrical clusters still are too large , and to describe nucleation , physical clusters defined via eq . should also be used . of course , it would be very desirable to carry these considerations over to nucleation in off - lattice models of fluids . however , a precise analogue of eq . is still not known , and hence other concepts to define physical clusters @xcite need to be used , if one wishes to study nucleation near the critical point . in the second part we present a first study of the time evolution of the cluster population based on the `` physical cluster '' definition . however , due to the large computer resources needed for this study , only data at a single temperature ( @xmath130 ) are presented . in order to allow a comparison of this part of the study with our results on static properties of critical droplets , as studied in the first part of the paper , we use a criterion to estimate the critical droplet size from the balance between droplet growth and shrinking processes . in the case of homogeneous nucleation , the results obtained in this way are roughly compatible with the results obtained from the static lever rule method . studying droplet volumes in the range from 100 to 200 , clear deviations from the classical nucleation theory are seen , which can be attributed to a decrease of the nucleation barrier due to fluctuation effects . however , in the case of heterogeneous nucleation , a rather large discrepancy between the results of the statics and dynamics of droplets is found . this discrepancy is not understood yet , and must be left as a challenging problem for the future . * acknowledgements * : we thank d. winter for providing us with the data from ref . @xcite that were included in fig . 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the conventional theory of homogeneous and heterogeneous nucleation in a supersaturated vapor is tested by monte carlo simulations of the lattice gas ( ising ) model with nearest - neighbor attractive interactions on the simple cubic lattice . these studies of nucleation kinetics are compared to studies where the relation between cluster size and supersaturation is estimated from equilibrium simulations of phase coexistence between droplet and vapor in the canonical ensemble .

the conventional theory of homogeneous and heterogeneous nucleation in a supersaturated vapor is tested by monte carlo simulations of the lattice gas ( ising ) model with nearest - neighbor attractive interactions on the simple cubic lattice . the theory considers the nucleation process as a slow ( quasi - static ) cluster ( droplet ) growth over a free energy barrier , constructed in terms of a balance of surface and bulk term of a `` critical droplet '' of radius , implying that the rates of droplet growth and shrinking essentially balance each other for droplet radius . for heterogeneous nucleation at surfaces , the barrier is reduced by a factor depending on the contact angle . using the definition of `` physical '' clusters based on the fortuin - kasteleyn mapping , the time - dependence of the cluster size distribution is studied for `` quenching experiments '' in the kinetic ising model , and the cluster size where the cluster growth rate changes sign is estimated . these studies of nucleation kinetics are compared to studies where the relation between cluster size and supersaturation is estimated from equilibrium simulations of phase coexistence between droplet and vapor in the canonical ensemble . the chemical potential is estimated from a lattice version of the widom particle insertion method . for large droplets it is shown that the `` physical clusters '' have a volume consistent with the estimates from the lever rule . `` geometrical clusters '' ( defined such that each site belonging to the cluster is occupied and has at least one occupied neighbor site ) yield valid results only for temperatures less than 60% of the critical temperature , where the cluster shape is non - spherical . we show how the chemical potential can be used to numerically estimate also for non - spherical cluster shapes .

1602.07522

i

this work is motivated by several physics goals , spanning fundamental and applied neutrino physics . reactor antineutrinos are emitted in huge quantities by reactor cores , and this feature has been used by many particle physicists since the late fifties to study the neutrino properties@xcite . in the seventies , was also born the idea that antineutrino detection could be used for reactor monitoring@xcite . in a reactor core , the production of antineutrinos arises from the beta decays of fission products . the distribution of the latter nuclei are inherently linked to the structure of the nucleus undergoing the fission process and to the energy of the impinging neutron . thus the resulting emitted antineutrinos reflect the composition of a reactor core , but also its thermal power . these latter features , combined with progresses in the r&d of small antineutrino detectors and the development of dedicated reactor simulations , could be of interest for the international atomic energy agency ( iaea ) in its task of safeguarding nuclear reactors worldwide@xcite . in parallel , with the advance of the next generation of reactor antineutrino experiments , new calculations of the main uranium and plutonium isotope antineutrino energy spectra have been recently developed@xcite and led to the so - called " reactor anomaly@xcite . several hypotheses have been raised to explain this anomaly , among which the existence of light sterile neutrinos@xcite . since then , short baseline experimental projects have been born at research reactors in order to evidence the existence of such sterile neutrinos , in addition to the ones already under development for applications of neutrino physics@xcite , or other physics goals such as neutrino nucleus coherent scattering experiments @xcite , or the measurement of the neutrino magnetic moment@xcite . originally designed to be a small detector dedicated to reactor monitoring with an optimized detection efficiency , the nucifer experiment@xcite is one of those experiments that could as well bring additional constraints on the phase space associated to a sterile neutrino in the ev@xmath1 range . this experiment has provided the framework of the results presented in this article : a simulation of the osiris reactor core close to which nucifer is installed , a prediction of the associated antineutrino emission , as well as of the gamma and neutron backgrounds generated by the reactor operation . most of worldwide research reactors use fuel enriched up to a maximum of 20% in @xmath0u , which is the upper limit to be qualified as low enriched uranium and is strongly supported by the international atomic energy agency @xcite . this enrichment guarantees that most of the fissions arises from @xmath0u thermal fission , but there may be a small contribution to the fissions coming from the @xmath2pu produced during irradiation from the 80% of @xmath3u composing this kind of fuel . this contribution has to be quantified as the @xmath2pu antineutrino energy spectrum shape differs from the one from @xmath0u , which requires the modelling of the reactor core and of the subsequent antineutrino emission . the reference antineutrino spectra are still the ones based on the integral beta spectra precisely measured at the high flux reactor of the institut laue langevin in the eighties @xcite , and lately the integral beta spectrum produced through fast fission of @xmath3u has been measured in munich at the garching reactor@xcite . currently antineutrino spectra obtained through the conversion of these spectra@xcite are the ones exhibiting the smallest systematic errors . however , it should be mentioned that these systematic errors are the object of numerous discussions , showing that there may be extra sources of systematics to be accounted for due to nuclear physics theoretical and experimental uncertainties , insufficiently considered up to now @xcite . the recent observation of a distorsion of the antineutrino energy spectra@xcite measured by double chooz@xcite , reno@xcite and daya bay@xcite above 4mev with respect to converted spectra reinforces the need for further investigations . reactor neutrino experiments have up to now mostly used converted spectra as predictions to compare their measurements to . as these spectra were measured after a short irradiation time of a target into a research reactor , an extra correction has to be applied to account for the `` off - equilibrium effects '' , due to the build - up of long lived fission products , and to neutron captures on fission products during the core cycle . an alternative to this methodology is to use the summation method@xcite , consisting in summing the contributions of all beta decayers to the antineutrino spectrum . up to now , the published summation method spectra were computed to match the conditions of the individual beta energy spectra of the main uranium and plutonium isotopes , measured at ill@xcite and garching@xcite , i.e. not under the physics conditions of a reactor core under operation . in this article , we have coupled the summation method for the first time with a complete reactor model , allowing us predicting the low energy part of the antineutrino spectrum , below the inverse beta decay process ( ibd ) detection threshold , and evidencing the important contribution of actinides to the antineutrino emission . the obtained antineutrino energy spectra span an energy range beyond the one of the measured ill and garching integral beta spectra , which is the energy range of the converted spectra , making of the summation method spectra the only available predictions in these energy regions ( below 1.8mev and beyond 7 - 8mev ) . in addition , are provided in this paper the corresponding off - equilibrium corrections , deduced for the first time from the simulation of a complete reactor core , that can only be computed with the summation method . experimental conditions at short distance from research reactors are challenging , because the reactor itself produces huge gamma and neutron backgrounds that induce accidental and correlated backgrounds in an antineutrino target . the understanding of these backgrounds is of utmost importance and triggered the second part of the work presented here . we have performed the simulation of the gamma rays and neutrons generated by the osiris research reactor and propagated them through the water and concrete shieldings which separate the core from the antineutrino detector . the background estimation at the core level presented in this article could be used for the optimization of the background rejection of other experimental setups , or to estimate the physics reach of a foreseen experiment in the phase space of the oscillation angle and squared mass difference . in summary , we have thus developed a model of the osiris research reactor core in order to : give orders of magnitude values of fission rates in small thermal research reactors using fuel enriched at about 20% in @xmath0u ; provide the required data to compute the emitted antineutrino energy spectrum , including fine effects such as off - equilibrium corrections ; and eventually give estimates of the reactor - generated neutron and gamma backgrounds and identify their production processes . the paper is organized as follows . a first section describes the osiris research reactor and its fuel elements . a second section describes the simulation tools which were used to perform these studies and the associated validation tests . in a third section , are presented the obtained results for the antineutrino energy spectrum and flux . the last section is dedicated to the neutron and gamma background studies . in appendix a , are provided the antineutrino energy spectrum computed with the complete osiris simulation and the summation method for a reactor at equilibrium and off - equilibrium effects . in appendix b , we provide a table containing the gamma energy spectrum emitted by the core , before its propagation through the specific shielding of the osiris reactor , so that it can be used as an input of a monte carlo simulation of another experimental site .

the detailed understanding of the antineutrino emission from research reactors is mandatory for any high sensitivity experiments either for fundamental or applied neutrino physics , as well as a good control of the gamma and neutron backgrounds induced by the reactor operation . in this article , the antineutrino emission associated to a thermal research reactor : the osiris reactor located in saclay , france , is computed in a first part . the calculation is performed with the summation method , which sums all the contributions of the beta decay branches of the fission products , coupled for the first time with a complete core model of the osiris reactor core . in addition , the required off - equilibrium corrections to be applied to converted antineutrino energy spectra of uranium and plutonium isotopes are provided . in a second part , the gamma energy spectrum emitted at the core level the origin of these gamma rays and neutrons is discussed and the associated energy spectrum of the photons transported after the concrete walls is displayed .

the detailed understanding of the antineutrino emission from research reactors is mandatory for any high sensitivity experiments either for fundamental or applied neutrino physics , as well as a good control of the gamma and neutron backgrounds induced by the reactor operation . in this article , the antineutrino emission associated to a thermal research reactor : the osiris reactor located in saclay , france , is computed in a first part . the calculation is performed with the summation method , which sums all the contributions of the beta decay branches of the fission products , coupled for the first time with a complete core model of the osiris reactor core . the mcnp utility for reactor evolution code was used , allowing to take into account the contributions of all beta decayers in - core . this calculation is representative of the isotopic contributions to the antineutrino flux which can be found at research reactors with a standard 19.75% enrichment inu . in addition , the required off - equilibrium corrections to be applied to converted antineutrino energy spectra of uranium and plutonium isotopes are provided . in a second part , the gamma energy spectrum emitted at the core level is provided and could be used as an input in the simulation of any reactor antineutrino detector installed at such research facilities . furthermore , a simulation of the core surrounded by the pool and the concrete shielding of the reactor has been developed in order to propagate the emitted gamma rays and neutrons from the core . the origin of these gamma rays and neutrons is discussed and the associated energy spectrum of the photons transported after the concrete walls is displayed .

0808.3164

i

modern x - ray observations show complex structures in both the spatial and spectral domains of various astrophysical sources . nonetheless , active galalactic nuclei ( agn ) including quasars nuclei remain spatially unresolved even with the highest - resolution x - ray telescopes . most of their energy is released within the unresolved core , and only spectral and timing information is available to study the nature of the x - ray emission . generally speaking , emission and absorption lines constitute an important part of the x - ray spectrum in that they can provide information as to the state of plasma . one of the goals of x - ray data analysis is to understand the components present in the spectrum , and to obtain information about the emission and absorption features , as well as their locations and relation to the primary quasar emission . the detection of weak lines in noisy spectra is the main statistical problem in such analyses : is a bump observed in the spectrum related to a real emission line or is it simply an artifact of the poissonian noise ? although quasars x - ray spectra are usually featureless as expected based on the comptonization process ( see for example * ? ? * ; * ? ? ? * ; * ? ? ? * ) , an important x - ray emission feature identified in agn and quasars spectra is the iron k emission line ( see recent review by * ? ? ? determining the origin and the nature of this line is one of main issues in agn and quasar research . this line is thought to come directly from illuminated accretion flow as a fluorescent process @xcite . the location of the line in the spectrum indicates the ionization state of iron in the emitting plasma , while the width of the line tells us the velocity of the plasma @xcite . the iron line provides a direct probe of the innermost regions of accretion flow and matter in close vicinity of a black hole . absorption features associated with the outflowing matter ( warm wind , partial covering absorber ) have also been observed in recent x - ray observations @xcite . although the location and width of absorption lines provide information as to the velocity of the absorber and its distance from the quasar , this article focuses on statistical issues in fitting the spectral location of narrow emission lines , i.e. , identifying the ionization state . there are two parts to the fe - k - alpha emission line observed in agn @xcite : one is a broad component thought to be a signature of a relativistic motion in the innermost regions of an accretion flow ; the other is a narrow component that is a result of a reflection off the material at larger distances from the central black hole . a detection of the broad component is challenging as it requires a spectral coverage over a large energy range , so the continuum emission is well determined and the broad line can be separated @xcite . the relativistic line profile is broad and skewed , and two strong peaks of the emission line that originates in a relativistic disk can be prominent and narrow . while the full profile of the broad line may not be easily separable from the continuum , these two peaks may provide a signature for this line in the x - ray spectrum . the broad fe - line gives an important diagnostic of the gas motion and can be used to determine the spin of a black hole @xcite ; see also an alternative model for the red wing " component by @xcite . the narrow component of the line gives diagnostics of the matter outside the accretion disk and conditions at larger distances from the black hole ; see fe - line baldwin effect discussion in @xcite . both line components are variable and the line may `` disappear '' from the spectrum @xcite . the spectral resolution of x - ray ccd detectors ( for example 100 - 200 ev in acis on _ chandra _ or epic on xmm-_newton _ ) is relatively low with respect to the predicted width of narrow ( @xmath0 km s@xmath1 ) emission or absorption lines in agn and quasars . observations with grating instruments ( rgs or heg ) can provide high resolution x - ray spectra , but the effective area of the present x - ray telescopes is too low for efficient agn detections , and only a handful of bright low redshift sources have been observed with gratings to date @xcite . therefore mainly the x - ray ccd spectra of lower resolution are used to study large samples of agn and quasars ( see for example * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . using these relatively low resolution x - ray detectors , the fe - k - alpha emission line can be narrow enough to be contained entirely in a single detector bin . in some cases ( for example in _ chandra _ ) the line may occupy a few bins . in this article we focus on the statistical problem of fitting the spectral location of an emission line or a set of emission lines that are narrow . this is a common objective in high - energy analyses , but as we shall discuss fitting these relatively narrow features poses significant statistical challenges . in particular we find evidence that using line profiles that are narrower than we actually expect the emission line to be can improve the statistical properties of the fitted emission line location . x - ray spectra , such as those available with the _ chandra x - ray observatory _ carry much information as to the quasar s physics . taking advantage of the spectral capacity of such instruments , however , requires careful statistical analysis . for example , the resolution of such instruments corresponds to a fine discretization of the energy spectrum . as a result , we expect a low number of counts in each bin of the x - ray spectrum . such low - count data make the gaussian assumptions that are inherent in traditional minimum @xmath2 fitting inappropriate . a better strategy , which we employ , explicitly models photon arrivals as an inhomogeneous poisson process @xcite . in addition , data are subject to a number of processes that significantly degrade the source counts , e.g. , the absorption , non - constant effective area , blurring of photons energy , background contamination , and photon pile - up . thus , we employ statistical models that directly account for these aspects of data collection . in particular , we design a highly structured multilevel spectral model with components for both the data collection processes and the complex spectral structures of the sources themselves . in this highly structured spectral model , a bayesian perspective renders straightforward methods that can handle the complexity of _ chandra _ data @xcite . as we shall illustrate , these methods allow us to use low - count data , to search for the location of a narrow spectral line , to investigate its location s uncertainty , and to construct statistical tests that measure the evidence in the data for including the spectral line in the source model . the energy spectrum can be separated into two basic parts : a set of continuum terms and a set of several emission lines . we begin with a standard spectral model that accounts for a single continuum term along with several spectral lines . throughout this paper , we use @xmath3 as a general representation of model parameters in the spectral model . the components of @xmath4 represent the collection of parameters for the continuum , ( emission ) lines , absorption , and background contamination , respectively . ( notice that the roman letters in the superscripts serve as a mnemonic for these four processes . ) because the x - ray emission is measured by counting the arriving photons , we model the expected poisson counts in energy bin @xmath5 , where @xmath6 is the set of energy bins , as @xmath7 where @xmath8 and @xmath9 are the width and mean energy of bin @xmath10 , @xmath11 is the expected counts per unit energy due to the continuum term at energy @xmath9 , @xmath12 is the set of free parameters in the continuum model , @xmath13 is the number of emission lines , @xmath14 is the expected counts due to the emission line @xmath15 , and @xmath16 is the proportion of an emission line centered at energy @xmath17 and with width @xmath18 that falls into bin @xmath10 . there are a number of smooth parametric forms to describe the continuum in some bounded energy range ; in this article we parameterize the continuum term @xmath19 as a power law , i.e. , @xmath20 where @xmath21 and @xmath22 represent the normalization and photon index , respectively . the emission lines can be modeled via the proportions @xmath16 using narrow gaussian distributions , lorentzian distributions , or delta functions ; the counts due to the emission line are distributed among the bins according to these proportions . while the gaussian or lorentzian function parameterizes an emission line in terms of center and width , the center is the only free parameter with a delta function ; the width of the delta function is effectively the width of the energy bin in which it resides . while the model in equation [ park : eq : ideal ] is of primary scientific interest , a more complex statistical model is needed to address the data collection processes mentioned in [ park : sec : hea ] . we use the term _ statistical model _ to refer to the model that combines the _ source _ or _ astrophysical model _ with a model for the stochastic processes involved in data collection and recording . thus , in addition to the source model , the statistical model describes such processes as instrument response and background contamination . specifically , to account for the data collection processes , equation [ park : eq : ideal ] is modified via @xmath23 where @xmath24 is the expected observed poisson counts in detector channel @xmath25 , @xmath26 is the set of detector channels , @xmath27 is the probability that a photon that arrives with energy corresponding to bin @xmath10 is recorded in detector channel @xmath28 ( i.e. , @xmath29 is the so - called redistribution matrix or rmf commonly used in x - ray analysis ) , @xmath30 is the effective area ( i.e. , arf , a calibration file associated with the x - ray observation ) of bin @xmath10 , @xmath31 is the probability that a photon with energy @xmath9 is _ not _ absorbed , @xmath32 is the collection of parameters for absorption , and @xmath33 is a poisson intensity of the background counts in channel @xmath28 . while the scatter probability @xmath27 and the effective area @xmath30 are presumed known from calibration , the absorption probability is parameterized using a smooth function ; see @xcite for details . to quantify background contamination , a second data set is collected that is assumed to consist only of background counts ; the background photon arrivals are also modeled as an inhomogeneous poisson process . unfortunately , the statistical methods and algorithms developed in @xcite can not be directly applied to fitting _ narrow _ emission lines . there are three obstacles that must be overcome in order to extend bayesian highly structured models to spectra containing narrow lines . in particular , we must develop ( 1 ) new computational algorithms , ( 2 ) statistical summaries and methods for inference under highly multimodal posterior distributions , and ( 3 ) statistical tests that allow us to quantify the statistical support in the data for including an emission line or lines in the model . our main objective in this paper is to extend the methods of @xcite in these three directions , and to evaluate and illustrate our proposals . here we discuss each of these challenges in detail . [ [ challenge-1-statistical - computation . ] ] challenge 1 : statistical computation . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + fitting the location of narrow lines requires new and more sophisticated computational techniques than those developed by @xcite . indeed , the algorithms that we develop require a new theoretical framework for statistical computation : they are not examples of any existing algorithm with known properties . although the details of this generalization are well beyond the scope of this article , we can offer a heuristic description ; a more detailed description is given in appendix [ ap : alg ] . readers who are interested in the necessary theoretical development of the statistical computation techniques are directed to @xcite and @xcite . the algorithms used by @xcite to fit the structured bayesian model described in [ park : sec : model ] are based on the probabilistic properties of the statistical models . for example , the parameters of a gaussian line profile can be fit by iteratively attributing a subset of the observed photons to the line profile and using the mean and variance of these photon energies to update the center and width of the line profile . the updated parameters of the line profile are used to again attribute a subset of the photons to the line , i.e. , to stochastically select a subset of the photons that are likely to have arisen out of the physical processes at the source corresponding to the emission line . these algorithms are typically very stable . for example , they only return statistically meaningful parameters because the algorithms themselves mimic the probabilistic characteristics of the statistical model . the family of expectation / maximization ( em ) algorithms @xcite and markov chain monte carlo ( mcmc ) methods such as the gibbs sampler @xcite are the examples of statistical algorithms of this sort . a drawback of these algorithms is that in some situations they can be slow to converge . when fitting the location of a gaussian emission line , for example , the location is updated more slowly if the line profile is narrower this is because only photons with energies very close to the current value of the line location can be attributed to the line . updating the line location with the mean of the energies of these photons can not result in a large change in the emission line location . the situation becomes chronic when a delta function is used to model the line profile : the line location parameter sticks at its starting value throughout the iteration . it is to circumvent this difficulty that we develop both new em - type algorithms @xcite and new mcmc samplers specially tailored for fitting narrow lines . our new samplers are motivated by the gibbs sampler , but constitute a non - trivial generalization of gibbs sampling known as partially collapsed gibbs sampling @xcite ; see appendix [ ap : alg ] . our updated versions of both classes of algorithms are able to fit narrow lines by avoiding the attribution of photons to the emission line during the iteration . such algorithms tend to require fewer iterations to converge regardless of the width of the emission line . because they involve additional evaluation of quantities evolving the large dimensional redistribution matrix , @xmath34 , however , each iteration of these algorithms can be significantly more costly in terms of computing time . a full investigation of the relative merit of the algorithms and a description of how the computational trade - offs can be played to derive optimal algorithms are beyond the scope of this paper . except in appendix [ ap : alg ] , we do not discuss the details of the algorithms further in this article ; interested readers are directed to @xcite and @xcite . [ [ challenge-2-multimodal - likelihoods . ] ] challenge 2 : multimodal likelihoods . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + the likelihood function for the emission line location(s ) is highly multimodal . each mode corresponds to a different relatively likely location for an emission line or a set of emission lines . standard statistical techniques such as computing the estimates of the line locations with their associated error bars or confidence intervals implicitly assume that the likelihood function is unimodal and bell shaped . because this assumption is clearly and dramatically violated , these standard summary statistics are unreliable and inadequate . unfortunately , there are no readily available and generally applicable simple statistical summaries to handle highly multimodal likelihoods . instead we must develop summaries that are tailored to the specific scientific goals in a given analysis . because general strategies for dealing with multimodal likelihood functions are little known to astronomers and specific strategies for dealing with multimodal likelihood functions for the location of narrow spectral lines do not exist , one of the primary goals of this article is to develop and illustrate these methods . a fully bayesian analysis of our spectral model with narrow emission lines is computationally demanding , even with our new algorithms . thus , we develop techniques that are much quicker and give similar results for the location of emission lines . these methods based on the so - called _ profile posterior distribution _ do not stand on as firm of a theoretical footing as a fully bayesian analysis , but are much quicker and thus better suited for _ exploratory data analysis_. the profile posterior distribution along with our exploratory methods are fully described and compared with the more sophisticated bayesian analysis . [ [ challenge-3-testing - for - the - presence - of - narrow - lines . ] ] challenge 3 : testing for the presence of narrow lines . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + in addition to fitting the location of one or more emission lines , we often would like to perform a formal test for the inclusion of the emission lines in the statistical model . that is , we would like to quantify the evidence in a potentially sparse data set for a particular emission line in the source . testing for a spectral line is an example of a notoriously difficult statistical problem in which the standard theory does not apply . there are two basic technical problems . first , the simpler model that does not include a particular emission line is on the boundary of the larger model that does include the line . that is , the intensity parameter of an emission line is zero under the simpler model and can not be negative under the larger model . an even more fundamental problem occurs if either the line location or width is fit , because these parameters have _ no value _ under the simpler model . the behavior ( i.e. , sampling distribution ) of the likelihood ratio test statistic under the simpler model is not well understood and can not be assumed to follow the standard @xmath2 distribution , even asymptotically . @xcite propose a monte - carlo - based solution to this problem based on the method of posterior predictive p - values @xcite . in this article we extend the application of protassov _ et al_. s solution to the case when we fit the location of a narrow emission line , a situation that was avoided in @xcite . the remainder of the article is organized into four sections . [ park : sec : model - based ] reviews bayesian inference and monte carlo methods with an emphasis on multimodal distributions , outlines our computation methods , proposes new summaries of multimodal distributions , and describes exploratory statistical methods in this setting . we introduce illustrative examples in [ park : sec : model - based ] , but detailed spectral analysis is postponed in order to allow us to focus on our proposed methods . in [ park : sec : simul ] , a simulation study is performed to investigate the statistical properties of our proposed methods , with some emphasis placed on the potential benefits of model misspecification . [ park : sec : quasar ] presents the analysis of the high redshift quasar pg1634 + 706 , and how to test for the inclusion of the line in the spectral model . concluding remarks appear in [ park : sec : conclusion ] . an appendix outlines the computational methods we developed specifically for fitting the location of narrow emission lines .

the poisson nature of the photon counts leads to local random fluctuations in the observed spectrum that often results in excess emission in a narrow band of energy resembling a weak narrow line . from a formal statistical perspective , this leads to a ( sometimes highly ) multimodal likelihood . bayesian methods offer a more direct paradigm for accounting for such complicated likelihood functions but even here multimodal likelihoods pose significant computational challenges . standard statistical quantities such as means and standard deviations can not adequately summarize inference and standard testing procedures can not be used to test for emission lines . in this paper we illustrate and validate our methods using simulation studies and apply them to the _ chandra _ observations of the high redshift quasar pg1634 + 706 .

the detection and quantification of narrow emission lines in x - ray spectra is a challenging statistical task . the poisson nature of the photon counts leads to local random fluctuations in the observed spectrum that often results in excess emission in a narrow band of energy resembling a weak narrow line . from a formal statistical perspective , this leads to a ( sometimes highly ) multimodal likelihood . many standard statistical procedures are based on ( asymptotic ) gaussian approximations to the likelihood and simply can not be used in such settings . bayesian methods offer a more direct paradigm for accounting for such complicated likelihood functions but even here multimodal likelihoods pose significant computational challenges . the new markov chain monte carlo ( mcmc ) methods developed in and , however , are able to fully explore the complex posterior distribution of the location of a narrow line , and thus provide valid statistical inference . even with these computational tools , standard statistical quantities such as means and standard deviations can not adequately summarize inference and standard testing procedures can not be used to test for emission lines . in this paper , we use new efficient mcmc algorithms to fit the location of narrow emission lines , we develop new statistical strategies for summarizing highly multimodal distributions and quantifying valid statistical inference , and we extend the method of posterior predictive p - values proposed by to test for the presence of narrow emission lines in x - ray spectra . we illustrate and validate our methods using simulation studies and apply them to the _ chandra _ observations of the high redshift quasar pg1634 + 706 .

0808.3164

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using a poisson model for the photon counts , the likelihood function of the parameter in the spectral model described in [ park : sec : model ] is given by @xmath35 $ ] where @xmath36 denotes the observed photon counts . with likelihood - based methods , the parameter value that maximizes the probability of the observed data is generally chosen as an estimate of @xmath3 ; this estimate is called the maximum likelihood estimate ( mle ) . in bayesian methods , prior knowledge for @xmath3 can be combined with the information in the observed data . prior distribution _ can be used to quantify information from other sources or to impose structure on a set of parameters . the prior distribution is combined with the likelihood to form a _ posterior distribution_. the prior distribution is denoted by @xmath37 and the posterior distribution by @xmath38 . bayesian inferences for @xmath3 are based on the posterior distribution . using bayes theorem , the prior distribution and the likelihood function are combined to form the posterior distribution via @xmath39 where the last proportionality holds because @xmath40 does not depend on @xmath3 and , given the observed data , is considered a constant . bayesian statistical inferences are made in terms of probability statements , which are quantified using various numerical summaries of the posterior distribution . to illustrate this , we consider a stylized right - skewed distribution ; see figure [ park : fig : skewed ] . this distribution is similar to the posterior distribution of the expected counts due to the emission line @xmath15 , @xmath14 , because this parameter is necessarily non - negative . although from a bayesian perspective the posterior distribution of a model parameter is the complete summary of statistical inference for that parameter , it is often useful to summarize the posterior distribution using point estimates or intervals . commonly used bayesian point estimates of a parameter are the mean , median , and mode(s ) of the posterior distribution . error bars for the point estimates can be computed based on the variation of the posterior distribution . the equal - tail interval and the highest posterior density ( hpd ) interval are both commonly used summaries of uncertainty . for example , a 68% equal - tail posterior interval is the central interval of the posterior distribution and corresponds to the range of values of the parameter above and below which lies exactly 16% of the posterior probability . a 68% hpd interval , on the other hand , is the interval of values that contains 68% of posterior probability and within which the density is never lower than that outside the interval . the 68% hpd interval is the shortest possible interval that accounts for 68% of the posterior probability . this is illustrated in figure [ park : fig : skewed](a ) and ( b ) . the equal - tail interval achieves the same probability as the hpd interval by excluding a more likely region and by including a less likely region . when the posterior distribution is unimodal and symmetric , the equal - tail interval and the hpd interval are identical . in addition to computing parameter estimates and their error bars , it is often important to check if model assumptions are supported by the data . one way to do this is to generate simulated data under the model and compare the simulated data with the observed data ; refer to @xcite where this strategy is used to determine whether emission line profiles should be included in the spectral model for a gamma - ray burst . if the simulated data vary systematically for the observed data , it is an indication that the model used to simulate the data may not be adequate . in a bayesian analysis , we might generate such simulated data from the _ posterior predictive distribution _ , denoted by @xmath41 , i.e. , @xmath42 where @xmath43 represents an unknown future observation and the last equation follows because @xmath43 and @xmath44 are conditionally independent given @xmath3 . in words , the posterior predictive distribution averages the likelihood function over the posterior distribution of @xmath3 . data are simulated from the posterior predictive distribution and then used to make predictive inferences ; see [ park : sec : model - check ] for details . posterior simulation plays a central part in applied bayesian analysis because of the usefulness of a simulation that can often be relatively easily generated from a posterior distribution . in performing simulations , given a large enough sample , a histogram of a monte carlo simulation can provide practically complete information about an actual posterior distribution . figure [ park : fig : skewed](c ) shows that the histogram of the monte carlo simulation carries the same information as the posterior distribution itself . thus , once a monte carlo simulation is obtained , it can be used to compute the mean , variance , percentiles , and other summaries of the posterior distribution . in particular , with a random simulation of size @xmath45 , the posterior mean can be approximated as @xmath46 where @xmath47 is a simulation from the posterior distribution , @xmath38 . a 68% equal - tail posterior interval is computed by generating a monte carlo simulation of size @xmath45 from the posterior distribution , sorting the simulated values into increasing order , and choosing the @xmath48$]th and the @xmath49$]th values in the list . with the monte carlo simulation , a 68% hpd region is computed by segmenting the range of possible parameter values into bins , approximating the posterior probability of each bin as the proportion of the simulated values in that bin , and computing a region by beginning with the bin with the largest posterior probability and adding additional bins in the order of their posterior probabilities until the resulting region contains at least 68% of the posterior probability . our search for a narrow emission line begins by finding modes of its posterior distribution that correspond to plausible locations of an emission line . to find the modes ( and to compte the profile posterior distribution ) , we use an algorithm optimized for this problem ( i.e. , the rotation(9 ) em - type algorithm , see appendix [ ap : alg ] and @xcite for details ) . because the posterior distribution of the line location is highly multimodal ( see [ park : sec : mm ] ) , the algorithm is run using multiple starting values selected across the entire energy range of possible line locations , e.g. , 50 starting values for the line location equally spaced between 1.0 kev and 6.0 kev . using multiple starting values enables us to identify the important local modes of the posterior distribution . it is important to use enough starting values to ensure all of the important modes are identified . this is a standard strategy , long advocated in texts on bayesian data analysis @xcite and is closely related to the computation of the profile posterior distribution described in [ park : sec : advise ] . the profile posterior distribution is computed by fixing the line location at each value of a fine grid , finding the posterior modes of the other model parameters , and plotting the resulting maximum posterior probability as a function of the line location . this procedure corresponds to the projected delta - chi - square method in the chi - square setting , see @xcite and @xcite . mode finding also begins with a fine grid of starting values , but we run the mode finder allowing all parameters including the line location to be fit . after the modes are found , monte carlo simulation techniques optimized to this problem can be run to further investigate the uncertainty of the possible line locations . we employ state - of - the - art mcmc samplers , i.e. , partially collapsed gibbs ( pcg ) i for the delta function emission line and pcg ii for the gaussian emission line to obtain the posterior distribution of line location ; see appendix [ ap : alg ] , @xcite , and @xcite for details . to ensure the convergence of a markov chain constructed by the mcmc samplers , we run multiple chains with overdispersed starting values ( e.g. , 1 kev , 3 kev , and 5 kev for the line location parameter ) and monitor the convergence qualitatively and quantitatively . for example , we compute the estimate of the potential scale reduction @xcite , denoted by @xmath50 , for all parameters of interest . if @xmath50 is near 1 ( e.g. , below 1.2 ) for each of the parameters , we collect the second halves of the chains together and use these monte carlo draws for inference ; see @xcite for theoretical justification and discussion . there are of course many strategies that one might employ to construct efficient monte carlo samplers . methods based on annealing or tempering , or that use explicitly parallel methods are often useful for exploring multimodal posterior distributions . given the low autocorrelation of the simulated values produced by our method , we have not pursued these strategies . fitting a narrow emission line often tends to yield a highly multimodal posterior distribution of the line location , as shown in figure [ park : fig : hpd ] . thus , we are interested in the two types of intervals for the posterior distributions : an equal - tail posterior interval and an hpd region . figure [ park : fig : hpd ] illustrates a 68% equal - tail posterior interval and a 68% hpd region for the line location when its posterior distribution is highly multimodal . this is only an example of a highly multimodal posterior distribution . we come to the details of our analysis of a line location in [ park : sec : simul ] . the 68% equal - tail posterior interval is a central interval , so that it includes segments with nearly zero posterior probability here and there within the interval . because the posterior distribution of the line location in figure [ park : fig : hpd ] is multimodal , the 68% hpd region consists of the four shaded disjoint intervals ; notice that the height of each of the histogram bars outside the hpd region is less than that of those within the region . in such a multimodal posterior distribution , the hpd region not only is shorter in length but also conveys more information as to likely locations of the line than does the equal - tail interval . in figure [ park : fig : hpd ] , we use a coarse binning to illustrate the distinction between the equal - tail posterior interval and hpd region . this results in a posterior region that is relatively imprecise ; in our spectral analysis , we use a finer binning to construct a more precise region from a monte carlo simulation . when the posterior distribution of the line location is plotted with the same fine binning as the _ chandra _ energy spectrum , however , it may not be smooth due to monte carlo errors , as shown in the top panel of figure [ park : fig : hpd - illust ] . an hpd region computed from the unsmoothed posterior distribution may result in a combination of too many posterior intervals . to avoid such fragmentation of hpd regions , we use gaussian kernel smoothing to smooth the posterior distribution before we compute hpd regions . the middle panel of figure [ park : fig : hpd - illust ] presents the smoothed posterior distribution resulting from applying gaussian kernel smoothing with standard deviation equal to the bin size of the _ chandra _ energy spectrum , i.e. , 0.01 kev . the smoothed posterior distribution smooths out lower posterior probabilities but does not flatten higher posterior probabilities too much . we propose a new graphical summary to better describe the hpd regions of a ( smoothed ) multimodal posterior distribution . an _ hpd graph _ is constructed by plotting a series of hpd regions against their corresponding hpd levels . for example , for the data set used to compute the posterior distribution in figure [ park : fig : hpd - illust ] , we compute 100 hpd regions , one for each of 100 levels , 1% , 2% , @xmath51 , and 100% . each of these regions is a union of possible values of the line location . we can plot the line location on the horizontal axis and the level on the vertical axis . each of the 100 hpd regions can then be plotted as a union of horizonal line intervals at the appropriate level of the hpd region on the vertical axis . the resulting hpd graph lets us visualize many hpd regions with varying levels , so that all the important modes of a multimodal distribution can be effectively summarized with their relative posterior probabilities . as an illustration , we computed the three hpd regions with levels 50% , 68% , and 95% , and plotted them in the middle panel of figure [ park : fig : hpd - illust ] along with the smoothed posterior distribution . the solid lines indicate the disjoint intervals that compose each hpd region , and the dotted lines the intervals outside the hpd region . the bottom panel in figure [ park : fig : hpd - illust ] shows the hpd graph in grey with the three hpd intervals from the middle plot superimposed . , where each marginal standard deviation corresponds to the size of an energy bin in the _ chandra _ spectrum . based on the smoothed posterior distribution , we compute ten 2-d hpd regions with levels ranging from 10% to 100% . these regions are plotted with different shades of grey in the 2-d hpd graph shown in the right panel.,width=576 ] when there are two parameters of interest , the 1-d hpd graph can be extended to a 2-d hpd graph . that is , a joint posterior distribution is computed from a monte carlo simulation by using bivariate gaussian kernel smoothing and used to construct 2-d hpd regions with various levels . these hpd regions can then be plotted with different shades of grey . for example , figure [ park : fig : twod - hpd - illust ] shows the 2-d hpd graph computed for the joint posterior distribution of two possible line locations ; see [ park : sec : simul2 ] for further discussion on the scatter plot . the left panel of figure [ park : fig : twod - hpd - illust ] is an unsmoothed joint posterior distribution . after applying bivariate gaussian kernel smoothing , 10 hpd regions ( one for each of 10 levels , 10% , 20% , ... , and 100% ) are computed and plotted with different shades of grey from black ( 10% ) to white ( 100% ) , as shown in the right panel of figure [ park : fig : twod - hpd - illust ] . hpd regions with lower levels contain pixels with higher posterior probabilities , so that darker pixels indicate more probable regions of the two line locations . multimodal likelihoods and posterior distributions pose another challenge for statistical analysis . the calibration of many standard statistical procedures is based on the asymptotic gaussian nature of the likelihood and posterior distribution . thus , standard methods for computing error bars and confidence intervals rely on the likelihood being at least approximately gaussian . when the likelihood function exhibits the multimodal features that we see in figures [ park : fig : hpd - illust ] and [ park : fig : twod - hpd - illust ] , these standard results simply do not apply . one consequence of this is that the nominal level of an interval may not match its frequency coverage . that is , if we were able to repeat our observation many times , we would find that percentage of intervals that contain the true line location might differ from the nominal level of the interval . in [ park : sec : simul ] , we find that the posterior distribution is highly multimodal when the true emission line is weak or there are several emission lines in a spectrum . in this case , we also find that by _ misspecifying _ the model we are able to improve the frequency properties of our proposed method . in particular , we find that using a delta function line profile improves the properties of our procedure even when the true line has appreciable width . as discussed in [ park : sec : mm ] , the posterior distribution of a narrow emission line location tends to be highly multimodal . in this case , the profile posterior distribution can be used as a handy and quick - to - compute summary of the posterior distribution to explore the possible locations of a spectral line . the profile posterior distribution is the posterior distribution of a parameter evaluated at the values of the other parameters that maximize the posterior distribution . the profile posterior distribution is a bayesian analogue to the profile likelihood , a standard likelihood method for dealing with nuisance parameters ; see @xcite or @xcite for applications of the profile likelihood . in the context of parameter estimation , the distribution of the minimum @xmath2 statistic described by @xcite is closely related to the profile posterior distribution . generally we do not advocate using the profile posterior distribution as a substitute for the marginal posterior distribution because interval or region estimates computed with the profile posterior distribution have rather unpredictable statistical properties . the marginal posterior distribution is obtained by integrating out ( i.e. , averaging over ) the other parameters and computing the marginal posterior distribution requires sophisticated numerical integration methods such as mcmc especially when the dimension of the nuisance parameters is large . however , the profile posterior distribution can be computed without mcmc and , as an analogue to the marginal posterior distribution , can be used to roughly examine the posterior distribution of a model parameter . thus , we believe the profile posterior distribution is well suited for the initial exploration of the data because it gives a clear and reliable set of potential locations for spectral lines . the profile posterior distribution can be computed on a fine grid of the possible values of the line location by running an optimizer to maximize over the other model parameters for each value of the line location on the grid ; we recommend using stable optimizers such as em - type algorithms @xcite . the profile posterior distribution of the line location computed in this way is computationally less demanding and cheaper in terms of cpu time than the marginal posterior distribution produced by monte carlo methods such as mcmc .

many standard statistical procedures are based on ( asymptotic ) gaussian approximations to the likelihood and simply can not be used in such settings . the new markov chain monte carlo ( mcmc ) methods developed in and , however , are able to fully explore the complex posterior distribution of the location of a narrow line , and thus provide valid statistical inference . even with these computational tools ,

the detection and quantification of narrow emission lines in x - ray spectra is a challenging statistical task . the poisson nature of the photon counts leads to local random fluctuations in the observed spectrum that often results in excess emission in a narrow band of energy resembling a weak narrow line . from a formal statistical perspective , this leads to a ( sometimes highly ) multimodal likelihood . many standard statistical procedures are based on ( asymptotic ) gaussian approximations to the likelihood and simply can not be used in such settings . bayesian methods offer a more direct paradigm for accounting for such complicated likelihood functions but even here multimodal likelihoods pose significant computational challenges . the new markov chain monte carlo ( mcmc ) methods developed in and , however , are able to fully explore the complex posterior distribution of the location of a narrow line , and thus provide valid statistical inference . even with these computational tools , standard statistical quantities such as means and standard deviations can not adequately summarize inference and standard testing procedures can not be used to test for emission lines . in this paper , we use new efficient mcmc algorithms to fit the location of narrow emission lines , we develop new statistical strategies for summarizing highly multimodal distributions and quantifying valid statistical inference , and we extend the method of posterior predictive p - values proposed by to test for the presence of narrow emission lines in x - ray spectra . we illustrate and validate our methods using simulation studies and apply them to the _ chandra _ observations of the high redshift quasar pg1634 + 706 .

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uranium and thorium are regarded as potentially useful cosmochronometers because their long radioactive decay half - lives ( @xmath3th : 14.05 gyr , @xmath2u : 4.468 gyr ) are significant fractions of the expected age of the universe . all of the actinides , including uranium and thorium , are thought to be pure @xmath0-process elements , since the alternative neutron - capture process , the @xmath7-process , terminates at @xmath8bi . the excellent agreement of the relative abundances of neutron - capture elements in the extremely metal - poor ( @xmath9 } = - 3.1 $ ] ) , @xmath0-process - element - enhanced star cs 22892 - 052 with the solar @xmath0-process pattern initially suggested that thorium might serve as a precise cosmochronometer @xcite . the time that has passed since the production of the thorium that is now observed in the outer atmosphere of such an old halo star can be regarded as a hard lower limit on the age of the universe .- process ) species that have been incorporated into the outer atmosphere of a low - mass ( @xmath10 ) star that has not yet evolved past the giant branch stage of evolution , and hence is amenable to spectroscopic study . ] sneden et al . ( 1996 ) estimated the age of this star to be @xmath11 gyr , comparing the measured th / eu ratio with an initial production ratio constrained by theory . this age limit , albeit with a rather large error bar , is in good agreement with the age limits derived by completely different techniques , e.g. , for globular clusters ( @xmath12 gyr ; carretta et al . 2000 ) , for type ia supernovae ( @xmath13 gyr ; perlmutter et al . 1999 ) , and from the shape of acoustic peaks in the cosmic microwave background spectrum ( @xmath14 gyr ; knox , christensen , & skordis 2001 ) . one advantage of the thorium chronology is that , once the initial and current values of th/@xmath0 in the star are specified , the age of the star depends only on the half - life of @xmath3th determined in the laboratory . that is , one is not forced to invoke complex ( and no doubt incomplete ) models of galactic chemical evolution , although insight from making simple attempts can still be obtained ( e.g. , cowan et al . 1997 ) . here , @xmath0 denotes one of the stable @xmath0-process elements , often taken to be eu . in the most simple model , the initial value of th/@xmath0 may be regarded as that arising from a single supernova that exploded in the near vicinity ( and perhaps may have even triggered the formation of ) the presently observed star , e.g. , cs 22892 - 052 , early in the history of the galaxy . in fact , the large dispersion of eu / fe observed in halo stars ( more than 2 orders of magnitude ) has been naturally explained by chemical evolution models that make such assumptions @xcite . thus far , the initial production of th/@xmath0 has been determined by fitting theoretical nucleosynthesis results to the solar @xmath0-process pattern , with the assumption that the @xmath0-pattern was _ universal _ in all astrophysical environments @xcite . however , a recent abundance analysis of cs 22892 - 052 with keck i ( hires ) has shown that the lighter neutron - capture elements ( @xmath15 ) are distinctly underabundant with respect to the solar pattern , which is well fit by species with @xmath16 @xcite . this implies that there likely exists at least two @xmath0-process sites that must be invoked to account for the entire set of elements associated with the @xmath0-process @xcite . furthermore , it should be noted that although johnson & bolte ( 2001 ) have derived an estimate of the minimum age of the universe , @xmath17 gyr , based on the abundances of thorium and other stable neutron - capture elements in five metal - poor stars , the estimated ages of these stars are very widely spread , from @xmath18 to 18 gyr ( with overlapping error bars ) . in addition , recent spectroscopic studies of several extremely metal - poor halo stars with subaru ( hds ) has revealed that the spread of estimated chronometric ages from the th - eu pair appears to exceed the abundance uncertainties ( honda et al . 2002 , in preparation ) . taken at face value , these results imply that the universality of the @xmath0-pattern may not hold over the actinides either . the second discovered @xmath0-process - enhanced , extremely metal - poor star , cs 31082 - 001 ( @xmath9 } = -2.9 $ ] ) has provided a new , potentially quite powerful cosmochronometer , uranium @xcite . in principle , uranium might be expected to be a more precise chronometer than thorium owing to its shorter half life . cayrel et al . ( 2001 ) concluded that the age of this star is @xmath19 gyr , based on comparisons of the observed ratios of u / th , u / os , and u / ir with their estimated production ratios @xcite . the discovery of uranium in cs 31082 - 001 has also prompted additional laboratory work to refine the oscillator strengths , for both uranium and thorium ( nilsson et al . 2002a , b ) , that are required to turn spectroscopic observations into measured abundances . however , analysis of this star has also provided conclusive evidence that the @xmath0-process pattern is _ not universal _ over the actinides ; the ratio th / eu in this star is _ higher _ than that of the solar @xmath0-process ratio . cs 31082 - 001 would be younger than the solar system if the initial th / eu were taken to be universal , in conflict with the ages derived from ratios involving u and other stable @xmath0-process elements close to the third @xmath0-process peak . therefore , any age estimates that demand assumption of the universality of the @xmath0-process pattern may in fact be unreliable . in addition to the above non - universality problem , the initial @xmath0-process pattern has thus far been determined theoretically by the superposition of nucleosynthesis results , where one is forced to assume constant temperatures , neutron number densities , and exposure times ( or the number of captured neutrons ) the most recent exploration of this approach is presented in schatz et al . these approximations have been necessary because of the lack of a reliable astrophysical model for the @xmath0-process site ( at least that associated with the heavy @xmath0-process elements ) . at the moment , the neutrino - wind scenario is considered to be the most promising , ever since the work by woosley et al . ( 1994 ) , although alternative models involving neutron - star mergers have also shown some promise @xcite . however , even the neutrino - wind model encounters serious problems , e.g. , the high entropy ( @xmath20 ) that led to the robust @xmath0-processing in the woosley et al . scenario has not been duplicated by other work @xcite . the purpose of this paper is , therefore , to construct a realistic @xmath0-process model based on the neutrino - wind scenario , in order to derive initial production ratios that might be useful for estimation of the minimum age of the universe , in particular by use of the u - th chronometer pair . recently , wanajo et al . ( 2001 ) have demonstrated that the solar @xmath0-process pattern for @xmath21 is well reproduced in such a model from a compact proto - neutron star , owing to the inclusion of general relativistic effects . although recent hydrodynamic studies have encountered difficulties attaining the required compactness , we use their model along with some improvements to be discussed in 2 . although some severe problems yet remain , it is clearly important to determine the initial @xmath0-process pattern based on site - specific , rather than only site - independent , models . in 3 the @xmath0-process nucleosynthesis calculation is described , and the results are compared to the solar @xmath0-process pattern . the initial electron fraction , @xmath22 , is varied from 0.39 to 0.49 , but taken constant with time during the neutron - capture process . in 4 , the age of cs 31082 - 001 is derived by comparison of the nucleosynthesis results obtained for each @xmath22 with the abundance pattern of heavy elements in this star . the implications of this study are discussed in 5 .

the discovery of the second highly-process - enhanced , extremely metal - poor star , cs 31082 - 001 ( [ fe / h ] ) has provided a powerful new tool for age determination , by virtue of the detection and measurement of the radioactive species uranium and thorium . one of the serious limitations of this approach , however , is that predictions of the production ratio of u and th have not been made in the context of a realistic astrophysical model of the-process . we have endeavored to produce such a model , based on the `` neutrino winds '' that are expected to arise from the nascent neutron star of a core - collapse supernova . in this model , the proto - neutron star mass and the ( asymptotic ) neutrino sphere radius recent hydrodynamic studies indicate that there may exist difficulties in obtaining such a compact ( massive and/or small in radius ) remnant . the electron fraction is taken to be a free parameter , constant with time . the mass - integrated-process yields , obtained by assuming a simple time evolution of the neutrino luminosity , are compared to the available spectroscopic elemental abundance data of cs 31082 - 001 . as a result , the `` age '' of this star

the discovery of the second highly-process - enhanced , extremely metal - poor star , cs 31082 - 001 ( [ fe / h ] ) has provided a powerful new tool for age determination , by virtue of the detection and measurement of the radioactive species uranium and thorium . because the half - life ofu is one - third that ofth , the u - th pair can , in principle , provide a far more precise cosmochronometer than the th - eu pair that has been used in previous investigations . in the application of this chronometer , the age of ( the progenitor of ) cs 31082 - 001 can be regarded as the minimum age of the galaxy , and hence of the universe . one of the serious limitations of this approach , however , is that predictions of the production ratio of u and th have not been made in the context of a realistic astrophysical model of the-process . we have endeavored to produce such a model , based on the `` neutrino winds '' that are expected to arise from the nascent neutron star of a core - collapse supernova . in this model , the proto - neutron star mass and the ( asymptotic ) neutrino sphere radius are assumed to be and 10 km , respectively . recent hydrodynamic studies indicate that there may exist difficulties in obtaining such a compact ( massive and/or small in radius ) remnant . nevertheless , we utilize this set of parameter choices since previous work suggests that the third-process peak ( and thus u and th ) is hardly reached when one adopts a less compact proto - neutron star in the framework of the neutrino - wind scenario . the temperature and density histories of the material involved in the neutron - capture processes are obtained with the assumption of a steady flow of the neutrino - powered winds , with general relativistic effects taken into account . the electron fraction is taken to be a free parameter , constant with time . the-process nucleosynthesis in these trajectories is calculated with a nuclear reaction network code including actinides up to . the mass - integrated-process yields , obtained by assuming a simple time evolution of the neutrino luminosity , are compared to the available spectroscopic elemental abundance data of cs 31082 - 001 . as a result , the `` age '' of this star is determined to be gyr , in excellent agreement with lower limits on the age of the universe estimated by other dating techniques , as well as with other stellar radioactive age estimates . future measurements of pt and pb in this star , as well as expansion of searches for additional-process - enhanced , metal - poor stars ( especially those in which both u and th are measurable ) , are of special importance to constrain the current astrophysical models for the-process .

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we have constructed a robust model of the @xmath0-process based on the neutrino - wind scenario for application to the u - th cosmochronology . the model of neutrino winds was taken from otsuki et al . ( 2000 ) and wanajo et al . ( 2001 ) , along with some improvements described above . the @xmath0-process with various neutron star masses ( @xmath175 ) and radii ( @xmath176 ) has already been explored extensively by wanajo et al . thus , @xmath175 and ( asymptotic ) @xmath105 were fixed to be @xmath4 and 10 km , respectively , for which the most robust @xmath0-processing was realized . on the other hand , the initial electron fraction @xmath22 ( assumed constant with time ) was taken to be a free parameter , rather than fixed to be 0.40 as in wanajo et al . ( 2001 ) . the model was tuned to fit the solar @xmath0-process pattern , since recent spectroscopic studies of extremely metal - poor stars have indicated a _ universal _ ( solar @xmath0-like ) abundance pattern , at least between the second and third r - process peaks . attention was paid to reproduce the pattern near @xmath177 , being close to th and u in mass number . we introduced the freezeout temperature , @xmath35 , as the most crucial parameter for constructing the model . comparing the nucleosynthesis results with the solar @xmath0-process pattern , @xmath35 was determined to be @xmath178 k. the nucleosynthesis yields were mass - integrated assuming simple evolutions of @xmath32 and @xmath105 . the results between @xmath134 and 200 for @xmath133 models were in good agreement with the solar @xmath0-pattern , although the production of th and u differed from model to model . the results of our nucleosynthesis predictions were compared to the spectroscopic abundance pattern of the @xmath0-process - enhanced metal - poor star cs 31082 - 001 . explorations of various combinations between the actinides and stable isotopes indicated that the @xmath179 case was found to be the best models for the age determination in this study . as a result , the age of cs 31082 - 001 was determined to be @xmath6 gyr by use of the u - th chronometer , which can be regarded as a hard lower limit on the age of the universe . in fact , this age is in excellent agreement with the age of the universe derived by other dating techniques ( e.g. , globular clusters , type ia supernovae , and the cosmic - microwave background ) , as well as with other stellar radioactive age estimates using the th - eu @xcite and u - th @xcite pairs . such a strong constraint on the age of this star was only made possible by the use of u and th in conjunction with one another . without uranium , the chronometers involving th alone presented only rather loose constraints . in this study the pb abundance in cs 31082 - 001 was not available for age determination , since only an upper limit on its abundance has been presented to date . it should be noted that the predicted pb abundance for @xmath180 case is _ higher _ than this upper limit , which seems difficult to solve @xcite . it is noteworthy , however , that freezeout effects can increase the ratio th - u / pb - bi ( see 3 ) , which should be examined further , as well as with other nuclear data sets . it remains possible that the solar @xmath0-process pb abundance , inferred from the residual of the solar @xmath7-process components , is not correct @xcite . clearly , re - investigation of the pb abundance in cs 31082 - 001 , as well expansion of the searches for additional @xmath0-process - enhanced metal - poor stars , in which both u and th are measurable , are highly desirable in the near future . it is also of importance to obtain measurements of the pt abundance in cs 31082 - 001 ( which is only possible with the strong pt absorption features observable in the near uv from space ) , so as to constrain the height , as well as the position , of the third peak @xcite . we emphasize that the conclusions in this study should be considered as merely the first step toward a better understanding of the dating technique involving the u - th chronometer . in particular , we note that the inferred age of cs 31082 - 001 could be significantly changed if we had utilized a different nuclear mass model , as demonstrated by griely and arnould ( 2001 ) . we expect , however , that a detailed comparison of the nucleosynthesis results with the solar @xmath0-process pattern , as in 3 , can distinguish better mass models . we suggest that the freezeout temperature , @xmath35 ( or the asymptotic temperature in more realistic models ) , is a useful parameter , as the freezeout effects are of importance to the final @xmath0-process pattern . while the waiting - point approximation , often referred to as the `` classical @xmath0-process model , '' has been an effective ( and thus far , the only ) method used to test the nuclear mass models , we should keep in mind that non - equilibrium processes can lead to non - negligible effects , as discussed in 3 ( e.g. , the positions of the @xmath0-process peaks , the smoothness of abundance pattern , and the ratio th - u / pb - bi ) . it should also be noted that we would not insist that the neutrino - wind model explored in this study is necessarily the best ( or only ) astrophysical site for the @xmath0-process . in fact , the physical conditions in this model , namely , the rather massive proto - neutron star ( @xmath4 ) with rapid contraction of @xmath105 to be 10 km , seem difficult to be achieved according to the current hydrodynamic studies . clearly , more study is needed to seek the true @xmath0-process site . nevertheless , it is encouraging that the age of the cs 31082 - 001 determined in this study is in excellent agreement with the age of the universe derived by other dating techniques . we hope our results provide some fresh insights to the future modeling of the true astrophysical @xmath0-process site . we would like to acknowledge v. hill for providing an up - to - date abundance table for cs 31082 - 001 prior to publication . we also thank h. schatz for helpful discussions , and the referee , j. j. cowan , who helped us to improve this paper . s. w. thanks k. sumiyoshi and h. utsunomiya for providing data for the @xmath181be reaction . this work was supported by a grant - in - aid for scientific research ( 13740129 ) from the ministry of education , culture , sports , science , and technology of japan . t.c.b acknowledges partial support from nsf grants ast-00 98549 and ast-00 98508 . t.c.b . would also like to recognize partial support from an international scholar fellowship from the ministry of education , culture , sports , science , and technology of japan , which supported his sabbatical stay in tokyo , where discussions leading to the present paper were initiated . ccccccccccc 0.60 & 0.24 & 0.02 & 0.08 & 0.21 & 0.11 & 0.01 & 0.04 & 0.10 & 0.44 & 0.47 + 0.70 & 0.36 & 0.02 & 0.09 & 0.27 & 0.17 & 0.01 & 0.04 & 0.13 & 0.47 & 0.46 + 0.80 & 0.55 & 0.02 & 0.13 & 0.36 & 0.25 & 0.01 & 0.06 & 0.17 & 0.46 & 0.45 + 0.90 & 0.46 & 0.02 & 0.14 & 0.50 & 0.23 & 0.01 & 0.07 & 0.25 & 0.50 & 0.44 + 1.00 & 0.38 & 0.02 & 0.15 & 0.45 & 0.19 & 0.01 & 0.07 & 0.22 & 0.49 & 0.52 + 1.10 & 0.41 & 0.03 & 0.14 & 0.47 & 0.18 & 0.02 & 0.06 & 0.21 & 0.44 & 0.41 + 1.20 & 0.17 & 0.06 & 0.09 & 0.46 & 0.06 & 0.02 & 0.03 & 0.16 & 0.36 & 0.40 + 1.30 & 0.05 & 0.09 & 0.05 & 0.23 & 0.01 & 0.03 & 0.02 & 0.07 & 0.32 & 0.24 + 1.40 & 0.03 & 0.15 & 0.06 & 0.27 & 0.01 & 0.03 & 0.01 & 0.05 & 0.18 & 0.19 ccccc 0.39 & @xmath182 & @xmath183 & 0.50 & 0.042 + 0.40 & @xmath184 & @xmath185 & 0.50 & 0.025 + 0.41 & @xmath186 & @xmath187 & 0.52 & 0.014 + 0.42 & @xmath188 & @xmath189 & 0.51 & 0.005 + 0.43 & @xmath190 & @xmath191 & 0.51 & 0.002 + 0.49 & @xmath192 & @xmath193 & 0.40 & 0.000 rrrrrrrrrr 0.39 & 0.18 & @xmath1940.18 & @xmath1940.60 & @xmath1941.08 & @xmath1940.11 & @xmath1940.47 & @xmath1940.89 & @xmath1941.37 & @xmath1940.29 + 0.40 & 0.05 & @xmath1940.41 & @xmath1940.84 & @xmath1941.27 & @xmath1940.24 & @xmath1940.70 & @xmath1941.13 & @xmath1941.57 & @xmath1940.29 + 0.41 & @xmath1940.11 & @xmath1940.68 & @xmath1941.10 & @xmath1941.48 & @xmath1940.40 & @xmath1940.97 & @xmath1941.39 & @xmath1941.76 & @xmath1940.29 + 0.42 & @xmath1940.58 & @xmath1941.16 & @xmath1941.56 & @xmath1941.85 & @xmath1940.89 & @xmath1941.47 & @xmath1941.87 & @xmath1942.16 & @xmath1940.31 + 0.43 & @xmath1940.92 & @xmath1941.43 & @xmath1941.82 & @xmath1942.06 & @xmath1941.24 & @xmath1941.75 & @xmath1942.13 & @xmath1942.38 & @xmath1940.32 + 0.49 & @xmath1942.75 & @xmath1942.50 & @xmath1942.83 & @xmath1943.17 & @xmath1943.13 & @xmath1942.89 & @xmath1943.21 & @xmath1943.55 & @xmath1940.38 rrrrrrrr 0.39 & 18.77 & 57.52 & 27.18 & 15.63 & 27.95 & 18.30 & 14.16 + 0.40 & 12.61 & 46.73 & 16.09 & 13.62 & 24.47 & 14.73 & 14.10 + 0.41 & 5.17 & 34.01 & 3.64 & 11.32 & 20.49 & 10.83 & 14.19 + 0.42 & @xmath19416.90 & 11.67 & @xmath19417.55 & 3.97 & 13.05 & 3.76 & 13.70 + 0.43 & @xmath19432.54 & @xmath1940.84 & @xmath19429.64 & @xmath1941.12 & 8.96 & @xmath1940.20 & 13.53 + 0.49 & @xmath194118.21 & @xmath19451.05 & @xmath19476.97 & @xmath19429.30 & @xmath1947.94 & @xmath19416.18 & 12.16 aboussir , y. , pearson , j. m. , dutta , a. k. , & tondeur , f. 1995 , at . data nucl . data tables , 61 , 127 arlandini , c. , kppeler , f. , wisshak , k. , gallino , r. , busso , m. , & straniero , o. 1999 , , 525 , 886 burrows , a. , hayes , j. , & fryxell , b. a. 1995 , , 450 , 830 cardall , c. y. & fuller , g. m. 1997 , , 486 , l111 carretta , e. , gratton , r. g. , clementini , & g. , fusi pecci , f. 2000 , , 533 , 215 cayrel , r. , hill , v. , beers , t.c . , barbuy , b. , spite , m. , spite , f. , plez , b. , andersen , j. , bonifacio , p. , franois , p. , molaro , p. , nordstrm , b. , & primas , f. 2001 , , 409 , 691 cowan , j. j. , thielemann , f. -k . , & truran , j. w. 1991 , , 208 , 267 cowan , j. j. , mcwilliam , a. , sneden , c. , & burris , d. l. 1997 , , 480 , 246 cowan , j. j. , pfeiffer , b. , kratz , k. -l . , thielemann , f. -k . , sneden , c. , burles , s. , tytler , d. , & beers , t. c. 1999 , , 521 , 194 cowan , j. j. et al . 2002 , , in press ( astro - 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verlag , berlin , p. 189 itoh , n. , hayashi , h. , nishikawa , a. , & kohyama , y. 1996 , , 102 , 411 johnson , j. a. & bolte , m. 2001 , , 554 , 888 kppeler , f. , beer , h. , & wisshak , k. 1989 , rep . phys . , 52 , 945 knox , l. , christensen , n. , & skordis , c. 2001 , , 563 , l95 meyer , b. s. , mclaughlin , g. c. , & fuller g. m. 1998 , , 58 , 3696 mller , p. , nix , j. r. , myers , w. d. , & swiatecki , w. j. 1995 , at . data nucl . data tables , 59 , 131 nilsson , h. , ivarsson , s. , johansson , s. , & lundberg , h. 2002a , , 381 , 1090 nilsson , h. , zhang , z. , lundberg , h. , johansson , s. , & nordstrm , b. 2002b , , in press 381 , 1090 otsuki , k. , tagoshi , h. , kajino , t. , & wanajo , s. 2000 , , 533 , 424 perlmutter , s. et al . 1999 , , 517 , 565 qian , y. -z . & woosley , s. e. 1996 , , 471 , 331 qian , y. -z . 2000 , , 534 , l67 schatz , h. , toenjes , r. , kratz , k .- pfeiffer , b. , beers , t.c . , cowan , j.j . , & hill , v. 2002 , , submitted sneden , c. , mcwilliam , a. , preston , g. w. , cowan , j. j. , burris , d. l. , & armosky , b. j. 1996 , , 467 , 819 sneden , c. , cowan , j. j. , ivans , i. i. , fuller , g. m. , burles , s. , beers , t. c. , lawler , j. e. 2000 , , 533 , l139 sneden , c. , cowan , j. j. , lawler , j. e. , burles , s. , beers , t. c. , & fuller , g. m. 2002 , , 566 , l25 takahashi , k. , witti , j. , & janka , h. -th . 1994 , , 286 , 857 terasawa , m. , sumiyoshi , k. , kajino , t. , mathews , g. j. , & tanihata i. 2001 , , 562 , 470 thompson , t. a. , burrows , a. , & meyer , b. s. 2001 , , 562 , 887 tsujimoto , t. , shigeyama , t. , & yoshii , y. 2000 , , 531 , l33 utsunomiya , h. , yonezawa , y. , akimune , h. , yamagata , t. , ohta , m. , fujishiro , m. , toyokawa , h. , & phgaki , h. 2001 , , 63 , 18801 wanajo , s. , kajino , t. , mathews , g. j. , & otsuki , k. 2001 , , 554 , 578 woosley , s. e. , wilson , j. r. , mathews , g. j. , hoffman , r. d. , & meyer , b. s. 1994 , , 433 , 229

, the age of ( the progenitor of ) cs 31082 - 001 can be regarded as the minimum age of the galaxy , and hence of the universe . is determined to be gyr , in excellent agreement with lower limits on the age of the universe estimated by other dating techniques , as well as with other stellar radioactive age estimates . future measurements of pt and pb in this star , as well as expansion of searches for additional-process - enhanced , metal - poor stars ( especially those in which both u and th are measurable ) , are of special importance to constrain the current astrophysical models for the-process .

the discovery of the second highly-process - enhanced , extremely metal - poor star , cs 31082 - 001 ( [ fe / h ] ) has provided a powerful new tool for age determination , by virtue of the detection and measurement of the radioactive species uranium and thorium . because the half - life ofu is one - third that ofth , the u - th pair can , in principle , provide a far more precise cosmochronometer than the th - eu pair that has been used in previous investigations . in the application of this chronometer , the age of ( the progenitor of ) cs 31082 - 001 can be regarded as the minimum age of the galaxy , and hence of the universe . one of the serious limitations of this approach , however , is that predictions of the production ratio of u and th have not been made in the context of a realistic astrophysical model of the-process . we have endeavored to produce such a model , based on the `` neutrino winds '' that are expected to arise from the nascent neutron star of a core - collapse supernova . in this model , the proto - neutron star mass and the ( asymptotic ) neutrino sphere radius are assumed to be and 10 km , respectively . recent hydrodynamic studies indicate that there may exist difficulties in obtaining such a compact ( massive and/or small in radius ) remnant . nevertheless , we utilize this set of parameter choices since previous work suggests that the third-process peak ( and thus u and th ) is hardly reached when one adopts a less compact proto - neutron star in the framework of the neutrino - wind scenario . the temperature and density histories of the material involved in the neutron - capture processes are obtained with the assumption of a steady flow of the neutrino - powered winds , with general relativistic effects taken into account . the electron fraction is taken to be a free parameter , constant with time . the-process nucleosynthesis in these trajectories is calculated with a nuclear reaction network code including actinides up to . the mass - integrated-process yields , obtained by assuming a simple time evolution of the neutrino luminosity , are compared to the available spectroscopic elemental abundance data of cs 31082 - 001 . as a result , the `` age '' of this star is determined to be gyr , in excellent agreement with lower limits on the age of the universe estimated by other dating techniques , as well as with other stellar radioactive age estimates . future measurements of pt and pb in this star , as well as expansion of searches for additional-process - enhanced , metal - poor stars ( especially those in which both u and th are measurable ) , are of special importance to constrain the current astrophysical models for the-process .

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bars and spirals are an important part of the morphology of disk galaxies . these showy disk morphological features which characterize the ( hubble ) tuning fork " ( firmani & avila - reese 2003 ) play a role in general classification schemes ( e.g. , hubble 1926 ; sandage 1961 ; de vaucouleurs 1959 ; sandage & bedke 1994 ) , and also can be tied to disk galaxy evolution ( e.g. , kormendy & kennicutt 2004 ) . over the past two decades , there has been a great deal of interest in the properties of bars , including quantification of bar strength ( e.g. , elmegreen & elmegreen 1985 ; martin 1995 ; wozniak et al . 1995 ; martinet & friedli 1997 ; rozas et al . 1998 ; aguerri et al . 1998 ; seigar & james 1998 ; aguerri 1999 ; chapelon et al . 1999 ; abraham & merrifield 2000 ; shlosman et al . 2000 ; buta & block 2001 ; laurikainen & salo 2002 ; knapen et al . 2002 ) , bar pattern speeds ( elmegreen et al . 1996 ; corsini et al . 2003 , 2004 ; debattista and williams 2004 ; aguerri et al . 2003 ; debattista et al . 2002 ; gerssen et al . 1999 ; merrifield and kuijken 1995 ) , mass inflow rates ( quillen et al . 1995 ) , and studies of the distribution of bar strengths ( block et al . 2002 ; whyte et al . 2002 ; buta , laurikainen , & salo 2004 ) . the most recent studies have indicated , on one hand , that bar and spiral strength can be quantified in a reasonable manner from near - infrared images and , on another hand , that such quantifications are useful for probing both bar and spiral evolution . the distribution of bar strengths is a particularly important issue . it is well known that as much as 70% of normal bright galaxies are barred at some level ( e.g. , eskridge et al . 2002 ) , which suggests that bars might be long - lived features . however , in the presence of gas , bars are not expected to be permanent features of galaxies , but should dissolve in much less than a hubble time owing to mass inflow into the nuclear region which can build up a central mass concentration and destroy a bar ( pfenniger and norman 1990 ) . the high frequency of bars has thus led to the idea that bars dissolve and reform many times during a hubble time ( combes 2004 ) . if this is the case , the distribution of bar strengths will tell us the relative amount of time a galaxy stays in a given bar state ( strong , weak , or non - barred ; bournaud & combes 2002 ; block et al . 2002 ) . block et al . ( 2002 ) and buta , laurikainen , & salo ( 2004=bls04 ) used the gravitational torque method ( gtm ; buta & block 2001 ; laurikainen & salo 2002 ) to derive maximum relative nonaxisymmetric torque strengths @xmath4 for the ohio state university bright galaxy survey ( osubgs , eskridge et al . 2002 ) , a statistically well - defined sample of nearby bright galaxies . block et al . ( 2001 , 2004 ) , bls04 , and laurikainen , salo , & rautiainen ( 2002 ) showed that @xmath4 correlates with deprojected bar ellipticity , a popular parameter suggested by athanassoula ( 1992 ) to be a useful ( although incomplete ) measure of bar strength ( e.g. , martin 1995 ; whyte et al . the correlation was found by laurikainen , salo , & rautiainen ( 2002 ) to be much better when objectively - measured near - ir ellipticities are used as opposed to the optical ellipticities estimated by martin ( 1995 ) from blue light photographs . the good correlation is very important , because the shape of the bar relates to the shape of the orbits which build up the bar , which should depend on the global force field . also , bls04 found that @xmath4 correlates well with the bar ellipticity parameter @xmath5 measured by whyte et al . @xmath4 is a bar strength indicator that is sensitive to the mass of the bar , and as such should be a better measure of bar strength than bar ellipticity . however , @xmath4 is affected also by spiral arm torques which can dominate over the torques due to weak bars . thus , @xmath4 alone can not tell us the actual distribution of bar strengths , but only the distribution for stronger bars . one way to derive the distribution of real bar strengths is to remove the spiral contribution to @xmath4 . buta , block , and knapen ( 2003=bbk03 ) developed a fourier - based method of separating bars from spirals that utilizes a symmetry assumption ( section 3 ) . block et al . ( 2004 ) applied this method to deep near - ir images of 17 bright galaxies to derive true bar strengths @xmath0 and spiral strengths @xmath3 . this analysis detected a possible correlation between @xmath0 and @xmath3 in the sense that among bars having @xmath0 @xmath6 0.3 , spiral strength increases with increasing bar strength . block et al . suggested that the apparent correlation implies that for stronger bars , the bar and the spiral grow together and have the same pattern speed . our goal with the present paper is to apply the bbk03 method to nearly 150 spiral galaxies in the osubgs , a database of @xmath7-band ( 1.65@xmath8 m ) images that have enough depth of exposure to allow reliable fourier analyses . in the @xmath7-band , the extinction is only 19% that in the @xmath9-band ( cardelli , clayton , & mathis 1989 ) , and such images are suitable for the derivation of gravitational potentials using fast - fourier transform techniques ( quillen , frogel , and gonzlez 1994 ; salo et al . 1999 ; laurikainen & salo 2002 ) . from the separated images , we derive the distributions of bar and spiral strengths and investigate what these tell us about disk galaxies . we also further investigate the correlation between @xmath0 and @xmath3 .

we have applied the bar / spiral separation method of buta , block , and knapen to derive the distribution of maximum relative gravitational bar torques , , for 147 spiral galaxies in the statistically well - defined ohio state university bright galaxy survey ( osubgs ) sample . our goal is to examine the properties of bars as independently as possible of their associated spirals .

the distribution of bar strengths in disk galaxies is a fundamental property of the galaxy population that has only begun to be explored . we have applied the bar / spiral separation method of buta , block , and knapen to derive the distribution of maximum relative gravitational bar torques , , for 147 spiral galaxies in the statistically well - defined ohio state university bright galaxy survey ( osubgs ) sample . our goal is to examine the properties of bars as independently as possible of their associated spirals . we find that the distribution of bar strength declines smoothly with increasing , with more than 40% of the sample having 0.1 . in the context of recurrent bar formation , this suggests that strongly - barred states are relatively short - lived compared to weakly - barred or non - barred states . we do not find compelling evidence for a bimodal distribution of bar strengths . instead , the distribution is fairly smooth in the range 0.0 0.8 . our analysis also provides a first look at spiral strengths in the osu sample , based on the same torque indicator . we are able to verify a possible weak correlation between and , in the sense that galaxies with the strongest bars tend also to have strong spirals .

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galaxies are complex systems consisting of a multitude of components that often require different approaches for both analytical and numerical study . the gaseous component can be described with the classic hydrodynamics equations ( che ) thanks to frequent collisions between constituent particles that act to isotropise the local pressure . on the other hand , stellar and dark matter particles lack collisions which effectively means the local pressure is anisotropic and should be described by a stress tensor . although this modification is rather straightforward to implement in the che ( see e.g. * ? ? ? * ; * ? ? ? * ) , this approach has mostly been applied to analytical and semi - analytical studies of growing instabilities in stellar systems ( e.g. * ? ? ? when it comes to numerical simulations of collisionless galactic components , n - body methods have often been the method of choice ( e.g. * ? ? ? one owes this to the relative ease with which they can be implemented and one can start modelling three - dimensional collisionless systems - often with rather small numbers of particles . in particular , large dark - matter - only n - body simulations ( e.g. the _ millennium simulation _ * ) have led to significant advances in our understanding of cosmological structure formation , allowing some of the founding tenets of the current paradigm to be tested . as simulations have grown in complexity , incorporating the effects of baryonic matter , it has become necessary for theorists to develop a wider range of techniques to model the gaseous component . for this , there exist two dominant approaches ; that of smooth particle hydrodynamics ( sph ) and alternatively , grid codes . whilst both approaches agree for simple tests where analytic solutions are available , discrepancies are still often found when modelling more complex phenomena . sph is very robust and memory efficient , allowing large cosmological runs to self - consistently model the effects of gas physics and collisionless matter ( see for example the _ owls _ and _ gimic _ simulations ; * ? ? ? * ; * ? ? ? * ) . however , due to the higher shock capturing powers and more flexible refinement criteria of mesh codes , along with the tendency of sph to suppress the formation of hydrodynamic instabilities and turbulent mixing @xcite , grid codes present a powerful alternative . in particular , grid based schemes are better suited to modelling small - scale physical processes such as heat conduction and radiative transfer . unfortunately , when coupling the collisionless matter to the collisionally dominated baryonic matter , it begins to become clear that the n - body approach is not always ideally suited to grid codes . in sph the gas is discretised into particles of a given mass , allowing the effects of gravity to be calculated using an n - body method in a very convenient self - consistent manner for all components . grid codes however require the mapping of the collisionless particle masses to the mesh , from which the global density field can be used to obtain the gravitational potential . this can be done using the multigrid technique @xcite with either a nested grid or adaptive mesh refinement ( amr ) . alternatively a fourier transform or a hybrid of the two can accelerate this process . once the gravitational acceleration is computed on the grid , it is then interpolated back to the particles . these are updated using a leapfrog method . this particle - mesh approach , a mapping of discrete particle properties to and from the mesh , represents a series of scientific and technical limitations to grid codes which degrade the physical reliability of their results and hampers the scalability of grid based simulations . these include : * _ spurious generation of entropy _ - the particle - mesh technique allows numerical noise to be introduced if insufficient particles are present in a given resolution element or `` cell . '' it has been argued by @xcite that in regions where the mesh is over - sampled relative to the number density of particles , then some cells may receive mass mapped from particles whilst their neighbours may not . this can lead to strong variations in the local density field when realistically the field should be smooth and continuous . this can drive spurious weak shocks and turbulence on small scales , generating an unphysical entropy excess . @xcite cites this as the origin of the higher entropy cores seen in galaxy cluster simulations when run using grid codes , compared to those run with sph codes which have cuspy low entropy cores @xcite . + as actually these particles should represent a continuous mass field , this effect can be limited by mapping the discrete mass of a given particle over a larger region using some pre - defined kernel function ( for example the cloud - in - cell technique ; * ? ? ? * ) , this however leads to more technical problems . * _ increased communication overhead _ - in massively parallel programs , a large amount of effort is often put into minimising communication between different nodes over the network . such communication is relatively time consuming , with latencies ( the time taken to establish and terminate a communication ) many orders of magnitude greater than the clock speed of the processor . as such , many calculations could be performed whilst waiting for a given group of processes to communicate , and if there is a list of different processes to communicate with , the time adds up . therefore any common communication scheme and grouping of messages , along with a reduction in the number of different nodes to which we must communicate with , presents a significant speed up in the code . + when particle masses are mapped using a kernel , there will inevitably be some overlap with neighbouring cells which may or may not reside on different nodes . although communication over the network is natural for any parallel simulation , it is lower when dealing with a system which advects only fluxes through cell surfaces instead of a system which can map mass to any neighbouring cell , whether it is directly adjacent to a face or merely in contact with an edge or vertex of the cell . this is demonstrated in figure [ fig : pmvsflux ] in which a schematic layout of two dimensional ( 2d ) block of cells ( as used in the flash code ) is shown along with the dashed outline of the neighbouring blocks which surround it . the internal cells in the block are shown in red and a surrounding layer four guardcells deep contains boundary data copied from neighbouring blocks . grey cells are guardcells which do not need to be updated or communicated for the given scheme , whilst green cells are guardcells which need to be updated or exchanged with neighbours . a 2d hydrodynamic simulation ( top panel ) requires the communication of boundary data to compute the four fluxes through its cell faces with the grey corner guardcells not being used . the bottom panel however , shows how mapping of particle mass over a kernel of finite size can lead to particle properties being mapped to any of the surrounding guardcells . this data then needs to be communicated to the internal cells of the blocks to which they correspond . thus in 2d the communication overhead is doubled , whilst in 3d it can increase by a factor of 3.3 ( 6 face fluxes / 20 edge and corner cells to which mass may be mapped ) . sophisticated space filling curves can help optimise the distribution of blocks ( or individual cells ) across nodes so that as many adjacent neighbours as possible reside on the same processor , minimising inter - node communication . however increased overhead remains unavoidable , especially as we always remain bottle - necked by the slowest processor if the simulation is to proceed in lock - step . * _ poor load balancing _ - the use of particles in conjunction with a mesh also presents a load - balancing issue as many forms of astrophysical structure formation result in the natural concentration of the majority of mass in dense compact regions . this leads to too many particles accumulating in one or two cells whilst the remaining cells have few or none , even if the initial particle distribution is fairly uniform . ultimately , the mass field ends up poorly sampled in the under - dense regions of the simulation whilst the mapping of properties to and from the mesh is performed by a limited number of cells within the densest regions . as already mentioned , the hydrodynamics requires that as many neighbouring cells as possible be stored on the same processor . therefore these heavily occupied dense cells are all stored on the same few processors leading to extremely poor load balancing . although distributing these dense blocks more evenly would improve the load balancing for the particle - mesh algorithm , it would ruin the load balancing for the hydrodynamics , creating an impossible system to optimise . fortunately the use of the collisionless boltzmann moment equations allows us to overcome all of these limitations since it allows the stellar and dark matter components to be represented as a collisionless fluid in a near identical manner to the standard baryonic gas . this removes the need to develop a separate parallelisation scheme for the particle - mesh approach and allows us to use the same well parallelised hydrodynamics scheme . instead of communicating guardcell data for the gas and stellar material separately , the data can now be grouped and communicated all at once , minimising the latency overhead and maximising bandwidth usage . ideal load - balancing is also achieved as the time taken to calculate the inter - cell fluxes is independent of the amount of collisionless mass within a cell . thus processors will not be left idle whilst others calculate , provided that the cells are evenly distributed across processors . given that the hydrodynamics in the flash amr code we use has been shown to scale well for tens of thousands of processors @xcite , then by using the same parallelisation scheme for the collisionless material , we naturally preserve this scaling . in an era of increasingly large and complex simulations , this scalability is vital in keeping performance in - line with scientific requirements . most importantly , as the density of the collisionless material is now represented in each cell continuously , this removes the potential for spurious generation of entropy through discreteness effects introduced when mapping particle properties to the mesh . it also removes limitations involved when converting gas into stars of discrete masses - problematic if cells contain insufficient mass but yet have densities that satisfy star formation criteria . we present in this paper our new implementation of the boltzmann moment equations which allows collisionless material to be modelled as a collisionless fluid on the mesh . a major application of this technique will be in modelling the behaviour of large collections of stars , such as those in a galaxy , as a collisionless fluid in much the same way that we model gas hydrodynamics in grid codes . we will therefore refer to it from here on as `` collisionless stellar hydrodynamics . '' we begin in [ sec : boltzmanneqns ] with a derivation of the zeroth , first and second order moment equations of the collisionless boltzmann equation and then proceed in [ sec : numericalschemes ] to outline the flash hydrodynamic code ( [ sec : flashcode ] ) and the different numerical schemes we use to numerically integrate the equations . these include both a simpler riemann solver free technique ( [ sec : ktscheme ] ) and a more sophisticated riemann solver scheme with characteristic tracing ( [ sec : riemannsolver ] ) . in [ sec : tests ] we outline our discovery of how standard hydrodynamic test problems for which analytic solutions are known , can be modified under special conditions to reproduce the results of a collisionless fluid . this enables us to use the sod - shock - tube test problem to test our results , the findings of which are given in [ sec : sodshock ] . we continue our tests with both a pressure - free spherical collapse test ( [ sec : sphercollapse ] ) and an anisotropic collapse with non - isotropic dispersion tensor in [ sec : anisocollapse ] . as a more complex test of our collisionless stellar hydrodynamics , in [ sec : diskgal ] we track the growth of a two armed spiral in a stellar disc , contrasting the resulting structure with the predictions of the swing amplification theory . we then conclude our findings with an overview of our results , a discussion of the runtime performance of our code and the future implications of our work in [ sec : summary ]

the dominant constituents of the universe s matter are believed to be collisionless in nature and thus their modelling in any self - consistent simulation is extremely important . for simulations that deal only with dark matter or stellar systems , the conventional n - body technique is fast , memory efficient , and relatively simple to implement . we propose the use of the collisionless boltzmann moment equations as a means to model the collisionless material as a fluid on the mesh , implementing it into the massively parallel flash amr code . this approach which we term `` collisionless stellar hydrodynamics '' enables us to do away with the particle - mesh approach and since the parallelisation scheme is identical to that used for the hydrodynamics , it preserves the excellent scaling of the flash code already demonstrated on peta - flop machines . we conclude by demonstrating the ability of our code to model complex phenomena by simulating the evolution of a two armed spiral galaxy whose properties agree with those predicted by the swing amplification theory . methods : numerical hydrodynamics

the dominant constituents of the universe s matter are believed to be collisionless in nature and thus their modelling in any self - consistent simulation is extremely important . for simulations that deal only with dark matter or stellar systems , the conventional n - body technique is fast , memory efficient , and relatively simple to implement . however when extending simulations to include the effects of gas physics , mesh codes are at a distinct disadvantage compared to sph codes . whereas implementing the n - body approach into sph codes is fairly trivial , the particle - mesh technique used in mesh codes to couple collisionless stars and dark matter to the gas on the mesh , has a series of significant scientific and technical limitations . these include spurious entropy generation resulting from discreteness effects , poor load balancing and increased communication overhead which spoil the excellent scaling in massively parallel grid codes . in this paper we propose the use of the collisionless boltzmann moment equations as a means to model the collisionless material as a fluid on the mesh , implementing it into the massively parallel flash amr code . this approach which we term `` collisionless stellar hydrodynamics '' enables us to do away with the particle - mesh approach and since the parallelisation scheme is identical to that used for the hydrodynamics , it preserves the excellent scaling of the flash code already demonstrated on peta - flop machines . we find that the classic hydrodynamic equations and the boltzmann moment equations can be reconciled under specific conditions , allowing us to generate analytic solutions for collisionless systems using conventional test problems . we confirm the validity of our approach using a suite of demanding test problems , including the use of a modified sod shock test . by deriving the relevant eigenvalues and eigenvectors of the boltzmann moment equations , we are able to use high order accurate characteristic tracing methods with riemann solvers to generate numerical solutions which show excellent agreement with our analytic solutions . we conclude by demonstrating the ability of our code to model complex phenomena by simulating the evolution of a two armed spiral galaxy whose properties agree with those predicted by the swing amplification theory . methods : numerical hydrodynamics

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in this paper we have outlined a series of important limitations that are encountered in mesh codes when using the particle - mesh technique . used to consistently integrate collisionless stellar or dark matter components into simulations which model gas physics on an eulerian mesh , the particle - mesh technique has the advantage of being relatively straight forward to implement but is unfortunately subject to several key limitations . from a technical perspective these include poor load balancing and increased communication overhead . from a physical point of view , discreteness effects incurred when discrete particle properties are mapped to the mesh , are believed to result in spurious entropy generation . in galaxy formation simulations , this can have a significant influence on the reservoir of cold gas available to form stars , potentially changing the entire dynamics of the system . to overcome these limitations we have proposed the use of the collisionless boltzmann moment equations as a powerful alternative . such an approach allows us to model the collective properties of collisionless objects such as stars as a fluid , instead of relying upon the traditional n - body approach . in this paper we refer to this approach as `` collisionless stellar hydrodynamics '' given its primary use in the modelling of the properties of large collections of stars , such as those in a galaxy , in much the same way as we model gases in eulerian grid codes . although direct integration of the collisionless boltzmann equation has been undertaken by other authors , it is often prohibitively expensive to perform . this arises as it is necessary to track both the spatial domain and its corresponding velocity phase space . however @xcite demonstrates that the ability to resolve small scale velocity fluctuations is much greater in these codes than for conventional n - body simulations . instead of a costly direct integration of the boltzmann equation , we opt to derive the zeroth , first and second order moments under the usual zero heat flux approximation and taking the third order moments to be negligible . although ultimately an approximation , we show that this yields results in - line with a series of demanding test problems , requiring a factor of @xmath159 less memory than is needed using direct integration over the complete velocity phase space . we implement these new collisionless stellar hydrodynamic equations into the massively parallel flash amr code using two different numerical solvers for hyperbolic partial differential equations . the first scheme by @xcite , requires no information on the equation of state of a collisionless fluid or any assumptions about the behaviour of fluid interactions within the riemann fan . this riemann solver free prescription allows us to track sharp discontinuities with relatively low numerical diffusion and provides a very useful comparison with which to compare our more sophisticated second scheme . in future , its extensibility is hoped to be used to explore the impact of including the higher order moments which we exclude here . by assuming a diagonalised dispersion tensor , we have derived the eigenvalues and eigenvectors for the first three moments of the collisionless boltzmann equations . these have been implemented into a characteristic tracing method based on the muscl - hancock unsplit advection scheme . this allows time averaged primitive states to be calculated at the cell interfaces using characteristic tracing , from which time averaged fluxes can be computed using a range of riemann solvers . we validate our code using a suite of tests with analytic solutions , including some commonly used to benchmark conventional hydrodynamic codes . by realising that the classic hydrodynamic equations and boltzmann moment equations can be reconciled under certain conditions , we are able to generate analytic solutions for the sod shock test which are applicable for collisionless systems . of particular note , we find that since a collisionless fluid has only one degree of freedom in a given direction and is unable to equipartition the kinetic energy of particles between the three dimensions through collisions , it has an effective ratio of specific heats , @xmath160 . thus in 1d , a sod shock solution for a collisionally dominated gas with @xmath160 , matches that for a collisionless fluid . using this insight , we confirm that our numerical schemes ; both the kt scheme and characteristic tracing method , accurately reproduce analytic solutions . although the kt scheme runs 22% faster with near identical memory consumption , our riemann solver based scheme shows notably better resolving power of sharp shocks and discontinuities , spreading them over roughly half the number of cells . through the use of a spherical pressure - free collapse problem , we confirm that the code can maintain good flow symmetry in convergent flows in the absence of any anisotropy in the dispersion tensor . agreement with the peak density within the collapsed sphere also confirms the validity of the poisson solver used in flash . through the inclusion of a non - negligible anisotropic dispersion tensor , we extend the spherical collapse to observe the behaviour of an initially homologous spherical cloud as it collapses and deforms into an elliptical profile . although initial behaviour of the system occurs in - line with expectations , the long term behaviour is more complicated with repeated transitions between an elliptical and spherical profile , along with switching of the major and minor axes after the initial core implosion . although the inclusion of gas physics may help to isotropise the internal structure of the cloud and damp these oscillations , they will nevertheless remain important to the dynamics outside of the core . we will explore in more detail interactions between the collisionally dominated gas physics and the stellar material in future papers . in particular , we will extend our scheme to include off - diagonal terms and a more thorough exploration of the effects of higher order terms . although powerful in its current form , the addition of off - diagonal terms in the velocity dispersion tensor will allow us to directly measure the vertex deviation , a key observable used for probing galactic structure . to date observers have made extensive measurements of our own milky way s vertex deviations which can hide detailed information about the kinematic properties of the bar and spiral arms . however noise in particle based simulations has made accurate theoretical predictions difficult , something which our new collisionless stellar hydrodynamics code can allow us to overcome . having already confirmed the applicability of the collisionless stellar hydrodynamics code to the formation of spiral structure , we have found excellent agreement between our numerical simulations of the growing spiral pattern and the predictions of the swing amplification theory , with the correct relation between the disc size and the outer lindblad resonances being observed . as a final note , we find the time taken in flash for the riemann solver based collisionless stellar hydrodynamics routine is only 7% greater than that for the original classic hydrodynamic scheme , allowing the collisionless stellar hydrodynamics to scale linearly with the classic hydrodynamics . we also find that instead of doubling the overall amount of time spent communicating when both gas and collisionless stellar hydrodynamics are included , our grouping of communications results in a net increase of only 1.2% to the overall communication time compared to that of just a single phase hydrodynamic scheme . thus we conclude by confirming that our new collisionless stellar hydrodynamic approach using the boltzmann moment equations both preserves the excellent scaling previously demonstrated in flash as well as enhancing the level of detail we can expect to be able to extract from our results , with none of the discreteness effects observed for particle - mesh techniques .

however when extending simulations to include the effects of gas physics , mesh codes are at a distinct disadvantage compared to sph codes . whereas implementing the n - body approach into sph codes is fairly trivial , the particle - mesh technique used in mesh codes to couple collisionless stars and dark matter to the gas on the mesh , has a series of significant scientific and technical limitations . these include spurious entropy generation resulting from discreteness effects , poor load balancing and increased communication overhead which spoil the excellent scaling in massively parallel grid codes . in this paper we find that the classic hydrodynamic equations and the boltzmann moment equations can be reconciled under specific conditions , allowing us to generate analytic solutions for collisionless systems using conventional test problems . we confirm the validity of our approach using a suite of demanding test problems , including the use of a modified sod shock test . by deriving the relevant eigenvalues and eigenvectors of the boltzmann moment equations , we are able to use high order accurate characteristic tracing methods with riemann solvers to generate numerical solutions which show excellent agreement with our analytic solutions .

the dominant constituents of the universe s matter are believed to be collisionless in nature and thus their modelling in any self - consistent simulation is extremely important . for simulations that deal only with dark matter or stellar systems , the conventional n - body technique is fast , memory efficient , and relatively simple to implement . however when extending simulations to include the effects of gas physics , mesh codes are at a distinct disadvantage compared to sph codes . whereas implementing the n - body approach into sph codes is fairly trivial , the particle - mesh technique used in mesh codes to couple collisionless stars and dark matter to the gas on the mesh , has a series of significant scientific and technical limitations . these include spurious entropy generation resulting from discreteness effects , poor load balancing and increased communication overhead which spoil the excellent scaling in massively parallel grid codes . in this paper we propose the use of the collisionless boltzmann moment equations as a means to model the collisionless material as a fluid on the mesh , implementing it into the massively parallel flash amr code . this approach which we term `` collisionless stellar hydrodynamics '' enables us to do away with the particle - mesh approach and since the parallelisation scheme is identical to that used for the hydrodynamics , it preserves the excellent scaling of the flash code already demonstrated on peta - flop machines . we find that the classic hydrodynamic equations and the boltzmann moment equations can be reconciled under specific conditions , allowing us to generate analytic solutions for collisionless systems using conventional test problems . we confirm the validity of our approach using a suite of demanding test problems , including the use of a modified sod shock test . by deriving the relevant eigenvalues and eigenvectors of the boltzmann moment equations , we are able to use high order accurate characteristic tracing methods with riemann solvers to generate numerical solutions which show excellent agreement with our analytic solutions . we conclude by demonstrating the ability of our code to model complex phenomena by simulating the evolution of a two armed spiral galaxy whose properties agree with those predicted by the swing amplification theory . methods : numerical hydrodynamics

1609.02176

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typically , an electronic system sustains average charge and heat current densities , @xmath6 , @xmath7 , when subjected to a uniform temperature gradient , @xmath8 , and constant electric field , @xmath9 . its linear thermoelectric response is described by [ eq : linres ] ( c j^e + j^h + ) = ( cc & + & + ) ( c + -t + ) , where @xmath10 is the conductivity tensor , @xmath11 and @xmath12 are the peltier tensors , and @xmath13 is the thermal conductivity tensor . in noninteracting systems , the electrical and heat - current operators are simply related to each other , giving rise to relations between @xmath10 , @xmath13 and @xmath11 . these relations continue to hold in fermi liquids , up to asymptotically vanishing corrections . an example is the wiedemann - franz law , @xmath14 , ( we use throughout @xmath15 . @xmath16 is the electron charge ) , whose breakdown has been interpreted as a signature of physics beyond the fermi liquid framework @xcite . another is the exact relation for noninteracting electrons @xcite between @xmath11 at a given temperature @xmath17 and chemical potential @xmath18 , and @xmath10 of the same system at zero temperature and shifted chemical potential [ eq : mott ] ( t , ) = _ - ^ d ( t=0,+ ) , where @xmath19 is the fermi function . this formula hence implies that in the absence of interactions , @xmath11 shares the same symmetry properties as @xmath10 . a similar conclusion is reached by solving the boltzmann equation within an energy - dependent relaxation - time approximation @xcite . owing to the pioneering works of onsager @xcite and subsequently of kubo @xcite it is well known that various linear - response transport coefficients are related via the time reversal symmetry of microscopic dynamics . consequently , one finds on general grounds that in the presence of a magnetic field @xmath20 , @xmath21 and @xmath22 , where @xmath23 . in turn , it is straightforward to show that even for an anisotropic system , as long as it is invariant under reflections , say with respect to the @xmath24 axis , @xmath25 . the above discussion implies that under similar conditions one also finds @xmath26 , provided that the system is noninteracting or considered within approximated boltzmann transport theory . a natural question then arises : is the relation @xmath26 valid beyond the limits of these two conditions ? beside its intrinsic theoretical appeal , this issue is also important for identifying non - fermi liquid behavior in the thermoelectric properties of correlated electronic systems . one such property is the nernst signal , defined by the off - diagonal elements @xmath27 and @xmath28 of the thermopower tensor @xmath29 . the latter relates the measured electric field to an applied temperature gradient , @xmath30 , in the presence of a magnetic field @xmath31 and in the absence of an electrical current . the dependence of @xmath32 on both the resistivity tensor @xmath33 and @xmath11 means that generally @xmath34 only for isotropic systems . therefore , the symmetry properties of @xmath32 do not carry direct information about interaction effects without independent knowledge of @xmath35 . however , such information may be gleaned from discrepancies between the measured nernst signal and the predictions of boltzmann transport theory . while this theory accounts for the observed data in a number of materials @xcite it underestimates the effect by orders of magnitude in several quasi - one - dimensional conductors @xcite . the nernst effect is also a sensitive probe of superconducting fluctuations , which contribute positively to the signal @xcite , in contrast to quasiparticles of various ordered normal states whose contribution is often of a negative sign @xcite . a positive nernst effect has been measured over a wide range above the critical temperature , @xmath36 , in a series of superconductors including the cuprates @xcite , as well as amorphous films of nb@xmath37si@xmath38 and ino@xmath39 @xcite . while the fluctuation contribution in the cuprates emerges from a high - temperature negative quasiparticle signal , the latter dominates the nernst effect down to , and even below , @xmath36 in other compounds such as the pnictides @xcite . it is therefore interesting to investigate the interplay between these opposing contributions in systems which exhibit concomitant strong fluctuations towards competing orders including superconductivity . motivated by the aforementioned issues we study in sec . [ sec : alpha ] the symmetry properties of @xmath11 within a generic model of interacting electrons . we begin by considering the thermoelectric linear response using the kubo formula . we show that the close relation which exists between the electrical and heat current operators in the noninteracting limit naturally leads , in the presence of reflection symmetry , to @xmath26 . however , contrary to the corresponding relation for the hall conductivities the property @xmath26 is not protected by reflection and time - reversal symmetries , and we demonstrate its explicit violation in the exactly solvable problem of two harmonically interacting electrons in a magnetic field . having established this point of principle we move on to consider the issue using boltzmann transport theory for the interacting system . we show that @xmath26 is obtained within the relaxation - time approximation of this theory , or more generally whenever inelastic processes can be neglected . since this is the case in a disordered fermi liquid at low temperatures we conclude that violation of the above relation under the specified conditions is a telltale sign of interactions beyond the fermi liquid framework . in sec . [ sec : nernst ] we consider a non - fermi liquid model of weakly coupled luttinger chains in the presence of a spin gap . we show that the antisymmetry of the off - diagonal elements of @xmath11 is indeed violated . furthermore , we calculate the nernst signal and show that interactions can lead to its substantial enhancement in such low dimensional systems . this may bare relevance to understanding the large signal observed experimentally in the quasi - one - dimensional materials . finally , we also find that the sign of the effect in the spin gapped system changes from negative to positive as the temperature is lowered and the magnetic field increased . we interpret this behavior as being due to the stronger superconducting fluctuations induced by the spin gap . various technical aspects of our study are relegated to the appendices .

the electrical hall conductivities of any anisotropic interacting system with reflection symmetry obey . in contrast , we show that the analogous relation between the transverse thermoelectric peltier coefficients , , does not generally hold in the same system . this fact may be traced to interaction contributions to the heat current operator and the mixed nature of the thermoelectric response functions . this suggests that quasiparticle - free groundstates ( so - called non - fermi liquids ) may be detected by examining the relationship between and in the presence of reflection symmetry and microscopic anisotropy . the latter lead to deviations that vanish as . ( iii ) we calculate the thermoelectric response in a model of weakly - coupled spin - gapped luttinger liquids and obtain strong breakdown of antisymmetry between the off - diagonal components of . we also find that the nernst signal in this model is enhanced by interactions and can change sign as function of magnetic field and temperature .

the electrical hall conductivities of any anisotropic interacting system with reflection symmetry obey . in contrast , we show that the analogous relation between the transverse thermoelectric peltier coefficients , , does not generally hold in the same system . this fact may be traced to interaction contributions to the heat current operator and the mixed nature of the thermoelectric response functions . remarkably , however , it appears that emergence of quasiparticles at low temperatures forces . this suggests that quasiparticle - free groundstates ( so - called non - fermi liquids ) may be detected by examining the relationship between and in the presence of reflection symmetry and microscopic anisotropy . these conclusions are based on the following results : ( i ) the relation between the peltier coefficients is exact for elastically scattered noninteracting particles ; ( ii ) it holds approximately within boltzmann theory for interacting particles when elastic scattering dominates over inelastic processes . in a disordered fermi liquid the latter lead to deviations that vanish as . ( iii ) we calculate the thermoelectric response in a model of weakly - coupled spin - gapped luttinger liquids and obtain strong breakdown of antisymmetry between the off - diagonal components of . we also find that the nernst signal in this model is enhanced by interactions and can change sign as function of magnetic field and temperature .

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camno@xmath0 and lamno@xmath0 are endpoint compounds in the series ca@xmath5la@xmath6mno@xmath0 , which has been thoroughly studied experimentally and theoretically @xcite . they have relatively simple atomic and magnetic structures , their magnetic excitations are well described by a spin wave hamiltonian @xcite and exchange constants , j , are well established by neutron scattering @xcite and from the nel temperature @xcite . exchange coupling in manganites has been extensively studied using model hamiltonian @xcite and _ ab initio _ calculations @xcite . this paper presents results of bulk _ ab initio _ unrestricted hartree - fock ( uhf ) and cluster configuration interaction ( ci ) calculations of exchange constants for both compounds . exchange constants obtained from ci calculations are in excellent agreement with experiment and the localised orbital ci wavefunctions are analysed to determine which quantum fluctuations are most important in exchange coupling . model hamiltonian calculations have attributed the exchange coupling energy to o@xmath7 to mn@xmath8 superexchange @xcite , mn d@xmath9 d@xmath9/mn d@xmath10 d@xmath11 t@xmath12 superexchange @xcite , or both @xcite . results of calculations presented below show that both exchange mechanisms operate and that o superexchange is the more important of the two . this was also found to be the case in the model hamiltonian calculations of meskine _ et al . _ @xcite . ci cluster calculations provide detailed information on exchange couplings between neighbouring mn ions , however a bulk electronic structure technique is required to study orbital ordering in lamno@xmath0 . total energies of lamno@xmath0 with a and g - type anti - ferromagnetic ( a - af and g - af ) and ferromagnetic ( fm ) spin orderings have been computed in several isovolume structures in order to establish whether or not orbital ordering and spin ordering terms in the hamiltonian for lamno@xmath0 are independent . obviously exchange constants will depend on orbital ordering , as the latter determines which empty orbitals are available to participate in exchange coupling . however , it is not known whether the e@xmath4 electron density in lamno@xmath0 for a particular orbital ordering depends on spin ordering . it is shown below that a common orbital ordering energy for any of several orbital orderings can be identified and that this energy is independent of spin ordering , to a high degree . spin and orbital ordering terms in the hamiltonian are therefore independent , although orbital ordering determines the exchange constants . at low temperatures , camno@xmath0 exists in a cubic perovskite structure ( lattice constant 3.73 ) with g - af magnetic ordering @xcite and a nel temperature of 130 k. using the rushbrooke - wood formula @xcite , this nel temperature implies an exchange constant j = 6.6 mev . note that throughout this work the spin hamiltonian is of the form due to domb and sykes @xcite @xmath13 @xmath14 is a spin operator , s is the magnitude of the total spin for an ion and j@xmath15 is the exchange constant for a pair of ions . this form is adopted for the hamiltonian as it is the same as that adopted in modelling spin wave dispersion in neutron scattering studies @xcite , except for a small dzyaloshinsky - moriya term . at low temperatures the space group of lamno@xmath0 is _ pnma _ @xcite . the ground state magnetic structure is a - af and the unit cell contains four formula units consisting of rotated and distorted octahedra . there is one more d electron per mn ion ( @xmath16 camno@xmath0 ) , which occupies an e@xmath4 orbital and induces a jahn - teller distortion in each mno@xmath17 octahedron , resulting in three distinct mn - o bond lengths of 1.91 , 1.97 and 2.18 @xcite . the occupied e@xmath4 orbital is a linear combination of d@xmath18 and d@xmath19 orbitals . the largest orbital component lies along the most elongated mn - o bond . the _ pnma _ structure is shown in fig . [ fig : fig1 ] . @xmath20 , @xmath21 and @xmath22 axes referred to below are indicated on this diagram . the results of a number of neutron and x - ray scattering studies of the structure of lamno@xmath0 @xcite over a range of temperatures are summarised in ref.@xcite . pnma _ structure can be viewed as containing planes of mn@xmath11 ions , each joined to its in - plane neighbours by pairs of short ( 1.91 ) and long ( 2.18 ) mn - o bonds . each mn@xmath11 ion in a particular plane is coupled to mn@xmath11 ions in planes immediately above and below by two mn - o bonds ( 1.97 ) . the symmetry of the _ pnma _ structure is such that there is one in - plane ( nearest neighbour ) exchange constant ( j@xmath23 ) and one out - of - plane constant ( j@xmath24 ) . both j@xmath23 and j@xmath24 have been determined from two independent neutron scattering studies to be -6.7 and 4.8 mev , respectively , @xcite . thus there is fm coupling within planes and af coupling between planes .

the equilibrium structure and exchange constants of camno and lamno have been investigated using total energy unrestricted hartree - fock ( uhf ) and localised orbital configuration interaction ( ci ) calculations on the bulk compounds and mno and mno clusters . computed exchange constants depend on orbital ordering . ci wave functions are analysed in order to determine which exchange processes are important in exchange coupling in camno and lamno .

the equilibrium structure and exchange constants of camno and lamno have been investigated using total energy unrestricted hartree - fock ( uhf ) and localised orbital configuration interaction ( ci ) calculations on the bulk compounds and mno and mno clusters . the predicted structure and exchange constants for camno are in reasonable agreement with estimates based on its nel temperature . a series of calculations on lamno in the cubic perovskite structure shows that a hamiltonian with independent orbital ordering and exchange terms accounts for the total energies of cubic lamno with various spin and orbital orderings . computed exchange constants depend on orbital ordering . exchange contributions to the total energy vary between -20 and 20 mev per mn ion , differences in orbital ordering energy vary between 3 and 100 mev and a jahn - teller distortion results in an energy reduction of around 300 mev . the lattice constant of the lowest energy cubic perovskite structure ( 3.953 ) is in good agreement with the lattice constant of the high temperature cubic phase of lamno ( 3.947 ) . the total energy of _ pnma _ lamno was minimised by varying lattice parameters and seven internal coordinates and a structure 194 mev per mn ion below that of a structure determined by neutron diffraction was found . this optimised structure is nearly isoenergetic with a cubic perovskite structure with a 5 percent jahn - teller distortion . uhf calculations tend to underestimate exchange constants in lamno , but have the correct sign when compared with values obtained by neutron scattering ; exchange constants obtained from ci calculations are in good agreement with neutron scattering data provided the madelung potential of the cluster is appropriate . cluster ci calculations reveal a strong dependence of exchange constants on mn d e orbital populations in both compounds . ci wave functions are analysed in order to determine which exchange processes are important in exchange coupling in camno and lamno .

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uhf total energy calculations were performed using the crystal98 code @xcite for fm , a- , c- , and g - af spin orderings . the energy of the cubic fm structure with the experimental lattice constant of 3.73 was adopted as the reference energy ( 0 mev ) ; calculations were also performed for each of the spin orderings with a lattice constant of 3.75 . total energies and magnetic moments from these calculations are given in table [ tab : tab1 ] . when these total energy differences are fitted to the hamiltonian in eq . [ eqn : eqn1 ] with nearest ( j@xmath46 ) and second nearest ( j@xmath26 ) neighbour interactions ( _ i.e. _ along [ a,0,0 ] and [ a , a,0 ] , where a is the lattice constant ) , the parameters obtained for a lattice constant of 3.73 are j@xmath46 = 10.7 mev , j@xmath26 = 0.3 mev and for a lattice constant of 3.75 , the parameters are j@xmath46 = 10.1 mev , j@xmath26 = 0.3 mev . it is generally believed that exchange interactions which connect magnetic ions along a linear chain are stronger than those which do not , such as the j@xmath26 interaction here . however , in the cubic perovskite structure , exchange interactions along [ 2a,0,0 ] , _ etc . _ contribute equally to all four spin orderings studied and so can not be extracted from the data presented here . similar values for j@xmath46 have been obtained from model hamiltonian calculations by meskine _ ( j@xmath46 = 9.5 mev ) @xcite . note that the definition used for the exchange energy in that work , the difference between the energy of a pair of ferro- and anti - ferromagnetically coupled mn ions , is @xmath47 the exchange energy defined in eq . [ eqn : eqn1 ] above . hence values for exchange energies from that work have been divided by two in order to compare them to values in the present work . exchange energies obtained from cluster ci calculations depend strongly on mn e@xmath4 and o 2p orbital populations . in turn these populations depend on the madelung potential of a sphere of point charges surrounding the mn@xmath1o@xmath2 cluster . the charges were located on crystal ion sites and mulliken populations of ions in bulk uhf calculations on camno@xmath0 were used as a guide in choosing the magnitudes of these charges . the sphere of point charges had a radius of just over 20 and contained around 3300 charges . the radius was chosen so that the sphere was overall almost charge neutral ; each unit cell of point charges was also neutral . the dependence of exchange energies in camno@xmath0 and lamno@xmath0 on mn ion charge , measured by the mulliken population of that ion in the scf cluster calculation , is shown in fig . [ fig : fig5 ] . the charge on the two mn ions @xmath48 was adjusted by transferring charge from mn point charge sites to ca or la point charge sites @xmath49 . the total charge of the mn and ca ( or la ) point charges was kept constant and the o ion charge was maintained at the uhf mulliken population value . it can be seen that the magnitude of the exchange energy increases as charge is removed from the mn ion , which is reasonable as charge is mainly being transferred to / from the e@xmath4 orbitals which are directly involved in the exchange coupling mechanism - as the e@xmath4 orbital becomes filled , the exchange energy diminishes . the ci calculation value of j@xmath46 = 8.1 mev quoted for camno@xmath0 in table [ tab : tab2 ] is the value obtained for an mn cluster ion charge of + 2.13 , the mn ion charge determined from the uhf calculation . this is to be compared to an estimate of the experimental value of j@xmath46 = 6.6 mev , derived from the nel temperature of camno@xmath0 . the fundamental saf s for the septet and singlet states of the mn@xmath1o@xmath2 cluster were given in eq . [ eqn : eqn2 ] and [ eqn : eqn4 ] . in the fundamental saf wave functions for either spin state , each has a saf coefficient , c@xmath50 , of unity , however when additional saf s are permitted in the wave function ( _ i.e. _ permitting o@xmath7 ion 2p to e@xmath4 excitations , _ etc . _ ) the weights of fundamental saf s are around 0.9950 and additional saf s corresponding to o superexchange and t@xmath12 exchange enter the wave function with saf coefficients of order 0.01 . even for limited active spaces ( as in these calculations ) the number of saf s entering the wavefunction means that a convenient way to analyse the wavefunction is to tabulate the summed occupancies ( _ i.e. _ @xmath51 ) of configurations of a particular type . there are , for example , several saf s in which one electron is excited from an o 2p orbital to an mn e@xmath4 orbital @xcite . the relative magnitudes of these occupancies are a measure of the importance of each type of fluctuation about the fundamental saf configurations . summed occupation numbers for the mn@xmath1o@xmath2 cluster are given in table [ tab : tab3 ] . it can be seen that the fundamental ( or main ) saf has occupancy 0.9926 for the singlet state while it has occupancy 0.9943 in the septet state and therefore that there are larger correlation effects in the singlet state . saf s in which a t@xmath12 electron has hopped from one mn ion to the other have an occupancy of 0.0005 , while these fluctuations are absent from the septet state owing to the pauli exclusion principle , as noted above . however , the main difference in septet and singlet wave functions is in the occupancy of states in which one electron is transferred from an o 2p orbital to an e@xmath4 orbital , the occupancy being 0.0038 for the singlet state and 0.0027 for the septet state . the occupancy of saf s in which a pair of electrons is transferred from o 2p to one mn e@xmath4 orbital is the same for both spin states . the energies of both spin states relative to the energy of the fundamental septet saf are also given in table [ tab : tab3 ] . the septet state with o superexchange fluctuations is 133.4 mev below the fundamental septet saf . this is the correlation energy for that state @xcite . the singlet state with o superexchange and t@xmath12 fluctuations is 149.6 mev below the reference energy and 153.2 mev below the fundamental singlet saf energy . the latter energy is the correlation energy for the singlet state . correlation energies for the mn@xmath1o@xmath2 and mn@xmath1o@xmath3 cluster ci wave functions are illustrated schematically in figure [ fig : fig6 ] . correlation energies are around 50 percent larger in mn@xmath1o@xmath2 than in mn@xmath1o@xmath3 and this is reflected in the larger exchange energy in camno@xmath0 . it is worth noting that when the ci cluster calculation for the exchange energy in camno@xmath0 was performed with no point charge array surrounding the cluster , the exchange energy obtained was 57 mev , well in excess of the experimental value . this emphasises the importance of madelung terms in the crystal hamiltonian in determining exchange energies in strongly correlated materials . total energy calculations were performed on lamno@xmath0 in the ideal perovskite ( cubic ) structure , a tetragonal perovskite structure , a cubic structure with a jahn - teller distortion of the mno@xmath17 octahedra and the _ pnma _ structure with atomic coordinates derived from experiment @xcite and by minimising the total energy by varying lattice parameters and internal coordinates not determined by symmetry . these structures are summarised in table [ tab : tab4 ] . the jahn - teller distortion consisted of elongation or contraction of mn - o bonds parallel to the @xmath52 axes of the unit cell . these are the mn - o bonds which induce fm coupling between mn ions in the _ pnma _ structure . the cubic structure with the lowest energy had a lattice constant of 3.953 ( volume 61.77 @xmath53 per mn ion ) which is comparable to the lattice constant of the cubic phase of lamno@xmath0 ( 3.947 ) which occurs at temperatures above 750k @xcite . all relative energies and lattice volumes will be assumed to be per mn ion hereafter . when this structure is changed by a 5 percent jahn - teller distortion ( table [ tab : tab4 ] ) the energy is lowered by 304 mev and the magnetic ground state of the structure switches from d@xmath18 d@xmath19 fm to d@xmath54 d@xmath55 fm ( see below ) . the total energy of the _ pnma _ structure using coordinates from experiment @xcite ( table [ tab : tab4 ] ) is 200 mev above the jahn - teller distorted structure . the total energy of the _ pnma _ structure was minimised @xcite by varying the lattice parameters and 7 internal coordinates not determined by symmetry of the _ pnma _ space group . the total energy of the energy minimised structure is 6 mev above the jahn - teller distorted structure . the optimised lattice parameters and internal coordinates are given in table [ tab : tab4 ] ; the @xmath20 lattice vector is essentially unchanged while the @xmath21 and @xmath22 lattice vectors increase in magnitude by 1.1 and 1.6 percent , respectively . the lattice volume rises from 60.89 to 62.53 @xmath53 . probably the most important changes which occur on minimising the total energy are : the degree of jahn - teller distortion is reduced ; la - o distances increase significantly . in the lowest energy cubic structure there is one mn - o distance of 1.976 and an la - o distance of 2.795 . on introducing the 5 percent jahn - teller distortion these become mn - o distances of 1.877 , 1.976 and 2.075 and la - o distances of 2.795 and 2.797 . in the experimental _ pnma _ structure @xcite the mn - o distances are 1.903 , 1.957 and 2.185 and the la - o distances are 2.433 , 2.461 and 2.548 . these change to 1.910 , 1.944 and 2.135 and 2.609 , 2.666 and 2.684 in the energy minimised structure . hence lower energies are found for structures with larger la - o distances and a reduced jahn - teller distortion . the combined ionic radii of la@xmath11 and o@xmath7 are 2.76 @xcite . la - o distances in the energy minimised _ pnma _ and cubic structures lie just below the combined ionic radii distance , whereas the la - o distances in the experimental _ pnma _ structure lie well below this distance . the cubic structure with a jahn - teller distortion and the energy minimised _ pnma _ structure are both lower in energy than the lowest energy cubic structure by around 300 mev . this energy lowering by a jahn - teller distortion is half of the lowering assumed by millis @xcite in a calculation of electron - phonon coupling in ca@xmath5la@xmath6mno@xmath0 . the uhf calculations reported here are similar to those reported by su _ they report an energy lowering of 1055 mev when the cubic structure is changed to the experimental _ pnma _ structure with no volume change . this calculation will overestimate the energy difference between such structures as the cubic structure with the _ pnma _ structure equilibrium volume is not the mimimum energy cubic structure . for the cubic perovskite structure it was found that variations of the total energies of different spin and orbital orderings can be fitted very well by a hamiltonian of the form @xmath56 where @xmath57 is an orbital ordering term which depends only on the orbital order . for these calculations the cubic unit cell was doubled along [ 110 ] , [ 101 ] and [ 011 ] directions ( g - af spin and orbital ordering ) and along the [ 001 ] direction ( a - af spin and orbital ordering ) and total energies and charge density difference plots @xcite were computed for d@xmath18 d@xmath18 , d@xmath18 d@xmath19 and d@xmath19 d@xmath19 orbital orderings and fm , a - af and g - af spin orderings . the d@xmath18 d@xmath19 a - af combination is incompatible with the unit cell doublings chosen and was omitted . total energies are given in table [ tab : tab5 ] and charge density difference plots for each of these orbital orderings are shown in fig . [ fig : fig7 ] . for d@xmath18 d@xmath18 and d@xmath19 d@xmath19 orbital ordering , distinct exchange constants in the @xmath58 plane , j@xmath23 , and in the @xmath59 plane , j@xmath24 , are postulated , whereas for d@xmath18 d@xmath19 ordering a single exchange constant , j = j@xmath23 = j@xmath24 , is postulated . exchange constants for each orbital ordering are given in table [ tab : tab6 ] . af exchange constants are obtained when adjacent mn orbital ordering is the same and fm coupling is observed when adjacent mn e@xmath4 orbitals differ . this observation also applies to _ pnma _ structures studied : fm coupling is observed between in - plane mn ions with alternating e@xmath4 orbital orientations ; af coupling is observed when adjacent mn e@xmath4 orbitals have the same orientation . magnitudes of af couplings vary between 5.1 and 14.2 mev and one fm coupling of -6.0 mev is observed in the d@xmath18 d@xmath19 a - af ordering . once exchange constants have been computed for a particular orbital ordering , comparison of structures with the same magnetic structure but different orbital ordering permits differences in orbital ordering energies to be calculated . the actual magnitude of orbital ordering energy , @xmath57 , of course depends on the reference energy chosen . the choice of the fm d@xmath18 d@xmath18 structure as the reference energy structure yields values of -17.4 , -20.0 and -113.4 mev for the d@xmath18 d@xmath18 , d@xmath19 d@xmath19 and d@xmath18 d@xmath19 relative orbital ordering energies . the important result here is that an alternating orbital order ( d@xmath18 d@xmath19 ) is around 90 mev below those with the same orbital order on each site ( d@xmath18 d@xmath18 or d@xmath19 d@xmath19 ) in the cubic perovskite structure . when the values of @xmath57 and exchange constants just mentioned are used to compute the relative energies of the eight spin and orbital orderings considered , the maximum deviation from the relative energies reported in table [ tab : tab4 ] is 0.2 mev , demonstrating the suitability of the hamiltonian in eq . [ eqn : eqn7 ] . the fact that charge density difference plots for different spin ordering and the same orbital ordering are very similar suggests that this should be the case . using the fact that orbital and spin contributions to the hamiltonian are independent , differences in total energy of a particular spin order as a function of lattice distortion may be attributed to differences in orbital ordering energy . [ fig : fig8 ] is a plot of total energy for each orbital ordering with g - af magnetic order as a function of isovolume , tetragonal lattice distortion . these calculations were performed using p4/mmm space group symmetry . it can be seen that d@xmath18 d@xmath19 orbital ordering is the most stable ordering only within a small parameter range about the cubic structure . when the tetragonal distortion is such that the lattice is elongated along the @xmath60 axis , d@xmath19 d@xmath19 ordering is favoured and when it is compressed along this axis , d@xmath18 d@xmath18 ordering is favoured . this may be explained by a simple electrostatic argument - the ordering which is favoured in either case is the one where the occupied e@xmath4 orbitals are oriented along the elongated axis or axes , thereby reducing the coulombic repulsion energy . the greatest stabilisation relative to the cubic lattice is found for an @xmath61/@xmath60 ratio of 0.94 where the energy is 164 mev below that of the cubic g - af reference energy . this stabilisation is still significantly less than the stabilisation of 298 mev which results when the energy minimised _ structure is adopted . relative energies and exchange constants for the jahn - teller distorted structure and both _ pnma _ structures studied are given in tables [ tab : tab7 ] and [ tab : tab8 ] , respectively . charge density difference plots for the jahn - teller distorted and energy minimised _ pnma _ structures are shown in fig . [ fig : fig9 ] . the magnetic ground state of the jahn - teller distorted structure is fm , but this is almost isoenergetic with the a - af structure . this is because the in - plane exchange constant is fm while the out - of - plane exchange constant is fm ( but small ) . the magnetic ground state of the cubic structure is g - af with af coupling between all neighbouring mn ions . the switch to fm coupling between neighbouring mn ions in - plane is due to the jahn - teller distortion in - plane . both _ structures studied have a - af magnetic ground states ( as is the case in nature ) but magnitudes of exchange constants obtained from these calculations are smaller than those obtained from neutron scattering data @xcite ( table [ tab : tab8 ] ) . values of 0.6 and -3.7 mev for j@xmath24 and j@xmath23 may be compared to 0.8 and -3.5 mev obtained in a similar uhf calculation @xcite and 4.8 and -6.7 mev from experiment @xcite . a local spin density approximation ( lsda ) calculation @xcite found values of -3.1 and -9.1 mev for j@xmath24 and j@xmath23 . this calculation did find an a - af ground state for _ pnma _ lamno@xmath0 , however , as second nearest neighbour exchange constants are significant in the lsda calculation and favour an a - af magnetic ground state . cluster ci calculations for lamno@xmath0 were performed using mn@xmath1o@xmath3 clusters with the mn ions in the same configuration as a pair of mn ions in the @xmath52 plane ( fig . [ fig : fig1 ] ) and with the mn ions along a line parallel to the @xmath21 axis . the former cluster corresponds to a pair of mn ions which is expected to be fm coupled while the latter corresponds to a pair of ions which is expected to be af coupled . mn e@xmath4 orbital ordering in the former cluster had the form illustrated schematically in fig . [ fig : fig2]c while the latter had orbital ordering as in fig [ fig : fig2]b . clusters and surrounding point charges with the experimental _ pnma _ structure @xcite and the energy minimised structure were used . exchange constants for lamno@xmath0 derived from these cluster calculations are given in table [ tab : tab8 ] . cluster ci calculations with mn , o and la surrounding point charges of 2.6 , -1.8 and 2.8 ( close to mulliken population values from uhf calculations ) result in exchange constants of 3.3 and -3.6 mev for j@xmath24 and j@xmath23 when the experimental structure is used . these values change to 5.1 and -7.4 mev when the energy minimised structure ( table [ tab : tab4 ] ) is used . the madelung potential has an important role in determining exchange constants in manganites . obviously ions several lattice constants or more distant from the ions in the central cluster may be treated as point charges rather than distributed charges without significantly altering the potential within the central cluster . however point charges adjacent to the central cluster may cause a significantly different potential within the cluster and affect the results of the exchange constant calculation . this question has previously been addressed by other workers @xcite . in order to estimate the effect of terminating the cluster with point charges , cluster ci calculations were performed with the 12 la point charges nearest to the central cluster ions replaced by la@xmath11 pseudopotentials @xcite . this resulted in a small increase in j@xmath24 and no change in j@xmath23 compared to the calculation where only point charges were used . the values obtained for j@xmath24 and j@xmath23 from these calculations were 5.2 and -7.4 mev , which are in good agreement with the experimental values : 4.8 and -6.7 mev . values for the exchange constants derived from the model hamiltonian calculations of meskine _ et al . _ @xcite are also given in table [ tab : tab8 ] . relative energies and saf occupancies for the mn@xmath1o@xmath3 clusters used for calculating exchange constants in lamno@xmath0 in the energy minimised structure are given in table [ tab : tab9 ] . the fundamental saf singlet states are 11.9 mev ( j@xmath24 ) and 17.9 mev ( j@xmath23 ) above the nonet states of the clusters . when additional saf s are permitted in the wave function the singlet(nonet ) states are lowered by 105.4(83.3 ) mev ( j@xmath24 ) and 82.8(79.7 ) mev ( j@xmath23 ) . these are the correlation energies for these states . the singlet state of the cluster used to calculate j@xmath24 is 10.2 mev lower in energy than the nonet state giving a value for j@xmath24 of 5.1 mev while the nonet state of the cluster used to calculate j@xmath23 is 14.7 mev lower in energy than the singlet state giving a value of -7.4 mev for j@xmath23 . from table [ tab : tab9 ] it can be seen that o to e@xmath4 ( 1e ) excitations are the main fluctuations about the fundamental saf state . the weight of the fundamental saf in the singlet states of either cluster is less than in the nonet states , reflecting the greater degree of correlation in the singlet states . in the j@xmath24 calculation the greater correlation energy of the singlet state _ c.f . _ the nonet state is sufficient to make the singlet state the ground state and give an af exchange constant . on the other hand , in the j@xmath23 calculation the singlet correlation energy is just greater than that of the nonet state and , together with the fact that the singlet state of the fundamental saf wave function is 17.9 mev above the nonet state , this results in a nonet ground state and an fm exchange constant .

a series of calculations on lamno in the cubic perovskite structure shows that a hamiltonian with independent orbital ordering and exchange terms accounts for the total energies of cubic lamno with various spin and orbital orderings . the lattice constant of the lowest energy cubic perovskite structure ( 3.953 ) is in good agreement with the lattice constant of the high temperature cubic phase of lamno ( 3.947 ) . the total energy of _ pnma _ lamno was minimised by varying lattice parameters and seven internal coordinates and a structure 194 mev per mn ion below that of a structure determined by neutron diffraction was found . this optimised structure is nearly isoenergetic with a cubic perovskite structure with a 5 percent jahn - teller distortion . cluster ci calculations reveal a strong dependence of exchange constants on mn d e orbital populations in both compounds .

the equilibrium structure and exchange constants of camno and lamno have been investigated using total energy unrestricted hartree - fock ( uhf ) and localised orbital configuration interaction ( ci ) calculations on the bulk compounds and mno and mno clusters . the predicted structure and exchange constants for camno are in reasonable agreement with estimates based on its nel temperature . a series of calculations on lamno in the cubic perovskite structure shows that a hamiltonian with independent orbital ordering and exchange terms accounts for the total energies of cubic lamno with various spin and orbital orderings . computed exchange constants depend on orbital ordering . exchange contributions to the total energy vary between -20 and 20 mev per mn ion , differences in orbital ordering energy vary between 3 and 100 mev and a jahn - teller distortion results in an energy reduction of around 300 mev . the lattice constant of the lowest energy cubic perovskite structure ( 3.953 ) is in good agreement with the lattice constant of the high temperature cubic phase of lamno ( 3.947 ) . the total energy of _ pnma _ lamno was minimised by varying lattice parameters and seven internal coordinates and a structure 194 mev per mn ion below that of a structure determined by neutron diffraction was found . this optimised structure is nearly isoenergetic with a cubic perovskite structure with a 5 percent jahn - teller distortion . uhf calculations tend to underestimate exchange constants in lamno , but have the correct sign when compared with values obtained by neutron scattering ; exchange constants obtained from ci calculations are in good agreement with neutron scattering data provided the madelung potential of the cluster is appropriate . cluster ci calculations reveal a strong dependence of exchange constants on mn d e orbital populations in both compounds . ci wave functions are analysed in order to determine which exchange processes are important in exchange coupling in camno and lamno .

cond-mat0111536

c

uhf and ci cluster calculations for the exchange constant in camno@xmath0 are in reasonable agreement with estimates for its value based on the rushbrooke - wood formula @xcite and its nel temperature . the calculated exchange constants are larger than the estimate based on experiment . the single af exchange constant is mainly a result of o to e@xmath4 ( 1e ) excitations which lower the energy of the singlet state of a pair of adjacent mn ions below that of the septet state . the magnitude of the exchange constant derived from ci cluster calculations depends strongly on the madelung potential within the cluster and there is agreement between theory and estimates based on experiment only when that potential results in ionic charges in the cluster similar to those in the bulk uhf calculation . lamno@xmath0 is more complex than camno@xmath0 . it is also more ionic than camno@xmath0 with mulliken populations of ions closer to the formal ion charges . a number of orbital and spin ordered states exist within a small energy range , say 300 mev , close to the ground state . the energies of several spin and orbital ordered states of cubic lamno@xmath0 are well described by the hamiltonian in eq . [ eqn : eqn7 ] . in the remainder of this section exchange constants in cubic and jahn - teller distorted lamno@xmath0 are correlated with mn@xmath11 ion orbital ordering and o@xmath7 ion charge density distortions and mn@xmath11 ion interactions are identified as type i , ii or iii according to goodenough s scheme @xcite . finally , the role of correlation and availability of empty orbitals on magnetic ion sites in af and fm coupling is discussed . cubic lamno@xmath0 has a d@xmath18 d@xmath19 fm ground state and a lattice constant of 3.953 . exchange constants depend on orbital ordering and range from -6.0 to 14.2 mev . charge density difference plots ( fig . [ fig : fig7 ] ) show that the charge density on an mn ion is essentially independent of charge densities on neighbouring ions . that density is determined solely by the ion s orbital ordering . however , charge densities on more polarisable o@xmath7 ion sites depend on charge densities at both neighbouring mn ion sites . for d@xmath19 d@xmath19 orbital ordering ( fig . [ fig : fig7 ] , top panels ) , o@xmath7 ions in mn - o bonds in the @xmath58 plane undergo a quadrupolar distortion in which charge is displaced from the mn - o bond axis into directions perpendicular to the bond while o@xmath7 ions in mn - o bonds along the @xmath60 axis are much less severly distorted and the ions tend to elongate along the bond axes . the d@xmath19 character of the ordered mn e@xmath4 orbitals can be seen clearly in the top right panel of fig . [ fig : fig7 ] . the exchange constant for mn@xmath11 ions in the @xmath58 plane with this orbital ordering is j@xmath23 = -0.1 mev while the exchange constant for mn@xmath11 ions along the @xmath60 axis is 14.2 mev . thus a weak exchange coupling is associated with the quadrupolar distortion of charge away from the bond axis while a much stronger coupling is associated with a nearly spherical ion in which charge density tends to concentrate along the bond axis , compared to the spherical o@xmath7 ion . for d@xmath18 d@xmath18 orbital ordering the d@xmath18 character of the ordered mn e@xmath4 orbitals is clearly seen in the middle left panel of fig . [ fig : fig7 ] . there is a relatively weak quadrupolar distortion of the o@xmath7 ions in the @xmath58 plane and a stronger quadrupolar distortion of o@xmath7 ions along the @xmath60 axis . the exchange constant for mn@xmath11 ions in the @xmath58 plane is 5.1 mev while it is 7.2 mev for mn@xmath11 ions along the @xmath60 axis . the d@xmath18 or d@xmath19 character of orbital ordering can be seen in both bottom panels in fig . [ fig : fig7 ] . in the @xmath58 and @xmath59 planes the o@xmath7 ion charge density is polarised in a circulating pattern , even though the o@xmath7 ions are situated midway between the mn@xmath11 ions . charge is polarised towards regions at mn@xmath11 ion sites where there is a reduction in charge density below that of spherical mn@xmath9 ions , as indicated by negative contours in the charge density difference plots . around each mn@xmath11 ion with the d@xmath19 e@xmath4 orbital occupied , charge is deformed towards the d@xmath19 ion in the @xmath58 plane and away from it along the @xmath60 axis , whereas for mn@xmath11 ions with the d@xmath18 e@xmath4 orbital occupied , charge is deformed towards it along the @xmath60 axis and away from it in the @xmath58 plane . thus each mn@xmath11 ion is coupled to each neighbouring mn@xmath11 ion by a polarised o@xmath7 ion and there is one fm exchange constant of -6.0 mev . a simple pattern of orbital ordering is obtained for the jahn - teller distorted structure where the unit cell was doubled in the [ 001 ] direction ( fig . [ fig : fig9 ] ) . this pattern of orbital ordering was obtained without biasing the initial guess wave function in anyway ( appendix a ) . orbital ordering in the @xmath58 plane is an alternating d@xmath54 d@xmath55 pattern which is repeated with period one along the @xmath60 axis . this is the a - type orbital ordering discussed in ref . the fm exchange constant between mn@xmath11 ions in the @xmath58 plane is -8.1 mev and the weak fm exchange constant along the @xmath60 axis is -0.1 mev . there is strong deformation of o@xmath7 ion charge density in the @xmath58 plane towards regions of reduced charge density at the mn@xmath11 ion sites , associated with strong fm exchange coupling ( fig . [ fig : fig9 ] , left panel ) . there is strong quadrupolar distortion of the charge density at o@xmath7 ion sites coupling mn@xmath11 ions along the @xmath60 axis , associated with a weak fm exchange coupling . the same a - type orbital ordering is also found in the _ pnma _ structures studied . there is a similar pattern of circulating charge polarisation towards regions at mn@xmath11 ion sites where the charge density is reduced and there is strong fm exchange coupling between mn@xmath11 ions lying approximately in the @xmath52 plane ( -3.7 and -6.0 mev , uhf calculations table [ tab : tab8 ] ) . the three mn - mn interactions described by goodenough @xcite are now tentatively identified in cubic and jahn - teller distorted lamno@xmath0 using charge densities on the o@xmath7 sites and orbital ordering at the neighbouring mn ion sites . type i interactions are found for : d@xmath18 d@xmath18 orbital ordering in cubic lamno@xmath0 for both j@xmath23 = 5.1 mev and j@xmath24 = 7.2 mev ( fig . [ fig : fig7 ] , middle panels ) ; d@xmath19 d@xmath19 orbital ordering for j@xmath24 = 14.2 mev ( fig . [ fig : fig7 ] , top right panel ) . type ii interactions are found for : d@xmath18 d@xmath19 orbital ordering in cubic lamno@xmath0 ( fig . [ fig : fig7 ] , bottom panels ) for both j@xmath24 and j@xmath23 = -6.0 mev ; d@xmath54 d@xmath55 orbital ordering in jahn - teller distorted lamno@xmath0 ( fig . [ fig : fig9 ] , left panel ( j@xmath23 = -8.1 mev ) . charge densities are characterised by breaking of symmetry of the o@xmath7 ion along the mn - o - mn axis . obviously this can only occur when the orbital orderings on adjacent mn ions differ , however this observation is worth making as such symmetry breaking is characteristic of fm exchange coupling . type iii interactions are found for d@xmath19 d@xmath19 orbital order in cubic lamno@xmath0 ( fig . [ fig : fig7 ] , top left panel ) where j@xmath23 = -0.1 mev ; for j@xmath24 = -0.6 mev in the jahn - teller distorted structure ( fig . [ fig : fig9 ] , right panel ) . in both cases the weak exchange coupling is associated with strong , quadrupolar o@xmath7 charge density deformation . cluster ci calculations provide detailed information on the exchange coupling mechanism . fundamental saf singlet states for clusters representing both camno@xmath0 and lamno@xmath0 lie above the fundamental saf high spin multiplicity states ; this is expected to be the case for a wide range of magnetic ions exchange coupled _ via _ a closed shell anion . the ground state for the pair of magnetic ions is af when the _ difference _ in correlation energies of the singlet and high spin multiplicity states exceeds the singlet / high spin state splitting , otherwise it is fm . correlation energies for singlet states exceed correlation energies of the corresponding high spin multiplicity states in the three cases studied here ( fig . [ fig : fig6 ] ) . this is also likely to be true for a wide range of magnetic ions which are exchange coupled _ via _ a closed shell anion as there are many more singlet saf s than high spin saf s in any particular active space . for example , in the active space used for the lamno@xmath0 cluster ci calculations there are over 18,000 singlet saf s compared to over 1,500 nonet saf s , which simply reflects the fact that there are many more ways to arrange spin - coupled electrons to form singlet states than there are to form nonet states for a specific number of electrons . only a few of either the singlet or nonet saf s appear in the ground state wave functions with a signicant weight , but since there are so many more singlet than nonet saf s , it is not surprising that the singlet state correlation energy is larger . when one empty mn e@xmath4 orbital is available to accept one or two electrons from an o@xmath7 ion , as is the case for j@xmath23 in _ pnma _ lamno@xmath0 , the singlet state correlation energy is only slightly larger than the nonet state correlation energy ( 82.8 versus 79.7 mev ) and the nonet state is the ground state . however , when two empty mn e@xmath4 orbitals are available , as is the case for j@xmath24 in _ pnma _ lamno@xmath0 and j in camno@xmath0 ( fig . [ fig : fig6 ] ) , singlet state correlation energies are significantly larger than the nonet(septet ) state correlation energies ( 105.4 versus 83.3 mev ( lamno@xmath0 ) and 153.2 versus 133.4 mev ( camno@xmath0 ) ) and the ground states are singlets . exchange coupling in camno@xmath0 and lamno@xmath0 is largely due to quantum fluctuations in the ground state in which one electron is excited from an o@xmath7 ion into an mn e@xmath4 orbital . fluctuations in which an electron is exchanged between t@xmath12 orbitals enter the singlet state in mn@xmath1o@xmath2 and mn@xmath1o@xmath3 clusters but are not the main contributors to the exchange interaction . parallel studies of exchange coupling in la@xmath26cuo@xmath62@xcite show that d@xmath18 d@xmath18 exchange interactions dominate the exchange coupling in la@xmath26cuo@xmath62 and o to d@xmath18 excitations have a lesser weight than cu@xmath63cu@xmath11 excitations in the la@xmath26cuo@xmath62 ground state . this difference in exchange coupling mechanism most likely reflects trends in effective hubbard u parameters for mn@xmath8 and cu@xmath64 and o 2p to metal d excitation energies . this work was supported by enterprise ireland under grant number sc/00/267 . m. n. wishes to acknowledge support by the trinity trust .

the predicted structure and exchange constants for camno are in reasonable agreement with estimates based on its nel temperature . uhf calculations tend to underestimate exchange constants in lamno , but have the correct sign when compared with values obtained by neutron scattering ; exchange constants obtained from ci calculations are in good agreement with neutron scattering data provided the madelung potential of the cluster is appropriate .

the equilibrium structure and exchange constants of camno and lamno have been investigated using total energy unrestricted hartree - fock ( uhf ) and localised orbital configuration interaction ( ci ) calculations on the bulk compounds and mno and mno clusters . the predicted structure and exchange constants for camno are in reasonable agreement with estimates based on its nel temperature . a series of calculations on lamno in the cubic perovskite structure shows that a hamiltonian with independent orbital ordering and exchange terms accounts for the total energies of cubic lamno with various spin and orbital orderings . computed exchange constants depend on orbital ordering . exchange contributions to the total energy vary between -20 and 20 mev per mn ion , differences in orbital ordering energy vary between 3 and 100 mev and a jahn - teller distortion results in an energy reduction of around 300 mev . the lattice constant of the lowest energy cubic perovskite structure ( 3.953 ) is in good agreement with the lattice constant of the high temperature cubic phase of lamno ( 3.947 ) . the total energy of _ pnma _ lamno was minimised by varying lattice parameters and seven internal coordinates and a structure 194 mev per mn ion below that of a structure determined by neutron diffraction was found . this optimised structure is nearly isoenergetic with a cubic perovskite structure with a 5 percent jahn - teller distortion . uhf calculations tend to underestimate exchange constants in lamno , but have the correct sign when compared with values obtained by neutron scattering ; exchange constants obtained from ci calculations are in good agreement with neutron scattering data provided the madelung potential of the cluster is appropriate . cluster ci calculations reveal a strong dependence of exchange constants on mn d e orbital populations in both compounds . ci wave functions are analysed in order to determine which exchange processes are important in exchange coupling in camno and lamno .

physics0111165

i

discrete symmetry violations in atoms are important phenomena to probe for physics beyond the standard model(sm ) of the particle physics . the electric dipole moment(edm ) of an atom , which is a signature of the simultaneous parity and time - reversal ( p - t ) symmetry violations is one such . there are several possible sources of p - t violation effects within an atom , the tensor pseudo - tensor electron nucleus interaction is an example which is semi - leptonic in nature . the atomic yb , which is a closed - shell atom having a @xmath3 is a very good candidate for atomic edm experiments to probe for the nuclear sector effects . an additional advantage of using a rare earth atom like yb is the closely spaced energy levels . the experimental results when compared with the theoretical results can yield signatures of physics beyond the sm . among the closed - shell atoms , the atom edm of xe@xcite and hg@xcite have been measured . though the hg experiment has set the record of being the most sensitive spectroscopy ever done , the result obtained is null and sets an upper bound to atomic hg edm as @xmath4 . still , it has set bounds on the parameters in particle physics models@xcite . improving the accuracy further is an important challenge in atomic edm experiments . atomic yb offer a possibility of achieving this by using the techniques of laser cooling and trapping . it is also desirable that the edm measurements be done in other closed - shell atoms to verify the physical effects observed . atomic yb also has the advantage of being relatively simple in level structure among the rare earth elements . it has been studied theoretically using a variety of atomic many - body methods and there are ongoing experimental studies . the excitation energies has been studied using relativistic coupled - cluster method@xcite ; the hyperfine structure constants and electric - dipole transition properties have been studied using multireference relativistic many - body perturbation theory@xcite ; and the oscillator strength of some of the important transitions were investigated using multi - configuration relativistic hartree - fock@xcite . the lifetime of some of the crucial levels have been measured experimentally@xcite and atomic yb has been laser cooled and trapped@xcite . it is the candidate for the atomic edm experiments using the methods of laser cooling and trapping of atoms which are in progress@xcite . the p - t violating effects which can be probed using atomic yb are the tensor pseudotensor ( t - pt ) electron - nucleus interaction@xcite and the schiff moment@xcite . an observation of a finite edm of atomic yb could mean nonzero @xmath1 , which is a signature of physics beyond the sm as @xmath1 is zero within sm . hence the theories which allow t - pt electron - nucleus interactions would play a role in understanding nature . the parameter @xmath1 is extracted from the experimental result of atomic edm by combining with the theoretical calculations . accurate atomic theory calculations are needed to obtain precise @xmath1.the atomic edm can also put bounds on the parameters of alternative models in particle physics . the schiff moment which arises due to either nucleon edm or p - t violating interactions between the nucleons can also contribute to the yb edm and can be used to extract the nuclear p - t violation parameters . we have calculated the contribution to atomic yb edm from both these effects but in this paper we will present the result of our calculations for t - pt contribution alone , in a later paper we will present the result of our schiff moment computation . the calculation of yb edm within a limited set of configuration state functions ( csfs ) using diagonalization and bloch equation based many - body perturbation theory ( mbpt ) methods was reported in an earlier paper@xcite . for convenient of reference this paper is called as paper - i hereafter . as a followup , in this paper we present results of calculations using much larger csf space . in addition , we discuss the drawbacks common to the diagonalization and bloch equation based perturbation methods , improvements are discussed and results of using these methods are presented . in this paper we present the method of the calculation .

the existence of a finite electric dipole moment ( edm ) of the closed - shell atom yb implies parity and time reversal violations involving the nuclear sector . an important effect which can contribute to the yb edm if a finite of yb is observed in experiments , then an estimate of can be obtained by combining with the theoretical calculations . a non - zero implies physics beyond the standard model . in this paper we present the result of our _ ab initio _ calculation of the edm yb using different many - body methods .

the existence of a finite electric dipole moment ( edm ) of the closed - shell atom yb implies parity and time reversal violations involving the nuclear sector . an important effect which can contribute to the yb edm is the tensor - pseudotensor electron - nucleus interaction characterized by the coupling constant . within the standard model ( sm ) of particle physics , as this form of interaction is not allowed . if a finite of yb is observed in experiments , then an estimate of can be obtained by combining with the theoretical calculations . a non - zero implies physics beyond the standard model . in this paper we present the result of our _ ab initio _ calculation of the edm yb using different many - body methods .

astro-ph0508177

i

the last few years haven seen the establishment of the lyman-@xmath0 forest as one of the major observational tools to probe the matter power spectrum . measurements of the matter power from the lyman-@xmath0 forest data extend to smaller scales and probe a complementary redshift range than those using the cosmic microwave background ( cmb ) , galaxy surveys or weak gravitational lensing . the lyman-@xmath0 forest is thus ideally suited to constrain cosmological parameters which affect the power spectrum on small scales like the neutrino mass and the mass of dark matter ( dm ) particles ( seljak et al . 2004 ; viel et al . 2005 ) . in a combined analysis with cmb data the lyman-@xmath0 forest results have also been pivotal in tightening constraints on the power law index of the power spectrum of primordial density fluctuations @xmath3 . a consistent picture emerges suggesting that the fluctuation amplitude of the matter power spectrum @xmath1 is rather high , that the spectral index of primordial density fluctuations is consistent with the value @xmath9 and that there is no evidence for a running of the spectral index , significant neutrino mass or a deviation from a cold dark matter spectrum at small scales ( croft et al . 1998 , mcdonald et al . 2000 , hui et al . 2001 , croft et al . 2002 [ c02 ] , mcdonald 2003 , viel et al . 2003 , viel , haehnelt & springel 2004 [ vhs ] , desjacques & haehnelt 2004 , viel , weller & haehnelt 2004 , mcdonald et al . 2004 [ m04a ] , mcdonald et al . 2004b [ m04b ] , viel et al . 2005 , lidz et al . 2005 ) . major uncertainties are thereby the assumed effective optical depth and thermal history of the intergalactic medium ( igm ) and the numerical limitations in obtaining accurate theoretical predictions for the flux power spectrum for a large parameter space ( see vhs and m04a for a detailed discussion ) . vhs and viel , weller & haehnelt ( 2004 ) recovered the linear dark matter power spectrum amplitude and its slope from a new set of 27 high resolution high signal - to - noise qsos ( the luqas sample , kim et al . 2004 [ k04 ] ) and reanalysed the earlier results of c02 . viel et al . found @xmath10 , @xmath11 ( @xmath8 ) and no evidence for a ( large ) running spectral index when they combined the lyman-@xmath0 forest data with the wmap data . similar results have have been obtained subsequently by the sdss collaboration from a much larger sample of 3035 low - resolution low s / n spectra with significantly wider reshift coverage ( m04b ; seljak et al . these findings corrected earlier claims of spergel et al . ( 2003 ) who used the data of c02 combined with cmb and galaxy survey data to argue for a significant tilt away from the canonical harrison - zeldovich @xmath9 spectrum and possibly also for a running of the spectral index ( see seljak et al . ( 2003 ) for the first suggestion that this result may be due to the assumption of an unplausibly large effective optical depth ) . large samples of qso absorption spectra offer the opportunity to obtain the flux power spectrum for a wide range of redshifts with an accuracy at the percent level . despite the generally good agreement between different groups achieved in the last couple of years there are , however , still major open issues of what and how large the uncertainties in the cosmological and astrophysical parameters inferred from the flux power spectrum are ( see vhs and m04b for discussions with different views ) . it will be important to resolve these issues if further progress is to be made . the two data sets used by vhs and m04b and their theoretical modelling were very different . the sdss qso data set analysed by m04a consists of @xmath12 qso spectra at low resolution ( @xmath13 ) and low s / n ( @xmath14 per pixel ) spanning a wide range of redshifts , while the luqas and the c02 samples contain mainly high resolution ( @xmath15 ) , high signal - to - noise ( @xmath16 per pixel ) qso spectra with median redshifts of @xmath17 and @xmath18 , respectively . the analysis methods to infer cosmological and astrophysical parameters were also very different . m04b modelled the flux power spectrum using a large number of hpm simulations ( gnedin & hui 1998 ; viel , haehnelt & springel 2005 ) exploring a large multi - dimensional parameter space . viel et al . ( 2004 ) improved instead the effective bias method developed by c02 . they used a grid of full hydrodynamical simulations run with the tree - sph code ( springel , yoshida & white 2001 ; springel 2005 ) to invert the non - linear relation between flux and matter power spectrum . both methods have their own set of problems . m04b had to use the approximate hpm method which they could only calibrate on a small number of hydro simulations of small box size ( see viel , haehnelt & springel ( 2005 ) for a discussion of the accuracy of hpm simulations ) . m04b further had to compromise on box size and even time - stepping in order to explore a large parameter space . this lead to large number of uncertain corrections which added to another large set of corrections necessary because of the rather low resolution and s / n of their data . the method used by vhs on the other hand requires differentiating the 1d flux power spectrum to obtain the `` 3d '' flux power spectrum , which introduces rather large errors . this makes the assessment of statistical errors somewhat difficult . we refer to zaldarriaga , hui & tegmark ( 2001 ) ; gnedin & hamilton ( 2002 ) ; zaldarriaga , scoccimarro & hui ( 2003 ) and seljak , mcdonald & makarov ( 2003 ) for a further critical assessments of the use of the effective bias method to infer cosmological parameters . vhs concluded that the best they can do was to give an estimate of the many systematic uncertainties involved and to combine these in a conservative way in the final result . however , for attemtps to take advantage of the full redshift coverage and smaller errors of the observed sdds flux power spectrum the effective bias stops being useful . further motivated by the differences in the data and in the theoretical modelling performed by the two groups , we will analyse here the sdss flux power spectrum with high resolution , large box - size full hydrodynamical simulations . ideally , one would like to be able to repeat the analysis made by the sdss collaboration by using a very fine grid of full hydrodynamical simulations in order to be able to sample the multi - dimensional parameter space . however , at present , this approach is not feasible since hydrodynamical simulations are very time consuming . we therefore decided to concentrate most of the analysis on a small region of the parameter space , around the best - fit models obtained by the two groups . we thereby use a taylor expansion to approximate the flux power spectrum around a best - guess model . this approximation should be reasonably accurate for little displacements in parameter space . we have checked the validity of the approximation for a few models . however , we caution the reader that the final error bars on recovered astrophysical and cosmological parameters is likely to be somewhat underestimated due to unaccounted errors of this approximation . the plan of this paper is as follows . in section [ data ] we briefly describe the sdss data set , while the hydrodynamical simulations are discussed in section [ hydro ] . section [ results ] describes the technical details of our modelling of the flux power spectrum and the reader more interested in the results may go straight to section [ chifitting ] where we discuss our findings for the cosmological and astrophysical parameters . section [ conclu ] contains a summary and an outline of possible ways of improving these measurements .

is very challenging . , we investigate how the interplay between astrophysical and cosmological parameters affects their measurements using the recently published flux power spectrum obtained from 3035 sdss qsos ( mcdonald et al . 2004 ) . we argue , however , that the major uncertainties in this measurement are still systematic rather than statistical . = 6.5truein # 1*mh : # 1 * [ 2]@series cosmology : intergalactic medium , cosmological parameters large - scale structure of universe quasars : absorption lines

the flux power spectrum of the lyman- forest in quasar ( qso ) absorption spectra is sensitive to a wide range of cosmological and astrophysical parameters and instrumental effects . modelling the flux power spectrum in this large parameter space to an accuracy comparable to the statistical uncertainty of large samples of qso spectra is very challenging . we use here a coarse grid of hydrodynamical simulations run with to obtain a `` best guess '' model around which we calculate a finer grid of flux power spectra using a taylor expansion of the flux power spectrum to first order . in this way , we investigate how the interplay between astrophysical and cosmological parameters affects their measurements using the recently published flux power spectrum obtained from 3035 sdss qsos ( mcdonald et al . 2004 ) . we find that the sdss flux power spectrum alone is able to constrain a wide range of parameters including the amplitude of the matter power spectrum , the matter density , the spectral index of primordial density fluctuations , the effective optical depth and its evolution . the thermal history of the intergalactic medium ( igm ) is , however , poorly constrained and the sdss data favour either an unplausibly large temperature or an unplausibly steep temperature - density relation . by enforcing a thermal history of the igm consistent with that inferred from high - resolution qso spectra , we find the following values for the best fitting model ( assuming a flat universe with a cosmological constant and zero neutrino mass ) : , , ( error bars ) . the values for and are consistent with those obtained by mcdonald et al . with different simulations for similar assumptions . we argue , however , that the major uncertainties in this measurement are still systematic rather than statistical . = 6.5truein # 1*mh : # 1 * [ 2]@series cosmology : intergalactic medium , cosmological parameters large - scale structure of universe quasars : absorption lines

astro-ph0508177

c

in table [ tab3 ] we list results for the most important parameters describing the matter distribution ( @xmath1 and @xmath3 ) obtained by recent studies using the lyman-@xmath0 forest by a variety of authors . the most direct comparison is again with m04b . at @xmath105 our results correspond to an fluctuation amplitude and effective slope at the pivot wavenumber @xmath256 s / km as defined by m04b of @xmath257 and @xmath258 . the values are consistent within @xmath259 with those of m04b . the agreement with otherauthors including our own work is at the same level . for comparison we also show the value for wmap alone . a consistent picture emerges for the lyman-@xmath0 forest data with a rather high fluctuation amplitude and no evidence for a significant deviation from @xmath9 or a running of the spectral index . this results holds for the lyman-@xmath0 forest data alone but is considerably strengthened if the lyman-@xmath0 forest data is combined with the cmb and other data . as discussed in section [ system ] there are many systematic uncertainties that affect the measurement of cosmological parameters with the lyman-@xmath0 flux power spectrum . in order to test the stability of the results we have removed the correction for high column density systems and the errors for the noise and resolution corrections in the case with priors . if we take out the correction due to strong absorption systems @xmath3 , decreases to @xmath260 , and the best fit value for @xmath261 becomes 0.381 , all the other parameters remain practically unchanged . the measured values do therefore practically not change but the value of @xmath42 increases by 0.5 . if we do not allow for the error to the noise and resolution corrections the inferred values do again not change but the value of @xmath42 increases by 1.8 . note that m04a have also subtracted an estimate of the contribution of associated metal absorption from the flux power spectrum and have applied a suite of other ( smaller ) corrections to the data ( see m04a for more details ) . many of these corrections would either not be necessary or substantially easier for spectra with somewhat better resolution ( @xmath262 ) and higher s / n . obtaining large samples of such spectra is observationally feasible and there is certainly room for improvement . note further that the sdss team will soon release a further measurement of the flux power spectrum performed by an independent group within the collaboration . we also note again that calculating the flux power spectrum by using a taylor expansion to first order around the best guess model is just an approximation . this was an important part of our analysis as it reduced the amount of cpu time necessary dramatically , but could be further improved by getting more accurate fits around the `` best guess '' model . we have also not attempted to correct for the possible effects of spatial fluctuations of the ionization rate , galactic winds , temperature fluctuation or the reionization history . this is because we are not convinced that it is already possible to model these effects with sufficient accuracy . this should hopefully change in future with improved observational constraints and numerical capabilities . one should further keep in mind that so far very little cross checking of hydrodynamical simulation run with different codes has been performed . in our study the rather poorly known thermal state of the igm is one of the major remaining uncertainties . further high - resolution spectroscopy and improved modelling will hopefully soon improve this . accurate modelling of the effect of high column density systems/ damped lyman-@xmath0 systems and improvement in the determination of the column density distribution of observed absorption systems in the poorly determined range around @xmath263 should also be a priority in further studies ( see the discussion in mcdonald et al . 2005 ) . it is certainly encouraging that the differences between our analysis and that of m04b are moderate despite considerable differences between their approximate hpm simulations calibrated with hydrodynamical simulations of rather small box size and our analysis with full hydrodynamical simulations of much larger box size here and in vhs . for the time being we would advice the conservative reader to double the formal errors quoted here . this will bring the error estimates to about the same size as the also conservative estimates for the errors of the fluctuation amplitude from the lyman-@xmath0 forest data alone in the analysis of vhs . the actual errors lie probably somewhere in between . we have compared the flux power spectra calculated from a suite of full large box - size high resolution ( @xmath264 mpc , @xmath109 particles ) hydrodynamical simulations with the sdss flux power spectrum as published by mcdonald et al . ( 2005 ) . we have identified a best - guess model which provides a good fit to the data . we have used a taylor expansion to first order to calculate flux power spectra in a multi - dimensional space of parameters describing the matter power spectrum and the thermal history of the igm with values close to those of our best - guess model . we have investigated the combined effect of cosmological and astrophysical parameters on the flux power spectrum with an adapted version of the markov - chain code cosmomc . our main results can be summarized as follows . * the flux power spectrum calculated directly from the simulation of a @xmath265cdm model ( @xmath63 , @xmath266 , @xmath65 and @xmath66,@xmath267 ) with a temperature density relation described by @xmath268 and @xmath269 gives an acceptable fit to the sdss flux power spectrum in the redshift range @xmath270 ( @xmath271 for 88 degrees of freedom ) . the fit can easily be further improved by small changes in the cosmological and astrophysical parameters . * at higher redshift the deviations from the observed flux power spectrum become significantly larger ( @xmath272 for 12 additional data points at @xmath26 ) suggesting either some problem with the data or a physical effect that changes rapidly with redshift . * we confirm the claim by mcdonald et al . ( 2004 ) that the degeneracy of the dependence of the flux power spectrum on the amplitude of the matter power spectrum and the effective optical depth can be broken for the published sdss flux power spectrum . it will be interesting to see if the same is true for the independent analysis of the sdss data to be released soon . * the sdss power spectrum alone can constrain the amplitude of the matter power spectrum , the matter density and the power - law index of primordial density fluctuation to within @xmath273 . the thermal state of the igm is however , poorly constrained and the sdss power spectrum formally prefers models with unplausible values of the parameters describing the thermal state . the dependence of the flux power spectrum on the assumed hubble constant is also very weak and the hubble constant is not well constrained . the exact values for the other cosmological parameters depend somewhat on the assumed prior for the thermal state and the details of the correction which have been applied to the data . * with a prior on the thermal history and the hubble constant motivated by the observations by schaye et al . ( 2000 ) and freedman et al . ( 2001 ) we obtain the following best - fitting values for the cosmological parameters @xmath5 , @xmath6 , @xmath7 ( @xmath8 error bars ) , and the effective optical depth is well described by the following power - law relation : @xmath244^{3.22\pm0.24}$ ] . the errors were obtained by marginalizing over a set of 22 parameters describing the matter distribution , thermal history of the universe , the effective optical depth and errors to various corrections to the data . the values for @xmath60 and @xmath3 are consistent with those found by m04a for the same data set with different simulations . they are also consistent with the results of other recent studies of lyman-@xmath0 forest data . the inferred optical depth is in good agreement with that measured directly from continuum - fitted high - quality absorption spectra .

we use here a coarse grid of hydrodynamical simulations run with to obtain a `` best guess '' model around which we calculate a finer grid of flux power spectra using a taylor expansion of the flux power spectrum to first order . in this way we find that the sdss flux power spectrum alone is able to constrain a wide range of parameters including the amplitude of the matter power spectrum , the matter density , the spectral index of primordial density fluctuations , the effective optical depth and its evolution . the thermal history of the intergalactic medium ( igm ) is , however , poorly constrained and the sdss data favour either an unplausibly large temperature or an unplausibly steep temperature - density relation . by enforcing a thermal history of the igm consistent with that inferred from high - resolution qso spectra , we find the following values for the best fitting model ( assuming a flat universe with a cosmological constant and zero neutrino mass ) : , , ( error bars ) . the values for and are consistent with those obtained by mcdonald et al . with different simulations for similar assumptions .

the flux power spectrum of the lyman- forest in quasar ( qso ) absorption spectra is sensitive to a wide range of cosmological and astrophysical parameters and instrumental effects . modelling the flux power spectrum in this large parameter space to an accuracy comparable to the statistical uncertainty of large samples of qso spectra is very challenging . we use here a coarse grid of hydrodynamical simulations run with to obtain a `` best guess '' model around which we calculate a finer grid of flux power spectra using a taylor expansion of the flux power spectrum to first order . in this way , we investigate how the interplay between astrophysical and cosmological parameters affects their measurements using the recently published flux power spectrum obtained from 3035 sdss qsos ( mcdonald et al . 2004 ) . we find that the sdss flux power spectrum alone is able to constrain a wide range of parameters including the amplitude of the matter power spectrum , the matter density , the spectral index of primordial density fluctuations , the effective optical depth and its evolution . the thermal history of the intergalactic medium ( igm ) is , however , poorly constrained and the sdss data favour either an unplausibly large temperature or an unplausibly steep temperature - density relation . by enforcing a thermal history of the igm consistent with that inferred from high - resolution qso spectra , we find the following values for the best fitting model ( assuming a flat universe with a cosmological constant and zero neutrino mass ) : , , ( error bars ) . the values for and are consistent with those obtained by mcdonald et al . with different simulations for similar assumptions . we argue , however , that the major uncertainties in this measurement are still systematic rather than statistical . = 6.5truein # 1*mh : # 1 * [ 2]@series cosmology : intergalactic medium , cosmological parameters large - scale structure of universe quasars : absorption lines

0811.0610

i

two - dimensional honeycomb lattice of carbon atoms may be viewed as the mother of all other forms of carbon . its crucial electronic property , which arises as a consequence of the absence of the inversion symmetry around the lattice site , is that the usual fermi surface is reduced to just two points . the electronic dispersion may be linearized around these two points , after which it becomes isotropic and dependent on the single dimensionful parameter , fermi velocity @xmath4 . the pseudo - relativistic nature of the electronic motion in graphene has since its synthesis placed this material at the center stage of condensed matter physics . many qualitatively novel phenomena that take , or may take place in such a system of `` dirac '' electrons are actively discussed in the rapidly growing literature on the subject . @xcite in this paper we discuss the low - energy theory and the metal - insulator quantum phase transitions of the _ interacting _ dirac electrons on the honeycomb lattice , building upon and expanding significantly the earlier work by one of us . @xcite in the first approximation , _ all _ weak interactions of dirac electrons in graphene may be neglected at half filling , when the fermi surface consists of the dirac points . this is because short - range interactions are represented by local terms which are quartic in the electron fields , which makes them irrelevant near the non - interacting fixed point by power counting . the same conclusion turns out to apply to the long - range tail of the coulomb interaction , which remains unscreened in graphene , although only marginally so . @xcite nevertheless , if strong enough , the same interactions would turn graphene into a gapped mott insulator . as an example , at a strong on - site repulsion the system is likely to be the usual nel antiferromagnet . @xcite it is not _ a priori _ clear on which side of this metal - insulator transition graphene should be . with the standard estimate for the nearest - neighbor hopping in graphene of @xmath5 and the hubbard interaction of @xmath6 , it seems that the system is below yet not too far from the critical point estimated to be at @xmath7 . @xcite if sufficiently weak , the electron - electron interactions only provide corrections to scaling of various quantities , which ultimately vanish at low temperatures or frequencies . at , what is probably a more realistic , an intermediate strength , the flow of interactions and the concomitant low - energy behavior may be influenced by the existence of metal - insulator critical points . it is possible that some of the consequences of such interaction - dominated physics have already been observed in the quantization of the hall conductance at filling factors zero and one . @xcite as we argued elsewhere , the anomalously large value of the minimal conductivity in graphene @xcite may be yet another consequence of the coulomb repulsion between electrons . @xcite the above discussion raises some basic questions . what is the minimal description of interacting electrons in graphene at `` low '' energies ? what is the symmetry of the continuum interacting theory , and how does it constrain the number of coupling constants ? what kinds of order may be expected at strong coupling , and what is the nature of the metal - insulator quantum phase transition ? in this paper we address these and related issues . in the rest of the introduction we give a preview of our main results . the simplest prototypical system that exhibits the physics of interacting dirac fermions which we seek to understand is the collection of spinless electrons interacting via short - range interactions , at half - filling . for present purposes an interaction may be considered as `` short - ranged '' if its fourier transform at the vanishing wavevector is finite . @xcite the least irrelevant quartic terms one can add to the non - interacting dirac lagrangian will then be local in space - time , and of course quartic in terms of the four - component dirac fields that describe the electronic modes near the two inequivalent dirac points at wavevectors @xmath8 at the edges of the brillouin zone . the most general local quartic term in the lagrangian would be of the form @xmath9 where @xmath10 and @xmath11 are four - dimensional hermitian matrices . the symmetry alone , however , immediately drastically reduces the number of independent couplings from the apparent @xmath12 to just fifteen . although the point group of the honeycomb lattice is @xmath13 , the exact spatial discrete symmetry of the lagrangian is only the _ dihedral group _ @xmath1 , or the _ vierergruppe _ , which consists of the reflections through the two coordinate axis shown in fig . 1 , and the inversion through the origin . such a small symmetry results from the very choice of two inequivalent dirac points out of six corners of the brillouin zone , which reduces the symmetry to the simple exchange of the two sublattices ( reflection around a axis ) , the exchange of dirac points ( reflection around b axis ) , and their product ( the inversion through the origin ) . @xmath1 , the time - reversal , and the translational invariance are shown to leave fifteen possible different local quartic terms in the lagrangian . fortunately , not all of these still numerous quartic terms are independent , and there are linear constraints between them implied by the algebraic fierz identities . @xcite the fierz transformations are rewritings of a given quartic term in terms of others , and we provide the general formalism for determining the number and the type of independent quartic couplings of a given symmetry . for the case at hand we find that spinless electrons interacting with short - range interactions on honeycomb lattice are in fact described by only _ six _ independent local quartic terms . the inclusion of electron spin would double this number to twelve . the linearized noninteracting lagrangian for dirac electrons , @xmath14 as well - known , exhibits the lorentz and the global @xmath3 ( `` chiral '' ) symmetry . the latter , generated by @xmath15 , with @xmath16 , is nothing but the `` rotation '' of the `` pseudospin '' , or `` valley '' , corresponding to two inequivalent dirac points . @xcite a general quartic term allowed by the lattice symmetry , on the other hand , has a much smaller symmetry , as already mentioned . nevertheless , we will argue that near the metal - insulator quantum critical points , all , or nearly all of the larger symmetry possessed by the non - interacting part of the lagrangian gets restored . this conclusion is supported by the , admittedly uncontrolled , but nevertheless quite informative one - loop calculation . first , we find three distinct critical points in the theory , all of which have not only the rotational , but the full lorentz - symmetric form . this immediately implies that the dynamical critical exponent is always @xmath17 . this is quite remarkable in light of the fact that the microscopic theory is not even rotationally invariant , and that the critical points in question are purely short - ranged . @xcite the fact that @xmath17 has important implications for several key physical observables near the critical point , as we discuss shortly . furthermore , we find that two out of three critical points in the theory exhibit a full chiral symmetry as well . we identify the three fixed points in the theory as corresponding to three possible order parameters , or `` masses '' that develop in the insulating phase at strong coupling . \1 ) @xmath18 , which preserves chiral , but breaks time - reversal symmetry . microscopically , this order parameter may be understood as a specific pattern of circulating currents , as discussed in the past . @xcite \2 ) @xmath19 , which preserves the time - reversal symmetry , and the single chiral generator @xmath20 , which will be shown to correspond to translational invariance . this order parameter describes a finite staggered density , i. e. the difference between the average densities on the two sublattices of the honeycomb lattice . @xcite \3 ) @xmath21 , which preserves the time - reversal , but breaks translational invariance ( @xmath20 ) . this order parameter can be understood as the specific `` kekule '' modulation of the nearest - neighbor hopping integrals . @xcite in one - loop calculation all three critical points have the same correlation length exponent @xmath22 , which we believe is an artifact of the quadratic approximation . the result that the dynamical critical exponent @xmath17 is , on the other hand , possibly exact . if we denote the relevant interaction parameter with @xmath23 , the fermi velocity near the transition scales as @xmath24 so the above value of @xmath25 would simply imply that it stays regular at the transition . this appears to be in agreement with the picture of the transition as the opening of the relativistic `` mass '' in the spectrum . the mass - gap in the insulating phase scales as usual @xcite as @xmath26 the transition on the metallic side is manifested as vanishing of the residue of the quasiparticle pole @xcite @xmath27 where we assumed @xmath17 . ( a more general power - law is discussed in the text . ) at one - loop the fermion anomalous dimension @xmath28 vanishes , but in general it is a positive , small , and critical - point - dependent number . the overall picture of the metal - insulator transition that emerges is presented in fig . 2 . for graphene s @xmath29-orbitals well localized on carbon sites , a further significant simplification takes place . all the terms without the equal number of creation and annihilation operators for each of the two sublattices must vanish . assuming again the emergent lorentz symmetry at low energies this allows one to finally write the simplest internally consistent interacting theory as @xmath30 this lagrangian provides the minimal low - energy description of interacting spinless electrons on honeycomb lattice . it has two critical points , corresponding to transitions into insulators 1 ) and 2 ) in the above , both corresponding to the gross - neveu criticality in 2 + 1 dimensions . we discuss the internal consistency and the sufficiency of this lagrangian and some of the peculiarities of the ensuing phase diagram . the rest of the paper is organized as follows . we discuss the point symmetry , translational symmetry , and the time - reversal symmetry of the interacting lagrangian as dictated by the microscopic hamiltonian for the system in the next section . in section iii it is shown how further enlargements of the symmetry would reduce the number of coupling constants . we introduce the notion of `` maximally symmetric '' theory , which shares the full lorentz and chiral symmetry with the quadratic term in the lagrangian . the general formalism of fierz transformations is developed and applied to the cases of interest in section iv . the change of the coupling constants with the ultraviolet cutoff in the theory is studied in section v. the atomic limit of the general interacting theory is described in section vi , and the critical exponents are discussed in section vii . in section viii we discuss the scaling of the electron propagator and the power - laws for various quantities of interest . the discussion of the long - range coulomb interaction and the critical behavior of the specific heat and the optical conductivity are given in section ix , and the summary in section x. finally , in appendixes we present some of the requisite technical details : the fierz transformation , the spectral form of the asymmetric matrix needed in section iv , and an alternative implementation of the renormalization group in presence of linear constraints .

the general low - energy theory of electrons interacting via repulsive short - range interactions on graphene s honeycomb lattice at half filling is presented . the exact symmetry of the lagrangian with local quartic terms for the dirac four - component field dictated by the lattice is identified astime reversal , where is the dihedral group , and is a subgroup of the `` chiral '' group of the non - interacting lagrangian , that represents translations in dirac language . we show how first imposing the rotational , then lorentz , and finally chiral symmetry to the quartic terms - in conjunction with the fierz transformations - eventually reduces the set of couplings to just two , in the `` maximally symmetric '' local interacting theory . in contrast to these two critical quantities , we argue that the fermi velocity is non - critical as a consequence of the dynamical exponent being fixed to unity by the emergent lorentz invariance near criticality . possible effects of the long - range coulomb interaction , and the critical behavior of the specific heat and conductivity are discussed .

the general low - energy theory of electrons interacting via repulsive short - range interactions on graphene s honeycomb lattice at half filling is presented . the exact symmetry of the lagrangian with local quartic terms for the dirac four - component field dictated by the lattice is identified astime reversal , where is the dihedral group , and is a subgroup of the `` chiral '' group of the non - interacting lagrangian , that represents translations in dirac language . the lagrangian describing spinless particles respecting this symmetry is parameterized by six independent coupling constants . we show how first imposing the rotational , then lorentz , and finally chiral symmetry to the quartic terms - in conjunction with the fierz transformations - eventually reduces the set of couplings to just two , in the `` maximally symmetric '' local interacting theory . we identify the two critical points in such a lorentz and chirally symmetric theory as describing metal - insulator transitions into the states with either time - reversal or chiral symmetry being broken . the latter is proposed to govern the continuous transition in both the thirring and nambu - jona - lasinio models in 2 + 1 dimensions and with a single dirac field . in the site - localized , `` atomic '' , limit of the interacting hamiltonian , under the assumption of emergent lorentz invariance , the low - energy theory describes the continuous transitions into the insulator with either a finite haldane s ( circulating currents ) or semenoff s ( staggered density ) masses , both in the universality class of the gross - neveu model . the simple picture of the metal - insulator transition on a honeycomb lattice emerges at which the residue of the quasiparticle pole at the metallic , and the mass - gap in the insulating phase both vanish continuously as the critical point is approached . in contrast to these two critical quantities , we argue that the fermi velocity is non - critical as a consequence of the dynamical exponent being fixed to unity by the emergent lorentz invariance near criticality . possible effects of the long - range coulomb interaction , and the critical behavior of the specific heat and conductivity are discussed .

mtrl-th9602004

i

the possibility of hydrogen metallization under high pressure was first discussed by wigner and huntington in the thirties @xcite . this particular subject was included in the more general conjecture that any system becomes metallic if sufficient pressure is applied . electrons , which are bound in the isolated atomic or molecular species , hybridize in a condensed phase to form extended states which gather in energy bands . when pressure is applied , the bands widen due to the enhancement of the overlap between neighboring atoms orbitals , up to the point at which the energy gap between the valence and the conduction band vanishes , thus giving rise to metallic behavior . this enhancement of the overlap can also be viewed as the growing importance of the electronic kinetic energy relative to the ion - electron potential ; the latter tends to bind electrons to the ions ( also in the form of interatomic , intramolecular or intermolecular bonds ) . in the case of pure hydrogen , metallization was estimated to occur around 2.5 mbars ( 1 mbar = 100 gpa ) , i.e. at pressures that have become accessible to experiment in diamond anvil cells only very recently @xcite . the absence of clear signs of metallic behaviour up to 2.9 mbar @xcite certainly adds to the challenge , and stimulates the continuous improvement of experimental setups in the search for the _ reluctant _ metallization . an additional difficulty in the description of this particular metal - insulator phase transition arises from the fact that at low pressures the low - temperature phase is not a monoatomic but a molecular solid , i.e. an hexagonal close packed ( hcp ) arrangement of h@xmath5 molecules @xcite . in this sense , h behaves more like a halogen than like an alkali metal @xcite . up to pressures of the order of 1 mbar , experiment indicates that the hcp arrangement is preserved . at pressures of the order of 110 gpa , the low - pressure free - rotator phase of para - h@xmath5 freezes into an orientationally ordered phase , whose nature is not yet fully understood . the observation of more than one vibron mode @xcite precludes the hcp structure with all the molecules pointing along the c - axis . however , other more complex hcp structures with tilted molecules ( herringbone - like ) are compatible with experiment @xcite . it is also possible that orientational order is not complete , thus giving rise to a sequence of weak phase transitions until the perfectly ordered phase is reached . an intriguing phase transition at 150 gpa , signalled by a discontinuity in the molecular vibron @xcite , has been ascribed either to a relative reorientation of the h@xmath5 groups @xcite , to metallization arising from an electronic band - overlap mechanism without molecular reorientation @xcite , and to both occuring at the same time @xcite . density functional ( dft ) calculations indicate that arrangements with complex molecular orientations ( non parallel ) are energetically preferred in the high pressure phase @xcite . another study @xcite concentrated on other classes of structures including cubic @xmath6 and rutile , and also two hcp structures , namely @xmath7 and @xmath8 . the hexagonal @xmath7 was found to be the favorable one above the 150 gpa transition . very recently , tse and klug performed ab initio simulated annealing calculations with 96 h atoms in the supercell , and found as a ground state an orthorombic structure , instead of hcp , composed of groups of three strongly interacting @xmath9 molecules @xcite . all these candidates were found to be insulating , and the reason for this was claimed to be the opening of a hybridization gap at the fermi level @xcite . diffusion monte carlo ( dmc ) calculations by natoli et al . @xcite have essentially confirmed results by kaxiras et al . @xcite , also at the quantitative level for the angles between different molecular units . they considered neither nagara s @xmath7 nor tse s orthorombic structure . this dmc calculation also finds an insulating behaviour and , interestingly , zero - point - motion effects due to the protons appear to be quite structure independent . as a consequence , zero - point - motion would turn out to be irrelevant as regards the 150 gpa transition , contrarily to the claims of surh et al . @xcite . well - converged local density functional ( lda ) calculations supplemented with the zero - point - motion energy contribution taken from frozen - phonon calculations @xcite , suggest that the molecular - hcp phase goes over directly to an atomic squeezed - hexagonal phase , by breaking the intramolecular bonds , at a pressure of 380 gpa . however , this calculation did not take into account non - hexagonal structures . hence , also from the theoretical point of view , it is not clear up to now whether metallization happens already in the molecular phase , or whether it is a consequence of dissociation , thus occuring simultaneously with the molecular - atomic transition @xcite . a rhombohedral structure was also postulated to supersede the squeezed - hexagonal phase at higher pressures ( above 400 gpa ) @xcite , while the transition to a body - centered - cubic ( bcc ) phase was located at around 1100 gpa @xcite . in general , static methods suffer from the drawback of having to carry out the investigation by _ guessing _ different structures . in this respect , the molecular dynamics results by tse and klug seem to be the most reliable . however , there is still some doubt because it is not obvious that their 96-atom supercell with @xmath10-point sampling and fixed cell volume and shape calculation is a sufficiently good description . a recently proposed method that combines state - of - the - art electronic structure calculations with variable cell shape molecular dynamics simulations @xcite , thus avoiding every undesired bias , is currently being used to investigate the low - temperature phase of h as a funcion of pressure @xcite . it is important to remark that , in general , energy differences between different structures are quite small , so that different levels of approximation often lead to different ground - state structures . in this respect , fully quantum - mechanical dmc calculations are very indicative . ceperley and alder @xcite located the molecular - to - atomic phase transiton at a pressure of about 300 gpa , by studying only cubic structures . further refinements of these dmc calculations have shown how dramatic the effect of improving the description can be @xcite . eventually , it appears that the atomic ground state structure in the vicinity of the molecular - atomic transition is the diamond structure , but the energy difference with respect to others is very small and , in particular , with respect to @xmath11-sn and hexagonal diamond , it is well within the error bars . the diamond structure was considered as a candidate for the ground state in one of the previous dft calculations , but found to be less favorable than a distorted hexagonal phase @xcite . the monoatomic bcc structure is unequivocally identified as the ground state in the very high density limit . there , the electronic kinetic energy is largely dominant over the remaining contributions , such that the electrons behave essentially as free fermions ; i.e. the electronic subsystem decouples from the protons and becomes a rigid , homogeneous electron gas , which acts only as a neutralizing background for the protons . this is well - known as the one - component plasma ( ocp ) model , whose classical version was shown to crystallize into the bcc structure . this follows from a simple calculation of the madelung energy , although the energy differences relative to other structures turn out to be rather small . in the classical ocp , which was thoroughly studied during the past two decades @xcite , the bcc structure turns out to be the stable one also at finite temperature and up to the melting point . the quantum version of the ocp at finite temperature has not yet been studied in detail . a numerical study using the path integral monte carlo technique ( pimc ) is currently under development @xcite . at higher temperatures the protons begin to behave as classical particles . the degeneracy temperature for the protons can be estimated to be of the order of @xmath12 , by comparing the mean interprotonic distance and the thermal de broglie wavelength . the electron degeneracy temperature ( @xmath13 ) lies well above ( by a factor @xmath14 ) such that , at temperatures lower than @xmath15 , electrons can be considered to follow the protons adiabatically , always staying in the the ground state compatible with the current protonic configuration ( fermi temperatures are about twice these numbers , e.g. @xmath16 ) . this latter approximation allowed hohl et al . @xcite to examine the hot , dense _ molecular _ phase by means of ab initio molecular dynamics ( aimd ) simulations , and also to make some progress regarding the low - temperature structure . the aimd study of the _ atomic _ phase is the subject of this and of a previous publication @xcite . the effect of excited electronic states in the same regime has very recently been explored by a novel ab initio molecular dynamics scheme using mermin s density functional @xcite , and the fully - quantum pimc method was applied to simulate the very high - temperature fluid phase @xcite , where the number of excited electronic states involved becomes too large to be treated efficiently with mermin s functional . the low - temperature regime , where protons in turn become degenerate , requires different simulation techniques which are currently being developed @xcite . high - temperature high - pressure measurements on hydrogen have been very recently reported in shock wave experiments @xcite . pressures between 1 and 2 mbar and temperatures of some thousand @xmath17 are now feasible and rather controllable , and further expansion of this range is in sight . in such experiments , nellis et al . observed the metallization of fluid molecular hydrogen at @xmath18 mbar and @xmath19 , a temperature which is significantly lower than that predicted for the plasma phase transition by chabrier et al . @xcite on the basis of a multicomponent thermodynamic theory that employs an approximate equation of state . although more accurate pimc simulations have essentially confirmed the predictions of the theory , including the existence of a first order phase transition at high pressures and a somewhat lower value for the transition temeprature @xcite , the discrepancy with respect to shock wave experiments and aimd results @xcite still holds . the latter would rather indicate a continuous transition in which metallization and dissociation of h@xmath5 molecules are closely related phenomena . a possible scenario would be the existence of two phase transitions : a continuous one , at relatively low temperatures , where molecular hydrogen already metallizes and begins to dissociate , and a discontinuous one at higher temperatures where a massive dissociation occurs with a concomitant jump in the electrical conductivity . hydrogen at finite temperatures and high densites consitutes , hence , a strongly coupled proton - electron plasma which is of great astrophysical interest since it is , in particular , the major constituent in jovian planet interiors . actually , the latter are basically h plasmas with a few percent admixture of he , and the statistical properties of the mixture ( mixing / demixing transition ) are of great importance to account for experimental observations and to establish models for the evolution of these planets @xcite . nevertheless , the answer to many relevant questions in astrophysics requires a full understanding of the statistical properties of the pure main constituents . hydrogen is present in both atomic and molecular fluid phases . these are separated by a boundary located at some distance from the center of the planet . the characteristics of this boundary , e.g. precise location , width , etc . depend on the density and temperature profile , i.e. on the equation of state . the matter of dissociation and metallization is particularly relevant because the large magnetic field measured in jupiter would include a non neglgible component generated in the outer molecular fluid phase , provided that temperature is above the metallization threshold . to quantify this effect the important quantities are the dissociated fraction and the electrical conductivity , which can be obtained from simulations in the molecular phase . the hydrogen plasma is perhaps the most fundamental , simple many - body system , with _ all _ the interactions ( proton - proton , proton - electron and electron - electron ) described exactly by the _ coulomb potential . in spite of this , the phase diagram appears to be surprisingly rich . the purpose of this article is to present a detailed study of the very high pressure physical properties and phase diagram of this simple and fascinating system . we are going to deal always with atomic phases , the molecular phases appearing at lower densities than those studied here . in section ii we briefly describe some details of the simulations , and we address some important technical issues such as the interplay between pseudopotentials and basis set expansions . section iii is devoted to the analysis of the validity of linear response theory in its ability to describe proton - proton interactions in terms of an effective pair potential of the screened coulomb form . in section iv we address a crucial problem that arises in the ab initio simulation of metallic systems , in particular liquid metals , i.e. size effects and fermi surface sampling . in section v we enter directly into the properties of the hydrogen plasma by describing the solid phases and the melting at very high pressure . section vi is concerned with the fluid phase , which we characterize as atomic - like . diffusion and vibrational properties are presented in section vii , while section viii is devoted to a thorough study of the collective dynamics , as a approach to the metal - insulator transition coming from the metallic side . the behavior of the longitudinal collective mode is studied as a function of density and temperature , and proposed as a probe for the metal - insulator transition at finite temeprature . finally , we conclude in section ix . in the remaining part of this section we define some useful parameters and ratios . the plasma is made up of @xmath20 electrons and as many ions ( protons ) per unit volume , such that the usual dimensionless density parameter is @xmath21 , where @xmath22 is the mean interionic distance ( ion - sphere radius ) and @xmath23 is the bohr radius . adopting atomic units throughout , the fermi momentum is @xmath24 , and the thomas - fermi screening length is @xmath25 . the dimensionless coulomb coupling constant associated with the classical ions is @xmath26 . note that @xmath27 , and that the electron degeneracy parameter is @xmath28 . typical densities inside jovian planets are between 1 and 10 @xmath29 and temperatures are of the order of 100 to 10000 @xmath17 , i.e. @xmath30 ranging from 0.5 to 1.5 , and @xmath31 @xcite . note that within this range @xmath32 and for the present calculations , whose aim is precisely to address some aspects of astrophysical plasmas , we can resort to the adiabatic approximation by assuming that the electrons are always in their instantaneous ground state for any given ionic configuration . higher temperatures require the relaxation of this hypothesis .

the hydrogen plasma is studied in the very high density ( atomic and metallic ) regime by extensive ab initio molecular dynamics simulations . these values are typical of jovian planets interiors . finite - size and brillouin zone sampling effects in metallic systems are studied and shown to be very delicate also in the fluid ( liquid metal ) phase . we analyse the low - temperature phase diagram and the melting transition . the structure of the fluid is found to be reminiscent of the underlying bcc ( solid ) phase .

the hydrogen plasma is studied in the very high density ( atomic and metallic ) regime by extensive ab initio molecular dynamics simulations . protons are treated classically , and electrons in the born- oppenheimer framework , within the local density approximation ( lda ) to density functional theory . densities and temperatures studied fall within the strong coupling regime of the protons . we address the question of the validity of linear screening , and we find it to yield a reasonably good description up to , but already too crude for ( with the ion sphere radius ) . these values are typical of jovian planets interiors . finite - size and brillouin zone sampling effects in metallic systems are studied and shown to be very delicate also in the fluid ( liquid metal ) phase . we analyse the low - temperature phase diagram and the melting transition . a remarkably fast decrease of the melting temperature with decreasing density is found , up to a point when it becomes comparable to the fermi temperature of the protons . the possible vicinity of a triple point bcc - hcp(fcc)-liquid is discussed in the region of and . the fluid phase is studied in detail for several temperatures . the structure of the fluid is found to be reminiscent of the underlying bcc ( solid ) phase . proton - electron correlations show a weak temperature dependence , and proton - proton correlations exhibit a well - defined first coordination shell , thus characterizing fluid h in this regime as an atomic liquid . diffusion coefficients are computed and compared to the values for the one - component plasma ( ocp ) . vibrational densities of states ( vdos ) show a plasmon renormalization due to electron screening , and the presence of a plasmon - coupled single - particle mode up to very high temperatures . collective modes are studied through dynamical structure factors . in close relationship with the vdos , the simulations reveal the remarkable persistence of a weakly damped high - frequency ion acoustic mode , even under conditions of strong electron screening . the possibility of using this observation as a diagnostic for the plasma phase transition to the fluid molecular phase at lower densities is discussed .

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the main conclusions to be drawn from the present aimd simulations of the hydrogen plasma in the high - density ( @xmath154 ) regime may be summarized as follows : \a ) due to the significant spacing between the quantized electronic states in the vicinity of the fermi surface , the n - dependence of the statistical averages must be treated with great care , in order to extract meaningful results . \c ) the bcc structure , which is the stable low temperature solid phase at least up to @xmath39 , becomes unstable at lower densities , where hcp and simple - hexagonal phases appear . more work is needed to determine the full low - temperature phase diagram , also including zero - point - motion effects . \d ) the melting temperature drops sharply with decreasing density , due to the enhanced efficiency of electron screening of the effective interaction between ions . new interesting physics is likely to arise in the region of @xmath3 and @xmath4 , where the existence of a bcc - hcp(fcc)-liquid triple point is argued , in a region where quantum effects in the protons are non - negligible . \e ) the fluid metallic phase behaves very much like a simple atomic liquid from a structural point of view , but the longitudinal collective dynamics of the ions retain a strong plasma - like character at intermediate wavenumbers . this reflects itself in unusually sharp peaks in the charge - fluctuation spectrum , which are gradually shifted to lower frequencies with decreasing density , as a result of electron screening . the damping , however , appears to be surprisingly insensitive to density , but is significantly enhanced by temperature . the acoustic character of the longitudinal mode is recovered at sufficiently small wavenumbers ( @xmath155 ) , in qualitative agreement with a simple linear screening picture . a strong damping of the mode at intermediate wavenumbers should be a clear - cut signature of the plasma - to - molecular phase transition , which is expected to start at @xmath83 around @xmath156 , and to move to finite temperatures of the order of a few thousand @xmath17 at lower densities ( @xmath157 ) @xcite . \f ) the single - particle motion of the ions couples to the longitudinal collective mode , and reflects itself in a striking oscillatory behaviour of the velocity autocorrelation function , which is reminiscent of the behavior of the ocp , despite the action of strong electron screening . the resulting ionic self - diffusion constant is strongly enhanced at lower densities , for identical values of the plasma coupling constant @xmath10 , but follows a power law similar to that observed in the ocp . one of us ( jk ) would like to thank furio ercolessi for facilitating his code to fit the two - body potential , and ruben weht for helping with the fp - lmto calculations . we acknowledge helpful discussions with ali alavi , detlef hohl , hong xu , gilles zerah , stephane bernard , carlo pierleoni , pietro ballone , erio tosatti , giorgio pastore and sandro scandolo . e. wigner and h. b. huntington , j. chem . phys . * 3 * , 764 ( 1935 ) ; h. k. mao and r. j. hemley , science * 244 * , 1462 ( 1989 ) . see h. k. mao and r. j. hemley , rev . phys . * 66 * , 671 ( 1994 ) and references therein . see also i. f. silvera in _ simple molecular systems at very high pressure _ , eds . a. polian , p. loubeyre and n. bocarra ( plenum , ny , 1989 ) . l. cui , n. h. chen and i. f. silvera , phys . . lett . * 74 * , 4011 ( 1995 ) . a. ruoff , private communication . n. w. ashcroft , physics world , july 1995 , p. 43 . m. hanfland , r. j. hemley and h. k. mao , phys . lett . * 70*,3760 ( 1993 ) . r. j. hemley and h. k. mao , phys . * 61 * , 857 ( 1988 ) . e. kaxiras , j. broughton and r. j. hemley , phys . . lett . * 67 * , 1138 ( 1991 ) ; e. kaxiras and j. broughton , europhys . * 17 * , 151 ( 1992 ) . h. chacham and s. g. louie , phys . lett . * 66 * , 64 ( 1991 ) . m. p. surh , t. w. barbee iii and c. mailhiot , phys . * 70 * , 4090 ( 1993 ) . h. nagara and t. nakamura , phys . * 68 * , 2468 ( 1992 ) . j. s. tse and d. d. klug , nature ( in press ) . i. i. mazin and r. e. cohen , phys . b * 52 * , r8597 ( 1995 ) . v. natoli , r. m. martin and d. m. ceperley , phys . lett . * 70 * , 1952 ( 1995 ) . t. w. barbee iii , a. garcia , m. l. cohen and j. l. martins , phys . lett . * 62 * , 1150 ( 1989 ) . t. w. barbee iii and m. l. cohen , phys . b * 44 * , 11563 ( 1991 ) . p. focher , g. l. chiarotti , m. bernasconi , e. tosatti and m. parrinello , europhys . lett . * 36 * , 345 ( 1994 ) . j. kohanoff , s. scandolo , g. l. chiarotti and e. tosatti , unpublished . d. m. ceperley and b. j. alder , phys . rev . b * 36 * , 2092 ( 1987 ) . v. natoli , r. m. martin and d. m. ceperley , phys . lett . * 70 * , 1952 ( 1993 ) . m. baus and j .- p . hansen , phys . reports * 59 * , 1 ( 1980 ) ; s. ichimaru , h. iyetomi and s. tanaka , _ ibid _ * 149 * , 91 ( 1987 ) . d. m. ceperley , private communication . d. hohl , v. natoli , d. m. ceperley and r. m. martin , phys . lett . * 71 * , 541 ( 1993 ) . j. kohanoff and j .- p . hansen , phys . lett . * 74 * , 626 ( 1995 ) . a. alavi , j. kohanoff , m. parrinello and d. frenkel , phys . lett . * 73 * , 2599 ( 1994 ) . c. pierleoni , d. m. ceperley , b. bernu and w. r. magro , phys . * 73 * , 2145 ( 1994 ) . j. kohanoff , c. pierleoni and d. m. ceperley ( unpublished ) . w. j. nellis , m. ross and n. c. holmes , science * 269 * , 1249 ( 1995 ) , s. t. weir , a. c. mitchell , and w. j. nellis , preprint . g. chabrier , d. saumon , w. b. hubbard , and j. i. lunine , astrophys . j. * 391 * , 817 ( 1992 ) , and references therein . w. r. magro , d. m. ceperley , c. pierleoni , and b. bernu , phys . rev . lett * 76 * , 1240 ( 1996 ) . a. alavi , m. parrinello and d. frenkel , science * 269 * , 1252 ( 1995 ) . d. saumon , w. b. hubbard , g. chabrier , and h. m. van horn , astrophys . j. * 391 * , 827 ( 1992 ) . r. car and m. parrinello , phy . lett . * 55 * , 2471 ( 1985 ) ; for a recent review see g. galli and m. parrinello in _ computer simulations in materials science _ , , m. meyer and v. pontikis ( eds . ) ( kluwer , dodrecht , 1991 ) . for a comprehensive treatise see , e.g. r. g. parr and w. yang , _ density functional theory of atoms and molecules _ , o.u.p . h. xu , j .- hansen and d. chandler , europhys . * 26 * , 419 ( 1994 ) . d. m. ceperley and b. j. alder , phys . * 45 * , 566 ( 1980 ) ; d. m. ceperley , phys . b * 18 * , 3126 ( 1978 ) . z. lin and j. harris , j. phys . : condens . matter * 4 * , 1055 ( 1992 ) . w. b. hubbard and m. s. marley in _ strongly coupled plasma physics _ , nato asi series b * 154 * , eds . d. rogers and h. e. dewitt . s. galam and j .- p . hansen , phys . a * 14 * , 816 ( 1976 ) . j. p. perdew and a. zunger , phys . b * 23 * , 5048 ( 1981 ) . f. ercolessi and g. b. adams , europhys * 26 * , 583 ( 1994 ) . j. hafner , _ from hamiltonians to phase diagrams _ , springer series in solid - state sciences * 70 * ( springer , berlin , 1987 ) . p. blchl and m. parrinello , phys . b * 45 * , 9413 ( 1992 ) . t. a. arias , m. c. payne and j. d. joannopoulos , phys . lett . * 69 * , 1077 ( 1992 ) . grumbach , d. hohl , r. m. martin , and r. car , j. phys . : condens . matter * 6 * , 1999 ( 1994 ) . g. pastore , e. smargiassi and f. buda , phys . a * 44 * , 6334 ( 1991 ) . m. o. robbins , k. kremer and g. s. grest , j. chem . phys . * 88 * , 3286 ( 1988 ) . m. w. c. dharma - wardana and f. perrot , phys . a * 26 * , 2096 ( 1982 ) . c. pierleoni , private communication . a. alavi , private communication . j. p. hansen , i. r. mcdonald and e. l. pollock , phys . a * 11 * , 1025 ( 1975 ) . g. zrah , j. clrouin and e. l. pollock , phys . lett . * 69 * , 446 ( 1992 ) . f. postogna and m. p. tosi , nuovo cimento * 55 b * , 399 ( 1980 ) . j. l. barrat , j. p. hansen and h. totsuji , j. phys . c * 21 * , 4511 ( 1988 ) . b. mosser et al . , astron . astrophys . * 267 * , 604 ( 1993 ) .

a remarkably fast decrease of the melting temperature with decreasing density is found , up to a point when it becomes comparable to the fermi temperature of the protons . the simulations reveal the remarkable persistence of a weakly damped high - frequency ion acoustic mode , even under conditions of strong electron screening . the possibility of using this observation as a diagnostic for the plasma phase transition to the fluid molecular phase at lower densities is discussed .

the hydrogen plasma is studied in the very high density ( atomic and metallic ) regime by extensive ab initio molecular dynamics simulations . protons are treated classically , and electrons in the born- oppenheimer framework , within the local density approximation ( lda ) to density functional theory . densities and temperatures studied fall within the strong coupling regime of the protons . we address the question of the validity of linear screening , and we find it to yield a reasonably good description up to , but already too crude for ( with the ion sphere radius ) . these values are typical of jovian planets interiors . finite - size and brillouin zone sampling effects in metallic systems are studied and shown to be very delicate also in the fluid ( liquid metal ) phase . we analyse the low - temperature phase diagram and the melting transition . a remarkably fast decrease of the melting temperature with decreasing density is found , up to a point when it becomes comparable to the fermi temperature of the protons . the possible vicinity of a triple point bcc - hcp(fcc)-liquid is discussed in the region of and . the fluid phase is studied in detail for several temperatures . the structure of the fluid is found to be reminiscent of the underlying bcc ( solid ) phase . proton - electron correlations show a weak temperature dependence , and proton - proton correlations exhibit a well - defined first coordination shell , thus characterizing fluid h in this regime as an atomic liquid . diffusion coefficients are computed and compared to the values for the one - component plasma ( ocp ) . vibrational densities of states ( vdos ) show a plasmon renormalization due to electron screening , and the presence of a plasmon - coupled single - particle mode up to very high temperatures . collective modes are studied through dynamical structure factors . in close relationship with the vdos , the simulations reveal the remarkable persistence of a weakly damped high - frequency ion acoustic mode , even under conditions of strong electron screening . the possibility of using this observation as a diagnostic for the plasma phase transition to the fluid molecular phase at lower densities is discussed .

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we are living exciting times in cosmology . roughly 15 years after the discovery of the inconsistency of a @xmath15 universe with the magnitude - redshift observed relation for the type ia supernova @xcite , many cosmological probes have pointed towards the universe passing through a phase of accelerated expansion : the cosmic microwave background anisotropies ( e.g. @xcite ) , the baryonic acoustic oscillations @xcite , the clustering of galaxies ( e.g. @xcite ) and the growth of massive galaxy clusters ( e.g. @xcite ) , among others . one possible explanation for this acceleration can be postulated by introducing a new energy component in the form of a dark energy with negative pressure ( for a review , see @xcite ) . consequently , the dark energy task force ( detf , @xcite ) has been created , urging the cosmology community to invest its effort in understanding the origin and nature of the dark energy . with this goal in mind , a number of surveys have been planned for the upcoming years intending to constrain the values of the dark energy by a factor of @xmath1610 times better than at present ( the so - called stage iv surveys , @xcite ) . some of these surveys , cited in chronological order of predicted start off , are : the javalambre physics of the accelerating universe astrophysical survey ( j - pas @xcite ) , the dark energy spectroscopic instrument ( desi , @xcite ) survey , the large synoptic sky telescope ( lsst , @xcite ) survey , the euclid @xcite survey and the wide - field infrared survey telescope ( wfirst ) , among many others . for an excellent review of some of these surveys , we refer the reader to @xcite . these surveys will follow complementary observational strategies , allowing constraints covering different regions of the cosmological parameter space for testing competing cosmological models . @xcite recently explored the properties of the photometric redshift capabilities we may expect for the euclid and lsst surveys , showing their different behaviours . in this work , we explore the unique photometric capability of the impending j - pas multiple ( @xmath6 50 ) narrow - band survey now being commissioned . this survey samples the optical spectrum with 54 narrow - bands of @xmath17 , providing photometric redshift accuracies close to what we would expect for a low resolution spectroscopic survey , where emission and absorption features will be detected photometrically . this kind of data , in the frontier between spectroscopic and photometric surveys , has never been explored before and it will allow us to reliably map the large - scale structure in 3d down to fainter magnitudes and larger areas than previous spectroscopic samples . to realise the full scientific potential of these data , new algorithms and techniques are being developed and tested and cosmological constraints will be forecasted @xcite . in particular , we focus on the expected performance of j - pas for galaxy clusters and groups related to cosmology . clusters , by virtue of their extreme masses are of great importance for the purpose of setting cosmology constraints and the study of the large - scale structure ( e.g. @xcite or see for a review @xcite ) . modeling accurately the cluster selection function and the uncertainties in the observable- theoretical mass relation is of major importance for extracting cosmological information from j - pas . the amplitude of the cluster power - spectrum ( e.g @xcite and references herein ) is expected to be rapidly evolving over the redshift range accessible to j - pas ( z@xmath21.5 ) , hence becoming very sensitive to the growth rate of structure ( see review by @xcite ) . presently , only relatively weak constraints are derived from redshift space distortions ( e.g. sdss , wiggle - z , boss , etc ) and even less derived from massive clusters owing to the current difficulties of completing even modest sized surveys with sufficient redshift information . furthermore , current wide angle surveys sensitive to clusters through weak lensing ( wl ) , x - ray measurements or the sunyaev - zeldovich ( sz ) effect are still dealing with alleviating the tension between the different scaling of the sz , wl and x - ray observable mass and the theoretical cluster mass in order to make the connection to the cosmological predictions ( e.g. @xcite ) . numerous techniques have been developed to detect galaxy clusters using x - ray data , the sz effect , wl or optical / ir data ( see @xcite and references herein ) , being their selection function carefully modeled . for the optical and ir techniques , there is a large diversity of selection functions depending on the technique or the survey considered ( for a review see @xcite ) . for instance , only few surveys with large number of medium or narrow - bands ( i.e. good photometric redshift resolution ) had their cluster samples fully exploited ( cosmos , @xcite ; alhambra , @xcite ) . therefore , the selection function of clusters in narrow - band surveys such as j - pas are still in the process of being explored . in this paper we provide a comprehensive estimate of the cluster selection function for j - pas , accounting for the expected photometric limits and redshift accuracy of our multi - narrow - bands . it must be stressed that j - pas provides near optimal efficiency for separating cluster members from foreground and background galaxies because of its photometric redshift precision . this accuracy of the photometric redshifts is matched to the typical velocity dispersion of massive clusters , and therefore we can detect clusters above the noise to much lower masses and to higher redshifts than the wide - field surveys using conventional filters . this cluster selection function will be useful not only for providing cosmological forecasts from cluster counts but also for performing extended studies on galaxy evolution and large - scale structure in clusters the structure of the paper is as follows . in section 2 , we describe j - pas , the survey used in this paper , giving an overview of its main characteristics . 3 describes the simulation used in this work , the original mock catalogue and the posterior modification with ` photreal ` intended to mimic the photometry and photometric redshifts realistically . in section 4 , we describe the photometric redshift properties of the j - pas data and compare with other next - generation surveys such as the lsst and euclid . section 5 presents the results of detecting galaxy clusters in these mocks . it first provides an explanation of the bayesian cluster finder , the cluster detector used in this work . then , it shows the results regarding the cluster selection function expected from the j - pas - mock catalogue and it finally models the cluster observable - halo mass relation and its evolution with redshift . finally , we draw conclusions of the work in section 6 . the cosmology adopted throughout this paper is @xmath18 @xmath19 , @xmath20 , @xmath21 , @xmath22 , @xmath23 , corresponding to the cosmology assumed in the millennium simulation used in this work for consistency . all the magnitudes in this work are provided in the ab system @xcite .

the impending javalambre physics of the accelerating universe astrophysical survey ( j - pas ) will be the first wide - field survey of 8500 deg to reach the ` stage iv ' category . because of the redshift resolution afforded by 54 narrow - band filters , j - pas is particularly suitable for cluster detection in the range z . cosmology : large - scale structure of universe - cosmology : observations - surveys - cosmology : dark matter - cosmology : miscellaneous - galaxies : clusters : general

the impending javalambre physics of the accelerating universe astrophysical survey ( j - pas ) will be the first wide - field survey of 8500 deg to reach the ` stage iv ' category . because of the redshift resolution afforded by 54 narrow - band filters , j - pas is particularly suitable for cluster detection in the range z . the photometric redshift dispersion is estimated to be only with few outliers 4% for galaxies brighter than ab , because of the sensitivity of narrow band imaging to absorption and emission lines . here we evaluate the cluster selection function for j - pas using n - body+semi - analytical realistic mock catalogues . we optimally detect clusters from this simulation with the bayesian cluster finder , and we assess the completeness and purity of cluster detection against the mock data . the minimum halo mass threshold we find for detections of galaxy clusters and groups with both% completeness and purity is up to . we also model the optical observable ,-halo mass relation , finding a non - evolution with redshift and main scatter of down to a factor two lower in mass than other planned broad - band stage iv surveys , at least . for the planck mass limit , j - pas will arrive up to with a . therefore j - pas will provide the largest sample of clusters and groups up to with a mass calibration accuracy comparable to x - ray data . [ firstpage ] cosmology : large - scale structure of universe - cosmology : observations - surveys - cosmology : dark matter - cosmology : miscellaneous - galaxies : clusters : general

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in this work , we have first characterized the photometric redshift properties of the j - pas survey in terms of photometric redshift bias , photometric redshift dispersion and rate of catastrophic outliers using an n - body and semi - analytical simulations @xcite and a posterior modification with ` photreal ` ( @xcite , bentez et al . in prep ) . we have seen that the mean photometric redshift precision of j - pas is @xmath133 down to @xmath134 23.0 , is in agreement with what was expected from previous simulations @xcite . furthermore , the photometric redshift bias is fully consistent with zero down to the same magnitude limit and up to moderate redshift ( z@xmath24 0.7 ) without performing any preselection of the survey . the rate of outliers , @xmath45 , is always lower than 4% down to @xmath134 22.5 and at least within @xmath135 . in addition , we have compared the photometric redshift predictions for j - pas with similar predictions obtained for the lsst and euclid , using the same techniques to transform the same original mock catalogues @xcite . in this comparison , we conclude that the photometric redshift performance of j - pas will be outstanding in comparison with other next - generation surveys up to z@xmath240.7 at least . the photometric redshift dispersion becomes more than 20 times smaller than euclid+des or the lsst and more than 10 times smaller than euclid+des+lsst surveys together . complementarily , we have also explored the performance of the bayesian cluster finder ( bcf ) applied to our narrow - band next - generation j - pas survey . we have demonstrated with realistic simulations that we will be able to recover groups and masses down to @xmath136 up to redshifts 0.7 with completeness @xmath670% and purity higher than 80% and higher masses at @xmath137 . restricting completeness to be @xmath680% makes the minimum mass to be detected to be @xmath138 up to redshift 0.7 . we have compared these selection functions with other selection functions coming from different surveys in different wavelengths and we have concluded that j - pas will reach at least a factor of 2 lower mass threshold than other similar next - generation and present surveys such as the des and lsst , done with bigger telescopes ( 4 m and 8 m respectively ) . in addition , as the mass function will be sampled to lower mass limits , the absolute total number of detected clusters and groups will be comparable to those detected with the lsst . this is a very important result since the lsst will image more than twice the area of j - pas . additionally , since j - pas will cover a substantial part of the northern sky , whereas the des and lsst will focus on the southern hemisphere , the j - pas optical cluster sample will result in an exquisite sample to follow - up clusters detected with erosita , for instance . in addition , we have model the @xmath94 relation to a model in order to estimate the relevance of our cluster sample for cosmological purposes . we have considered a log - log normal model with a linear dependence with redshift . the results are compatible with a non - evolution of this relation with redshift . also , the main scatter obtained from the limited subsample of clusters down to @xmath139 and within @xmath140 is @xmath141 . these value is comparable to the results presented in other works limited to a local sample @xcite or very massive clusters @xcite . this results highlight then the enormous potential of j - pas for constraining cosmological parameters with galaxy clusters . finally , we have also looked into the precision with which we will be able to measure dark matter halo masses by using as observable the total stellar mass of the cluster . the results , based on simulations , suggest that we can recover galaxy clusters halo masses with an average scatter of @xmath142 down to @xmath143 . we note that this quantity becomes comparable to what other work found for samples of clusters five times more massive both in observations @xcite and in simulations @xcite when restricted to similar mass ranges . similarly , high accuracies were usually reached with other techniques such as wl @xcite , x - rays @xcite or cmb data @xcite . the impressive calibrations in measuring masses using large number of narrow - bands ( @xmath650 ) photometry provides a new technique that can reinforce the existing ones . a forthcoming paper ( ascaso et al . in prep ) will be devoted to investigate the impact of this selection function on the cosmological parameters , paying particular attention to the dark energy constraints .

here we evaluate the cluster selection function for j - pas using n - body+semi - analytical realistic mock catalogues . , j - pas will arrive up to with a . therefore j - pas will provide the largest sample of clusters and groups up to with a mass calibration accuracy comparable to x - ray data . [ firstpage ]

the impending javalambre physics of the accelerating universe astrophysical survey ( j - pas ) will be the first wide - field survey of 8500 deg to reach the ` stage iv ' category . because of the redshift resolution afforded by 54 narrow - band filters , j - pas is particularly suitable for cluster detection in the range z . the photometric redshift dispersion is estimated to be only with few outliers 4% for galaxies brighter than ab , because of the sensitivity of narrow band imaging to absorption and emission lines . here we evaluate the cluster selection function for j - pas using n - body+semi - analytical realistic mock catalogues . we optimally detect clusters from this simulation with the bayesian cluster finder , and we assess the completeness and purity of cluster detection against the mock data . the minimum halo mass threshold we find for detections of galaxy clusters and groups with both% completeness and purity is up to . we also model the optical observable ,-halo mass relation , finding a non - evolution with redshift and main scatter of down to a factor two lower in mass than other planned broad - band stage iv surveys , at least . for the planck mass limit , j - pas will arrive up to with a . therefore j - pas will provide the largest sample of clusters and groups up to with a mass calibration accuracy comparable to x - ray data . [ firstpage ] cosmology : large - scale structure of universe - cosmology : observations - surveys - cosmology : dark matter - cosmology : miscellaneous - galaxies : clusters : general

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the information contained by an individual finite object ( like a finite binary string ) is objectively measured by its kolmogorov complexity the length of the shortest binary program that computes the object . such a shortest program contains no redundancy : every bit is information ; but is it meaningful information ? if we flip a fair coin to obtain a finite binary string , then with overwhelming probability that string constitutes its own shortest program . however , also with overwhelming probability all the bits in the string are meaningless information , random noise . on the other hand , let an object @xmath0 be a sequence of observations of heavenly bodies . then @xmath0 can be described by the binary string @xmath1 , where @xmath2 is the description of the laws of gravity , and the observational parameter setting , while @xmath3 is the data - to - model code accounting for the ( presumably gaussian ) measurement error in the data . this way we can divide the information in @xmath0 into meaningful information @xmath2 and data - to - model information @xmath3 . the main task for statistical inference and learning theory is to distil the meaningful information present in the data . the question arises whether it is possible to separate meaningful information from accidental information , and if so , how . in statistical theory , every function of the data is called a `` statistic '' of the data . the central notion in probabilistic statistics is that of a `` sufficient '' statistic , introduced by the father of statistics r.a . fisher @xcite : `` the statistic chosen should summarise the whole of the relevant information supplied by the sample . this may be called the criterion of sufficiency @xmath4 in the case of the normal curve of distribution it is evident that the second moment is a sufficient statistic for estimating the standard deviation . '' for traditional problems , dealing with frequencies over small sample spaces , this approach is appropriate . but for current novel applications , average relations are often irrelevant , since the part of the support of the probability density function that will ever be observed has about zero measure . this is the case in , for example , complex video and sound analysis . there arises the problem that for individual cases the selection performance may be bad although the performance is good on average . there is also the problem of what probability means , whether it is subjective , objective , or exists at all . to simplify matters , and because all discrete data can be binary coded , we consider only data samples that are finite binary strings . the basic idea is to found statistical theory on finite combinatorial principles independent of probabilistic assumptions , as the relation between the individual data and its explanation ( model ) . we study extraction of meaningful information in an initially limited setting where this information be represented by a finite set ( a model ) of which the object ( the data sample ) is a typical member . using the theory of kolmogorov complexity , we can rigorously express and quantify typicality of individual objects . but typicality in itself is not necessarily a significant property : every object is typical in the singleton set containing only that object . more important is the following kolmogorov complexity analog of probabilistic minimal sufficient statistic which implies typicality : the two - part description of the smallest finite set , together with the index of the object in that set , is as concise as the shortest one - part description of the object . the finite set models the regularity present in the object ( since it is a typical element of the set ) . this approach has been generalized to computable probability mass functions . the combined theory has been developed in detail in @xcite and called `` algorithmic statistics . '' here we study the most general form of algorithmic statistic : recursive function models . in this setting the issue of meaningful information versus accidental information is put in its starkest form ; and in fact , has been around for a long time in various imprecise forms unconnected with the sufficient statistic approach : the issue has sparked the imagination and entered scientific popularization in @xcite as `` effective complexity '' ( here `` effective '' is apparently used in the sense of `` producing an effect '' rather than `` constructive '' as is customary in the theory of computation ) . it is time that it receives formal treatment . formally , we study the minimal length of a total recursive function that leads to an optimal length two - part code of the object being described . ( `` total '' means the function value is defined for all arguments in the domain , and `` partial '' means that the function is possibly not total . ) this minimal length has been called the `` sophistication '' of the object in @xcite in a different , but related , setting of compression and prediction properties of infinite sequences . that treatment is technically sufficiently vague so as to have no issue for the present work . we develop the notion based on prefix turing machines , rather than on a variety of monotonic turing machines as in the cited papers . below we describe related work in detail and summarize our results . subsequently , we formulate our problem in the formal setting of computable two - part codes . kolmogorov in 1974 @xcite proposed an approach to a non - probabilistic statistics based on kolmogorov complexity . an essential feature of this approach is to separate the data into meaningful information ( a model ) and meaningless information ( noise ) . cover @xcite attached the name `` sufficient statistic '' to a model of which the data is a `` typical '' member . in kolmogorov s initial setting the models are finite sets . as kolmogorov himself pointed out , this is no real restriction : the finite sets model class is equivalent , up to a logarithmic additive term , to the model class of computable probability density functions , as studied in @xcite . related aspects of `` randomness deficiency '' were formulated in @xcite and studied in @xcite . despite its evident epistemological prominence in the theory of hypothesis selection and prediction , only selected aspects of the theory were studied in these references . recent work @xcite can be considered as a comprehensive investigation into the sufficient statistic for finite set models and computable probability density function models . here we extend the approach to the most general form : the model class of total recursive functions . this idea was pioneered by @xcite who , unaware of a statistic connection , coined the cute word `` sophistication . '' the algorithmic ( minimal ) sufficient statistic was related to an applied form in @xcite : the well - known `` minimum description length '' principle @xcite in statistics and inductive reasoning . in another paper @xcite ( chronologically following the present paper ) we comprehensively treated all stochastic properties of the data in terms of kolmogorov s so - called structure functions . the sufficient statistic aspect , studied here , covers only part of these properties . the results on the structure functions , including ( non)computability properties , are valid , up to logarithmic additive terms , also for the model class of total recursive functions , as studied here . it will be helpful for the reader to be familiar with initial parts of @xcite . in @xcite , kolmogorov observed that randomness of an object in the sense of having high kolmogorov complexity is being random in just a `` negative '' sense . that being said , we define the notion of sophistication ( minimal sufficient statistic in the total recursive function model class ) . it is demonstrated to be meaningful ( existence and nontriviality ) . we then establish lower and upper bounds on the sophistication , and we show that there are objects the sophistication achieves the upper bound . in fact , these are objects in which all information is meaningful and there is ( almost ) no accidental information . that is , the simplest explanation of such an object is the object itself . in the simpler setting of finite set statistic the analogous objects were called `` absolutely non - stochastic '' by kolmogorov . if such objects have high kolmogorov complexity , then they can only be a random outcome of a `` complex '' random process , and kolmogorov questioned whether such random objects , being random in just this `` negative '' sense , can occur in nature . but there are also objects that are random in the sense of having high kolmogorov complexity , but simultaneously are are typical outcomes of `` simple '' random processes . these were therefore said to be random in a `` positive '' sense @xcite . an example are the strings of maximal kolmogorov complexity ; those are very unsophisticated ( with sophistication about 0 ) , and are typical outcomes of tosses with a fair coin a very simple random process . we subsequently establish the equivalence between sophistication and the algorithmic minimal sufficient statistics of the finite set class and the probability mass function class . finally , we investigate the algorithmic properties of sophistication : nonrecursiveness , upper semicomputability , and intercomputability relations of kolmogorov complexity , sophistication , halting sequence .

the information in an individual finite object ( like a binary string ) is commonly measured by its kolmogorov complexity . one can divide that information into two parts : the information accounting for the useful regularity present in the object and the information accounting for the remaining accidental information . there can be several ways ( model classes ) in which the regularity is expressed . the resulting theory , known as algorithmic statistics , analyzes the algorithmic sufficient statistic when the statistic is restricted to the given model class . however , the most general way to proceed is perhaps to express the useful information as a recursive function . the resulting measure has been called the `` sophistication '' of the object .

the information in an individual finite object ( like a binary string ) is commonly measured by its kolmogorov complexity . one can divide that information into two parts : the information accounting for the useful regularity present in the object and the information accounting for the remaining accidental information . there can be several ways ( model classes ) in which the regularity is expressed . kolmogorov has proposed the model class of finite sets , generalized later to computable probability mass functions . the resulting theory , known as algorithmic statistics , analyzes the algorithmic sufficient statistic when the statistic is restricted to the given model class . however , the most general way to proceed is perhaps to express the useful information as a recursive function . the resulting measure has been called the `` sophistication '' of the object . we develop the theory of recursive functions statistic , the maximum and minimum value , the existence of absolutely nonstochastic objects ( that have maximal sophistication all the information in them is meaningful and there is no residual randomness ) , determine its relation with the more restricted model classes of finite sets , and computable probability distributions , in particular with respect to the algorithmic ( kolmogorov ) minimal sufficient statistic , the relation to the halting problem and further algorithmic properties . _ index terms_ constrained best - fit model selection , computability , lossy compression , minimal sufficient statistic , non - probabilistic statistics , kolmogorov complexity , kolmogorov structure function , sufficient statistic , sophistication

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branching brownian motions ( bbm ) and branching random walks ( brw ) are among the simplest stochastic models of a growing population in space and time . they describe particles which perform brownian motions or random walks and branch independently at random times @xcite . if one starts with a single particle , the size of the region of space occupied by the particles grows linearly with time . since the mid seventies , one has a precise understanding of the fluctuations of the size of this region @xcite . for example in the one dimensional case one knows that the probability distribution of the position of the rightmost particle of a bbm can be obtained by solving an fkpp ( fisher - kolmogorov - petrovskii - piskounov ) equation @xcite : for a bbm starting at the origin , where particles diffuse according to @xmath2 ^ 2 \rangle = \sigma^2 t\ ] ] and branch at rate @xmath3 , one can show @xcite that , at time @xmath4 , the probability @xmath5 that the rightmost particle is on the right of @xmath6 is the solution of the fkpp equation @xmath7 with a step initial condition @xmath8 ( where @xmath9 is the heaviside function ) . in the long time limit , it is known @xcite that the probability @xmath10 that the position of the rightmost particle @xmath11 is concentrated around @xmath12 . one can also show @xcite from ( [ kpp ] ) that the large deviation function @xmath13 of the position @xmath14 of the rightmost particle for @xmath15 @xmath16\ ] ] is given by @xmath17 in ( [ ld - bbm ] ) and everywhere below the symbol @xmath18 means that @xmath19 over the last decade a number of generalizations of the branching brownian motion have been considered where , due to some selection or coalescence mechanism , the density of particles generated by the bbm saturates . these extensions of the bbm are expected to be described by noisy versions of the fkpp equation @xcite . in these noisy versions , the main effect of the noise is to shift the velocity of the front @xcite and to make its position fluctuate @xcite . a phenomenological approach has been proposed in @xcite which gives a prediction for the cumulants of this position . our goal here is to understand the large _ positive _ deviations of this position . the case of large _ negative _ deviations ( studied in @xcite for branching random walks with coalescence ) would require a rather different approach and will not be discussed in this paper except for some comments in the conclusion ; in particular the large deviation function may depend on the number of particles one starts with . in the present work we try to study how ( [ psi - bbm ] ) is modified by these selection or coalescence mechanisms . we discuss three models : 1 . * the @xmath0-bbm @xcite : * + in the @xmath0-bbm , one starts at time @xmath20 with a single particle at the origin . this particle branches and diffuses like a usual branching brownian motion . the only difference with the usual bbm is that whenever a particle gets at a distance larger than @xmath0 from the rightmost particle , it is eliminated . therefore at any given time @xmath4 the system consists of a random number @xmath21 of particles at positions @xmath22 which all satisfy @xmath23 where @xmath24 . + this number of particles @xmath25 fluctuates but one can show ( see the discussion in section [ existence ] ) that the evolution of the @xmath0-bbm leads to a steady state where the event @xmath26 is recurrent . + for large @xmath4 one can also show ( see section [ existence ] ) that the probability distribution of the position @xmath14 of the rightmost particle has a large deviation form @xmath27 \ . \label{ld - lbbm}\ ] ] one of our results ( see sections [ physical ] and [ proofs ] ) is the following upper bound for @xmath28 and large @xmath0 @xmath29 with @xmath30 where @xmath31 in ( [ res - lbbm ] ) and everywhere else in this paper , the symbol @xmath32 means that @xmath33 2 . * the @xmath1-bbm @xcite : * + in the @xmath1-bbm one starts as above with a single particle at @xmath20 which diffuses and branches but the size of the population can not exceed a fixed value @xmath1 . as long as the number of particles @xmath25 is less than @xmath1 the evolution is exactly the same as for the bbm . however , when @xmath34 , as soon as a new branching event occurs , the leftmost particle is eliminated so that the total number of particles remains subsequently equal to @xmath1 . + for the @xmath1-bbm we will obtain ( see sections [ physical ] and [ proofs ] below ) for the large deviation function @xmath35 \label{ld - nbbm}\ ] ] an upper bound @xmath36 where @xmath37 where @xmath38 is given by ( [ vc - eq ] ) . in fact , as discussed in the conclusion , we believe that @xmath39 remains valid even for @xmath40 . this would follow from a conjecture ( [ conjecture ] ) that we formulate in the conclusion but that we did not succeed to prove . the cbrw ( coalescing branching random walk ) * @xcite + an important motivation in the study of the cbrw is its dual relation with the noised fkpp equation , rigorously established in @xcite . + to explain how the cbrw is defined let us first consider a branching random walk brw on a one dimensional lattice with lattice spacing @xmath41 : a particle on site @xmath6 jumps to site @xmath42 at rate @xmath43 , to site @xmath44 at rate @xmath43 and branches at rate @xmath45 to give rise to two new particles on the same site . + the trajectory of each particle is a random walk and in the long time limit the probability that such a random walk reaches a position @xmath46 is of the form @xmath47 + where @xmath48 using the fact that @xmath49 with @xmath50 the large deviation function ( [ fv ] ) can be easily obtained from the parametric form as @xmath51 + as the particles branch at rate @xmath45 , the distribution of the position @xmath52 of the rightmost particle of this brw , ( in absence of coalescence ) , is of the form @xcite @xmath53\ ] ] with @xmath54 + now in the coalescing branching random walk ( cbrw ) , in addition to the diffusion and the branching , we let each pair of particles on the same site coalesce at rate @xmath55 . we will show in section [ existence ] @xmath56\ ] ] and in sections [ physical ] and [ proofs ] that for @xmath57 , @xmath58 where @xmath59 and , where for each @xmath60 , @xmath61 is solution of @xmath62 with @xmath38 and @xmath63 given by @xmath64 ( i.e. @xmath63 is the value of @xmath60 such that @xmath65 ) . + + the general expression ( [ res1-cbrw ] ) simplifies when @xmath66 . one then has @xmath67 and in the whole range @xmath68 @xmath69 instead of ( [ g ] ) . all the other steps remain the same with @xmath70 , @xmath71 and therefore @xmath72 + if one would consider more general branching random walks , characterized by the rate @xmath73 at which a particle jumps a distance @xmath61 from the site it occupies , @xmath74 would be given by @xmath75 and all the rest ( [ parametric]-[vc - v1 ] ) would remain unchanged with only ( [ g ] ) replaced by ( [ gnew ] ) . + + _ remark : _ a way of looking for a solution @xmath61 of ( [ v ] ) is to work with the legendre transform @xmath74 related to @xmath76 by ( [ parametric ] ) . if @xmath77 and @xmath78 are defined by @xmath79 and @xmath80 , one can check that ( [ v ] ) becomes @xmath81 under this form , one can show using the convexity of @xmath74 that @xmath82 has a single minimum at some value @xmath83 , that @xmath84 and that as @xmath85 as @xmath86 or @xmath87 ( we restrict our discussions here and below to @xmath88 as @xmath89 ) , there is always a solution @xmath78 and therefore a solution @xmath61 of ( [ v ] ) .

the large deviation function has been known for a long time in the literature for the displacement of the rightmost particle in a branching random walk ( brw ) , or in a branching brownian motion ( bbm ) . more recently a number of generalizations of the bbm and of the brw have been considered where selection or coalescence mechanisms tend to limit the exponential growth of the number of particles . here one noticeable feature of our results is their non analytic dependence on the parameters ( such as the coalescence rate in the cbrw ) . + + + +

the large deviation function has been known for a long time in the literature for the displacement of the rightmost particle in a branching random walk ( brw ) , or in a branching brownian motion ( bbm ) . more recently a number of generalizations of the bbm and of the brw have been considered where selection or coalescence mechanisms tend to limit the exponential growth of the number of particles . here we try to estimate the large deviation function of the position of the rightmost particle for several such generalizations : the-bbm , the-bbm , and the cbrw ( coalescing branching random walk ) which is closely related to the noisy fkpp equation . our approach allows us to obtain only upper bounds on these large deviation functions . one noticeable feature of our results is their non analytic dependence on the parameters ( such as the coalescence rate in the cbrw ) . + + + +

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in the present paper we have tried to estimate the large deviation function for the position of the rightmost particle of three generalizations of the branching brownian motion and of the branching random walks , subjected to selection or coalescence mechanisms . we have proved the existence of a large deviation function ( [ ld - lbbm],[ld - nbbm],[ld - cbrw ] ) for positive deviations of the position of the rightmost particle of these three models : the @xmath0-bbm , the @xmath1-bbm and the cbrw . for large @xmath0 for the @xmath0-bbm , large @xmath1 for the @xmath1-bbm , and for small @xmath55 for the cbrw , we obtain upper bounds for these large deviation functions ( [ res - lbbm],[res2-lbbm ] ) , ( [ res - nbbm],[res1-nbbm ] ) , ( [ res - cbrw],[res1-cbrw ] ) . our results are limited to velocities larger than the typical velocity @xmath38 of the rightmost particle of the bbm or of the brw . our approach does not allow us to give lower bounds for these large deviation functions . it has been shown by duality @xcite that the coalescence branching random walk is closely related to the noisy version of the f - kpp equation . of course it would be interesting to see whether a direct analysis of the noisy f - kpp equation could confirm our result ( [ ld - cbrw],[res - cbrw],[1.22 ] ) . as recalled in the introduction , the f - kpp equation gives the evolution the the probability distribution of the position of the rightmost particle of a bbm and the large deviation function of this position is ( [ ld - bbm],[psi - bbm ] ) . one question we tried ( without success ) to solve and that we would like to raise in this conclusion is how to obtain the probability @xmath484 of finding @xmath1 particles on the right of position @xmath485 for @xmath486 . we could only get the following lower bound @xmath487 \label{conjecture}\ ] ] by considering the events where a single particle moves first a distance @xmath61 during a time @xmath96 and then gives rise to a regular tree which produces @xmath1 particles on the right of @xmath6 , i.e. @xmath488 \right]\ ] ] where @xmath61 and @xmath96 are related by @xmath489 the question of negative large deviations of the position of the rightmost particle ( as considered in @xcite for the cbrw ) would also be interesting to attack . in this case the result might strongly depend on whether one starts with a single particle or more than one particle ( in @xcite it was assumed that the initial number of particles is large and even infinite ) . if one starts with a single particle , one would get already for the large deviation function ( [ ld - bbm ] ) of the bbm @xmath491 ( where @xmath135 ) and the events which would dominate the contributions to the large deviations of the @xmath0-bbm , @xmath1-bbm and the cbrw would be rather different from those considered in the present paper . chauvin , b. , rouault , a. ( 1988 ) . kpp equation and supercritical branching brownian motion in the subcritical speed area . application to spatial trees . probability theory and related fields , 80 , 299 - 314 . doering , c. r. , mueller , c. , smereka , p. ( 2003 ) . interacting particles , the stochastic fisher - kolmogorov - petrovsky - piscounov equation , and duality . physica a : statistical mechanics and its applications , 325 , 243 - 259 . rouault , a. ( 2000 ) . large deviations and branching processes . proceedings of the 9th international summer school on probability theory and mathematical statistics ( sozopol , 1997 ) . pliska studia mathematica bulgarica 13 , 15 - 38 .

we try to estimate the large deviation function of the position of the rightmost particle for several such generalizations : the-bbm , the-bbm , and the cbrw ( coalescing branching random walk ) which is closely related to the noisy fkpp equation . our approach allows us to obtain only upper bounds on these large deviation functions .

the large deviation function has been known for a long time in the literature for the displacement of the rightmost particle in a branching random walk ( brw ) , or in a branching brownian motion ( bbm ) . more recently a number of generalizations of the bbm and of the brw have been considered where selection or coalescence mechanisms tend to limit the exponential growth of the number of particles . here we try to estimate the large deviation function of the position of the rightmost particle for several such generalizations : the-bbm , the-bbm , and the cbrw ( coalescing branching random walk ) which is closely related to the noisy fkpp equation . our approach allows us to obtain only upper bounds on these large deviation functions . one noticeable feature of our results is their non analytic dependence on the parameters ( such as the coalescence rate in the cbrw ) . + + + +

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there are many motivations to introduce an extended higgs sector . examples are , including obsolete ones , fine - tuning in the weak - scale higgs mass @xcite suggesting supersymmetry @xcite , @xmath0-violation @xcite , grand unification @xcite , extended gauge symmetry @xcite , strong @xmath0 problem @xcite , string theory @xcite , vacuum stability @xcite , light fermion mass / weak - scale hierarchy @xcite , fermion flavour structure @xcite , neutrino mass @xcite , dark matter ( see e.g. @xcite ) , cosmic rays @xcite , baryogenesis @xcite , inflation @xcite , novel collider phenomenology @xcite , as well as anomalies seen in precision ( see e.g. @xcite ) and accelerator ( see e.g. @xcite ) experiments . in this article , we entertain the possibility that an intriguing outcome from the lep experiment is in fact pointing to an extended higgs sector , which may be directly inspected at the large hadron collider ( lhc ) . specifically , we take as our framework the two higgs doublet model ( 2hdm ) of type - i with @xmath7 in the vicinity of the @xmath2-boson mass . the two main points of this paper are the following . ( 1 ) the charged higgs produced in association with the lightest neutral higgs can be discovered as an excess in the @xmath8 process at the lhc . moreover , this could happen even at the early stage with @xmath9 in a substantial portion of the parameter space . ( 2 ) with the lightest neutral higgs mass assumed to be @xmath10 , the charged higgs one - loop effect can enhance @xmath11 enough to produce the excess observed at the recent lhc analyses @xcite . this enhancement is particularly welcome since the @xmath12 production at hadron colliders is generically suppressed due to higgs mixing . this light charged higgs scenario was previously advocated in @xcite , whose contents we recap here . the lep elecroweak working group has performed an analysis of @xmath2 decay branching ratios . in their report , @xmath13 appears to be higher than @xmath14 and @xmath15 , to the level of 2.8 standard deviations @xcite . should this difference be real , it would violate the charged current lepton universality , that is predicted by the gauge invariance of the standard model ( sm ) and has been confirmed in many indirect tests . as a resolution of this puzzle , one of the authors pointed out that a significant portion of the apparent lepton non - universality can be attributed to production of light charged higgs pairs which predominantly decay to the @xmath16 final states @xcite . one of the most natural ways to realise a @xmath1 that has mass @xmath17 and is thus light enough to be on - shell produced at lep , is to employ the type - i two higgs doublet model ( 2hdmi ) . in this model , all the @xmath1fermion couplings are suppressed like @xmath18 , the ratio of the two vacuum expectation values ( vevs ) . with the choice of a high enough @xmath5 , this enables @xmath1 to escape from the severe flavour changing neutral current ( fcnc ) constraints as well as any process that probes the @xmath1fermion interaction such as @xmath19 , @xmath20 , and @xmath21 . presuming the above lep anomaly to be real , the following points make this scenario more appealing . first , invoking a light charge higgs ( discussed also in @xcite ) is the only proposed solution that does not spoil the other precision lepton universality tests using lepton or meson decays @xcite . second , the requirement of a light charged higgs plus @xmath22 singles out type - i out of the four types of 2hdms @xcite in which tree - level fcnc is forbidden by a @xmath23 symmetry @xcite . note that these assumptions already fix many aspects of the model that otherwise offer more than one option , i.e.the yukawa coupling structure , the charged higgs mass , and the viable range of @xmath5 . these combine to predict a distinct set of collider physics signatures . in this paper , we shall consider @xmath0-violation in the higgs sector , which can in general occur in a class of 2hdms . in this way , we can explore higgs mixing patterns which received relatively less attention . a practical advantage is that one can analyse both the scalar and the pseudo - scalar higgses in a unified manner : switching between the two sectors reduces to tuning the higgs mixing angles , which determine the composition of each neutral mass eigenstate . within the context of the minimal supersymmetric standard model ( mssm ) , there are earlier studies of @xmath0-violating higgs phenomenology . in particular , the general @xmath0-violating potential and mass spectrum can be found in the paper of a. pilaftsis and c. wagner @xcite , where the importance of the scalar pseudo - scalar transitions in higgs phenomenology was emphasised . in the same article , the couplings of the charged higgs boson to @xmath0-violating higgs bosons were also discussed . this article is organised as follows . we begin by giving an overview of the model in the next section . section [ sec : strategy ] is a summary of our search strategy , which leads to the main phenomenological results presented in section [ sec : res ] . section [ sec : h1 ] is devoted to the diphoton signal of the lightest neutral higgs . we deliver our conclusion in section [ sec : conclusions ] . in addition , we present : the ghost lagrangian for our setup of 2hdm in appendix [ appe : b ] , the relation between our parametrisation and perturbativity in appendix [ appe : perturbativity ] , and differential cross - sections of our main process in appendix [ appe : diff ] .

the large hadron collider is shown to have great scope for a light charged higgs discovery , in the context of the-violating type - i two higgs doublet model . this scenario with similar masses of and was suggested by the puzzling departure from charged current lepton universality found in the lep data . with the lightest neutral higgs mass set to the effect of scalar pseudo - scalar mixing on loop - induced higgs signals is also discussed .

the large hadron collider is shown to have great scope for a light charged higgs discovery , in the context of the-violating type - i two higgs doublet model . this scenario with similar masses of and was suggested by the puzzling departure from charged current lepton universality found in the lep data . with the lightest neutral higgs mass set to , the charged - neutral higgs associated production mechanism can cause a significant excess in the events over a vast range of as long as the higgs mixing pattern avoids a few limiting cases . thanks to the low mass , the charged higgs loop can play a striking role in neutral higgs decays into , thereby compensating for a suppressed gluon - gluon fusion rate . the effect of scalar pseudo - scalar mixing on loop - induced higgs signals is also discussed .

1603.06248

i

the mammalian hippocampus plays a key role in spatial cognition . place cells , the principal hippocampal neurons , manifest remarkable spatial specificity of spiking activity . they fire only in select locations in the environment . these locations are known as their respective place fields @xcite . as a result , the place cells spike trains contain information about the animal s current location @xcite , its future @xcite and past @xcite navigation routes , both in the wakeful state and even in sleep @xcite . moreover , damages to the hippocampal network produce impairments in spatial learning and difficulties in navigation planning @xcite . it is hence believed that the place cell ensembles encode an internalized map " that serves as a basis of animal s spatial awareness @xcite . * motivation*. an increasing amount of both direct @xcite and indirect @xcite experimental evidence suggests that this map is topological in nature , a rough - and - ready connectivity framework into which other brain regions integrate more detailed metrical information . a number of approaches have been deployed to understand the neuronal computations that could produce such a framework @xcite . in particular , the approach proposed in @xcite exploits the connection between the place fields covering an environment and the alexandrov - ech theorem , which points out the possibility of reconstructing the topology of a space @xmath0 from the pattern of overlaps between regions that cover @xmath0 . the fact that the place fields produce a dense cover of the environment suggests that the pattern of overlaps between them contains the information required to represent the environment s topology , which may hold the key to the way in which the hippocampus encodes its topological map of s pace . this observation is taken further by noticing that the domains where several place fields overlap are precisely the ones where the corresponding place cells cofire . in other words , the information about the overlap of place fields is represented via the place cell coactivity , which suggests that the alexandrov - ech construction can be carried out not only via geometric pattern of the place field overlaps , but also through the analysis of the place cell coactivities . * topological model*. the details of the topological model of the hippocampal map are discussed in @xcite , but in brief , the idea is to represent the combinations of coactive place cells ( @xmath1 , @xmath2 , ... , @xmath3 ) as multi - dimensional polyhedra the coactivity simplexes , " @xmath4 $ ] ( see methods ) . together , these coactivity simplexes form a simplicial coactivity complex " @xmath5 . in his construction , the individual cell groups , just like simplexes , provide local information about the space ; joined together into a simplicial complex , modeling a neuronal ensemble , they represent space as whole . numerical simulations demonstrate that @xmath5 captures the topological structure of the environment and serves as a schematic representation of the hippocampal map @xcite . for example , the sequences of place cell combinations ignited along the paths traversed by the animal are represented in @xmath5 by chains of coactivity simplexes the simplicial paths @xcite . a non - contractible simplicial path may represent a navigational path @xmath6 that encircles a physical obstacle , whereas topologically trivial simplicial paths correspond to contractible routes in the physical space ( figure [ figure1]a , b ) . the complex @xmath5 begins to form as soon as the rat starts navigating . every detected instance of place cell coactivity contributes a simplex to @xmath5 . at the early stages of navigation , when only a few cells had time to produce spikes , the coactivity complex is small , fragmented , and contains many holes , most of which do not represent physical obstacles in the environment . such holes , which may be viewed as transient gaps " in the cognitive map , tend to disappear as spatial learning continues . the minimal time , @xmath7 , after which the topology of @xmath5 matches the topology of the environment , or more precisely , when the correct number of topological loops emerges , figure [ figure1]c , can therefore be viewed as a theoretical estimate of the time required to learn the hippocampal map @xcite . * parameter dependence*. an important property of the model is that the structure of the coactivity complex @xmath5 and the time course of its formation during learning are sensitive to various parameters of the neuronal firing statistics , which allows studying the net effect produced by these parameters on spatial learning . for example , the oscillations of the extracellular electrical field potential , typically referred to as the local field potential ( lfp ) , are known to modulate the place cells activity at several timescales . first , each place cell tends to spike within a small range of the phases of the theta " component of the lfp ( @xmath8 , 4 - 12 hz @xcite ) , which depends on the distance that the animal has traveled into the corresponding place field . as a rat moves through the place field , the preferred @xmath8-range of a place cell progressively decreases with each new @xmath8-cycle , a phenomenon known as the @xmath8-phase precession @xcite . the preferred @xmath8-phases of different cells are additionally synchronized by the second major component of the lfp , the gamma " rhythm ( @xmath6 , 30 - 80 hz , @xcite ) . in fact , the period of the more rapid @xmath6-rhythm , @xmath9 , is believed to define the range of the preferred phases within the slower @xmath8-rhythm ; on average a @xmath8-period , @xmath10 , contains about seven @xmath6-cycles , @xmath11 ( see @xcite and figure [ sfigure1]a ) . * paths in the environment are represented in a simplicial complex*. ( * a * ) two topologically equivalent paths in a physical environment , @xmath12 and @xmath13 , encircle an obstacle ( white square ) that can not traversed by the rat s trajectory ( grey curve in the background ) and are therefore non - contractible . the path @xmath14 does not encircle the obstacle and therefore is contractible and topologically inequivalent to @xmath12 and @xmath13 . ( * b * ) a schematic representation of the @xmath15 skeleton of the coactivity complex @xmath5 ( vertices shown as black dots , the @xmath16 links as white lines and @xmath15 facets as grey triangles ) and of the simplicial paths @xmath17 , @xmath18 and @xmath19 , which represent the physical paths @xmath12 , @xmath13 and @xmath14 . the topological equivalences and inequivalences between the simplicial paths ( @xmath20 and @xmath21 , @xmath22 ) provide qualitative information about the physical paths , encoded via place cell coactivity . since we are primarily concerned with representing topological properties of the navigational paths , in the following we discuss only the @xmath15 skeleton of the coactivity complex . ( * c * ) timelines of the topological loops encoded in the coactivity complex . as the animal begins to explore its environment , the coactivity complex contains many spurious topological loops most of which do not represent the physical obstacle . this topological noise " disappears after about five minutes , which marks the learning time , @xmath7the moment when the correct topology of space ( one @xmath16 loop representing the obstacle and one @xmath23 loop that informs us that the environment is connected ) has emerged . ] numerous experimental @xcite and theoretical @xcite studies demonstrate that both the @xmath8- and the @xmath6-waves play key roles in spatial , working , and episodic memory functions . however , most theoretical analyses addressed the way in which the @xmath6-synchronization affects the informational contents of spiking in small networks or in the individual cells . in contrast , the topological approach allows modeling cognitive map as a whole . for example , it was used in @xcite to demonstrate that @xmath8-precession makes otherwise poorly performing ensembles more capable of spatial learning . the present analysis applies the topological model to study the effect produced on spatial learning by the @xmath6-waves and to demonstrate that @xmath6-synchronization of the place cell spiking activity enables the encoding or retrieval of the large - scale spatial representations of the environment by integrating place cell coactivity at a synaptic timescale .

the mammalian hippocampus plays a principal role in producing a cognitive map of space an internalized representation of the animal s environment . the neuronal mechanisms we demonstrate that gamma - modulation of neuronal activity generates a synchronized spiking of dynamical cell assemblies , which enables learning a spatial map at faster timescales .

the mammalian hippocampus plays a principal role in producing a cognitive map of space an internalized representation of the animal s environment . the neuronal mechanisms producing this map depend primarily on the temporal structure of the hippocampal neurons spiking activity , which is modulated by the oscillatory extracellular electrical field potential . in this paper , we discuss the integrative effect of the gamma rhythm , one of the principal components of these oscillations , on the ability of the place cell ensembles to encode a spatial map . using methods of algebraic topology and statistical physics , we demonstrate that gamma - modulation of neuronal activity generates a synchronized spiking of dynamical cell assemblies , which enables learning a spatial map at faster timescales .

1203.4470

i

mass measurements of 40 nuclides were made , most of which improved the precision and accuracy over literature values . results are largely consistent with previous results from penning traps , reaction energetics , and storage ring measurements , but are frequently much lower in mass than results from @xmath3-endpoint measurements . comparison with mass models shows only sporadic agreement , and suggests unsuitability of these models for precise astrophysical @xmath2-process simulations . reliable mass measurements yet closer to and on the @xmath2-process path are still needed . the cpt has been moved to the new californium rare isotope breeder upgrade ( caribu ) facility @xcite now operating at the atlas accelerator , and has begun a successor campaign to these measurements . the extent of the cpt s previous measurements was limited by the purity and rate of the available beam , and caribu offers several improvements over the system used here to overcome these limitations . the @xmath25-@xmath307 times more intense fission source and larger gas catcher will allow access to nuclides 3 - 5 neutrons farther from stability . a new compact higher - resolution in - flight isobar separator @xcite promises purification with a resolving power of four times that of the previous system while avoiding the saturation of ion traps that would have occurred otherwise with such an intense beam . the in - flight separation will also defer the limitation in nuclide lifetime that would be imposed by in - trap purification . many of the newly available nuclides lie directly on potential @xmath2-process paths near @xmath308 . the cpt will conduct a survey of all accessible @xmath2-process nuclides in this vicinity , as well as any other neutron - rich species made available with the goal of finding isomers , regions of deformation , and shell quenching . over 200 additional masses are expected to be measured by the cpt .

the measurements , of fission fragments from acf spontaneous fission source in a helium gas catcher , approach the predicted path of the astrophysical process . where overlap exists , this data set is largely consistent with previous measurements from penning traps , storage rings , and reaction energetics , but large systematic deviations are apparent in-endpoint measurements .

the masses of 40 neutron - rich nuclides from z = 51 to 64 were measured at an average precision of using the canadian penning trap mass spectrometer at argonne national laboratory . the measurements , of fission fragments from acf spontaneous fission source in a helium gas catcher , approach the predicted path of the astrophysical process . where overlap exists , this data set is largely consistent with previous measurements from penning traps , storage rings , and reaction energetics , but large systematic deviations are apparent in-endpoint measurements . differences in mass excess from the 2003 atomic mass evaluation of up to kev are seen , as well as systematic disagreement with various mass models .

1509.01653

i

millimeter wave ( mmwave ) communications is a key candidate technology for future 5 g cellular networks . this is mainly due to the availability of large spectrum resources at higher frequencies , which leads to much higher data rates . recent research suggests that mmwave systems will typically feature ( i ) large - dimensional antenna arrays with directional beamforming at the transmitter / receiver which is motivated by the small wavelength that allows packing a large number of antenna elements into small form - factors ; and ( ii ) a dense deployment of base stations ( bss ) to ensure comparable coverage to ultra high frequency ( uhf ) networks@xcite . these mmwave design features are also attractive for rf ( radio frequency ) energy harvesting where a harvesting device may extract energy from the incident rf signals@xcite . this could potentially power the massive number of low - power wireless devices in future paradigms such as the internet of things@xcite . the signal propagation at mmwave frequencies , however , suffers from poor penetration and diffraction characteristics , making it sensitive to blockage by buildings@xcite . it is , therefore , unclear if mmwave cellular networks will be more favorable for rf energy harvesting compared to the conventional ( below 6 ghz ) frequencies . further , the network level design principles for mmwave energy harvesting systems are not well understood . this motivates a network view of energy harvesting in a mmwave cellular network . in this paper , we provide a tractable framework to characterize the performance of wireless energy and information transfer aided by a large - scale mmwave cellular network . our analysis accounts for the key distinguishing features of mmwave systems , namely the sensitivity to blockage and the use of potentially large antenna arrays at the transmitter / receiver . we first consider mmwave energy harvesting , where devices only extract energy from the incident mmwave signals . our analysis models two operating scenarios , one where devices have their beams aligned to that of a mmwave bs , and the other where no such beam alignment is assumed . for both operating modes , we derive simple analytical expressions for metrics such as the energy coverage probability and the average harvested power using tools from stochastic geometry . we then extend the analysis to characterize the overall ( energy - and - information ) coverage probability for the general case where a device extracts both energy and information from the mmwave signals . to get design insights , we examine the network level performance trends in terms of key parameters such as the mmwave network density and the antenna geometry parameters for both operating modes of the energy harvesting devices . numerical results suggest that narrower antenna beams are preferred when the users are aligned with a bs , whereas wider beams are favorable when no beam alignment is assumed . our findings also suggest that there typically exists an optimum transmit antenna beamwidth that maximizes the network - wide energy coverage for a given user population . this implies that the mmwave bss will need to adapt the antenna beam patterns depending on the fraction of the users operating in each mode . similar to the bs - related parameters , we also investigate the role of device - related parameters on system performance . for example , the overall ( energy - and - information ) coverage probability can be improved by optimizing over a design parameter ( power splitting ratio ) to optimally portion the received signal between the energy harvesting and the information decoding modules . another important design feature at the user is the receive antenna array . similar to the bss , the mmwave users can , in principle , benefit from using large antenna arrays . for low - power energy harvesting devices , however , the associated antenna circuity could increase the power consumption , offsetting the potential gains of large antenna arrays . to leverage multiple antennas at the receiver without resorting to power - hungry circuit components , we propose a simple switch - based receiver architecture for simultaneous energy and information transfer . simulation results reveal that the proposed low - power solution performs reasonably well compared to more advanced but power - hungry receiver architectures . wireless energy harvesting is becoming increasingly feasible due to the reduction in the power consumption requirements of wireless sensors and the improvements in energy harvesting technologies @xcite . this has also led to considerable research in advancing the theoretical understanding of wireless powered systems ( see @xcite for a comprehensive overview ) . for example , wireless energy and information transfer has been studied for different information - theoretic setups such as a broadcast channel@xcite , a fading channel@xcite , and an interference channel @xcite . many of these papers highlight the fundamental trade - off between energy and information transfer efficiency and characterize the achievable rate - energy regions for different practical receiver architectures@xcite . wireless energy and/or information transfer in large - scale networks has also been investigated@xcite . in @xcite , the performance of ambient rf energy harvesting was characterized using tools from stochastic geometry . using a repulsive point process to model rf transmitters , it was shown that more repulsion helps improve the performance at an energy harvester for a given transmitter density . in @xcite , cognitive radio networks were considered , and opportunistic wireless energy harvesting was proposed and analyzed . in @xcite , a hybrid cellular network architecture was proposed to enable wireless power transfer for mobiles . in particular , an uplink cellular network was overlaid with power beacons and trade - offs between transmit power and deployment densities were investigated under an outage constraint on the data links . a broadband wireless network with transmit beamforming was considered in @xcite , where optimal power control algorithms were devised for improving the throughput and power transfer efficiency . simultaneous information and energy transfer in a relay - aided network was considered in @xcite . under a random relay selection strategy , the network - level performance was characterized in terms of the relay density and the relay selection area . our work differs from the prior work in that we investigate wireless energy and information transfer in a large - scale _ mmwave _ cellular network . due to different physical characteristics and design features at mmwave , prior work on energy / information transfer in lower frequency networks does not directly apply to mmwave networks . in another line of work , the performance of mmwave cellular networks in terms of signal - to - interference - and - noise ratio ( sinr ) coverage and rate has also been analyzed using stochastic geometry@xcite . none of this work on mmwave networks , however , provides a performance characterization from the perspective of wireless energy and information transfer . the paper is organized as follows . in section [ secsys ] , we introduce the system model . section [ seceh ] presents the analytical results for mmwave energy harvesting . the case with simultaneous information and energy transfer is treated in section [ secswipt ] . we conclude the paper in section [ secconc ] .

the millimeter wave ( mmwave ) band , which is a prime candidate for 5 g cellular networks , seems attractive for wireless energy harvesting . this is because it will feature large antenna arrays as well as extremely dense base station ( bs ) deployments . optimizing the antenna geometry parameters such as beamwidth can maximize the network - wide energy coverage for a given user population . at the device level is proposed for simultaneous energy and information transfer .

the millimeter wave ( mmwave ) band , which is a prime candidate for 5 g cellular networks , seems attractive for wireless energy harvesting . this is because it will feature large antenna arrays as well as extremely dense base station ( bs ) deployments . the viability of mmwave for energy harvesting though is unclear , due to the differences in propagation characteristics such as extreme sensitivity to building blockages . this paper considers a scenario where low - power devices extract energy and/or information from the mmwave signals . using stochastic geometry , analytical expressions are derived for the energy coverage probability , the average harvested power , and the overall ( energy - and - information ) coverage probability at a typical wireless - powered device in terms of the bs density , the antenna geometry parameters , and the channel parameters . numerical results reveal several network and device level design insights . at the bss , optimizing the antenna geometry parameters such as beamwidth can maximize the network - wide energy coverage for a given user population . at the device level , the performance can be substantially improved by optimally splitting the received signal for energy and information extraction , and by deploying multi - antenna arrays . for the latter , an efficient low - power multi - antenna mmwave receiver architecture is proposed for simultaneous energy and information transfer . overall , simulation results suggest that mmwave energy harvesting generally outperforms lower frequency solutions .

1509.01653

c

in this paper , we analyzed the energy harvesting performance at low - power devices powered by a mmwave cellular network . using a stochastic geometry framework , we derived analytical expressions characterizing the performance of mmwave energy and information transfer in terms of system , channel and network parameters . simulations results were used to validate the accuracy of the derived expressions . leveraging the analytical framework , we also provided useful network and device level design insights . for the connected case when the transmitter and receiver beams are aligned , results show that the energy coverage improves with narrower beams . in contrast , wider beams provide better energy coverage when the receivers are not aligned with a particular transmitter . this trade - off is evident in the more general scenario having both types of receivers , where there typically exists an optimal beamforming beamwidth that maximizes the network - wide energy coverage . moreover , we found that several device - related parameters can significantly impact the system performance . for example , the performance can be substantially improved by optimizing over the power splitting ratio and by leveraging large antenna arrays . to allow using multiple antennas at the mmwave receivers while keeping the power consumption low , we proposed a low - power receiver architecture for mmwave energy and information transfer using antenna switches . simulation results show that the proposed architecture can provide good gains for the overall mmwave energy harvesting performance . simulation results also reveal that mmwave cellular networks could potentially provide better energy coverage than lower frequency solutions .

numerical results reveal several network and device level design insights . at the bss , , the performance can be substantially improved by optimally splitting the received signal for energy and information extraction , and by deploying multi - antenna arrays . for the latter , an efficient low - power multi - antenna mmwave receiver architecture overall , simulation results suggest that mmwave energy harvesting generally outperforms lower frequency solutions .

the millimeter wave ( mmwave ) band , which is a prime candidate for 5 g cellular networks , seems attractive for wireless energy harvesting . this is because it will feature large antenna arrays as well as extremely dense base station ( bs ) deployments . the viability of mmwave for energy harvesting though is unclear , due to the differences in propagation characteristics such as extreme sensitivity to building blockages . this paper considers a scenario where low - power devices extract energy and/or information from the mmwave signals . using stochastic geometry , analytical expressions are derived for the energy coverage probability , the average harvested power , and the overall ( energy - and - information ) coverage probability at a typical wireless - powered device in terms of the bs density , the antenna geometry parameters , and the channel parameters . numerical results reveal several network and device level design insights . at the bss , optimizing the antenna geometry parameters such as beamwidth can maximize the network - wide energy coverage for a given user population . at the device level , the performance can be substantially improved by optimally splitting the received signal for energy and information extraction , and by deploying multi - antenna arrays . for the latter , an efficient low - power multi - antenna mmwave receiver architecture is proposed for simultaneous energy and information transfer . overall , simulation results suggest that mmwave energy harvesting generally outperforms lower frequency solutions .

0904.2079

r

figure 1 shows our 1.3-mm continuum map of l1551 irs5 at an angular resolution of @xmath9 . the continuum emission peaks at the location of the protostellar system , as seen in images at comparable angular resolution at 3 mm @xcite and 0.8 mm @xcite . we fitted a two - dimensional gaussian to the continuum source to derive a total flux density of 1.20@xmath100.01 jy and a deconvolved size at full - width half - maximum ( fwhm ) of @xmath11 along a position angle of @xmath12 . the size of the continuum source is much larger than the separation of the two main protostellar components ( @xmath00.3@xmath13 ) , implying that at least a part of the emission arises from the surrounding envelope . @xcite found that , at 3 mm , about half of the continuum emission arises from the circumstellar dust disks of the two main protostellar components ( their observation did not have sufficient angular resolution to spatially separate the candidate third protostellar component ) , and about half from the surrounding dust envelope . the continuum source detected here has an orientation similar to but size much smaller than the pseudodisk traced in c@xmath2o by @xcite , suggesting that the extended part of the continuum emission traces the inner regions of the pseudodisk . both free - free emission from ionized jets and thermal emission from dust can contribute to the continuum emission . in l1551 irs5 , as in many protostellar systems , the ionized jets dominate the emission at cm wavelength , whereas dust contributes an increasingly larger fraction of the emission towards shorter wavelengths . to assess the relative contribution from each component at a given wavelength , we have collected all relevant measurements of the continuum emission for l1551 irs5 at centimeter to submillimeter wavelength as listed in table 2 . figure 2 shows the spectral energy distribution ( sed ) of the continuum emission based on the tabulated data . we modeled the sed as the sum of two power - law components with each component having @xmath14 , where @xmath15 is the intensity at a given frequency @xmath16 and @xmath17 the power - law index . a chi - squared fit to the data gives one component with @xmath18 that dominates at low frequencies ( short - dashed line in fig . 2 ) , consistent with optically - thin free - free emission . the other component has @xmath19 that dominates at high frequencies ( long - dashed line in fig . 2 ) , consistent with thermal emission from dust . as can be seen , the contribution from free - free emission to the continuum at 1.3 mm is only @xmath0@xmath20 . assuming that the dust temperature ( @xmath21 ) is uniform , we can estimate the total dust mass of the continuum source from the relationship @xmath22 where @xmath23 is the distance to the source , @xmath24 is the blackbody function , @xmath21 the dust temperature and @xmath25 the dust mass opacity coefficient given by @xmath26 @xcite . the quantity @xmath27 is related to the spectral index , @xmath17 , of the dust continuum emission by the relationship @xmath17 = 2 + @xmath27 . assuming @xmath21 = 47 k @xcite , the dust mass inferred from equation ( 1 ) is @xmath28 . this value is in reasonable agreement with those derived at 2.7 mm that are sensitive to the same size scales @xcite . figure 3 shows our co ( 21 ) channel maps of l1551 irs5 . for presentation purposes , none of the maps displayed in this manuscript have been corrected for the primary beam response of the sma ; the quantities we computed were , of course , derived from maps corrected for the primary beam response . emission is detectable over the velocity range 0.2@xmath29 measured with respect to the local standard of rest ( @xmath30 ) . we estimate based on the symmetry of the features observed ( see below ) a systemic velocity of @xmath06.5 km s@xmath6 for the l1551 irs5 protostellar system , comparable to previous estimates @xcite . the absence of emission within @xmath0@xmath31 of the systemic velocity is likely caused by extended emission ( mostly from the ambient molecular cloud ) that is resolved out by the interferometer . figure 4 shows the integrated co(21 ) intensity map at blueshifted velocities spanning 0.2@xmath32 ( blue contours ) and redshifted velocities spanning 7.4@xmath29 ( red contours ) separately . to make this map , we first applied hanning smoothing ( a triangular function of width five channels at zero intensity ) to the channel maps , and then excluded all features in the channel maps where the intensity in the corresponding smoothed maps is less than 1.5@xmath33 . the most prominent feature in this map is an x - shaped structure ( as indicated by the diagonal lines ) that has its blueshifted pair of arms lying west and its redshifted pair of arms lying east of the protostellar system . in the channel maps of figure 3 , the blueshifted part of this x - shaped structure can be most clearly seen at velocities spanning 2.3@xmath34 and the redshifted part 7.6@xmath29 . both pairs of arms have an opening angle of @xmath0@xmath35 , and extend @xmath02030 ( @xmath030004000 au ) from center . they have a symmetry axis along the ne sw direction at a position angle of about @xmath36 , which is close to the orientation of the major axes of the ionized jets as well as the large - scale bipolar molecular outflow . furthermore , the x - shaped structure exhibits the same velocity pattern ( i.e. , redshifted to the e and blueshifted to the w ) as the large - scale bipolar molecular outflow . in both the channel maps of figure 3 and integrated - intensity map of figure 4 , the blueshifted nw arm can be seen to be much broader than the other three arms of the x - shaped structure . a close examination of the channel maps reveals that the nw arm comprises several distinct and relatively compact ( bullet - like ) spatial - kinematic components . for example , the broadest portion of the nw arm at about 10@xmath13 from center ( see fig . 4 ) is dominated by a pair of comparatively high - velocity bullets that can be best seen in the channel maps ( fig . 3 ) at velocities of 2.1@xmath373.4@xmath37 . the tip of the nw arm is dominated by two lower - velocity bullets that can be best seen in the channel maps at 3.7@xmath374.7@xmath37 . on the other hand , the two redshifted arms each comprise only one spatial - kinematic component ( see below ) . in this way , the properties of the x - shaped component seem to mirror that of the large - scale bipolar molecular outflow . several distinct spatial - kinematic components have been seen in single - dish co(21 ) observations spaced at semi - regular intervals along the blueshifted outflow lobe of l1551 irs5 @xcite . curiously , no such distinct components are present in the same observations of the redshifted outflow lobe . figure 5 shows position - velocity ( pv- ) diagrams along each opposing set of arms as indicated by the diagonal lines in figure 4 . the straight lines drawn in figure 5 are not meant to guide the eye , but instead are our model fits to the pv - diagrams as we shall describe later in @xmath38 . the pv - diagrams along the ne ( fig . 5(a ) , upper right quadrant ) and se ( fig . 5(b ) , upper right quadrant ) arms look very similar , with each having a velocity at peak intensity that increases with radial distance ( i.e. , hubble - like expansion ) out to @xmath020 from center . the sw arm ( fig . 5(a ) , lower left quadrant ) is only weakly detected in the pv - diagram , but nevertheless can be seen to have a velocity gradient comparable to the ne and se arms . on the other hand , the pv - diagram along the nw arm ( fig . 5(b ) , lower left quadrant ) , shows at least two distinct velocity components . the component labeled nw - a increases comparatively quickly in velocity with radial distance out to @xmath010@xmath13 from center . the component labeled nw - b increases more slowly in velocity with radial distance out to @xmath030@xmath13 from center . nw - a corresponds to the pair of higher - velocity bullets , and nw - b to the pair of lower - velocity bullets , mentioned above . neither of these components have a velocity gradient that matches the comparable velocity gradients of the other three arms of the x - shaped component . the next most prominent feature in the integrated - intensity map of figure 4 is located between the blueshifted and redshifted arms of the x - shaped structure and extends to @xmath010@xmath13 from center . the outer portion of this feature on the ne side appears to twist north and that on the sw side twist south , creating a s - shaped structure . its symmetry axis is oriented at a position angle of about 55@xmath5 , approximately aligned with the symmetry axis of the x - shaped component as well as major axis of the large - scale bipolar molecular outflow . the s - shaped structure exhibits blueshifted velocities ne of center , and redshifted velocities sw of center . the velocity pattern of the s - shaped structure is therefore opposite to that of both the x - shaped structure and large - scale bipolar molecular outflow . in the channel maps of figure 3 , the blueshifted part of the s - shaped structure can be seen most clearly at velocities spanning 3.4@xmath32 and the redshifted part 7.4@xmath39 . the line - of - sight velocity of the s - shaped structure therefore does not reach velocities as high ( far from @xmath40 ) as the x - shaped structure . as described in @xmath41 , this structure exhibits an approximately sinusoidal variation in its radial velocity along its length . finally , a compact component centered on the location of l1551 irs5 can be seen in the channel maps of figure 3 extending to higher blueshifted and redshifted velocities than either the x- or s - shaped components . it is the only detectable or dominant component visible at blueshifted velocities spanning 0.2@xmath42 and redshifted velocities spanning 9.2@xmath29 . in the integrated - intensity map of figure 4 , although difficult to visually separate from the base of the x- or s - shaped structures , the compact central component comprises the closest redshifted and blueshifted intensity peaks straddling the l1551 irs5 protostellar system . to better extract the properties of the compact central component , we have fitted a two - dimensional gaussian structure to this component at each velocity where it is detectable in the channel maps . figure 6 shows the integrated co(21 ) intensity map made from the derived fits with the blueshifted and redshifted emission plotted separately . the centroids of the redshifted and blueshifted emissions are displaced by @xmath01.4 ( @xmath0200 au ) ne and sw from center , respectively , at a position angle of about 65 . the kinematic axis of this component is therefore closely aligned with the symmetry / major axis of , and has the same velocity pattern as , the x - shaped component and large - scale bipolar molecular outflows . to better study the structure of the x- and s - shaped components near their base , we have subtracted the compact central component from the channel maps using the above - mentioned fits to this component ( @xmath43 ) . figure 7 shows the integrated co(21 ) intensity maps made before ( upper row ) and after ( lower row ) the compact central component was subtracted , separated into two different velocity regimes . the higher velocity regime ( fig . 7 , left column ) spans 0.2@xmath42 ( i.e. , @xmath44 ) at blueshifted velocities ( blue contours ) and 8.9@xmath29 ( @xmath45 ) at redshifted velocities ( red contours ) . the lower velocity regime ( fig . 7 , right column ) spans 3.7@xmath32 ( @xmath46 ) at blueshifted velocities ( blue contours ) and 7.4@xmath47 ( @xmath48 ) at redshifted velocities ( red contours ) . like before , to make these maps we first applied hanning smoothing ( a triangular function of width five channels at zero intensity ) to the channel maps , and then excluded all features in the channel maps where the intensity in the corresponding smoothed maps is less than 1.5@xmath33 . the s - shaped component , which as mentioned above does not reach velocities as high as the x - shaped component , is barely detectable in the higher velocity regime . in this regime , the compact central component can be well separated from the x - shaped component as can be seen by comparing the map made before and after subtraction . in the lower velocity regime , all three components are detectable . the compact central component dominates the emission close to the protostellar system as can be seen by comparing the map made before and after subtraction . we have estimated physical parameters for all three components separately after correcting our maps for the primary beam response of the sma antennas . for simplicity , we assumed that the observed co(21 ) emission is optically thin , in local thermal equilibrium ( lte ) , and has an excitation temperature of 10 k as derived by @xcite based on the intensity ratio between co(32 ) and co(10 ) . we also assumed a h@xmath49-to - co abundance ratio of @xmath50 . we adopted an inclination of @xmath51 with respect to the plane of the sky for all three components , such that their major axes are orthogonal to the equatorial plane of the circumstellar disks of the two main protostellar components and their surrounding flattened condensation @xcite . as we shall discuss later ( 4.3 ) , the adopted inclination is probably appropriate for the x - shaped and compact central components , and close to median value in the allowed range from our model fit for the s - shaped component ( but with the ne side the near side , opposite to the x - shaped and compact central components ) . in table 3 , we tabulate for each component its estimated mass @xmath52 , outflow momentum @xmath53 , kinetic energy @xmath54 , mass loss rate @xmath55 , and dynamical age corresponding to the maximum derived dynamical time @xmath56 = @xmath57 , where @xmath58 is the distance from the driving source to the emission peak of the outflowing gas at a given velocity @xmath59 . note that all these values except for dynamical age are lower limits , in part because we have assumed that the co(2 - 1 ) emission is optically thin , and in part because emission close to the systemic velocity was entirely resolved out . the x - shaped component , which is the most obvious component in our map , dominates in mass , momentum , and energy . it also has the oldest dynamical age . the mass - loss rate is highest for the compact central component , which also has the youngest dynamical age .

the multiple protostellar system l1551 irs5 exhibits a large - scale bipolar molecular outflow that spans.5 pc on both the ne ( redshifted ) and sw ( blueshifted ) sides of the system . our co(21 ) image at ( au ) resolution reveals three distinct components : 1 ) an x - shaped structure spanning from center with a similar symmetry axis and velocity pattern as the large - scale outflow ; 2 ) an s - shaped structure spanning from center also with a similar symmetry axis but opposite velocity pattern to the large - scale outflow ; and 3 ) a compact central component spanning.4 from center again with a similar symmetry axis and velocity pattern as the large - scale outflow .

the multiple protostellar system l1551 irs5 exhibits a large - scale bipolar molecular outflow that spans.5 pc on both the ne ( redshifted ) and sw ( blueshifted ) sides of the system . we have studied this outflow within au of its driving source(s ) with the submillimeter array . our co(21 ) image at ( au ) resolution reveals three distinct components : 1 ) an x - shaped structure spanning from center with a similar symmetry axis and velocity pattern as the large - scale outflow ; 2 ) an s - shaped structure spanning from center also with a similar symmetry axis but opposite velocity pattern to the large - scale outflow ; and 3 ) a compact central component spanning.4 from center again with a similar symmetry axis and velocity pattern as the large - scale outflow . the x - shaped component likely comprises the limb - brightened walls of a cone - shaped cavity excavated by the outflows from the two main protostellar components . the compact central component likely comprises material within this cavity newly entrained by one or both outflows from the two main protostellar components . the s - shaped component mostly likely comprises a precessing outflow with its symmetry axis inclined in the opposite sense to the plane of the sky than the other two components , taking the s - shaped component out of the cone - shaped cavity along most if not all of its entire length . this outflow may be driven by a recently reported candidate third protostellar component in l1551 irs5 , whose circumstellar disk is misaligned relative to the two main protostellar components . gravitational interactions between this protostellar component and its likely more massive northern ( and perhaps also southern ) neighbor(s ) may be causing the circumstellar disk and hence outflow of this component to precess .

0904.2079

i

l1551 irs5 exhibits the first recognized bipolar molecular outflow from a protostellar system . single - dish maps show that this outflow can be traced in both co(10 ) and co(21 ) to 1.4 pc on the sky along the ne ( redshifted lobe ) and sw ( blueshifted lobe ) sides of the system along a position angle of @xmath0@xmath1 . this outflow is presumably driven by the two main protostellar components in l1551 irs5 , each of which exhibits an ionized jet that is closely aligned with the major axis of the larger scale molecular outflow . here , we imaged the molecular outflow within @xmath04000 au of l1551 irs in co(21 ) with the submillimeter array ( sma ) at an angular resolution of @xmath04 ( linear resolution of @xmath0560 au ) . our observations revealed three distinct spatial - kinematic components : * an x - shaped structure centered on l1551 irs with arms that can be traced to @xmath02030 ( @xmath02800 - 4200 au ) from the system . it has a symmetry axis along the ne ( redshifted side ) to sw ( blueshifted side ) direction at a position angle of @xmath0@xmath36 . this component is therefore closely aligned with , and exhibits the same velocity pattern as , the large - scale bipolar molecular outflow . * a previously unknown s - shaped structure centered on l1551 irs5 that can be traced to @xmath015 ( @xmath02100 au ) from the system . it has a symmetry axis along the ne ( blueshifted side ) to sw ( redshifted side ) direction at a position angle of @xmath0@xmath146 . although also closely aligned with the major axis of the large - scale bipolar molecular outflow , this component exhibits a velocity pattern in the opposite sense . there is no known counterpart to this outflow on large ( @xmath147 pc ) scales . this component has the smallest linewidth of all three components . * a previously unknown compact component centered on l1551 irs5 that can be traced to @xmath01.4 ( @xmath0200 au ) from the system . it has a major axis along the ne ( redshifted side ) to sw ( blueshifted side ) direction at a position angle of @xmath0@xmath118 . this component is therefore closely aligned with , and exhibits the same velocity pattern as , the large - scale bipolar molecular outflow . it has the largest linewidth of all three components . * the x - shaped component comprises the limb - brightened walls of a cone - shaped outflow cavity . the molecular gas originally in this cavity was likely entrained by the high - velocity collimated winds of the two main protostellar components , and subsequently excavated by the low - velocity wide - angle winds of the same components . the opening angle of this cavity is @xmath090@xmath5 , comparable to that seen in other class i protostellar systems . * the s - shaped component is unlikely to be the front and back walls of the same outflow cavity whose limb - brightened walls are seen as the x - shaped component . instead , the s - shaped component is most likely a precessing outflow whose symmetry axis is inclined in the opposite sense to the plane of the sky compared with the x - shaped and compact central components , as well as the large - scale bipolar molecular outflow . this precessing outflow may driven by the candidate third protostellar component in l1551 irs5 discovered by @xcite , who found that the circumstellar disk of this component is misaligned relative to the two main protostellar components . gravitational interactions between the third protostellar component and its likely more massive northern ( and perhaps also southern ) neighbor(s ) may be causing the circumstellar disk and hence jet of this component to precess . * the compact central component likely comprises material newly entrained by one or both jets from the two main protostellar components . the relatively short dynamical age for this component of @xmath0200 yrs may suggest a recent enhancement in the strength of one or both ionized jets responsible for driving this outflow . previous single - dish observations suggest multiple ejection episodes in the large - scale bipolar molecular outflow of l1551 irs5 @xcite . our study reveals multiple bipolar molecular outflow components near the base of this large - scale outflow . it adds additional evidence for a third protostellar component in l1551 irs5 that may be related to that discovered by @xcite . we thank chin - fei lee for his advice in constructing the model for the x - shaped cavity , and n. ohashi and m. saito for fruitful discussions . we thank the anonymous referee for suggesting we consider whether an outflow that winds due to orbital motion can explain the s - shaped component , and the editor ( e. fiegelsen ) for bringing to our attention the possibility that the x - ray source seen at the base of the optical jets could be related to the compact central concentration . j. lim and s. takakuwa acknowledge grants from the national science council of taiwan ( nsc 96 - 2112-m-001 - 020-my2 and nsc 97 - 2112-m-001 - 003-my2 respectively ) in support of this work . the grant to j. lim also provides a masters student stipend for p .- f . wu . arce , h. g. & sargent , a. i. 2006 , , 646 , 1070 duquennoy , a. , & mayor , m. 1991 , , 248 , 485 bachillar , r. , tafalla , m. , cernicharo , j. 1994 , , 425 , 93 bachillar , r. , prez gutirrez , m. , kumar , m. s. , tafalla , m. 2001 , , 372 , 899 bally , j. , feigelson , e. , reipurth , b. 2003 , , 584 , 843 barsony , m. , scoville , n. z. , & chandler , c. j. 1993 , , 409 , 275 bate , m. r. , bonnell , i. a. , clarke , c. j. , lubow , s. h. , ogilvie , g. i. , pringle , j. e. , tout , c. a. 2000 , , 317 733 beckwith , s. v. w. & sargent , a. i. 1991 , 381 , 250 bieging , j. h. , cohen , m. 1985 , , 292 , 249 bourke , t. l. , garay , g. , lehtinen , k. k. , koehnenkamp , i. , launhardt , r. , nyman , l. , may , j. , robinson , g. , hyland , a. r. 1997 , , 476 , 781 eislffel , j. , smith , m. d. , davis , c. j. , ray , t. p. 1996 , , 112 , 2086 fendt , c. & zinnecker , h. 1998 , , 334 , 750 fridlund , c. v. m. , sandqvist , a. , nordh , h. l. , olofsson , g. 1989 , , 213 , 310 fridlund , c. v. m. , liseau , r. 1998 , , 499 , 75 fridlund , c. v. m. , bergman , p. , white , g. j. , pilbratt , g. l. , tauber , j. a. 2002 , , 382 , 573 gueth , f. & guilloteau , s. 1999 , 343 , 571 ho , p. t. p. , moran , j. m. , lo , k. y. 2004 , , 616 , 1 hodapp , k. 1994 , , 94 , 615 jgensen , j. k. , bourke , t. l. , myers , p. c. , di francesco , j. , van dishoeck , e. f. , lee , c. , ohashi , n. , sch@xmath148ierm f. l. , takakuwa , s. , wilner , d. j. , zhang , q. 2007 , , 659 , 479 keene , j. , masson , c. r. 1990 , , 355 , 635 lim , j. & takakuwa , s. 2006 , , 653 , 425 looney , l. w. & mundy , l. g. , & welch , w. j. 1997 , , 484 , 157 masciadri , e. & raga , a. c. 2002 , , 568 , 733 mathieu , r. d. 1994 , ar , 32 , 465 momose , m. , ohashi , n. , kawabe . r. , nakano , t. , & hayashi , m. 1998 , 504 , 314 ohashi , n. , kawabe , r. , ishiguro , m. , hayashi , m. 1991 , , 102 , 2054 pyo , t. , hayashi , m. , kobayashi , n. , terada , h. , goto , m. , yamashita , t. 2002 , , 570 , 724 pyo , t. , hayashi , m. , kobayashi , n. , tokunage , a. t. , terada , h. , tsujimoto , m. , hayashi , s. s. , usuda , t. , yamashita , t. , takami , h. , takato , n. , kendachi , k. 2005 , , 618 , 817 rodrguez , l. f. , dalessio , p. , wilner , d. j. , ho , p. t. p. , torrelles , j. m. , curiel , s. , gmez , y. , lizano , s. , pedlar , a. , cant , j. , rage , a. c. 1998 , , 395 , 355 rodrguez , l. f. , curiel , s. , cant , j. , loinard , l. , raga , a. c. , & torrelles , j. m. 2003a , , 421 , 330 rodrguez , l. f. , porras , a. , claussen , m. j. , curiel , s. , wilner , d. j. , & ho , p. t. p. 2003b , , 586 , l137 saito , m. , kawabe , r. , kitamura , y. , sunada , k. 1996 , , 473 , 464 sault , r. j. , teuben , p. j. , wright , m. c. h. 1995 , aspc , 77 , 433 scoville , n. z. , carlstrom , j. e. , chandler , c. j. , phillips , j. a. , scott , s. l. , tilanus , r. p. j. , wang , z. 1993 , , 105 , 1482 snell , r. l. , loren , r. b. , plambeck , r. l. 1980 , , 239 , 844 stojimirovi , i. , narayanan , g. , snell , r. l. & bally , j. 2006 , apj , 649 , 280 strom , k. m. , strom , s. e. & vrba , f. j. 1976 , , 81 , 320 tafalla , m. , myers , p. c. , mardones , d. , bachiller , r. 2000 , , 359 , 967 takakuwa , s. , ohashi , n. , ho , p. t. p. , qi , c. , wilner , d. j. , zhang , q. , bourke , t. l. , hirano , n. , choi , m. , yang , j. 2004 , , 616 , 15 tohline , j. e. 2002 , ar , 40 , 349 , 3 , 6 , 9 , 15 , 25 , 35 and 45@xmath33 , where @xmath149 . the central @xmath30 of each channel is shown at the top left corner of each panel . crosses indicate the positions to the two main protostellar components as in figure 1 . the field of view of the sma at fwhm is shown by the large circle , and the synthesized beam by the filled ellipse at the bottom left corner . ] and the red contours 8.9@xmath150 . in the lower velocity regime ( right column ) , the blue contours span velocities 3.7@xmath32 and the red contours 7.4@xmath47 . in the left column , blue contours levels are plotted at @xmath151 , 1.0 , 2.0 , 3.0 , 5.1 , 8.5 , 11.9 and 15.3 @xmath152 and red contours levels are plotted at @xmath153 , 0.8 , 1.5 , 2.3 , 3.8 , 6.3 , 8.8 and 11.3 @xmath152 . in the right column , blue contours levels are plotted at @xmath153 , 0.8 , 1.6 , 2.4 , 3.9 , 6.5 , 9.1 and 11.7 @xmath152 and red contours levels are plotted at @xmath154 , 0.7 , 1.4 , 2.1 , 3.5 , 5.8 , 8.1 and 10.4 @xmath152 . ]

the compact central component likely comprises material within this cavity newly entrained by one or both outflows from the two main protostellar components . the s - shaped component mostly likely comprises a precessing outflow with its symmetry axis inclined in the opposite sense to the plane of the sky than the other two components , taking the s - shaped component out of the cone - shaped cavity along most if not all of its entire length . this outflow may be driven by a recently reported candidate third protostellar component in l1551 irs5 , whose circumstellar disk is misaligned relative to the two main protostellar components . gravitational interactions between this protostellar component and its likely more massive northern ( and perhaps also southern ) neighbor(s ) may be causing the circumstellar disk and hence outflow of this component to precess .

the multiple protostellar system l1551 irs5 exhibits a large - scale bipolar molecular outflow that spans.5 pc on both the ne ( redshifted ) and sw ( blueshifted ) sides of the system . we have studied this outflow within au of its driving source(s ) with the submillimeter array . our co(21 ) image at ( au ) resolution reveals three distinct components : 1 ) an x - shaped structure spanning from center with a similar symmetry axis and velocity pattern as the large - scale outflow ; 2 ) an s - shaped structure spanning from center also with a similar symmetry axis but opposite velocity pattern to the large - scale outflow ; and 3 ) a compact central component spanning.4 from center again with a similar symmetry axis and velocity pattern as the large - scale outflow . the x - shaped component likely comprises the limb - brightened walls of a cone - shaped cavity excavated by the outflows from the two main protostellar components . the compact central component likely comprises material within this cavity newly entrained by one or both outflows from the two main protostellar components . the s - shaped component mostly likely comprises a precessing outflow with its symmetry axis inclined in the opposite sense to the plane of the sky than the other two components , taking the s - shaped component out of the cone - shaped cavity along most if not all of its entire length . this outflow may be driven by a recently reported candidate third protostellar component in l1551 irs5 , whose circumstellar disk is misaligned relative to the two main protostellar components . gravitational interactions between this protostellar component and its likely more massive northern ( and perhaps also southern ) neighbor(s ) may be causing the circumstellar disk and hence outflow of this component to precess .

1212.1201

i

near - infrared ( nir ) observations ( 0.92.5@xmath0 ) are important in practically all areas of astronomy and astrophysics . for example , low - mass stars and brown dwarfs emit a substantial fraction of their light at these wavelengths and nir spectroscopy is the most efficient way to study these objects . nir spectroscopy is also one of the best ways to study the early universe because optical and ultraviolet emission lines from distant galaxies are redshifted to nir wavelengths due to hubble expansion . unfortunately , deep nir observations from the ground are extremely difficult to make due to the presence of a bright atmospheric background . the background in the range 0.91.8@xmath0 is predominantly from the de - excitation of atmospheric hydroxyl ( oh ) molecules at an altitude of @xmath1 90 km @xcite . the nir background is @xmath1 1000 times brighter than the optical background and can not be simply subtracted from astronomical observations @xcite because its brightness fluctuates on short timescales @xcite . solving the nir sky background problem is an important challenge in observational astronomy . previous attempts at a ground - based solution have not been able to suppress oh emission lines over a broad wavelength range while maintaining high throughput between the lines , which is critical for a wide range of science cases . for example , observations may be made in a very narrow wavelength range between oh emission lines using ultra - narrow band filters @xcite . however , this requires a specific unambiguously identifiable feature within the narrow wavelength range from the object . as a result , the number and nature of objects that may be observed by this technique is severely limited . more sophisticated approaches attempt to remove oh emission lines by dispersing the light with a diffraction grating at high resolution , selectively masking out the oh lines , and then recombining the light @xcite . unfortunately , the diffraction grating and the system optics ( which the light must pass through twice ) unavoidably scatters the bright oh light and the scattered portions can not be effectively removed . thus , oh emission lines are better dealt with before the light reaches any dispersing element . there have been attempts to use holographic filters for this purpose . @xcite demonstrated a device with 10 notches 10db deep and 0.1 nm wide with 85% throughput between the notches . using several of these holographic filters in series would be sufficient to suppress on the order of 100 oh doublets pre - dispersion , but the internotch throughput would be very low in this configuration . see @xcite for an in - depth comparison of these oh suppression techniques . oh suppression using aperiodic fiber bragg gratings @xcite overcomes many of the shortcomings of these previous approaches and is the best available solution to the nir sky background problem from the ground @xcite . fiber bragg gratings ( fbgs ) are common photonic devices widely used in telecommunications . basic fbgs are single - mode fibers ( smfs ) with a periodic refractive index modulation written into the fiber core by exposing it to ultraviolet light . the periodic refractive index modulation induces strong reflections at the bragg wavelength , @xmath2 , where @xmath3 is the spatial period of the refractive index modulation , and @xmath4 is the effective index of the core . reflectivities close to 100% and narrow bandwidths of 0.1 nm are possible with simple periodic fbgs @xcite . however , basic periodic fbgs have limited use for oh suppression . each periodic index modulation can be thought of as producing a single notch . a very large number of periodic index modulations would be required to suppress the dense forest of oh lines in the @xmath5 and @xmath6 bands . writing multiple periodic index modulations in succession in the same fiber results in high loss in the spectral regions between the notches because of the excessive exposure to ultraviolet light @xcite . aperiodic fbgs are designed with all notches treated simultaneously resulting in a single complex refractive index modulation that encodes @xmath150 irregularly spaced notches over a span of @xmath1100 nm with high internotch throughput . figure [ fig : afbgresponse ] shows the wavelength response of a single aperiodic fbg with 50 notches between 1.47 and 1.58@xmath0 . aperiodic fbgs are an attractive means of filtering atmospheric oh lines . however , when used in astronomy , where the wavefront exiting the telescope is distorted by atmospheric turbulence , coupling light into small core diameter smfs is challenging . as a result , large core diameter multi - mode fibers ( mmfs ) are more commonly used in astronomy . unfortunately , mmfs smear out the narrow notches of fbgs into broad , shallow notches because the bragg condition is different for each fiber mode . oh suppression requires a fiber with the light collecting ability of an mmf and the suppression characteristics of an smf fbg . the solution to this problem is a device called a photonic lantern @xcite . the device consists of a multi - mode ( mm ) port connected to an array of smfs by a taper transition . the photonic lantern converts the modes of the mm port into the supermodes of the smf array and vice versa . by splicing photonic lanterns to an array of fbgs , we have an `` oh suppression fiber '' that is easy to couple light into and exhibits the exact same transmission characteristics as an fbg in an smf . the gnosis grating unit is the first oh suppression unit to utilize these oh suppression fibers . it is independent of telescope and spectrograph but we commissioned the unit at the 3.9 m anglo - australian telescope ( aat ) at siding spring observatory with the existing iris2 infrared imaging spectrograph @xcite to demonstrate the potential of oh suppression fibers . in addition to the grating unit , gnosis consists of a fore - optics unit and an iris2 interface unit , which connects the grating unit to the telescope and spectrograph , respectively . the optical light path is shown in figure [ fig : opticalpath ] . light exiting the back of the aat is collected by a 7 element integral field unit ( ifu ) spanning 1.2@xmath7 mounted inside the fore - optics unit . the light is transported by a fiber bundle to the grating unit , where oh suppression occurs . the oh suppressed light is transported by another fiber bundle to the iris2 spectrograph for measurement . in this paper , we present the design and performance of each gnosis subsystem and as a whole . we begin by discussing the two components of our oh suppression fibers , the fbgs and the photonic lanterns in sections [ section : fbg ] and [ section : photoniclantern ] . the oh suppression fibers are housed in the gnosis grating unit , which is described in section [ section : gratingunit ] . in sections [ section : foreoptics ] and [ section : iris2interface ] we discuss the gnosis fore - optics unit and iris2 interface unit , which connects the grating unit to the telescope and iris2 , respectively . section [ section : onsky ] summarizes the on - sky performance of gnosis and section [ section : discussion ] contains a discussion on the future of oh suppression fibers . with the best - fitting butterworth profile ( red line ) . the notch is deep , narrow , and square , which is ideal for oh suppression.[fig : h1notch],scaledwidth=45.0% ]

however , deep near - infrared observations are extremely difficult to make from ground - based telescopes due to the bright background from the atmosphere . nearly all of this background comes from the bright and narrow emission lines of atmospheric hydroxyl ( oh ) molecules . the atmospheric background can not be easily removed from data because the brightness fluctuates unpredictably on short timescales . gnosis is a prototype astrophotonic instrument that utilizes gnosis was commissioned at the 3.9 m anglo - australian telescope with the iris2 spectrograph to demonstrate the potential of oh suppression fibers , but may be potentially used with any telescope and spectrograph combination . unlike previous atmospheric suppression techniques gnosis suppresses the lines before dispersion and in a manner that depends purely on wavelength . we present the instrument design and report the results of laboratory and on - sky tests from commissioning .

the near - infrared is an important part of the spectrum in astronomy , especially in cosmology because the light from objects in the early universe is redshifted to these wavelengths . however , deep near - infrared observations are extremely difficult to make from ground - based telescopes due to the bright background from the atmosphere . nearly all of this background comes from the bright and narrow emission lines of atmospheric hydroxyl ( oh ) molecules . the atmospheric background can not be easily removed from data because the brightness fluctuates unpredictably on short timescales . the sensitivity of ground - based optical astronomy far exceeds that of near - infrared astronomy because of this long - standing problem . gnosis is a prototype astrophotonic instrument that utilizes oh suppression fibers " consisting of fiber bragg gratings and photonic lanterns to suppress the 103 brightest atmospheric emission doublets between 1.47 and 1.7 . gnosis was commissioned at the 3.9 m anglo - australian telescope with the iris2 spectrograph to demonstrate the potential of oh suppression fibers , but may be potentially used with any telescope and spectrograph combination . unlike previous atmospheric suppression techniques gnosis suppresses the lines before dispersion and in a manner that depends purely on wavelength . we present the instrument design and report the results of laboratory and on - sky tests from commissioning . while these tests demonstrated high throughput ( 60% ) and excellent suppression of the skylines by the oh suppression fibers , surprisingly gnosis produced no significant reduction in the interline background and the sensitivity of gnosis+iris2 is about the same as iris2 . it is unclear whether the lack of reduction in the interline background is due to physical sources or systematic errors as the observations are detector noise dominated . oh suppression fibers could potentially impact ground - based astronomy at the level of adaptive optics or greater . however , until a clear reduction in the interline background and the corresponding increasing in sensitivity is demonstrated optimized oh suppression fibers paired with a fiber - fed spectrograph will at least provide a real benefit at low resolving powers .

1212.1201

c

in this paper , we have given a thorough description of each subsystem of gnosis , the first instrument to use fiber bragg grating oh suppression fibers . these fibers were designed to demonstrate a reduction of the interline background increasing sensitivity by a factor of 40 or more when suppressing the brightest oh doublets in the @xmath6-band . the line spread function of iris2 shows that the spectrograph s diffraction grating scatters light many pixels from the line center and simulations show that the cumulative contribution from multiple lines leads to a continuum of scattered light that dominates the interline background @xcite . if the emission lines are suppressed before the light has the opportunity to be scattered by the spectrograph , the continuum of scattered light and therefore the interline background will be reduced . with the oh lines corresponding to @xmath48 transitions from @xcite shown by the dashed blue lines . these @xmath48 lines were not suppressed by design based on their relative strengths in @xcite but they match up well with the residual features in the spectrum.[fig : abramsr],scaledwidth=45.0% ] to demonstrate this effect , we carried out observations of blank sky with gnosis at the 3.9 m aat with the iris2 spectrograph . although the oh suppression fibers successfully suppressed most of the brightest oh doublets in the range 1.51.7@xmath0 at the target level or greater and reduced the integrated background by a factor of @xmath110 , the spectra showed no significant reduction in the interline background and thus the same median signal to noise per pixel when compared to a control fiber without oh suppression . a reduction in the interline background and the associated increase in sensitivity would led to oh suppression fibers having an impact on astronomy at the level of adaptive optics or greater . therefore , it is critically important to identify why no reduction was observed in these experiments and determine if improvements can be made to realize the full benefit of oh suppression . only observations that are detector noise - dominated have been made with oh suppression fibers . if no interline background reduction is seen in oh - suppressed observations that are not detector noise - dominated it would indicate either oh suppression fibers do not suppress scattered light or the atmosphere is more complex than modeled by @xcite . specifically , the oh spectrum may be different than the model of @xcite used to design the fbgs , which would result in poor suppression . we have presented evidence of this above and poorly suppressed lines such as these would scatter more light into the interline regions . alternatively , there may be unaccounted for atmospheric continuum sources from other molecular species that creates a continuum floor . it may also be possible that the unsuppressed oh lines are not as weak as indicated by @xcite and they scatter more light into the interline regions . as evidence , we found that the @xmath48 transitions found in @xcite match up well with residual features in our oh - suppressed spectrum of the sky as seen in figure [ fig : abramsr ] . these doublets according to @xcite are stronger than indicated by @xcite and would contribute more scattered light to the interline region . the evidence that inaccuracies in the fbg design because of inaccuracies in the oh line model of @xcite , which may result in more scattered light in the interline region than expected , is certainly suggestive . however , this is based on the assumption that oh suppression fibers suppress scattered light , which has yet to be demonstrated . thus , it is critically important that the next step be a clear demonstration of scattered light suppression with observations that are not detector noise - dominated . such observations require that the interline signal is greater and/or the detector noise is lower . in general , this may be accomplished by increasing the brightness of the source , increasing the throughput of the system and/or utilizing a low - noise detector . the system throughput may be increased mostly significantly by optimizing the oh suppression fibers and/or the spectrograph . presently , without first demonstrating that oh suppression fibers suppress scattered light , fabricating optimized fibers would be difficult to justify . thus , @xcite suggested that pairing gnosis with a fiber - fed spectrograph with a high efficiency volume phase holographic ( vph ) grating is the best way to go about improving system throughput . if a high - performance detector , a 1.7@xmath0 cutoff hawaii-2rg for example , were included the spectrograph would simultaneously increase throughput and lower detector noise , which would be ideal for oh - suppressed observations of blank sky . the australian astronomical observatory has plans to build such a spectrograph called praxis for further testing of oh suppression fibers on - sky by early 2014 @xcite . however , for the purpose of demonstrating scattered light suppression , observations of blank sky are not ideal because the sky spectrum may be considerably more complex than the spectrum the fbgs are designed to suppress . thus , the ideal source would be an oh line source in the laboratory , such as that created by @xcite . this would remove any complications from additional atmospheric sources , but the weaker suppressed oh lines are still present . alternatively , scattered light suppression may also be demonstrated with a single emission line from a bright arc lamp ( xenon has at least one line at 1.6733@xmath0 that coincides with one of the fbg notches ) . these observations only require gnosis and the iris2 spectrograph without any telescope , which is advantageous because they do not require building a new spectrograph . regardless of whether or not oh suppression fibers can be used to reduce the interline background and increase sensitivity , they provide real benefits for observations at low resolving powers ( 500@xmath493000 ) , which was shown by @xcite using observations of [ ] emission lines in seyfert galaxies and ch@xmath50 absorption in brown dwarfs . previously , observations at these resolving powers have been too low to resolve out the oh lines , but that is no longer necessary with oh suppression fibers . the performance of the oh suppression fibers is very good , but there is room for improvement especially the throughput . the biggest single loss in the oh suppression fibers comes from mm to sm conversion of the input photonic lantern . the beam feeding the delivery fiber of the input photonic lanterns is @xmath1@xmath32/5 and we argued in section [ section : photoniclantern ] that the oh suppression fibers must be fed at @xmath35 @xmath32/7 to avoid overfilling the mm port ( @xmath32/5.8 ) of the 1@xmath2419 photonic lanterns . thus , the mm to sm conversion throughput will increase if we slow the beam feeding the oh suppression fiber from @xmath32/5 to @xmath32/7 . for a back - to - back system with 1@xmath2419 photonic lanterns , the total throughput increases by @xmath10.5db ( 11% ) when slowing the input beam from @xmath32/5 to @xmath32/7 @xcite . however , doing so will decrease the fiber s fov . by conservation of tendue , the product of the fiber fov on - sky and the telescope diameter is proportional to the product of the fiber input na and the fiber core diameter . therefore , it is not possible to underfill the photonic lantern mm port by reducing the core diameter or input na without sacrificing the fiber s fov . as an alternative to slowing the input beam from @xmath32/5 to @xmath32/7 to avoid overfilling the mm port , we may increase the mm port na to match the input @xmath32/5 beam . if we keep the core diameter fixed , this corresponds to increasing @xmath25 , the number of smfs in the photonic lantern . based on equation ( [ equation : lanternna ] ) an mm port na of 0.12 ( the @xmath32/5 beam arrives at the mm port at @xmath32/4.2 due to frd ) with @xmath30 corresponds to @xmath51 . thus , a back - to - back system with 1@xmath2437 photonic lanterns fed at f/5 would be equivalent to a system with 1@xmath2419 photonic lanterns fed at @xmath32/7 and should yield a similar increase in throughput over the current configuration . the wavelength - dependent loss of a symmetric photonic lantern system may be addressed by designing the mm port of the input and output photonic lanterns to have different nas . if @xmath25 is the number of smfs then the mm port of the input photonic lantern should be designed to support @xmath52 modes at the blue end of the suppression range . as @xmath53 there will be @xmath54 modes at the red end of the suppression range and no penalty will be incurred in the mm to sm conversion at any wavelength . the mm port of the output photonic lantern should be designed to support @xmath55 modes at the red end of the suppression range , which would correspond to @xmath56 modes at the blue end of the suppression range . thus , in the sm to mm conversion , none of the modes will be lost at any wavelength . photonic lanterns with large @xmath25 are very cumbersome to handle and the gnosis grating unit is rather bulky and heavy ( 100 kg ) . a significant reduction in size and weight may be possible with oh suppression fibers consisting of fbgs printed in multi - core fibers ( mcfs ) with each end tapered down into an mmf . @xcite demonstrated such a device with an mcf containing @xmath1120 cores within a 230@xmath0 cladding and a single notch . mcfs with 37 cores can be manufactured and it should be a simple matter to taper down each end of the mcf into a 50@xmath0 mmf following a similar process for the manufacturing of the photonic lanterns . in addition to the reduction in size and weight no splices would be required boosting the throughput by @xmath10.35db ( 8% ) . assuming complex refractive index modulations can be imprinted into each mcf core with the same level of performance as the current gnosis fbgs and incorporating all the suggestions above would result in a throughput of at least @xmath10.73 . these next - generation oh suppression fibers are currently under development @xcite . thus far we have discussed improvements to the oh suppression fibers themselves but the other subsystems also require optimization . retrofitting gnosis to the existing iris2 spectrograph was acceptable for an initial demonstration of oh suppression fibers , but a fiber - fed spectrograph like praxis would be ideal for future science observations . in the current configuration , the instrument thermal background is high ( see figure [ fig : cold ] ) and emanates almost entirely from the slit block of the iris2 interface unit reducing the sensitivity of observations . a spectrograph with a vacuum feed - through would make the iris2 interface unit unnecessary and significantly reduce the thermal background . also , it would reduce the number of optical surfaces and there would be no slit block alignment errors , which would increase the system throughput by @xmath115% in addition to the increase in throughput due to the high efficiency vph grating and the increase in sensitivity due to the high performance detector . oh suppression fibers have the potential to significantly expand our window to the universe from the ground if their suppression of scattered light can be confirmed and the atmosphere does not contain bright continuum sources that are un - filterable . nevertheless , these fibers provide real benefits for spectroscopic observations at low resolving powers and optimized systems utilizing these types of fibers are very feasible . the gnosis team acknowledges funding by arc lief grant le100100164 . we thank the referee for providing insightful comments and suggestions which have greatly improved this paper . c.q.t . gratefully acknowledges support by the national science foundation graduate research fellowship under grant no . thanks stuart gilchrist , stuart jackson , rene pelton , billy robbins , andrew sheinis , and tim white .

the near - infrared is an important part of the spectrum in astronomy , especially in cosmology because the light from objects in the early universe is redshifted to these wavelengths . oh suppression fibers " consisting of fiber bragg gratings and photonic lanterns to suppress the 103 brightest atmospheric emission doublets between 1.47 and 1.7 . while these tests demonstrated high throughput ( 60% ) and excellent suppression of the skylines by the oh suppression fibers , surprisingly gnosis produced no significant reduction in the interline background and the sensitivity of gnosis+iris2 is about the same as iris2 . it is unclear whether the lack of reduction in the interline background is due to physical sources or systematic errors as the observations are detector noise dominated . oh suppression fibers could potentially impact ground - based astronomy at the level of adaptive optics or greater . however , until a clear reduction in the interline background and the corresponding increasing in sensitivity is demonstrated optimized oh suppression fibers paired with a fiber - fed spectrograph will at least provide a real benefit at low resolving powers .

the near - infrared is an important part of the spectrum in astronomy , especially in cosmology because the light from objects in the early universe is redshifted to these wavelengths . however , deep near - infrared observations are extremely difficult to make from ground - based telescopes due to the bright background from the atmosphere . nearly all of this background comes from the bright and narrow emission lines of atmospheric hydroxyl ( oh ) molecules . the atmospheric background can not be easily removed from data because the brightness fluctuates unpredictably on short timescales . the sensitivity of ground - based optical astronomy far exceeds that of near - infrared astronomy because of this long - standing problem . gnosis is a prototype astrophotonic instrument that utilizes oh suppression fibers " consisting of fiber bragg gratings and photonic lanterns to suppress the 103 brightest atmospheric emission doublets between 1.47 and 1.7 . gnosis was commissioned at the 3.9 m anglo - australian telescope with the iris2 spectrograph to demonstrate the potential of oh suppression fibers , but may be potentially used with any telescope and spectrograph combination . unlike previous atmospheric suppression techniques gnosis suppresses the lines before dispersion and in a manner that depends purely on wavelength . we present the instrument design and report the results of laboratory and on - sky tests from commissioning . while these tests demonstrated high throughput ( 60% ) and excellent suppression of the skylines by the oh suppression fibers , surprisingly gnosis produced no significant reduction in the interline background and the sensitivity of gnosis+iris2 is about the same as iris2 . it is unclear whether the lack of reduction in the interline background is due to physical sources or systematic errors as the observations are detector noise dominated . oh suppression fibers could potentially impact ground - based astronomy at the level of adaptive optics or greater . however , until a clear reduction in the interline background and the corresponding increasing in sensitivity is demonstrated optimized oh suppression fibers paired with a fiber - fed spectrograph will at least provide a real benefit at low resolving powers .

1306.4142

i

the fractional occupation numbers @xmath0 of the correlated one - body reduced density matrix ( 1rdm ) have intrigued many scientists in the past decades . they are defined by the eigenvalue equation @xmath1 where the 1rdm itself is defined in terms of the usual creation and annihilation field operators as @xmath2 for a state @xmath3 where @xmath4 is space - spin coordinate . the one - particle orbitals @xmath5 in eq . are denoted as the natural orbitals ( no ) whereas the eigenvalues @xmath0 are called the no occupation numbers . as an integral kernel the 1rdm is a bounded linear hermitian operator with an infinite but countable eigenvalue spectrum and the set of all nos form a basis in the set of quadratically integrable functions . if the state @xmath3 is fermionic it is not difficult to prove that @xmath6 @xcite . in the following we will restrict ourselves to electronic systems such that this property holds . the fact that the occupation numbers can also have non - integer values between zero and one is one of the most distinct features of interacting systems compared to non - interacting systems which can only have integer occupation numbers typically . therefore the occupation numbers reflect strongly the electronic correlations present in the system under consideration . a system is considered weakly correlating when the occupation numbers differ only slightly from zero or one , in which case the full many - electron wavefunction can well be approximated by a single slater determinant ( non - interacting wavefunction ) . if a system is strongly correlated , the occupation numbers deviate strongly from integer values and multiple determinants are required to obtain a sufficiently accurate approximation to the many - body wavefunction which captures the physics of the system . the ability of the 1rdm occupation numbers to signal strong correlation has encouraged people to develop 1rdm functional theory as an alternative to traditional density function theory ( dft ) to handle strongly correlated systems such as dissociating molecules @xcite , mott insulators @xcite and quantum hall systems @xcite , for which the current approximate density functionals fail miserably . the sum of the occupation numbers equals the number of electrons in the system . therefore , if we order the occupation numbers , @xmath7 , from the highest to the lowest one , their values need to decay to zero sufficiently fast for @xmath8 , i.e. @xmath9 or even become zero after some point @xmath10 . the question whether they actually do become zero or only approach zero for @xmath8 is not only an academic question , but is also of practical interest for methods that try to build an accurate approximation to the wavefunction by making an expansion in terms of slater determinants , e.g. configuration interactions ( ci ) . this question has recently been addressed for the dissociating hydrogen molecule @xcite . one would expect that an optimal set of orbitals exists which leads to the fastest convergence of the expansion of the wavefunction in terms of slater determinants @xcite . one can prove that if all determinants are taken into account ( full ci ) , that the highest occupied nos are the orbitals which give the fastest convergence towards the exact one in the @xmath11-norm @xcite . the nos become even more interesting if the occupation numbers become all zero for @xmath12 sufficiently large , since this would imply that only a finite set of nos would already be sufficient to expand the full many - electron wavefunction . the question if zero occupation numbers exist in coulomb systems is maybe even more important for 1rdm functional theory . basic theorems in 1rdm functional theory @xcite follow similar arguments as the famous hohenberg kohn theorem @xcite of density functional which establishes a one - to - one correspondence between densities , potentials and non - degenerate ground states . the main difference between 1rdm functional theory and density functional theory is that the natural conjugate variable to the 1rdm is a non - local external potential of the form @xmath13 rather than the local potential of density - functional theory . it therefore immediately follows that the energy contribution of the nonlocal external field to the total energy is given by @xmath14 with this expression the hohenberg kohn proof can be followed exactly as in density - functional theory and gilbert @xcite in fact did this to establish that there is a one - to - one correspondence between non - degenerate ground states @xmath3 and their corresponding 1rdm @xmath15 . this is already sufficient to establish 1rdm functional theory , since the ground state energy can be written as a functional of the 1rdm @xmath16 $ ] . in density - functional theory one can further prove that two different ( up to a gauge ) potentials can not have the same non - degenerate ground state . the analogous proof fails in 1rdm theory since there can exist nonlocal potentials @xmath17 with the property that @xmath18 for a given ground state @xmath3 of some hamiltonian @xmath19 . such a potential can therefore always be added to this hamiltonian without affecting the ground state ( it could be that @xmath3 is now an excited state but by multiplying @xmath17 by a small enough number we can ensure that @xmath3 is still the ground state ) . let us now see how eq . can come about . let us first define the annihilation operator @xmath20 which annihilates the no @xmath21 from any many - body quantum state . suppose now that @xmath22 for some of the labels @xmath23 , which means that the orbital @xmath21 does not appear in any slater determinant of a ci expansion of @xmath3 . this implies that @xmath24 such that the corresponding no occupation number vanishes . we can then construct the following one - body potential @xmath25 where @xmath26 is an arbitrary hermitian matrix and where we sum only over the labels for which @xmath27 for the state @xmath3 . it is clear that this potential exactly has the property @xmath28 . in real space this corresponds to a nonlocal spatial potential of the form of eq . where @xmath29 we therefore see that eq . can be satisfied whenever the state @xmath3 has vanishing no occupations . the non - vanishing of the no occupation numbers for electronic ground states is therefore a necessary condition for the existence of a one - to - one mapping between nonlocal potentials and 1rdms . to the best of our knowledge the answer to the question whether the necessary condition is also a sufficient one is unknown . the one - to - one mapping between non - local potentials and 1rdms would be relevant for the foundations of linear response 1rdm functional theory and also its time - dependent extension would greatly benefit from the resulting simplifications . other consequences of vanishing occupation numbers arise in the extended koopmans theorem @xcite . the extended koopmans theorem is an extension to arbitrary wavefunctions of the well known theorem by koopmans that the occupied hartree fock orbital energies provide approximations to the ionization energies @xcite . if the exact wavefunction is used in the extended koopmans procedure , even the exact ionization energies should result , provided the set of partially occupied nos is complete , i.e. none of the occupation numbers vanishes . a less restrictive condition has been derived by pernal and cioslowski @xcite , though in practice it simply implies that none of occupation numbers should vanish . for systems with coulombic interactions the extended koopmans theorem is found to hold to very high numerical accuracy @xcite although this does not prove its validity . we have therefore seen that the possible vanishing of no occupation numbers has important consequences for ci expansions as well as for the validity of fundamental theorems in many - body theory . this then immediately raises the question in which cases the no occupation numbers vanish . if none of the occupation numbers vanishes , then every no is needed in an expansion of the ground state wave function . one general observation that one can make is that infinite expansions are typically required when expanding non - smooth functions in terms of smooth ones . in the case of electronic ground states the coulomb interaction requires the wavefunction to have a cusp at the positions where the electrons come together of the form @xmath30 where @xmath31 . this cusp gives an infinite kinetic energy which exactly compensates the infinity from the coulomb interaction between the electrons @xcite . due to this non - analytic behavior of the wavefunction , a full expansion of the wavefunction in one - electron functions requires in general all functions to be present . hence , one may expect in the particular case of an expansion in nos , none of the nos should have an occupation number equal to zero , since that would imply that the no is not required in the expansion . although this argument sounds very reasonable , it is certainly not a proof that zero occupations do not occur in coulomb systems . though infinitely many occupation numbers are required to be non - zero , it might be that some of them are still zero in some special situations . in the case of the homogeneous electron gas ( heg ) , however , this argument can be turned into a proof . since the nos of the heg are simply plane waves , the occupation numbers are then given by the momentum distribution , @xmath32 . kimball has shown that the momentum distribution is required to decay as @xmath33 due to the inter - electronic cusp condition @xcite , so the occupation numbers never become exactly zero . in the case of the heg we were in the fortunate situation that the nos are plane waves and , so that their occupation numbers are simply given by the momentum distribution . for general systems we are not in such a convenient position , because a straightforward expansion in a finite basis set effectively smoothens the electron - electron cusp and the argument does not apply anymore . for two - electron systems we are in a more fortunate situation , however , since for singlet two - electron systems there is a strong connection between the nos and the wavefunction . the spatial part of the singlet two - electron wavefunction is symmetric and can therefore be diagonalized @xmath34 by calculating the corresponding spin - integrated 1rdm , one readily finds that the eigenfunctions are nos and that the coefficients are related to the occupation numbers as @xmath35 . though we are not in such a good position as the for the heg , this connection is quite useful , since it allows us to connect the behavior of the occupation numbers directly to the analytic properties of the wavefunction , instead of going via the 1rdm in which much of the analytic properties are integrated out . therefore , we will focus our attention in this paper mainly to singlet two - electron systems to demonstrate how the form of the interaction determines the analytic properties of the wavefunction , which in turn dictates the asymptotic decay of the occupation numbers .

the non - vanishing of the natural orbital occupation numbers of the one - particle density matrix of many - body systems has important consequences for the existence of a density matrix - potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the extended koopmans theorem . on the basis of weyl s theorem we further derive a more general criterium for the non - vanishing of no occupations for two - particle wave functions with a certain separability structure . on the basis of this criterium we show that for a two - particle system of harmonically confined electrons with a coulombic interaction ( the so - called hookium ) the natural orbital occupations never vanish .

the non - vanishing of the natural orbital occupation numbers of the one - particle density matrix of many - body systems has important consequences for the existence of a density matrix - potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the extended koopmans theorem . on the basis of weyl s theorem we give a connection between the differentiability properties of the ground state wave function and the rate at which the natural occupations approach zero when ordered as a descending series . we show , in particular , that the presence of a coulomb cusp in the wave function leads , in general , to a power law decay of the natural occupations , whereas infinitely differentiable wave - functions typically have natural occupations that decay exponentially . we analyze for a number of explicit examples of two - particle systems that in case the wave function is non - analytic at its spatial diagonal ( for instance , due to the presence of a coulomb cusp ) the natural orbital occupations are non - vanishing . we further derive a more general criterium for the non - vanishing of no occupations for two - particle wave functions with a certain separability structure . on the basis of this criterium we show that for a two - particle system of harmonically confined electrons with a coulombic interaction ( the so - called hookium ) the natural orbital occupations never vanish .

astro-ph9910548

r

in creating a composite model , we first scaled the contributions from highion to provide a rough fit to the high ionization lines such as c iv @xmath41550 , [ ne v ] @xmath43426 , and [ fe vii ] @xmath46087 and lowion to fit lines such as [ n ii ] @xmath46584 , [ o ii ] @xmath43727 , with the result that the contribution of highion to the total h@xmath13 flux is 3 times that of lowion . due to the uncertainties in the atomic data , we have elected not to include the predicted forbidden line strengths from coronal in our scaling . since the balmer lines are associated kinematically with the non - coronal emission lines , it seems reasonable to expect that the contribution from coronal is @xmath31 15% of the total h@xmath13 flux , which is only slightly more than the uncertainty in measurement . in table 2 , we compare the predicted line ratios for highion and lowion and the composite model to the observed / dereddened values . given the simplicity of the model , we have obtained very satisfactory fits for the vast majority of the observed emission lines . there is good agreement over nearly the full ionization sequence , for example c iv @xmath41550 , c iii ] @xmath41909 , and c ii ] @xmath42325 , and o iv ] @xmath41402 , [ o iii ] @xmath45007 , [ o ii ] @xmath43727 , and [ o i ] @xmath46300 . the predicted [ o iii ] @xmath125007,4959/[o iii ] @xmath44363 ratio is 46 , which indicates that t@xmath30 in the o@xmath45 , averaged over the two components , is correct . the [ fe vii ] @xmath43759/[fe vii ] @xmath46087 ratio is 0.55 , lower than the observed value , which indicates a somewhat higher temperature in the fe@xmath19 zone than predicted , which is not surprising since given our model requirement that this zone is co - located with the o@xmath45 zone . the predicted [ s ii ] @xmath46716/@xmath46731 ratio is 1.15 , identical to that observed within the errors , which confirms our assumptions regarding the density and ionization structure of lowion . in general , the model predictions demonstrate that our assumptions regarding the elemental abundances are approximately correct . however , the models do underpredict the strengths of the neon lines somewhat , which may indicate that the neon is supersolar , but probably less than a factor of two . the model prediction for the he ii @xmath44686/h@xmath13 and ratio is only slightly higher than observed . the predicted strengths of the lines formed in the partially neutral envelope of the low ionization gas , such as [ s ii ] @xmath126716 , 6731 and [ o i ] @xmath46300 , are in reasonable agreement with the observations . this indicates that the combined effects of sed and column density are well represented by the models . this result is of particular importance , given the assumption that the components are ionized by different continua . also listed in table 2 are the model predictions for the emitted h@xmath13 flux , the emitting surface area ( the scaled to the reddening - corrected h@xmath13 luminosity divided by the emitted flux ) , and covering factor for each component , assuming a distance of @xmath0 25 pc from the hidden continuum source . at the distance of ngc 1068 ( 14.4 mpc , bland - hawthorne 1997 ) , the 01 slit width corresponds to 7.2 pc , yielding a covering factor for the slit of @xmath0 0.05 . since the covering factor of these components are substantially lower than 0.05 , there is no evidence that we are seeing substantial effects of superimposition of clouds along our line - of - sight . our photoionizaton code does not include pumping of uv resonance lines by scattering of continuum radiation and continuum fluoresence ( cf . ferguson , ferland , & pradhan 1994 ) , which may explain the underpredictions of the strengths of several uv resonance lines , including n v @xmath41240 , c ii @xmath41335 and mg ii @xmath42800 . therefore , we recomputed the lowion model using cloudy90 , assuming a turbulent velocity of 50 km s@xmath3 . although pumping of uv resonance lines is most efficient for gas with large turbulent velocities ( @xmath5 1000 km s@xmath3 ; ferguson et al . 1994 ) , it can still be an important process if the covering factor of the emitting gas is sufficiently large ( cf . hamann & korista 1996 ) and/or if the optical depths of the scattered lines are small ( ferland 1992 ) . we derive a relatively large covering factor for lowion ( @xmath0 20% that of the slit ) , and thus it is not surprising that the model predicts a significant contribution to resonance lines from scattered continuum radiation ( interestingly , this is all due to direct pumping of the uv resonance line , since there is insufficient ionizing radiation incident upon lowion to pump the euv driver lines ) . the cloudy90 predictions for c ii @xmath41335 and mg ii @xmath42800 are listed in table 2 , alongside those from our code ( the predictions for the non - resonance lines were quite similar for the two codes ) , and the agreement with observed flux ratios is quite good . in addition to the large column densities of c@xmath39 ( 3.22 x 10@xmath49 @xmath14 ) and mg@xmath39 ( 1.54 x 10@xmath50 @xmath14 ) , lowion predicts a large column density for o@xmath47 ( 6.02 x 10@xmath49 @xmath14 ) . o i @xmath41302 is present in the far - uv spectrum ( see figure 1 ) and we expect that is also formed by continuum scattering ( unfortunately , it is not included in the code output ) . however , continuum scattering does not appear to have a similarly strong affect in boosting the n v @xmath41240 line , as we discuss below . in table 3 , we list the predictions of the coronal model for the mean ionization fractions ; ions with observed lines are flagged . we elected not to list the predicted emission - line ratios since they may be misleading given the lack of reliable atomic data ( cf . moorwood et al . the model predicts non - negligible populations for each of the observed ionic states , except si@xmath19 and fe@xmath19 , however it is clear that the [ fe vii ] lines arise in lower ionization gas . if we assume that coronal contributes 15% of the observed h@xmath13 flux , the covering factor is 2.2 x 10@xmath51 . assuming isotropic scattering , at small electron scattering optical depths , @xmath52@xmath53 @xmath54 1 , the reflected fraction of continuum radiation , f@xmath55 @xmath7 n@xmath30f@xmath56@xmath57 , where n@xmath30 is the column density of electrons , f@xmath56 is the covering factor , and @xmath57 is the thomson cross - section . for coronal , f@xmath55 @xmath7 7.4 x 10@xmath23 . however , the observed reflected continuum fraction in our spectrum , based on the estimated central source luminosity ( pier et al . 1994 ) , is f@xmath55 @xmath0 1.4 x 10@xmath51 ( the total reflected fraction is f@xmath55 @xmath7 1.5 x 10@xmath58 , consistent with the larger region sampled ; miller et al . thus , the coronal - line emitting gas near the hot spot makes a neglible contribution to the scattered continuum radiation .

the spectra were taken with the _ hubble space telescope_/space telescope imaging spectrograph ( _ hst_/stis ) , through the 01x520 slit , covering the full stis 1200 to 10000 waveband , and are from a region that includes the hot spot , extending 02 , or 14 pc ( for h 75 km sec mpc ) , in the cross - dispersion direction . the combination of covering factor and thomson optical depth of the high ionization components is insufficient to scatter the observed fraction of continuum radiation into our line - of - sight .

the physical conditions near the optical continuum peak ( `` hot spot '' ) in the inner narrow line region ( nlr ) of the seyfert 2 galaxy , ngc 1068 , are examined using ultraviolet and optical spectra and photoionization models . the spectra were taken with the _ hubble space telescope_/space telescope imaging spectrograph ( _ hst_/stis ) , through the 01x520 slit , covering the full stis 1200 to 10000 waveband , and are from a region that includes the hot spot , extending 02 , or 14 pc ( for h 75 km sec mpc ) , in the cross - dispersion direction . the spectra show emission - lines from a wide range of ionization states for the most abundant elements , similar to archival faint object spectrograph spectra of the same region . perhaps the most striking feature of these spectra is the presence of strong coronal emission lines , including [ s xii ] which has hitherto only been identified in spectra of the solar corona . there is an apparent correlation between ionization energy and velocity of the emission lines with respect to the systemic velocity of the host galaxy , with the coronal lines blueshifted , most other high excitation lines near systemic , and some of the low ionization lines redshifted . from the results of our modeling , we find that the emission - line gas is photoionized and consists of three principal components : 1 ) one in which most of the strong emission - lines , such as [ o iii ] , [ ne v ] , c iv , arise , 2 ) a more tenuous , highly ionized component , which is the source of the coronal - line emission , and 3 ) a component , which is not co - planar with the other two , in which the low ionization and neutral lines , such as [ n ii ] and [ o i ] , are formed . the first two components are directly ionized by the euv - xray continuum emitted by the central source , while the low ionization gas is ionized by a combination of highly absorbed continuum radiation and a small fraction of unabsorbed continuum scattered by free electrons associated with the hot spot . the combination of covering factor and thomson optical depth of the high ionization components is insufficient to scatter the observed fraction of continuum radiation into our line - of - sight . therefore , the scattering must occur in an additional component of hot plasma , which contributes little or no uv / optical line emission .

astro-ph9910548

c

as we have demonstrated , the ionic states indicated by the coronal emission - lines can co - exist in a large column of highly ionized gas . the ionization parameter , u @xmath2 1.7 , is characteristic of the x - ray absorbers present in many seyfert 1 galaxies ( cf . reynolds 1997 ) . it is tempting to associate the coronal - line emitting gas with the x - ray absorber , as reynolds et al . ( 1997 ) has done for the case of the seyfert 1 galaxy , mcg -6 - 30 - 15 . based on the fraction of seyfert 1s that possess an x - ray absorber , it is likely that the covering factor of the absorber is 0.5 1 ( cf . george et al . 1998 ) . however , we find that the covering factor of the coronal - line gas in ngc 1068 is quite low , and thus different from typical x - ray absorbers . the low covering factor of the coronal gas also makes it unlikely to be the continuum scattering region . furthermore , miller et al . ( 1991 ) estimated a temperature for the scattering medium , t@xmath30 @xmath0 3 x 10@xmath8 k , which is significantly greater than our model predictions . therefore , it is likely that the scattering occurs in a component of gas associated with the hot spot that is more highly ionized than our coronal component . if we use the initial conditions , n@xmath40 @xmath2 200 @xmath34 , u @xmath2 8 , and n@xmath40 @xmath0 10@xmath41 @xmath14 , cloudy90 predicts a mean t@xmath30 @xmath0 4.5 x 10@xmath8 k , which is close to miller et al.s value . if we , again , apply the constraint that this additional component contributes @xmath31 15% of the total h@xmath13 , the covering factor for this component is @xmath31 0.07 and , thus , f@xmath55 @xmath31 1.2 x 10@xmath51 , or approximately 85% that observed . we would expect to see some line emission from this component , but only from the most highly ionized species , such as [ s xii ] @xmath47611 . the covering factor for this component is slightly greater than that constrained by the slit width , which would not be surprising if the scatterer is indeed an x - ray absorber viewed across our line - of - sight , as suggested by krolik & kriss ( 1995 ) , and there was some superposition of clouds . to summarize , we think it is unlikely that the coronal - line gas has a sufficient covering factor to produce the scattered continuum radiation . it is plausible that the scattering occurs in a component of more highly ionized gas , with a high covering factor , which may contribute a fraction of the coronal - line emission . although the physical conditions of both components are within the range observed for x - ray absorbers ( cf . reynolds 1997 ) , we suggest that while the absorber may be associated with the scatterer , neither are associated with the coronal - line gas that we observe . the relative contributions of photoionization and collisional processes ( e.g. , shocks , heating by cosmic rays ) to the physical state of the emission - line gas in ngc 1068 has been a matter of some debate . while kriss et al . ( 1992 ) have attributed the strong c iii @xmath4977 and n iii @xmath4990 seen in _ hut _ spectra to shock heating , ferguson et al . ( 1994 ) suggest that the strength of these lines result from a combination of continuum fluoresence and dielectronic recombination . given the importance of continuum scattering to o i @xmath41302 , c ii @xmath41335 and mg ii @xmath42800 , it is not surprising that the same process enhances c iii @xmath4977 and n iii @xmath4990 . in fact , the recomputed lowion predicts relatively strong c iii @xmath4977 and n iii @xmath4990 ( see table 2 ) . the contribution to both lines from continuum scattering is @xmath0 90% for lowion and @xmath0 50% in highion , primarily from zones near the ionized face of the cloud , where the driver lines are optically thin and pumping is most efficient ( ferland 1992 ) . the models predict c iii ] @xmath41909/c iii @xmath4977 @xmath7 5.2 and n iii ] @xmath41750/n iii @xmath4990 @xmath7 1.1 , compared to 3.15 @xmath59 0.51 and 1.46 @xmath59 0.34 , respectively , from the _ hut _ spectra ( kriss et al . 1992 ) , noting that these ratios are quite sensitive to the atomic parameters used in the code . thus , although we can not rule out additional heating mechanisms , it is clear that continuum pumping can dramatically enhance these lines in photoionized gas . nevertheless , it is interesting to note that turbulent velocities as low as 50 km s@xmath3 can fully account for the resonance scattering . the full width at half maximum of c ii @xmath41335 is @xmath0 1240 km s@xmath3 , corrected for galactic absorption , which indicates that the line is broadened by the summation of different kinematic components . interestingly , the widths of the resolved kinematic components of instrinsic uv absorbers in seyfert 1 galaxies are also typically @xmath0 50 km s@xmath3 ( crenshaw et al . the lack of large scale turbulence implies a lack of violent disruption of the gas . in krc , we attributed the large h@xmath11/h@xmath13 ratio in at least one region to collisional excitation of h@xmath11 by an injection of energetic particles , possibly associated with the radio jet , into the nlr gas this effect was not as apparent in the optical nucleus , and we find no evidence in our stis data for enhancement of h@xmath11 beyond the predictions of the photoinization models . however , there may still be examples of jet / cloud interaction at other locations in the inner nlr of ngc 1068 . this will be addressed in a subsequent paper . one piece of evidence that heating processes other than photoionization are present is that the electron temperatures predicted by the models are somewhat lower than those estimated from the [ fe vii ] . however , the underprediction of the [ fe vii ] ratio is probably due to our assumption that these lines arise in the same gas as the [ o iii ] lines . therefore , while it is possible that collisional effects are important in some of the high ionization gas in the inner nlr , most of the observed properties are consistent with photoionization by the central source . while there is no additional evidence to support our proposed geometry for the inner nlr in ngc 1068 , assuming that the low ionization gas is screened by a large column absorber resolves a problem with the krc model regarding the covering factor of the screened gas . also , it is apparent that conditions in the nlr of ngc 4151 are due to absorption of the ionizing continuum by intervening gas ( alexander et al . 1999 ; kraemer et al . if a column of extremely optically thick gas is present , it may have an important effect in the collimation of the ionizing radiation . however , in order to do so , the absorber must have a large covering factor ( i.e. , 0.5 ) . in addition to ngc 4151 , a large column of x - ray absorbing gas has been detected in the seyfert 1.5 , mrk 6 ( feldmeier et al . 1999 ) , but there are not enough examples to make a statistical determination of the covering factor of the absorber , or its column density as a function of scale - height . nevertheless , if this component has a large covering factor , it will be important , along with the putative molecular torus and any intrinsic anisotropy of the radiation field , in determining the distribution of ionized gas in the nlr .

there is an apparent correlation between ionization energy and velocity of the emission lines with respect to the systemic velocity of the host galaxy , with the coronal lines blueshifted , most other high excitation lines near systemic , and some of the low ionization lines redshifted . from the results of our modeling , we find that the emission - line gas is photoionized and consists of three principal components : 1 ) one in which most of the strong emission - lines , such as [ o iii ] , [ ne v ] , c iv , arise , 2 ) a more tenuous , highly ionized component , which is the source of the coronal - line emission , and 3 ) a component , which is not co - planar with the other two , in which the low ionization and neutral lines , such as [ n ii ] and [ o i ] , are formed . the first two components are directly ionized by the euv - xray continuum emitted by the central source , while the low ionization gas is ionized by a combination of highly absorbed continuum radiation and a small fraction of unabsorbed continuum scattered by free electrons associated with the hot spot . therefore , the scattering must occur in an additional component of hot plasma , which contributes little or no uv / optical line emission .

the physical conditions near the optical continuum peak ( `` hot spot '' ) in the inner narrow line region ( nlr ) of the seyfert 2 galaxy , ngc 1068 , are examined using ultraviolet and optical spectra and photoionization models . the spectra were taken with the _ hubble space telescope_/space telescope imaging spectrograph ( _ hst_/stis ) , through the 01x520 slit , covering the full stis 1200 to 10000 waveband , and are from a region that includes the hot spot , extending 02 , or 14 pc ( for h 75 km sec mpc ) , in the cross - dispersion direction . the spectra show emission - lines from a wide range of ionization states for the most abundant elements , similar to archival faint object spectrograph spectra of the same region . perhaps the most striking feature of these spectra is the presence of strong coronal emission lines , including [ s xii ] which has hitherto only been identified in spectra of the solar corona . there is an apparent correlation between ionization energy and velocity of the emission lines with respect to the systemic velocity of the host galaxy , with the coronal lines blueshifted , most other high excitation lines near systemic , and some of the low ionization lines redshifted . from the results of our modeling , we find that the emission - line gas is photoionized and consists of three principal components : 1 ) one in which most of the strong emission - lines , such as [ o iii ] , [ ne v ] , c iv , arise , 2 ) a more tenuous , highly ionized component , which is the source of the coronal - line emission , and 3 ) a component , which is not co - planar with the other two , in which the low ionization and neutral lines , such as [ n ii ] and [ o i ] , are formed . the first two components are directly ionized by the euv - xray continuum emitted by the central source , while the low ionization gas is ionized by a combination of highly absorbed continuum radiation and a small fraction of unabsorbed continuum scattered by free electrons associated with the hot spot . the combination of covering factor and thomson optical depth of the high ionization components is insufficient to scatter the observed fraction of continuum radiation into our line - of - sight . therefore , the scattering must occur in an additional component of hot plasma , which contributes little or no uv / optical line emission .

1201.4804

i

the precision measurement of the mass of the @xmath0-boson , @xmath4 , is an important goal of the fermilab tevatron @xcite and the cern large hadron collider ( lhc ) . with precise knowledge of @xmath4 and the top quark mass , @xmath5 , indirect information on the mass of the higgs boson , @xmath6 , within the standard model ( sm ) can be extracted from the @xmath6 dependence of radiative corrections to the @xmath0 mass . global sm fits to all electroweak precision data performed by the gfitter collaboration and the lep electroweak working group predict the sm higgs mass to be @xmath7 gev ( @xmath8 ) @xcite and @xmath9 gev ( @xmath10 c.l . ) @xcite , respectively , which lies well within the mass range presently probed by the tevatron @xcite and lhc @xcite experiments . future more precise measurements of the @xmath0 and top quark masses together with improvements in the sm predictions of @xmath4 are expected to considerably improve the indirect determination of @xmath6 . at the tevatron , for an integrated luminosity of @xmath11 , an ultimate precision of @xmath1215 mev for the @xmath0 mass may be possible @xcite . for the lhc , estimates range from @xmath13 mev @xcite to @xmath14 mev @xcite for @xmath15 , depending on the assumptions made for detector resolutions and theoretical uncertainties . with a dedicated program @xcite , one may be able to achieve @xmath16 mev ) . in hadronic collisions , the @xmath0 boson mass can be determined from the transverse mass distribution of the lepton pair , @xmath17 , originating from the @xmath0 decay , @xmath2 , and the transverse momentum distribution of the charged lepton or neutrino . both qcd and electroweak ( ew ) corrections play an important role in the measurement of @xmath0 observables at hadron colliders . it is imperative to control predictions for observables relevant to @xmath0 production at least at the @xmath18 level . also the transverse momentum distribution of the @xmath0 boson is an important ingredient in the current @xmath0 mass measurement at the tevatron ( see , e.g. ref . @xcite for a review ) . in lowest order ( lo ) in perturbation theory , the @xmath0 boson is produced without any transverse momentum . only when qcd corrections are taken into account does the @xmath0 boson acquire a non - negligible transverse momentum , @xmath19 . for a detailed understanding of the @xmath19 distribution , it is necessary to resum the soft gluon emission terms , and to model non - perturbative qcd corrections . this has been done either by using calculations targeted specifically for resummation and parametrizing non - perturbative effects ( see e.g. refs . @xcite and @xcite ) , or interfacing a calculation of @xmath0 boson production at next - to - leading order ( nlo ) in qcd with a parton - shower monte carlo ( mc ) program and tuning the parameters used to describe the non - perturbative effects . this approach has been pursued in refs . @xcite , for instance . fixed higher - order predictions beyond nlo are known for fully differential distributions through next - to - next - to - leading order in qcd @xcite , and recently first steps towards a calculation of the complete mixed ew - qcd @xmath20 corrections to the drell - yan production process were made in ref . @xcite . while qcd corrections only indirectly affect the @xmath0 mass extracted from the @xmath17 distribution , ew radiative corrections can considerably distort the shape of this distribution in the region sensitive to the @xmath0 mass . for instance , final - state photon radiation is known to shift @xmath4 by @xmath21 mev ) @xcite . in the last few years , significant progress in our understanding of the ew corrections to @xmath0 boson production in hadronic collisions has been made . the complete @xmath1 ew radiative corrections to @xmath22 ( @xmath23 ) were calculated by several groups @xcite and found to agree @xcite . first steps towards going beyond fixed - order in qed radiative corrections in @xmath0 production were taken in refs . @xcite , for instance , by including the effects of final - state multiple photon radiation . for a review of the state - of - the - art of predictions for @xmath0 production at hadron colliders see , e. g. , refs . @xcite . as a result of all these studies , given the anticipated accuracy of a @xmath0 boson mass measurement at the tevatron and the lhc , it has become increasingly clear that it is necessary to not only fully understand and control the separate higher - order qcd and ew corrections , but also their combined effects . a first study of combined effects can be found in ref . @xcite , where final - state photon radiation was added to a calculation of @xmath0 boson production which includes nlo and resummed qcd corrections . this study showed that the difference in the effects of ew corrections in the presence of qcd corrections and of simply adding the two predictions may be not negligible in view of the anticipated precision . moreover , in the relevant kinematic region , i.e. around the jacobian peak , the qcd corrections tend to compensate some of the effects of the ew corrections . in ref . @xcite the full set of ew @xmath1 corrections of horace @xcite and the qcd nlo corrections to @xmath0 production were combined in the mc@nlo framework @xcite which is interfaced with the parton - shower mc program herwig @xcite . the results of a combination of the ew @xmath1 corrections to @xmath0 production as implemented in sanc @xcite with pythia @xcite and herwig can be found in ref . @xcite , without , however , performing a matching of nlo qcd corrections to the parton shower . in this paper , we present a combination of the full ew @xmath1 radiative corrections of ref . @xcite contained in the public mc code wgrad2 and the qcd corrections to @xmath2 production of powheg - w @xcite . one advantage of the powheg method @xcite for the use in a detector simulation is that it only generates positive weighted events . moreover , it provides an interface to both herwig and pythia . it is well suited as a starting point for combining ew and qcd corrections to @xmath0-boson production in one mc program to serve as an analysis tool in the @xmath0-mass measurement of the tevatron and lhc experiments . the resulting mc code , called in the following powheg - w_ew , is publicly available at the powheg box webpage @xcite and allows the simultaneous study of the effects of both qcd and nlo ew corrections with both pythia and herwig . we do not include the effects of photon - induced processes and of multiple photon radiation . as has been found in earlier studies @xcite , both effects , although small , still can have a non - negligible impact on the @xmath0-mass measurement and should be included in view of the anticipated final precision of the @xmath4 measurement at the tevatron . this is left to a future publication . the technical details of our calculation and implementation of ew @xmath24 corrections in powheg - w are described in section [ sec : theory ] . in section [ sec : results ] we first describe our crosschecks , and then present numerical results for total cross sections and distributions which are of interest for the @xmath0-mass measurement at the tevatron and the lhc . in particular , we study the combined effects of ew @xmath1 and qcd corrections on the @xmath25 and @xmath26 distributions in @xmath27 , taking into account detector resolution effects and using pythia to simulate parton showering . finally , our conclusions are presented in section [ sec : conclusions ] .

the precision measurement of the mass of the boson is an important goal of the fermilab tevatron and the cern large hadron collider ( lhc ) . we provide numerical results for total cross sections and kinematic distributions of relevance to the mass measurement at the tevatron and the lhc for the processes .

the precision measurement of the mass of the boson is an important goal of the fermilab tevatron and the cern large hadron collider ( lhc ) . it requires accurate theoretical calculations which incorporate both higher - order qcd and electroweak corrections , and also provide an interface to parton - shower monte carlo programs which make it possible to realistically simulate experimental data . in this paper , we present a combination of the full electroweak corrections of wgrad2 , and the next - to - leading order qcd radiative corrections to production in hadronic collisions in a single event generator based on the powheg framework , which is able to interface with the parton - shower monte carlo programs pythia and herwig . using this new combined qcd+ew monte carlo program for production , we provide numerical results for total cross sections and kinematic distributions of relevance to the mass measurement at the tevatron and the lhc for the processes . in particular , we discuss the impact of ew corrections in the presence of qcd effects when including detector resolution effects .

1201.4804

c

in this paper we described the combination of the complete ew @xmath1 corrections with nlo qcd+resummed corrections to @xmath0 production in hadronic collisions , based on implementing the ew corrections of wgrad2 in powheg - w . using the resulting mc program , powheg - w_ew , which is publicly available on the webpage of the powheg box , we presented results for the transverse @xmath0 mass and charged lepton momentum distributions , taking into account lepton identification requirements which are closely modeled after those used in the high - precision measurement of the @xmath0 mass at the tevatron . in view of the anticipated precision of the @xmath0 mass measurement at the tevatron and the lhc , predictions for these observables including higher - order radiative corrections have to be under excellent control . tools such as powheg - w_ew that allow the study of combined ew and qcd corrections are important in reducing the theoretical uncertainty in the @xmath0 mass measurement . we especially concentrated on studying whether there is a change of the impact of ew corrections when qcd radiation is present as described by powheg+pythia in the kinematic region where ew corrections are known to have a significant impact on the extracted @xmath0 mass . we found interesting qcd - ew interference effects in the @xmath26 distributions , i. e. effects that go beyond simply adding qcd and nlo ew corrections , that change the shape of the distribution around the jacobian peak . these effects are similar to those observed in refs . @xcite , and their impact on the @xmath0 mass extracted from the @xmath26 distribution should be studied in more detail by using realistic detector resolution effects , ideally in close collaboration with the experimentalists performing the @xmath0-mass measurement . moreover , these findings also suggest that a calculation of the complete mixed ew - qcd @xmath146 corrections is desirable to further reduce the theoretical uncertainty and to obtain an accurate estimate of the theory uncertainty due to missing higher - order corrections . further improvements that are planned for powheg - w_ew include the implementation of the known higher - order qed and ew effects , i. e. beyond nlo , of photon - induced processes , and the usage of an updated pdf that fully considers qed corrections , once available . since powheg - w_ew interfaces to both pythia and herwig it is also a convenient tool to perform a tuned comparison of qcd+ew effects when using either parton - shower mc . finally , since powheg - w_ew includes the complete nlo ew corrections , it is interesting to note that the effects of ew sudakov logarithms that become numerically important in distributions at high energies can now also be studied in the presence of qcd radiation . this is especially interesting for the search for @xmath147 bosons at the lhc . * note added * shortly after the submission of our arxiv paper , another implementation of ew corrections to single @xmath0 production into the powheg box became available @xcite .

it requires accurate theoretical calculations which incorporate both higher - order qcd and electroweak corrections , and also provide an interface to parton - shower monte carlo programs which make it possible to realistically simulate experimental data . in this paper , we present a combination of the full electroweak corrections of wgrad2 , and the next - to - leading order qcd radiative corrections to production in hadronic collisions in a single event generator based on the powheg framework , which is able to interface with the parton - shower monte carlo programs pythia and herwig . using this new combined qcd+ew monte carlo program for production ,

the precision measurement of the mass of the boson is an important goal of the fermilab tevatron and the cern large hadron collider ( lhc ) . it requires accurate theoretical calculations which incorporate both higher - order qcd and electroweak corrections , and also provide an interface to parton - shower monte carlo programs which make it possible to realistically simulate experimental data . in this paper , we present a combination of the full electroweak corrections of wgrad2 , and the next - to - leading order qcd radiative corrections to production in hadronic collisions in a single event generator based on the powheg framework , which is able to interface with the parton - shower monte carlo programs pythia and herwig . using this new combined qcd+ew monte carlo program for production , we provide numerical results for total cross sections and kinematic distributions of relevance to the mass measurement at the tevatron and the lhc for the processes . in particular , we discuss the impact of ew corrections in the presence of qcd effects when including detector resolution effects .

1503.08101

i

while many features of black hole spacetimes can be investigated in terms of the motion of ( massive and massless ) particles , wave propagation opens a perspective on additional phenomena such as interference effects , scattering of radiation at a black hole , its quasi - normal modes and black hole evaporation . scattering and interference patterns have proven to be very important tools in other branches of physics and yield observational properties of different physical systems . therefore , it is of great relevance to consider black - hole scattering as well and to describe the dynamics of fields in the presence of a black hole for different boundary and initial conditions . the central equation that describes the propagation of massless waves on schwarzschild background spacetime is the general ( time - dependent ) regge - wheeler equation which is a wave equation written in the usual schwarzschild time and the so - called tortoise coordinate . regge and wheeler found this equation for spin @xmath2 by investigating the stability of a schwarzschild black hole under gravitational perturbations in a linearized perturbation theory @xcite . to study electromagnetic wave propagation one can solve maxwell s equations on flat spacetime but consider a medium with specified constitutive relations @xcite . another possibility to derive the regge - wheeler equation for @xmath3 is to use the so - called debye equation , because the source - free maxwell equations reduce to this single scalar equation on a schwarzschild background @xcite . for scalar perturbations and their propagation the klein - gordon equation has to be employed and the regge - wheeler equation for @xmath4 follows from a straight - forward calculation @xcite . for each of the three different types of perturbations the respective regge - wheeler - type equation follows after an expansion of the fields into ( tensorial , vectorial and scalar ) spherical harmonics . assuming additionally a harmonic time dependence , i.e. , fourier expanding the solution of this wave equation , leads to a radial equation that is known as the stationary regge - wheeler equation . this radial equation is a schrdinger - type differential equation with a spin - dependent potential barrier . due to the form of this potential no exact solution is known as long as the tortoise coordinate is kept as the radial variable . changing the coordinate system and reconsidering the previous wave equations gives rise to new radial equations that admit analytic solutions in terms of series of special functions such as hypergeometric or coulomb wave functions , see e.g. ref . another very insightful method is to use the heun functions @xcite and the theoretical framework of singularity analysis to construct analytic ( local ) solutions to the radial equations . we will follow this strategy to a great extent in this article . we start with some necessary preparations in sec . [ sec : prep ] where we introduce the confluent heun equation and important notations concerning singularities of differential equations and local solutions around them . furthermore , we consider on a schwarzschild background a wave equation in the tortoise coordinate with an arbitrary potential term . this equation is transformed to usual schwarzschild coordinates . by considering a general coordinate transformation that keeps the angles unchanged we proceed to eddington - finkelstein , painlev - gullstrand and kruskal - szekeres coordinates . in the last part of this section we sketch how to derive the respective wave equations for the three different spin values . we combine the results to obtain the general regge - wheeler equation that has the form of the previously discussed wave equation in the tortoise coordinate and can , thus , be transformed to the respective wave equations in the other coordinate systems . in sec . [ sec : radialeqn1 ] we study the radial equation in the tortoise coordinate , which is the stationary regge - wheeler equation . a lot about the phenomenology can be learned from this simplest form of the radial equation . we describe asymptotic solutions that fulfill the causal boundary condition at the horizon , the so - called in - mode for scattering and the qnm - asymptotics . here and in the following , qnm stands for quasi - normal modes . since there is no known exact analytic solution of the stationary regge - wheeler equation beyond the asymptotic behavior , approximations or numerical methods have to be used to obtain the full solutions of this equation . afterwards , we derive the radial equation in the usual schwarzschild coordinate , which was already considered e.g. by leaver @xcite and fiziev @xcite . we briefly summarize their results and give properties as well as local solutions of this radial equation . all these solutions have only finite and non - sufficient domains of convergence and there is no regular solution at the black hole horizon that allows to penetrate this radius . in sec . [ sec : radialeqn2 ] we derive and discuss the radial equation in eddington - finkelstein coordinates in full detail , and we examine its properties and local solutions in terms of frobenius and thom series and using the confluent heun function @xmath5 . as far as we know , there is no previous work concerned with the analysis of the eddington - finkelstein radial equation to find analytic solutions of the perturbation equations on schwarzschild background , apart from a short remark on their asymptotic behavior at the horizon in ref . @xcite . to overcome the fact that the region where the local solutions converge is bounded , we show how an analytic continuation of the local frobenius solutions onto the entire interval @xmath60,\infty [ \,$ ] can be performed . in this way we construct an exact solution on this interval that is regular at the horizon and satisfies the causal boundary condition . in sec . [ sec : applications ] we examine some applications of our analytically continued solutions . we consider black hole scattering and briefly sketch how to calculate qnm - frequencies for the different perturbations . at the end of this section we use the method of damour and ruffini @xcite and our semi - analytically calculated graybody factors to reobtain the power spectrum of the hawking radiation emitted from a schwarzschild black hole .

the propagation of ( massless ) scalar , electromagnetic and gravitational waves on fixed schwarzschild background spacetime is described by the general time - dependent regge - wheeler equation . we collect properties of all the singular points and construct analytic ( local ) solutions in terms of the standard confluent heun function heunc , frobenius and asymptotic thom series . black hole scattering and quasi - normal modes are briefly considered as possible applications and we use semi - analytically calculated graybody factors together with the damour - ruffini method to reconstruct the power spectrum of hawking radiation emitted by the black hole .

the propagation of ( massless ) scalar , electromagnetic and gravitational waves on fixed schwarzschild background spacetime is described by the general time - dependent regge - wheeler equation . we transform this wave equation to usual schwarzschild , eddington - finkelstein , painlev - gullstrand and kruskal - szekeres coordinates . in the first three cases , but not in the last one , it is possible to separate a harmonic time - dependence . then the resulting radial equations belong to the class of confluent heun equations , i.e. , we can identify one irregular and two regular singularities . using the generalized riemann scheme we collect properties of all the singular points and construct analytic ( local ) solutions in terms of the standard confluent heun function heunc , frobenius and asymptotic thom series . we study the eddington - finkelstein case in detail and obtain a solution that is regular at the black hole horizon . this solution satisfies causal boundary conditions , i.e. , it describes purely ingoing radiation at . to construct solutions on the entire open interval,\infty [ \,$ ] , we give an analytic continuation of local solutions around the horizon . black hole scattering and quasi - normal modes are briefly considered as possible applications and we use semi - analytically calculated graybody factors together with the damour - ruffini method to reconstruct the power spectrum of hawking radiation emitted by the black hole .

0712.2823

c

we have modelled the pre - maximum spectra of 6 different sne ia ( see table [ tab : prop ] ) . three of these ( 2002bo , 2002dj and 2002er ) are classified as high velocity gradient ( hvg ) , and are characterized by a large si line velocity that evolves rapidly after maximum brightness . the other three sne ( 2001el , 2003cg , and 2003du ) , classified as low velocity gradient ( lvg ) , have a smaller si line velocity that evolves slowly after maximum . the parameters of our models are shown in tables [ tab : param ] ( luminosity and photospheric velocity ) and [ tab : abun ] ( abundances ) . in the following , we summarize the properties of hvg ( [ sec : hvg ] ) and lvg ( [ sec : lvg ] ) sne . their different appearance stems basically from a different photospheric velocity . the presence of iron - peak elements in the outer layers is revisited and its implications are discussed in [ sec : fe ] . then , the origin of the difference between hvg and lvg is discussed in [ sec : hvglvg ] . the variety of high velocity features ( hvfs ) is very large independently of the classification of hvg or lvg . the causes for hvfs are also discussed in [ sec : hvf ] . finally , possible influences to the lc width - luminosity relation are discussed ( [ sec : wlr ] ) . hvg sne 2002bo and 2002dj have the highest line velocities and the lowest photospheric temperatures of the 6 sne . the higher temperature for sn 2002er results from the high @xmath7 and the low @xmath8 . sn 2002er seems to be intrinsically more luminous than sn 2002bo at a similar epoch ( table 2 ) , although it has a larger decline rate . this is also supported by the analysis of nebular spectra ( mazzali et al . the velocity of sn 2002er is intrinsically lower than that of other hvg sne ( b05 ; kotak et al . although a sn may be classified as hvg , its @xmath63 can be as high as that of lvg sne if the sn has both a high enough @xmath7 and low enough @xmath8 . this suggests continuity between two groups ( branch et al . 2006 , 2007 ) . the @xmath06355 lines of sne 2002bo and 2002dj have well - defined p - cygni profiles with blue wings reaching @xmath82 km s@xmath2(blue lines in fig . [ fig : si ] ) . in the spectra of these sne , is not seen below at least @xmath39 km s@xmath2 . this suggests that the abundance distribution of hvg sne resembles that of 1d delayed detonation models ( khokhlov et al . 1991a ; hflich & khokhlov 1996 ; iwamoto et al . 1999 ) rather than that of the 1d deflagration model w7 ( nomoto et al . 1984 ) . the computed physical conditions in the ejecta of a representative hvg sn , 2002bo , and those of a typical lvg sn of similar @xmath132 , and thus presumably similar luminosity , sn 2001el , are shown in figure [ fig : ion ] . in the ionization plot , solid lines represent the lower of two states marked in each panel . the temperature structure , the number density of electrons , and the ionization state of sn 2002bo and sn 2001el computed under the assumptions described in [ sec : method ] are rather similar at all layers with @xmath133 km s@xmath2 . consequently , the ionization fractions are also similar . b05 show the evolution of the parameter @xmath134(si ) , the ratio of the lines at 5800 and 6000 . @xmath134(si ) is thought to be a temperature indicator ( nugent et al . 1995 ) . at pre - maximum epochs ( @xmath135 days ) , @xmath134(si ) is larger in hvg than in lvg sne ( see fig . 2 in b05 ) . as we have shown , a typical hvg sn has a lower photospheric temperature before maximum . the fact that sne 2002bo and 2001el have a similar @xmath132 , and therefore should have a similar luminosity , suggests that the lower temperature of sn 2002bo at pre - maximum epochs reflects its higher photospheric velocity . therefore , @xmath134(si ) is not a good indicator of sn luminosity at pre - maximum phases , when the dispersion of the photospheric velocity among different sne is still very large ( b05 ) . on the other hand , since the diversity in photospheric velocity is small at epochs near maximum , both @xmath134(si ) and the temperature more closely reflects the intrinsic luminosity . the three lvg sne have similar photospheric velocities and temperatures . the temperature structure , electron density , and ionization state of sn 2001el are shown in figure [ fig : ion ] ( green lines ) . the run of all physical quantities is similar to hvg sn 2002bo at comparable velocities , but the values at the photosphere are significantly different because @xmath8 is lower for lvg . in particular , important ions such as , , , and are a factor of @xmath136 less abundant near the photosphere of lvg sne ( at @xmath137 km s@xmath2 ) then near the photosphere of hvg sne ( at @xmath138 km s@xmath2 ) . the @xmath06578 line is likely to be present in the lvg sne 2001el and 2003du , and possibly also in sn 2003cg near the photosphere ( @xmath137 km s@xmath2 ) . the mass fraction of c required to suppress the @xmath06355 emission peak is however only 0.002 - 0.003 . the mass of c in sne 2001el and 2003du is only @xmath139 if we assume a homogeneous , spherically symmetric distribution above the photosphere . even if we consider that we can not estimate the c abundance at @xmath140 km s@xmath2 because of the blend with the line , and assume @xmath66(c)=0.5 at @xmath141 km s@xmath2 , the mass of c is at most @xmath142 . this is still less than predicted by the w7 model ( @xmath143 ) . although is used to estimate c abundance in marion et al . ( 2006 ) , is not the dominant ionization state as shown in figure [ fig : ion ] ( solid line ) , and the exact amount of is very sensitive to the temperature structure . in our calculations , lines never become visible even if makes a deep absorption , suggesting that is a better indicator of carbon abundance in this temperature range . alternatively , the emission peak of @xmath06355 may be suppressed if si is detached from the photosphere ( see branch et al . 2002 for the case of h@xmath88 ) . this is however not the case for the objects presented here because the velocity of decreases to @xmath144 km s@xmath2 at subsequent epochs and si is abundant at the corresponding velocities . in addition to this , the fact that the emission profile of the line is well - peaked at maximum light even in lvg suggests that the suppression is related to the conditions of the outer layers . both and lines are clearly present in pre - maximum spectra . we showed that about a few percent of fe in mass fraction , including both stable fe and decay products of @xmath4ni , are required to match the observed lines ( [ sec:02bofe ] ) . lines of both ions ( and ) are correctly reproduced , which suggests that the computation of the ionization state of fe is reliable . the fact that fe is not highly abundant indicates that the photosphere resides outside the fe - rich layers . in order to distinguish stable fe ( e.g. , @xmath145fe ) from the decay product of @xmath4ni ( i.e. , @xmath4fe ) , the abundances of ni and co were quantified from the spectra ( [ sec:02bofe ] ) . in 4 of our sne , we are able to estimate the @xmath4ni abundance near the photosphere , while only upper limits could be obtained in the remaining 2 cases . if @xmath4ni accounted for all the present fe abundance at such an early epoch ( when only 3% of @xmath4ni has decayed to @xmath4fe ) , the ejecta would be dominated by @xmath4ni . this is , however , clearly inconsistent with the observed spectra and the parameters obtained from the modeling . therefore , we conclude that not only @xmath4ni , but also stable fe must exist at the photosphere . the respective abundances obtained are always larger than solar suggesting that the origin is not the progenitor but nucleosynthesis during the explosion . the metal abundances in the outer layers suggest that the abundances are not sharply stratified with velocity . even in 1d , the region where @xmath4ni is synthesized extends to si - rich layers because the temperature changes smoothly during the explosion . @xmath145fe can also be synthesized in si - rich layers ( e.g. , iwamoto et al . another explanation for fe - group elements in outer layers may be large scale mixing , as seen in recent three - dimensional deflagration models ( e.g. , gamezo et al . 2003 ; rpke & hillebrandt 2005 ; rpke et al . 2006 ) . the presence of fe - group elements in the outer layers and the diversity of their abundances and a low abundance of unburned elements may hinder the use of pre - maximum spectra as indicators of the progenitor metallicity ( lentz et al . in fact , larger diversity than predicted by model computations is seen in uv spectra ( ellis et al . this may reflect diversity in the abundances of fe - group elements in the outer layers , or in the photospheric temperature ( [ sec : hvg ] and [ sec : lvg ] ) . the difference between hvg and lvg sne can be studied comparing the properties of sne with similar decline rates ( @xmath132 ) . for an optimal comparison at a similar epoch , we again take sne 2002bo ( hvg ; @xmath52 days , @xmath146 ) and 2001el ( lvg ; @xmath147 days , @xmath148 ) as examples . the marginal detection of carbon in the emission peak of @xmath06355 in lvg sne suggests that the burning is less powerful in lvg sne than in hvg sne . it is also interesting that other sne where c was detected ( sn 1998aq , branch et al . 2003 ; and possibly sn 1994d , branch et al . 2005 ) are also lvg . in addition , we find that hvg sne do not have carbon at least up to @xmath149 km s@xmath2 . if more burning occurs in hvg than in lvg sne , the former may have more kinetic energy . this would tend to make the photospheric velocity of hvg higher . the kinetic energy difference between hvg and lvg can estimated by a simple analysis . we assume that the outermost layer are fully burned to si in hvg while half of the material at @xmath141 km s@xmath2 is oxygen and carbon in lvg . since the mass above @xmath150 km s@xmath2 is @xmath112 assuming the w7 density structure , the difference in nuclear energy release is @xmath151 erg , which is less than @xmath152 of the typical kinetic energy of sne ia models . the expected difference in photospheric velocity is however only @xmath153% . therefore , it seems unlikely that the difference between hvg and lvg can be accounted for by a different kinetic energy alone . yet , such a difference in kinetic energy can not be ruled out . alternatively , hvg sne may have more massive ejecta than lvg sne . the limiting mass of a spinning wd can exceed the chandrasekhar mass of the static wd , @xmath154 ( uenishi , nomoto & hachisu 2003 ; yoon & langer 2004 , 2005 ; domnguez et al . since the density structure of a rotating wd is flatter than that of a static one , the photospheric velocity may be larger before maximum but then evolve more rapidly . unless the wd mass is extremely large such as the 2@xmath98 suggested for sn 2003fg by howell et al . ( 2006 ) , the expansion kinetic energy would not be significantly reduced by a higher binding energy . however , there is no evidence that hvg sne tend to synthesize more @xmath4ni , which does not support this interpretation . even though the mass and the kinetic energy of the ejecta are similar in hvg and lvg , a different fe - group abundance in the outer region could make their appearance different . some amount of fe - group elements is present in the outer layers of all 6 sne ( see [ sec : fe ] ) . line velocities are expected to be higher if more fe - group elements are present in the outer layers because of the larger opacity of these elements . our results show that the near - photospheric abundance of fe - group elements is not smaller in hvg than in lvg , even though the photospheric velocity is higher in hvg by @xmath155 km s@xmath2 . this might imply that hvg sne have more fe - group elements if the metal abundance is a decreasing function of radius ( velocity ) . therefore , the abundances of fe - group elements in the outer layers can be a cause of spectral diversity , while differences in the kinetic energy or the progenitor mass are less likely . to confirm this hypothesis , the metal abundance in the spectra of lvg with @xmath156 km s@xmath2 should be investigated with earlier spectra . high - velocity features ( @xmath1 km s@xmath2 ) are seen in both h&k and in the ir triplet . except for sn 2003cg , hvfs are not present in synthetic spectra based on w7 . they can be reproduced using the dd density structure and a relatively large ca abundance . alternatively , they can be also explained by an enhancement in density of the outer layer ( @xmath157 km s@xmath2 ) of a factor of 4 from the w7 value assuming some h ( @xmath158% in mass fraction ) in this region . interaction with csm may produce the latter situation ; mixing of h into the ejecta increases the fraction by a factor of 5 - 10 as it favors recombination ( mazzali et al . 2005a ) . the profiles of the ir triplet show variations ( fig . [ fig : ca ] ) . in hvg sne ( blue lines ) , the profile is round and the high - velocity component tends to blend with the photospheric component . in lvg sne , on the other hand , the profiles are less blended because of the weakness of the photospheric component ( green lines , see also sn 2003kf in mazzali et al . this is a natural consequence of the high @xmath159 and the low @xmath8 of lvg sne . the high temperature suppresses and lines near the photosphere , and the low photospheric velocity makes the position of the photospheric component redder . the combination of these two effects results in a weaker and redder photospheric absorption , so that the high - velocity component becomes more detached in lvg sne . the strength of the high - velocity component also varies from sn to sn . as our models show , this is not a temperature effect , because the temperature in the outer region is similar in all cases ( fig . [ fig : ion ] ) . although we could reproduce the strength of the hvf increasing the ca abundance , the abundances that are required show a large spread ( of a factor of 100 ; table [ tab : abun ] ) . this diversity may be a line - of - sight effect if hvfs are caused by aspherical structures , like a torus or clumps ( tanaka et al . 2006 ) , as also suggested by the high polarization level of the feature ( wang et al . 2003 ; kasen et al . 2003 ) . the very strong , broad blue wing of the @xmath06355 absorption in sne 2002bo , 2002dj and 2001el is not perfectly explained by our synthetic spectra ( figures [ fig:02bo ] , [ fig:02dj ] and [ fig:01el ] ) . this suggests the presence of hvfs in as well as in lines , although the velocity of the blue edge of the absorption is lower than that of the lines ( figures [ fig : si ] and [ fig : ca ] ) . on the other hand , sne 2002er , 2003cg and 2003du lack this feature ( figures [ fig:02er ] , [ fig:03cg ] , and [ fig:03du ] ) . the origin of hvfs is debated ( e.g. , hatano et al . 1999 ; wang et al . 2003 ; thomas et al . 2004 ; gerardy et al . 2004 ; mazzali 2005a ; kasen & plewa 2005 ; tanaka et al . the difficulty in using the dd model is that it still requires a high ca abundance in the high - velocity layers ( @xmath160 km s@xmath2 ; table [ tab : abun ] ) despite the absence of a very strong si absorption at similar velocities . one problem with the csm interaction scenario is that it requires the accumulation of a relatively large mass . the estimated mass in the high - velocity shell is @xmath142 . in order to accumulate this mass , a mass loss rate @xmath161 is required for a wind velocity of 10 km s@xmath2 . this mass loss rate is higher than that constrained from x - ray , optical and radio observations ( e.g. , cumming et al . 1996 ; mattila et al . 2005 ; immler et al . 2006 ; hughes et al . 2007 ; panagia et al . a combination of these two scenarios ( i.e. , dd model and csm interaction ) may relax these requirements ( gerardy et al . 2004 ) . alternatively , hvfs may reflect the pre - sn abundances of the progenitor wd . in the single - degenerate scenario , the wd accretes matter from a companion star ( see nomoto et al . 1994 for a review ) . at an accrretion rate suitable for stable h shell burning ( nomoto 1982 ) , he shell flashes are rather weak ( taam 1980 ; fujimoto & sugimoto 1982 ) , and their products can accrete onto the wd . the products of he shell flashes could be ca - rich depending on conditions such as the pressure at the burning shell ( hashimoto , hanawa & sugimoto 1983 ) . after many cycles of he flashes , when the mass of the wd reaches the chandrasekhar mass , the outermost layers of the wd should consist not only of c and o but also of heavier elements . if such matter resides in the outermost layers after the explosion , it could cause hvfs . to investigate this scenario further , the growth of the wd should be studied in detail . if and hvfs are caused by the explosion itself or by csm interaction , they should correlate ( see fig . 12 in tanaka et al . in fact , this seems to be the case for sne 2002bo , 2002dj , 2001el , and 2003cg , but the correlation is not clear for sne 2002er and 2003du ( figs . [ fig : si ] and [ fig : ca ] ) . this may be useful to discriminate the origin of the hvfs . the relation between lc width and luminosity in sne ia indicates that the properties of sne ia are determined by a single dominant parameter . however , dispersion is present in the relation , and it may due to uncertainties in distance and reddening or to intrinsic properties of sne ia ( mazzali & podsiadlowski 2006 ) . understanding the origins of the dispersion is important for a more precise cosmological use of sne ia . the earliest spectra of sne ia are clearly not determined by a single parameter , e.g. , sne with a similar maximum luminosity have different line velocities . therefore , the variation in the early phase spectra could , to some extent , reveal an intrinsic dispersion in the width - luminosity relation . since the variation of properties is larger in hvg than in lvg sne ( b05 ; mazzali et al . 2007 ) , the hvg group at least could be related to the dispersion in the width - luminosity relation . a first parameter to look at in this context is the kinetic energy of the ejecta . hvg sne may have higher kinetic energy than lvg by at most @xmath162% ( [ sec : hvglvg ] ) . since the light curve width ( @xmath163 ) scales roughly as @xmath164 ( arnett 1982 ) , where @xmath165 is the kinetic energy of the ejecta , the lc width of hvg sne may become narrower than that of lvg sne . this effect should not be significant given the dependence of @xmath163 . however , an earlier lc rise , accompanied by a brighter luminosity at maximum even when the ejecta contain the same amount of @xmath4ni , is a change orthogonal to the observed width - luminsity relation . thus , differences in @xmath165 could cause an intrinsic dispersion in the width - luminosity relation . the @xmath4ni distribution could also affect the lc rise time . if hvg sne have an extended @xmath4ni distribution as suggested in [ sec : hvglvg ] , their lc may peak earlier than in the case where @xmath4ni is confined in the innermost layers because the diffusion time is shorter for the outer @xmath4ni . an early lc rise would make the peak luminosity brighter even for the same @xmath4ni mass . consequently , sne with similar @xmath132 may have different peak luminosities in certain conditions of mixing ( e.g. , mazzali & podsiadlowski 2006 , woosley et al .

earlier than 1 week before maximum , sne with a rapidly evolving line velocity ( hvg ) have a larger photospheric velocity than sne with a slowly evolving line velocity ( lvg ) . since the two groups have comparable luminosities , the temperature at the photosphere is higher in lvg sne . different fe - group abundances in the outer layers may be one of the reasons for spectral diversity among sne ia at the earliest times .

the properties of the highest velocity ejecta of normal type ia supernovae ( sne ia ) are studied via models of very early optical spectra of 6 sne . at epochs earlier than 1 week before maximum , sne with a rapidly evolving line velocity ( hvg ) have a larger photospheric velocity than sne with a slowly evolving line velocity ( lvg ) . since the two groups have comparable luminosities , the temperature at the photosphere is higher in lvg sne . this explains the different overall spectral appearance of hvg and lvg sne . however , the variation of the and absorptions at the highest velocities ( km s ) suggests that additional factors , such as asphericity or different abundances in the progenitor white dwarf , affect the outermost layers . the line is marginally detected in 3 lvg sne , suggesting that lvg undergo less intense burning . the carbon mass fraction is small , only less than 0.01 near the photosphere , so that he mass of unburned c is only . radioactiveni and stable fe are detected in both lvg and hvg sne . different fe - group abundances in the outer layers may be one of the reasons for spectral diversity among sne ia at the earliest times . the diversity among sne ia at the earliest phases could also indicate an intrinsic dispersion in the width - luminosity relation of the light curve .

0712.2823

c

the outermost ejecta of type ia sne are studied by modeling very early spectra . of the 6 sne we studied , 2 ( sne 2002bo and 2002dj ) are classified as hvg , being characterized by a high photospheric velocity and a low photospheric temperature . all three lvg sne ( sne 2001el , 2003cg and 2003du ) have uniform properties and are characterized by a low photospheric velocity and a high photospheric temperature . the properties of sn 2002er , which is classified as hvg , are close to those of lvg , suggesting that there is continuity between the groups . this is consistent with suggestions by branch et al . ( 2006 , 2007 ) hvg sne have a @xmath06355 line with a pronounced emission peak and a broad blue absorption , suggesting that si is present at @xmath86 km s@xmath2 . the abundance distribution in hvg sne is similar to that of a delayed detonation model , i.e. , the burning front reaches the outermost layers . on the other hand , the @xmath06355 emission profile of lvg sne tends to be suppressed , possibly because of the presence of @xmath06578 . this suggests that the burning front in lvg sne is weaker than in hvg sne . however , the mass fraction of carbon at the photosphere of lvg sne is only @xmath66(c ) @xmath166 , and the estimated c mass is less than @xmath142 , which is less than predicted by w7 ( @xmath143 ) . the difference in the photospheric velocity explains the different appearance of hvg and lvg sne at pre - maximum phases through the temperature difference . at the highest velocities ( @xmath1 km s@xmath2 ) , however , the variety of the and features is not explained by this scenario . this may require additional factors such as asphericity or diversity in the element abundance of the progenitor wd . both stable fe and @xmath4ni are detected at the photosphere ( @xmath167 km s@xmath2 ) in all 6 sne , suggesting that fe - group elements are always present in the outer layers . the differece in their abundances may be an important reason for the diversity among sn ia spectra . on the other hand , the difference in kinetic energy between hvg and lvg sne is too small to be the origin of the spectral diversity . the diversity of sne ia seen in early phase spectra could cause the intrinsic dispersion in the lc width - luminosity relation , through the difference in kinetic energy and the amount of iron - group elements in the outer layers . m.t . is supported by the jsps ( japan society for the promotion of science ) research fellowship for young scientists . acknowledges support by the proyecto fondecyt 3070034 . this research was supported in part by the grant - in - aid for scientific research ( 18104003 , 18540231 ) and the 21st century coe program ( quest ) from the jsps and mext of japan

the properties of the highest velocity ejecta of normal type ia supernovae ( sne ia ) are studied via models of very early optical spectra of 6 sne . at epochs this explains the different overall spectral appearance of hvg and lvg sne . however , the variation of the and absorptions at the highest velocities ( km s ) suggests that additional factors , such as asphericity or different abundances in the progenitor white dwarf , affect the outermost layers . the line is marginally detected in 3 lvg sne , suggesting that lvg undergo less intense burning . the carbon mass fraction is small , only less than 0.01 near the photosphere , so that he mass of unburned c is only . radioactiveni and stable fe are detected in both lvg and hvg sne . the diversity among sne ia at the earliest phases could also indicate an intrinsic dispersion in the width - luminosity relation of the light curve .

the properties of the highest velocity ejecta of normal type ia supernovae ( sne ia ) are studied via models of very early optical spectra of 6 sne . at epochs earlier than 1 week before maximum , sne with a rapidly evolving line velocity ( hvg ) have a larger photospheric velocity than sne with a slowly evolving line velocity ( lvg ) . since the two groups have comparable luminosities , the temperature at the photosphere is higher in lvg sne . this explains the different overall spectral appearance of hvg and lvg sne . however , the variation of the and absorptions at the highest velocities ( km s ) suggests that additional factors , such as asphericity or different abundances in the progenitor white dwarf , affect the outermost layers . the line is marginally detected in 3 lvg sne , suggesting that lvg undergo less intense burning . the carbon mass fraction is small , only less than 0.01 near the photosphere , so that he mass of unburned c is only . radioactiveni and stable fe are detected in both lvg and hvg sne . different fe - group abundances in the outer layers may be one of the reasons for spectral diversity among sne ia at the earliest times . the diversity among sne ia at the earliest phases could also indicate an intrinsic dispersion in the width - luminosity relation of the light curve .

1507.00478

i

two major challenges of contemporary particle physics are the search for beyond - standard model physics and a better understanding of the non - perturbative low - energy sector of the strong interaction . typically both aspects intermix when it comes to high - precision determinations of low - energy quantities and the corresponding standard model predictions . if a low - energy observable is potentially influenced by quantum effects from new particles , then it is also influenced by hadronic loop effects . the latter often if not always constitute the main uncertainty of the standard model prediction . on the other hand , new physics can only be revealed if a significant deviation between experiment and standard model calculation is observed . of course , this requires small uncertainties for both the experimental and the standard model result . our poor understanding of non - perturbative qcd could provide a serious hurdle for a reliable standard model calculation and/or for a reliable uncertainty estimate of such a calculation . two quantities of current interest which might indicate some deviation between experiment and the standard model are the gyromagnetic ratio of the muon @xcite and the rare decay of the neutral pion into electron and positron @xcite . an important quantity that enters both observables is the pion transition form factor , i.e. the three - point correlator between a neutral pion and two electromagnetic currents . two tasks are carried out in the present work : first , the pion - vector - vector ( @xmath1 ) correlator is determined by combining high - energy quark - based information with low(er)-energy hadronic information . we follow the general approach proposed in @xcite with some refinements . second , we explore some phenomenological consequences of our correlator and focus in particular on the rare pion decay @xmath13 . here we include also qed radiative corrections along the lines of @xcite . two limits of qcd are of particular interest for low - energy hadron physics : the chiral limit where the masses of the two or three lightest quarks are neglected @xcite and the limit where the number of quark colors , @xmath14 , is sent to infinity @xcite . concerning the @xmath1 correlator the chiral anomaly fixes the low - energy strength unambiguously in the chiral limit . for a large number of colors there are infinitely many , infinitely narrow , i.e. stable , quark - antiquark states for every combination of quantum numbers . they show up as poles in the @xmath15-point correlators of quark currents . in the real world of three colors the hadrons generically turn to unstable resonances because the hadronic interactions do not vanish any more . the poles in the correlators turn to cuts ( and poles in other riemann sheets ) . the cuts start at the corresponding many - body thresholds . thus the relevance of the large-@xmath14 limit for the real world is highest , if one considers hadrons which are narrow and/or kinematical regions where there are no ( significant ) cuts . this is our guiding principle when exploring phenomenological consequences . concerning form factors there are no cuts in the space - like region . in the standard model the rare decay of the pion into electron and positron is caused by a loop where the pion first turns into a pair of ( real or virtual ) photons ; see fig . [ fig : piee ] below . at this vertex the pion transition form factor sneaks in . if the form factor was replaced by a constant , the loop would diverge @xcite . in qcd the pion transition form factor is suppressed for large virtualities @xcite . this leads to a finite result for the @xmath11-@xmath16-@xmath17 amplitude at the one - loop level of the standard model calculation . thus for a quantitative determination of the branching ratio of the considered rare pion decay it is necessary to know where and how fast the pion transition form factor reaches its asymptotic form which in turn depends on the various combinations of virtualities . these considerations show that one needs information from various qcd regimes : the threshold regime governed by the chiral anomaly , the regime of hadronic resonances , and , finally , the regime of asymptotically high energies dictated by quarks and asymptotic freedom . these regimes are connected in the approach of @xcite where the operator product expansion ( ope ) for various three - point correlators of quark currents is matched to a hadronic ansatz that satisfies the chiral constraints for the low - energy limit . this ansatz is furthermore based on a truncation of the infinite tower of stable hadronic states that appears in the limit of a large number of colors . in principle one can work out arbitrary many orders in the ope and match to the parameters that emerge with the tower of hadron states . however , the higher orders in the ope contain unknown quark and gluon condensates of high dimensionality . thus in practice the model dependence emerges from a selection of the to be matched ope constraints and from the choice where to truncate the tower of hadron states . using one hadron multiplet per channel and leading - order ope constraints has been studied in detail in @xcite . this truncation is called `` lowest - meson dominance '' ( lmd ) . in the present work we will explore the consequences of having two hadron multiplets per channel . in the language of @xcite our approach would be called `` lmd+v+p '' . to avoid this clumsy name we decided to introduce the name `` two - hadron saturation '' ( ths ) . concerning our quantity of interest , the @xmath1 correlator and the corresponding pion transition form factor , the starting point on the level of quark currents is the pseudoscalar - vector - vector ( @xmath0 ) correlator . the consequences of lmd for this quantity have been studied in @xcite . an application to the rare pion decay to electron and positron was presented in @xcite . two vector multiplets have also been considered in @xcite ; see also @xcite where this has been used for the rare pion decay . what makes our approach different from previous works is that we explore in detail the consequence of two multiplets in _ each _ channel and that we fit and/or compare to data on the @xmath18 correlator . in fact , including a second multiplet in the vector channel involves the energy region of about 1.4 gev @xcite . in this region there is also a pseudoscalar multiplet . thus the extension from lmd to two multiplets for a channel suggests to use two multiplets for _ every _ channel . concerning the second aspect , the interrelation to the @xmath18 correlator , we will come back to this issue below , after discussing in more detail the pertinent high - energy constraints . there is yet one more short - distance limit to be considered . instead of studying the high - energy limit of correlators of quark currents ( ope ) , one can also study the high - energy limit of correlators that involve specific asymptotic states like hadrons or photons together with one or several quark currents . in particular the high - energy behavior of the pion - photon - vector correlator has recently gained much attention since the babar data @xcite seem to contradict the brodsky lepage ( b - l ) scaling limit @xcite while the belle data @xcite seem to support it . using ths we are able to satisfy all leading - order ope constraints for the @xmath0 correlator and in addition the b - l constraint for the pion - photon - vector correlator . while lmd satisfies the same ope constraints , it violates the b - l constraint as can be easily deduced from the explicit form given in @xcite ; see also the discussion in @xcite . as we will show below , the constraints from the leading order of the ope , from b - l and from the chiral anomaly together fix the ths approach to the @xmath1 correlator up to one single parameter , which we call @xmath19 . if the invariant mass of one of the vector currents in this correlator is set to zero , i.e. for the pion - photon - vector correlator , then @xmath19 drops out . in other words we have full predictive power for this correlator . aiming at the rare pion decay into electron and positron one needs the full information on the @xmath1 correlator for arbitrary invariant masses of the two vector currents . in principle , the parameter @xmath19 would be best determined from data on the @xmath1 correlator with both invariant masses being different from real photons . unfortunately such data do not exist . in this situation we turn to the second - best choice . projecting the @xmath1 correlator on one of the vector mesons that we include in ths yields a 3-point correlator for the pion , the vector meson and a quark current with vector quantum numbers . given that our approach is based on the large-@xmath14 limit where mesons are approximated by infinitely narrow states , it is suggestive to use a narrow vector meson . since phenomenologically and in the large-@xmath14 limit the pion decouples from the @xmath20 meson @xcite , we are left with the @xmath4 meson as the best choice for a vector meson . consequently we will use data on the @xmath4-@xmath5 transition form factor @xcite to fix our remaining parameter @xmath19 . the @xmath1 correlator obtained in this way from ths shows an awesome behavior : if the virtuality of one vector current becomes large while the other is set to zero ( photon case ) , the asymptotic b - l limit is reached rather fast , resembling essentially strict vector - meson dominance ( vmd ) @xcite . the scale that defines where the approach to the asymptotic limit sets in is basically given by the mass of the @xmath21/@xmath4 meson . on the other hand , if both vector currents have the same large virtuality , the corresponding asymptotic limit is reached very late for the @xmath1 correlator as obtained from ths . this finding points to the relevance of details of hadronic physics above 1 gev . for this case the @xmath1 correlator from vmd falls off much faster than demanded by qcd , while for lmd the asymptotic limit is reached much earlier than for ths . since the rare decay @xmath13 is sensitive to both high- and low - energy physics , it is interesting to study how this intriguing behavior of the @xmath1 correlator obtained from ths influences the branching ratio of this rare process . before going into the details of our findings we shall compare our approach to related ones from the literature . the @xmath4-@xmath5 transition form factor and related quantities have also been addressed in @xcite where the ground - state vector mesons are treated as light degrees of freedom . by construction the approach is restricted to low energies , i.e. high - energy constraints were not considered . nonetheless , it turns out that the ths result for the @xmath4-@xmath5 transition form factor is numerically very close to the one from @xcite . conceptually close in spirit to ths is the lagrangian approach utilized , e.g. , in @xcite ( earlier references can be traced back from these works ) . also here hadron resonances in the large-@xmath14 limit are used to interpolate between the low - energy region governed by chiral perturbation theory and the high - energy region governed by the ope or quark scaling considerations . in @xcite a @xmath0 and a corresponding @xmath1 correlator are constructed with one multiplet in the vector channel and two multiplets in the pseudoscalar channel ( i.e. the goldstone bosons and one resonance multiplet ) . for an extension to two multiplets in the vector channel see @xcite . the @xmath1 correlator from @xcite satisfies the b - l constraint , but the @xmath0 correlator satisfies only one leading - order ope constraint , not all of them . as shown in @xcite the lagrangian utilized in @xcite is not capable to provide correlators that satisfy all ope constraints ; see also the discussion in @xcite . instead of the other ope constraints on the @xmath0 correlator a high - energy constraint based on quark counting rules is imposed on the @xmath22 correlator in @xcite . in our work we impose high - energy constraints on the @xmath0 correlator ( ths satisfies _ all _ leading - order ope constraints ) and on the @xmath1 correlator ( the b - l limit ) , but not on the @xmath22 or @xmath23 correlator . our philosophy is that we take the first multiplets to resemble the corresponding ground - state physical particles but the second multiplets to mimic the effect of the tower of infinitely many excited states . since we study with @xmath0 an order parameter of chiral symmetry breaking @xcite one expects that the second multiplets are close to the physical states that are the first excitations on top of the ground states . however , the weighted average of the whole tower of states might shift the effective mass higher up . in the present work we explore the uncertainty of the ths approximation by changing the masses of the second multiplets from the first to the second physical excitations . concerning the @xmath1 correlator we expect to obtain reasonable results because the pion might not resolve too many details of the intermediate - energy region . thus replacing the tower of excited resonances by the respective lowest excitation and demanding high - energy constraints for the @xmath1 correlator might be good enough . in contrast , a @xmath22 or @xmath23 correlator resolves more from the intermediate - energy region because the vector meson induces a larger mass scale . ( the same would apply to a @xmath24 correlator . ) therefore to satisfy high - energy constraints in this case we expect that one would need a more detailed modeling than just having ths , i.e. one excitation ( plus the ground state ) in each channel . it might be worth to explore a three - hadron saturation scenario , but this is beyond the scope of the present work . therefore we demand constraints on the @xmath0 and @xmath1 correlators , but disregard constraints for three - point correlators of one pseudoscalar meson , one vector meson and one vector quark current . for the same reason we only consider leading , but not subleading high - energy / ope constraints . from a formal point of view our approach is close to the successive pad approximations as utilized , e.g. , in @xcite . our correlators are also approximated by rational functions . in our approach , however , the poles of the correlators are related to physical states ( in the large-@xmath14 limit ) . in contrast , in the pad framework of @xcite one determines the rational functions by fits to data . it is not the purpose of this pad approach to look for the poles of the obtained rational functions . in fact , there are no physical restrictions from outside that would make sure that these poles correspond in any way to physical hadrons . but this is what s - matrix theory suggests ( in the large-@xmath14 limit ) : anything beyond polynomials should be caused by unitarity , analyticity , crossing symmetry and physical states . our work is complementary to the dispersion theoretical approach of @xcite ; see also @xcite . while we can not expect to reach the accuracy of a dispersive approach concerning low - energy quantities , our framework has the advantage to provide a smooth and physical connection between the low- and high - energy region and between the quark based and hadron based correlators . in practice , dispersive calculations are based on an excellent account of the low - energy region ( up to about 1 gev ) and a high - energy completion , i.e. a matching to the high - energy behavior deduced from s - matrix theory , qcd or qcd related approaches ; see the discussion in @xcite concerning the @xmath1 correlator . as already discussed , for our doubly virtual @xmath1 correlator there are regions in the virtualities where the asymptotic regime is reached only at very high energies . in practice this might imply that a naive matching of a dispersive calculation to the asymptotic regime might miss part of the physics present at intermediate energies . clearly it is worth to explore the interplay of a dispersive calculation with ths in the future . the rest of the paper is structured in the following way : in section [ sec : ff ] we construct the @xmath0 and @xmath1 correlators subject to high- and low - energy constraints . the results for the @xmath1 correlator are compared to data and to other approaches ( lmd and vmd ) . it is studied how the shape of the correlator changes when varying the remaining free parameter @xmath19 in a reasonable range . in addition , a model uncertainty is estimated by varying the mass of the second vector - meson multiplet between the _ physical _ masses of the first and second excitation . in section [ sec : pheno ] the @xmath23 correlator is constructed . the parameter @xmath19 is determined from a fit to the @xmath4-@xmath5 transition form factor . the widths or branching ratios , respectively , for the corresponding decays @xmath25 , @xmath26 , and @xmath27 are determined for ths ( and also for lmd and vmd ) . actually the first decay does not depend on @xmath19 . we find good agreement between ths and the experimental results . we address the rare pion decay to electron and positron in section [ sec : piee ] . including radiative corrections the branching ratio of this process is calculated and we compare again the ths result to other approaches . for the ths case this branching ratio is sensitive to @xmath19 . direct comparison to the experimental value from ktev @xcite seems to suggest that a discrepancy persists on the level of 2@xmath12 . in section [ sec : pieegam ] we study the properties of the singly virtual pion transition form factor in the low - energy region , such as slope and curvature . note that these quantities do not depend on the parameter @xmath19 . for the dalitz decay @xmath28 we calculate the decay width taking into account next - to - leading order ( nlo ) radiative corrections . these are evaluated along the lines of @xcite . again we compare ths to other approaches . with the full set of radiative corrections at hand , we take a fresh look on the ktev result . considering some radiative corrections that were not accounted for in the analysis suggests that the previously stated discrepancy might be even reduced to 1.5@xmath12 . the main message here , however , is that the radiative corrections are now theoretically under control @xcite and can be used in future data analyses . in section [ sec : outlook ] we provide an outlook how ths can be further utilized and how the scheme can be extended . finally , an appendix is added to provide the pseudoscalar form factors in terms of the loop integrals required for the rare pion decay . comparing in detail various approaches throughout the present work reveals that the vmd form factor proves to be phenomenologically very successful in most applications , in spite of the facts that vmd is so simple and partially possesses an improper high - energy behavior . however , the ths form factor , which satisfies all the considered constraints , works very well , too . still , the mean value of the ktev result remains a challenge for all approaches , even though the discrepancy has been reduced by a considerable level . we provide a brief discussion on this point in the corresponding sections .

the parameters are constrained by the operator product expansion at leading order where two or all three momenta are considered as large . demanding in addition the brodsky lepage limit one obtains ( in the chiral limit ) a pion - vector - vector ( ) correlator with only one free parameter . the singly virtual pion transition form factor and the decay width of are independent of this parameter and can serve as cross - checks of the results . the free parameter is determined from a fit of the- transition form factor . are compared to the ktev results . we find a deviation of 2 or less for the rare pion decay .

the pseudoscalar - vector - vector ( ) correlator is constructed using two meson multiplets in the vector and two in the pseudoscalar channel . the parameters are constrained by the operator product expansion at leading order where two or all three momenta are considered as large . demanding in addition the brodsky lepage limit one obtains ( in the chiral limit ) a pion - vector - vector ( ) correlator with only one free parameter . the singly virtual pion transition form factor and the decay width of are independent of this parameter and can serve as cross - checks of the results . the free parameter is determined from a fit of the- transition form factor . the resulting correlator is used to calculate the decay widths and and finally the widths of the rare decay and of the dalitz decay . incorporating radiative qed corrections the calculations of decays are compared to the ktev results . we find a deviation of 2 or less for the rare pion decay . 13.20.cz decays of mesons , 13.40.gp electromagnetic form factors , 11.30.rd chiral symmetry , 12.40.vv vector - meson dominance

astro-ph0001266

i

rrrrrrr & & & & + & & & & & & + 104 & 0.05 & 0.06 & -0.71 & -0.70 & -0.78 & 14.05 @xmath12 0.05 + 288 & 0.03 & 0.04 & -1.40 & -1.07 & -1.14 & 15.40 @xmath12 0.05 + 362 & 0.05 & 0.06 & -1.33 & -1.15 & -1.09 & 15.51 @xmath12 0.05 + 1261 & 0.01 & 0.01 & -1.32 & & -1.08 & 16.68 @xmath12 0.05 + 1851 & 0.02 & 0.03 & -1.23 & & -1.03 & 16.18 @xmath12 0.05 + 1904 & 0.01 & 0.01 & -1.67 & -1.37 & -1.37 & 16.15 @xmath12 0.05 + 3201 & 0.21 & 0.27 & -1.53 & -1.23 & -1.24 & 14.75 @xmath12 0.05 + 4590 & 0.04 & 0.05 & -2.11 & -1.99 & -2.00 & 15.75 @xmath12 0.10 + 4833 & 0.33 & 0.42 & -1.92 & -1.58 & -1.71 & 15.70 @xmath12 0.10 + 5272 & 0.01 & 0.01 & -1.66 & & -1.33 & 15.58 @xmath12 0.05 + 5466 & 0.00 & 0.00 & -2.22 & & -2.13 & 16.60 @xmath12 0.05 + 5897 & 0.08 & 0.10 & -1.93 & -1.59 & -1.73 & 16.30 @xmath12 0.10 + 5904 & 0.03 & 0.04 & -1.38 & -1.11 & -1.12 & 15.00 @xmath12 0.05 + 6093 & 0.18 & 0.23 & -1.75 & & -1.47 & 16.25 @xmath12 0.05 + 6171 & 0.33 & 0.42 & -1.09 & & -0.95 & 15.65 @xmath12 0.05 + 6205 & 0.02 & 0.03 & -1.63 & -1.39 & -1.33 & 14.95 @xmath12 0.10 + 6218 & 0.19 & 0.24 & -1.40 & & -1.14 & 14.70 @xmath12 0.10 + 6254 & 0.28 & 0.36 & -1.55 & -1.41 & -1.25 & 15.05 @xmath12 0.10 + 6341 & 0.02 & 0.03 & -2.24 & & -2.10 & 15.20 @xmath12 0.10 + 6352 & 0.21 & 0.27 & -0.50 & -0.64 & -0.70 & 15.25 @xmath12 0.05 + 6362 & 0.09 & 0.12 & -1.18 & -0.96 & -0.99 & 15.35 @xmath12 0.05 + 6397 & 0.18 & 0.23 & -1.94 & -1.82 & -1.76 & 12.95 @xmath12 0.10 + 6541 & 0.12 & 0.15 & -1.79 & & -1.53 & 15.40 @xmath12 0.10 + 6637 & 0.17 & 0.22 & -0.72 & & -0.78 & 15.95 @xmath12 0.05 + 6656 & 0.34 & 0.44 & -1.75 & & -1.41 & 14.25 @xmath12 0.10 + 6681 & 0.07 & 0.09 & -1.64 & & -1.35 & 15.70 @xmath12 0.05 + 6723 & 0.05 & 0.06 & -1.12 & & -0.96 & 15.45 @xmath12 0.05 + 6752 & 0.04 & 0.05 & -1.54 & -1.42 & -1.24 & 13.80 @xmath12 0.10 + 6779 & 0.20 & 0.26 & -1.94 & & -1.61 & 16.30 @xmath12 0.05 + 6809 & 0.07 & 0.09 & -1.80 & & -1.54 & 14.45 @xmath12 0.10 + 7078 & 0.09 & 0.12 & -2.13 & -2.12 & -2.02 & 15.90 @xmath12 0.05 + in very recent times , new determinations of galactic globular cluster ( ggc ) metallicities have provided us with new homogeneous @xmath13\textrm { } $ ] scales . in particular , carretta & gratton ( @xcite ; cg ) obtained metallicities from high resolution spectroscopy for 24 ggcs , with an internal uncertainty of 0.06 dex . for an even larger sample of 71 ggcs , metallicities have been obtained by rutledge et al . ( @xcite ; rhs97 ) based on spectroscopy of the caii infrared triplet . the equivalent widths of the caii triplet have been calibrated by rhs97 on both the cg scale and the older zinn & west ( @xcite ; zw ) scale . the compilation by rhs97 is by far the most homogeneous one which is currently available . in the same period , we have been building the largest homogeneous @xmath0 photometric sample of galactic globular clusters ( ggc ) based on ccd imaging carried out both with northern ( isaac newton group , ing ) and southern ( eso ) telescopes ( rosenberg et al . @xcite , @xcite ) . the main purpose of the project is to establish the relative age ranking of the clusters , based on the methods outlined in saviane et al . ( @xcite , @xcite ; srp97 , srp99 ) and buonanno et al . ( @xcite ; b98 ) . the results of this investigation are presented in rosenberg et al . ( @xcite ; rspa99 ) . here suffice it to say that for a set of clusters we obtained @xmath14 vs. @xmath15 color - magnitude diagrams ( cmd ) , which cover a magnitude range that goes from a few mags below the turnoff ( to ) up to the tip of the red giant branch ( rgb ) . at this point both a spectroscopic and photometric homogeneous databases are available : the purpose of this study is to exploit them to perform a thorough analysis of the morphology of the rgb as a function of the cluster s metallicity . as a first step , we want to obtain a new improved calibration of a few classical photometric metallicity indices . secondly , we want to provide to the community a self - consistent , * analytic , * family of giant branches , which can be used in the analysis of old stellar populations in external galaxies . photometric indices have been widely used in the past to estimate the mean metallicities of those stellar systems where direct determinations of their metal content are not feasible . in particular , they are used to obtain @xmath13\textrm { } $ ] values for the farthest globulars and for those resolved galaxies of the local group where a significant pop ii is present ( e.g. the dwarf spheroidal galaxies ) . the calibration of @xmath0 indices is particularly important , since with comparable exposure times , deeper and more accurate photometry can be obtained for the cool , low - mass stars in these broad bands than in @xmath16 . moreover , our huge cmd database allows a test of the new cg scale on a large basis : we are able to compare the relations obtained for both the old zw and new scale , and check which one allows to rank ggcs in the most accurate way . indeed , the most recent calibration of the @xmath0 indices ( carretta & bragaglia @xcite ) is based on just 8 clusters . a reliable metallicity ranking of ggc giant branches also allows studies that go beyond a simple determination of the _ mean _ metallicity of a stellar population . as an illustration , we may recall the recent investigation of the halo metallicity distribution function ( mdf ) of ngc 5128 ( harris et al . @xcite ) , which was based on the fiducial gc lines obtained by da costa & armandroff ( @xcite , hereafter da90 ) . these studies can be made more straightforward by providing a suitable analytic representation of the rgb family of ggcs . indeed , assuming that most of the ggcs share a common age ( e.g. rosenberg et al . @xcite ) , one expects that there should exist a `` universal '' function of @xmath17\ } $ ] able to map any @xmath18 $ ] coordinate pair into the corresponding metallicity ( provided that an independent estimate of the distance and extinction of the star are available ) . we will show here that such relatively simple mono - parametric function can actually be obtained , and that this progress is made possible thanks to the homogeneity of both our data set and analysis . in order to enforce a proper use of our calibrations , we must clearly state that , in principle , the present relations are valid only for rigorously old stellar populations ( i.e. for stars as old as the bulk of galactic globulars ) . at fixed abundance , giant branches are somewhat bluer for younger ages ( e.g. bertelli et al . moreover , in real stellar systems agb stars are also present on the blue side of the rgb ( cf . [ f : pars - partb ] ) . both effects must be taken into account when dealing with lg galaxies , since they could lead to systematic effects in both the mean abundances and the abundance distributions ( e.g. saviane et al . @xcite ) . the observational sample , on which this investigation is based , is presented in sect . [ s : sample ] . [ s : indices ] is devoted to the set of indices which are to be calibrated . they are defined in sect [ s : defindices ] . the reliability of our sample is tested in sect . [ s : checks ] , where we demonstrate that our methodology produces a set of well - correlated indices . in sect . [ s : newda90 ] we show that , once a distance scale is assumed for the ggcs , our whole set of rgbs can be approximated by a _ single _ analytic function , which depends on the metallicity alone . this finding allows a new and easier way to determine the distances and mean metallicities of the galaxies of the local group , extending the methods of da costa & armandroff ( @xcite ) , and lee et al . ( @xcite ) . the metallicity indices are calibrated in sect . [ s : calibrations ] , where analytic relations are provided both for the zw and for the cg scales . using these indices , we are able to test our analytic rgb family in sect [ s : testfits ] . our conclusions are in sect . [ s : conclusioni ] .

the purpose of this study is to carry out a thorough investigation of the changes in morphology of the red giant branch ( rgb ) of galactic globular clusters ( ggc ) as a function of metallicity , in the bands . to this aim , ) _ we measure a complete set of metallicity indices _ , based on the morphology and position of the red - giant branch . in particular , we provide here the first calibration of the , and indices in the plane . our new calibrations of the , , and indices are consistent with existing relations . *

the purpose of this study is to carry out a thorough investigation of the changes in morphology of the red giant branch ( rgb ) of galactic globular clusters ( ggc ) as a function of metallicity , in the bands . to this aim , two key points are developed in the course of the analysis . * ( a ) * using our photometric database for galactic globular clusters ( the largest homogeneous data sample to date ; rosenberg et al . ) _ we measure a complete set of metallicity indices _ , based on the morphology and position of the red - giant branch . in particular , we provide here the first calibration of the , and indices in the plane . we show that our indices are internally consistent , and we calibrate each index in terms of metallicity , both on the zinn & west ( 1984 ) and the carretta & gratton ( 1997 ) scales . our new calibrations of the , , and indices are consistent with existing relations . * ( b ) * using a grid of selected rgb fiducial points , _ we define a function in the $ ] space which is able to reproduce the whole set of ggc giant branches in terms of a single parameter _ ( the metallicity ) . as a first test , we show that the function is able to predict the correct trend of our observed indices with metallicity . the usage of this function will improve the current determinations of metallicity and distances within the local group , since it allows to easily map coordinates into,m_{i } $ ] ones . to this aim the `` synthetic '' rgb distribution is generated both for the currently used lee et al . ( 1990 ) distance scale , and for the most recent results on the rr lyr distance scale .

astro-ph0001266

c

in this work , we have provided the first calibration of a few metallicity indices in the @xmath137 plane , namely the indices @xmath1 , @xmath2 and @xmath3 . calibrations on both the zinn & west ( 1984 ) and carretta & gratton ( 1997 ) scales have been obtained . the metallicity indices @xmath5 , @xmath6 , @xmath7 and @xmath8 have been also calibrated on both scales , and we have shown that our new relations are consistent with existing ones . in the case of the latter two indices , we have obtained the first calibration on the cg scale ; for both scales , we have also obtained the first calibration that takes into account new results on the rr lyr distances . the accuracy of the calibrations is generally better than 0.2 dex , regardless of the metallicity scale that is used . our results are an improvement over previous calibrations , since a new approach in the definition of the rgb is used , and since our formulae are based on the largest homogeneous photometric database of galactic globular clusters . the availability of such database also allowed us a progress towards the definition of a standard description of the rgb morphology and location . we were able to obtain a function in the @xmath9 $ ] space which is able to reproduce the whole set of ggc giant branches in terms of a single parameter ( the metallicity ) . we suggest that the usage of this function will improve the current determinations of metallicity and distances within the local group , extending the methods of lee et al . ( 1993 ) . we thank the referee , gary da costa , for helpful suggestions that improved the final presentation of the manuscript . i.s . acknowledges the financial support of italian and spanish foreign ministries , through an ` azioni integrate / acciones integradas ' grant . aparicio a. , gallart c. , bertelli g. , 1997 , aj 114 , 680 armandroff t.e . , da costa g.s . , caldwell n. , seitzer p. , 1993 , aj 106 , 986 bertelli g. , bressan a. , chiosi c. , fagotto f. , nasi e. , 1994 , a&as 106 , 275 buonanno r. , corsi c.e . , pulone l. , fusi pecci f. , bellazzini m. , 1998 , a&a 333 , 505 ( b98 ) caldwell n. , armandroff t.e . , da costa g.s . , seitzer p. , 1998 , aj 115 , 535 carretta e. , bragaglia a. , 1998 , a&a 329 , 937 carretta e. , gratton r. , 1997 , a&as 121 , 95 ( cg ) carretta e. , gratton r.g . , clementini g. , fusi pecci f. , 1999 , apj , in press ( c99 ) da costa g.s . , armandroff t.e . , 1990 , aj 100 , 162 ( da90 ) dean j.f . , warren p.r . , cousins a.w.j . , 1978 , mnras 183 , 569 gallart c. , freedman w. , aparicio a. , bertelli g. , chiosi c. , 1999 , aj , , 118 , 2245 harris g.l.h . , harris w.e . , poole g.b . , 1999 , aj 117 , 855 harris w.e , 1996 , aj 112 , 1487 hartwick f.d.a . , 1968 , apj 154 , 475 held e.v . , saviane i. , momany y. , 1999a , a&a 345 , 747 held e.v . , saviane i. , momany y. , carraro g. , 1999b , apj , in press lee m.g . , freedman w.l . , madore b.f . , 1993 , apj 417 , 553 lee y.w . , demarque p. , zinn r. , 1990 , apj 350 , 155 ( ldz ) lloyd evans t. , 1983 , s. afr . circ . 7 , 86 martnez - delgado d. , aparicio . a. , gallart c. , 1999a , aj , 118 , 2229 martnez - delgado d. , gallart c. , aparicio a. , 1999b , aj , 118 , 862 rosenberg a. , saviane i. , piotto g. , aparicio a. , 1999a , aj , 118 , 2306 ( rspa99 ) rosenberg a. , piotto g. , saviane i. , aparicio a. , 1999b , a&as , in press rosenberg a. , aparicio a. , saviane i. , piotto g. , 1999c , a&as , submitted rutledge a.g . , hesser j.e . , stetson p.b . , 1997 , pasp 109 , 907 ( rhs97 ) sandage a. , smith l.l . , 1966 , apj 144 , 886 sandage a. , wallerstein g. , 1960 , apj 131 , 598 saviane i. , held e.v . , bertelli g. , 1999a , a&a , in press saviane i. , held e.v . , piotto g. , 1996 , a&a 315 , 40 saviane i. , rosenberg a. , piotto g. , 1997 . in : rood , a.renzini ( eds . ) advances in stellar evolution , cambridge university press , cambridge , p. 65 ( srp97 ) saviane i. , piotto g. , fagotto f. , et al . , 1998 , a&a 333 , 479 saviane i. , rosenberg a. , piotto g. , 1999b . in : b. k. gibson , t. s. axelrod , m. e. putman ( eds . ) , `` the third stromlo symposium : the galactic halo '' ( srp99 ) walker a. , 1992 , pasp 104 , 1063 zinn r. , west m. , 1984 , apjs 55 , 45 ( zw )

( a ) * using our photometric database for galactic globular clusters ( the largest homogeneous data sample to date ; rosenberg et al . we show that our indices are internally consistent , and we calibrate each index in terms of metallicity , both on the zinn & west ( 1984 ) and the carretta & gratton ( 1997 ) scales . ( b ) * using a grid of selected rgb fiducial points , _ we define a function in the $ ] space which is able to reproduce the whole set of ggc giant branches in terms of a single parameter _ ( the metallicity ) . as a first test , we show that the function is able to predict the correct trend of our observed indices with metallicity . the usage of this function will improve the current determinations of metallicity and distances within the local group , since it allows to easily map coordinates into,m_{i } $ ] ones . to this ( 1990 ) distance scale , and for the most recent results on the rr lyr distance scale .

the purpose of this study is to carry out a thorough investigation of the changes in morphology of the red giant branch ( rgb ) of galactic globular clusters ( ggc ) as a function of metallicity , in the bands . to this aim , two key points are developed in the course of the analysis . * ( a ) * using our photometric database for galactic globular clusters ( the largest homogeneous data sample to date ; rosenberg et al . ) _ we measure a complete set of metallicity indices _ , based on the morphology and position of the red - giant branch . in particular , we provide here the first calibration of the , and indices in the plane . we show that our indices are internally consistent , and we calibrate each index in terms of metallicity , both on the zinn & west ( 1984 ) and the carretta & gratton ( 1997 ) scales . our new calibrations of the , , and indices are consistent with existing relations . * ( b ) * using a grid of selected rgb fiducial points , _ we define a function in the $ ] space which is able to reproduce the whole set of ggc giant branches in terms of a single parameter _ ( the metallicity ) . as a first test , we show that the function is able to predict the correct trend of our observed indices with metallicity . the usage of this function will improve the current determinations of metallicity and distances within the local group , since it allows to easily map coordinates into,m_{i } $ ] ones . to this aim the `` synthetic '' rgb distribution is generated both for the currently used lee et al . ( 1990 ) distance scale , and for the most recent results on the rr lyr distance scale .

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randomized load balancing , where a job is assigned to a server from a small subset of randomly chosen servers , is very simple to implement , and can surprisingly deliver better performance ( for example reducing collisions , waiting times , backlogs ) in a number of applications , such as , data center , hash tables , distributed memory machines , path selection in networks , and task assignment at web servers . one useful model that has been extensively used to study the randomized load balancing schemes is the supermarket model . in the supermarket model , a key result by vvedenskaya , dobrushin and karpelevich @xcite indicated that when each poisson arriving job is assigned to the shortest one of @xmath0 randomly chosen queues with exponential service times , the equilibrium queue length can decay doubly exponentially in the limit as the population number @xmath1 , and the stationary fraction of queues with at least @xmath2 customers is @xmath3 , which is a substantially exponential improvement over the case for @xmath4 , where the tail of stationary queue length distribution in the corresponding m / m/1 queue is @xmath5 . the distributed load balancing strategies , in which individual job decisions are based on information on a limited number of other processors , have been studied analytically by eager , lazokwska and zahorjan @xcite and through trace - driven simulations by zhou @xcite . based on this , the supermarket model is developed by queueing theory and markov processes . most of recent research applied the density dependent jump markov processes to deal with a simple supermarket model with poisson arrival processes and exponential service times , a key result of which illustrates that there exists a unique fixed point which is decreasing doubly exponentially . that approach used in the literature relies on determining the behavior of the supermarket model as its size grows to infinity , and its behavior is naturally described as a system of differential equations , which leads to a closed form solution : doubly exponential structure , of the fixed point . readers may refer to , such as , analyzing a basic and simple supermarket model by azar , broder , karlin and upfal @xcite , vvedenskaya , dobrushin and karpelevich @xcite , mitzenmacher @xcite . certain generalization of the supermarket model have been explored , for example , simple variations by mitzenmacher and vcking @xcite , mitzenmacher @xcite , vcking @xcite , mitzenmacher , richa , and sitaraman @xcite and vvedenskaya and suhov @xcite ; and analyzing load information by mirchandaney , towsley , and stankovic @xcite , dahlin @xcite , mitzenmacher @xcite . furthermore , martin and suhov @xcite , martin @xcite , suhov and vvedenskaya @xcite studied the supermarket mall model by means of the fast jackson network , where each node in a jackson network is replaced by @xmath6 parallel servers , and a job joins the shortest of @xmath7 randomly chosen queues at the node to which it is directed . luczak and mcdiamid @xcite studied the maximum queue length of the original supermarket model with exponential service times when the service speed scales linearly with the number of jobs in the queue . li , lui and wang @xcite discussed the supermarket model with ph service times and the supermarket model with markovian arrival processes , respectively . readers may refer to an excellent overview by mitzenmacher , richa , and sitaraman @xcite . this paper is interested in analyzing the supermarket model with general service times , which is an open problem for determining whether or how the heavy - tailed service times can disrupt the doubly exponential structure of the fixed point . on the other hand , note that the supermarket model is a complex queueing system and has much different characteristics from the ordinary queueing systems , thus the general service times make its analysis more challenging than the exponential or ph service case . up to now , there has not been an effective method to be able to deal with the supermarket model with general service times . the main contributions of the paper are threefold . the first one is to provide a novel and simple approach to study the supermarket model with general service times . this approach is based on the supplementary variable method but is described as a new integral - differential structure for expressing and computing the fraction of queues efficiently . using the new approach , we setup an infinite - size system of integral - differential equations , which makes applications of the density dependent jump markov processes to be able to deal with the general distributions , such as general service times , involved in the supermarket model . the second one is to obtain a close - form solution : doubly exponential structure , for the fixed point satisfying the system of nonlinear equations , which is always a key in the study of supermarket models . furthermore , this paper analyzes the exponential convergence of the current location of the supermarket model to its fixed point , and studies the lipschitz condition in the kurtz theorem under general service times . also , this paper provides numerical examples to illustrate the effectiveness of our approach in analyzing the randomized load balancing schemes with the non - exponential service requirements . the third one is to obtain that the fixed point is decomposited into two groups of information under a product form : the arrival information and the service information . based on this , we indicate three important observations : ( a ) : : the fixed point for the supermarket model is different from the tail of stationary queue length distribution for the ordinary m / g/1 queue , because the fixed point is light - tailed but the stationary queue length is heavy - tail if the service times are heavy - tailed . note that such a difference is illustrated in this paper for the first time , while it can not be observed in the literature for the supermarket model with poisson arrivals and exponential service times , e.g. , see mitzenmacher , richa , and sitaraman @xcite . ( b ) : : the doubly exponential solution to the fixed point can extensively exist even if the service time distribution is heavy - tailed . this is an answer of the above open problem to illustrate the role played by the heavy - tailed service time distribution in the doubly exponential solution to the fixed point . ( c ) : : the doubly exponential solution to the fixed point is not unique for a more general supermarket model . note that we give three different doubly exponential solutions in the supermarket model with poisson arrivals and ph service times , thus it is very interesting to provide all the doubly exponential solutions for a more general supermarket model . based on this , one can gain the new and important understanding how the workload probing can help in load balancing jobs with general service times such as heavy - tailed service . the remainder of this paper is organized as follows . in section 2 , we first describe a supermarket model with general service times , which is always useful in the study of randomized load balancing schemes . then the supermarket model is expressed as a systems of integral - differential equations in terms of the density dependent jump markov processes . in section 3 , we first introduce a fixed point of the system of integral - differential equations , and set up a system of nonlinear equations satisfied by the fixed point . then we provide a close - form solution : doubly exponential structure , to the system of nonlinear equations . in section 4 , we provide a necessary discussion on the key parameter @xmath8 used in the doubly exponential structure , and indicate that the doubly exponential solution to the fixed point extensively exists even if the service time distribution is heavy - tailed . in section 5 , we give three methods to analyze the supermarket model with poisson arrivals and ph service times , and provide three different ways to determine the key parameter @xmath8 and compute the doubly exponential solution to the fixed point . we show that the doubly exponential solution to the fixed point is not unique for a more general supermarket . in section 6 , we study the exponential convergence of the current location of the supermarket model to its fixed point . not only does the exponential convergence indicates the existence of the fixed point , but it also explains such a convergent process is very fast . in section 7 , we apply the kurtz theorem to study the supermarket model with the general service times , and analyze the lipschitz condition with respect to general service times . some concluding remarks are given in section 8 .

the randomized load balancing model ( also called _ supermarket model _ ) is now being applied to the study of load balancing in data centers and multi - core servers systems . it is very interesting to analyze the general service times in the supermarket model , and specifically understand influence of the heavy - tailed service times on the doubly exponential solution . since the supermarket model is a complex queueing system , the general service times make its analysis more challenging than the exponential or ph service case . up to now , it still is an open problem whether or how the heavy - tailed service times can disrupt the doubly exponential structure of the fixed point in the supermarket model . in this paper , we provide a novel and simple approach to study the supermarket model with general service times . the fixed point is decomposited into two groups of information under a product form : the arrival information and the service information . based on this . 0.5 cm * keywords : * randomized load balancing , supermarket model , density dependent jump markov process , fixed point , doubly exponential solution , heavy - tailed distribution , exponential convergence , lipschitz condition .

the randomized load balancing model ( also called _ supermarket model _ ) is now being applied to the study of load balancing in data centers and multi - core servers systems . it is very interesting to analyze the general service times in the supermarket model , and specifically understand influence of the heavy - tailed service times on the doubly exponential solution . since the supermarket model is a complex queueing system , the general service times make its analysis more challenging than the exponential or ph service case . up to now , it still is an open problem whether or how the heavy - tailed service times can disrupt the doubly exponential structure of the fixed point in the supermarket model . in this paper , we provide a novel and simple approach to study the supermarket model with general service times . this approach is based on the supplementary variable method used in analyzing stochastic models extensively . we organize an infinite - size system of integral - differential equations by means of the density dependent jump markov process , and obtain a close - form solution : doubly exponential structure , for the fixed point satisfying the system of nonlinear equations , which is always a key in the study of supermarket models . the fixed point is decomposited into two groups of information under a product form : the arrival information and the service information . based on this , we indicate two important observations : the fixed point for the supermarket model is different from the tail of stationary queue length distribution for the ordinary m / g/1 queue , and the doubly exponential solution to the fixed point can extensively exist even if the service time distribution is heavy - tailed . furthermore , we analyze the exponential convergence of the current location of the supermarket model to its fixed point , and study the lipschitz condition in the kurtz theorem under general service times . based on these analysis , one can gain a new understanding how workload probing can help in load balancing jobs with general service times such as heavy - tailed service . 0.5 cm * keywords : * randomized load balancing , supermarket model , density dependent jump markov process , fixed point , doubly exponential solution , heavy - tailed distribution , exponential convergence , lipschitz condition .

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in this section , we provide a necessary discussion for the key parameter @xmath8 in the doubly exponential solution of theorem [ the : cfs ] . based on this , for the fixed point we give a new and important observation : the doubly exponential solution to the fixed point can extensively exist for @xmath127 , even if the service time distribution is heavy - tailed . note that@xmath157 ^{d}\text{d}x\nonumber\\ & = \frac{\int_{0}^{+\infty}\left [ \overline{g}\left ( x\right ) \right ] ^{d}\text{d}x}{\left [ \int_{0}^{+\infty}\overline{g}\left ( x\right ) \text{d}x\right ] ^{d } } , \label{dequ1}\ ] ] it is easy to see that @xmath158 if @xmath4 . thus , we need to analyze the case for @xmath48 as follows . since @xmath130 , we get that @xmath159 ^{d}\leq\overline{g}\left ( x\right ) \leq1 $ ] , which leads to@xmath160 ^{d}dx\leq\int_{0}^{+\infty}\overline{g}\left ( x\right ) dx=1/\mu.\ ] ] it is easy to see that @xmath161 , and thus if @xmath127 , then @xmath95 . in what follows we analyze five simple and useful examples . in first two examples , the service time distribution is light - tailed ; while in the last three examples , the service time distribution is heavy - tailed . specifically , the examples with heavy - tailed service times illustrate two important observations : the first one indicates that the fixed point for the supermarket model is different from the tail of stationary queue length distribution for the ordinary m / g/1 queue , and the second one is to show that the doubly exponential solution to the fixed point can exist extensively if the service time mean is non - zero and finite . * example one : * exponential distribution . let @xmath162 . then @xmath163 . it is easy to see that when @xmath164{d}$ ] , @xmath165 ; when @xmath166{d}$ ] , @xmath158 ; and when @xmath167{d}$ ] , @xmath168 . if @xmath169 , then @xmath8 is a linear function of @xmath170 , and if @xmath171 , then @xmath8 is a nonlinear function of @xmath170 . figures 3 and 4 show the functions @xmath172 and @xmath173 , respectively . is a linear function of @xmath170 for @xmath169,width=302 ] is a nonlinear function of @xmath170 for @xmath171,width=302 ] * example two : * erlang distribution @xmath174 . let @xmath175 . then @xmath8 is given by@xmath176 ^{d}\text{d}x.\ ] ] let @xmath177 . table 1 lists how @xmath8 depends on the parameter pair @xmath178 . as seen from table 1 , @xmath8 is decreasing for each of the two parameters @xmath179 and @xmath7 . [ c]|c||c|c|c|c|c||c|c|@xmath180 & ( 2 , 2 ) & ( 2 , 5 ) & ( 2 , 10 ) & ( 5 , 2 ) & ( 10 , 2 ) & ( 5 , 5 ) & ( 10 , 10 ) + @xmath8 & 0.52 & 0.19 & @xmath181 & @xmath182 & @xmath183 & @xmath184 & @xmath185 + * example three : * weibull distribution @xmath186 . let @xmath187 . it is easy to check that the mean of the weibull distribution is given by@xmath188 which follows that @xmath8 is given by@xmath189 ^{d-1}},\ ] ] where @xmath190d@xmath26 . obviously , the weibull distribution @xmath186 is heavy - tailed if @xmath191 ; and the weibull distribution @xmath186 is light - tailed if @xmath192 . to indicate the role played by the heavy - tailed parameter @xmath193 for @xmath191 , taking @xmath194 and @xmath169 we have@xmath195 table 2 indicates how @xmath8 depends on the heavy - tailed parameter @xmath193 , such as , @xmath168 if @xmath196 ; @xmath165 if @xmath197 . this example , together with theorem [ the : cfs ] , illustrates an important observation that the fixed point @xmath198 is doubly exponential ( clearly , it is light - tailed ) even if the service time distribution is heavy - tailed . based on this , the the fixed point is different from the tail of stationary queue length distribution of the ordinary m / g/1 queue , since for the ordinary m / g/1 queue , the stationary queue length distribution is heavy - tailed if the service time distribution is heavy - tailed , e.g. , see adler , feldman and taqqu @xcite . [ c]|c||c|c|c|c|c||c|c|c|@xmath193 & 0.2 & 0.3 & 0.4 & 0.5 & 0.6 & 0.7 & 0.8 & 0.9 + @xmath8 & @xmath199 & @xmath200 & 0.27 & 0.63 & 1.05 & 1.47 & 1.86 & 2.19 + * example four : * power law distribution . let @xmath201 . if @xmath202 , then the power law distribution does not exist the finite mean . in this case , we can not setup the system of integral - differential equations for the fraction density vector @xmath70 which leads to the analysis for the fixed point . thus we only deal with the case with @xmath203 . note that for each @xmath203 @xmath204 and@xmath160 ^{d}\text{d}x=\frac{1}{\mu},\ ] ] thus we obtain @xmath205 . it is easy to see that when @xmath206 , @xmath165 ; when @xmath177 , @xmath158 ; and when @xmath207 , @xmath168 . it follows from theorem [ the : cfs ] that for @xmath14@xmath208 this indicates that the fixed point @xmath209 is doubly exponential ( of course , it is light - tailed ) if the service time distribution is power law . * example five : * almost exponential distribution . let @xmath210 . then it is easy to see that the almost exponential distribution is heavy - tailed if @xmath211 @xmath212 ^{d}}\ ] ] table 3 lists how @xmath8 depends on the parameter pair @xmath213 . as seen from table 3 , @xmath8 is decreasing for each of the two parameters @xmath7 and @xmath214 . [ c]|c||c|c|c|c|@xmath215 & ( 2 , 2 ) & ( 4 , 2 ) & ( 2 , 4 ) & ( 4 , 4 ) + @xmath8 & @xmath216 & @xmath217 & @xmath218 & @xmath219 +

, we indicate two important observations : the fixed point for the supermarket model is different from the tail of stationary queue length distribution for the ordinary m / g/1 queue , and the doubly exponential solution to the fixed point can extensively exist even if the service time distribution is heavy - tailed .

the randomized load balancing model ( also called _ supermarket model _ ) is now being applied to the study of load balancing in data centers and multi - core servers systems . it is very interesting to analyze the general service times in the supermarket model , and specifically understand influence of the heavy - tailed service times on the doubly exponential solution . since the supermarket model is a complex queueing system , the general service times make its analysis more challenging than the exponential or ph service case . up to now , it still is an open problem whether or how the heavy - tailed service times can disrupt the doubly exponential structure of the fixed point in the supermarket model . in this paper , we provide a novel and simple approach to study the supermarket model with general service times . this approach is based on the supplementary variable method used in analyzing stochastic models extensively . we organize an infinite - size system of integral - differential equations by means of the density dependent jump markov process , and obtain a close - form solution : doubly exponential structure , for the fixed point satisfying the system of nonlinear equations , which is always a key in the study of supermarket models . the fixed point is decomposited into two groups of information under a product form : the arrival information and the service information . based on this , we indicate two important observations : the fixed point for the supermarket model is different from the tail of stationary queue length distribution for the ordinary m / g/1 queue , and the doubly exponential solution to the fixed point can extensively exist even if the service time distribution is heavy - tailed . furthermore , we analyze the exponential convergence of the current location of the supermarket model to its fixed point , and study the lipschitz condition in the kurtz theorem under general service times . based on these analysis , one can gain a new understanding how workload probing can help in load balancing jobs with general service times such as heavy - tailed service . 0.5 cm * keywords : * randomized load balancing , supermarket model , density dependent jump markov process , fixed point , doubly exponential solution , heavy - tailed distribution , exponential convergence , lipschitz condition .

1008.3788

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in this paper , we provide a novel and simple approach to study the randomized load balancing model with general service times , which is described as an infinite - size system of integral - differential equations . this approach is based on the supplementary variable method , which is always applied in dealing with stochastic models of m / g/1 type , e.g. , see li and zhao @xcite and li @xcite . we organize an infinite - size system of integral - differential equations by means of the density dependent jump markov process , and obtain a close - form solution : doubly exponential structure , for the fixed point satisfying the system of nonlinear equations , which is always a key in the study of supermarket models . since the fixed point is decomposited into two groups of information under a product form , we indicate three important observations : 1 . the fixed point for the supermarket model is different from the tail of stationary queue length distribution for the ordinary m / g/1 queue ; 2 . the doubly exponential solution to the fixed point can exist extensively for @xmath127 even if the service time distribution is heavy - tailed ; and 3 . the doubly exponential solution to the fixed point is not unique for a more general supermarket model . furthermore , we analyze the exponential convergence of the current location of the supermarket model to its fixed point , and study the lipschitz condition in the kurtz theorem under general service times . finally , we present numerical examples to illustrate the effectiveness of our approach in analyzing the randomized load balancing schemes with the non - exponential service requirements . based on this analysis , one can gain a new and important understanding how workload probing can help in load balancing jobs with general service times such as heavy - tailed service . the approach of this paper is useful in analyzing the randomized load balancing schemes in resource allocation in computer networks . we expect that this approach will be applicable to the study other randomized load balancing schemes with general service times , for example , generalizing the arrival process to non - poisson : the renewal arrival process or the markovian arrival process .

this approach is based on the supplementary variable method used in analyzing stochastic models extensively . we organize an infinite - size system of integral - differential equations by means of the density dependent jump markov process , and obtain a close - form solution : doubly exponential structure , for the fixed point satisfying the system of nonlinear equations , which is always a key in the study of supermarket models . furthermore , we analyze the exponential convergence of the current location of the supermarket model to its fixed point , and study the lipschitz condition in the kurtz theorem under general service times . based on these analysis , one can gain a new understanding how workload probing can help in load balancing jobs with general service times such as heavy - tailed service

the randomized load balancing model ( also called _ supermarket model _ ) is now being applied to the study of load balancing in data centers and multi - core servers systems . it is very interesting to analyze the general service times in the supermarket model , and specifically understand influence of the heavy - tailed service times on the doubly exponential solution . since the supermarket model is a complex queueing system , the general service times make its analysis more challenging than the exponential or ph service case . up to now , it still is an open problem whether or how the heavy - tailed service times can disrupt the doubly exponential structure of the fixed point in the supermarket model . in this paper , we provide a novel and simple approach to study the supermarket model with general service times . this approach is based on the supplementary variable method used in analyzing stochastic models extensively . we organize an infinite - size system of integral - differential equations by means of the density dependent jump markov process , and obtain a close - form solution : doubly exponential structure , for the fixed point satisfying the system of nonlinear equations , which is always a key in the study of supermarket models . the fixed point is decomposited into two groups of information under a product form : the arrival information and the service information . based on this , we indicate two important observations : the fixed point for the supermarket model is different from the tail of stationary queue length distribution for the ordinary m / g/1 queue , and the doubly exponential solution to the fixed point can extensively exist even if the service time distribution is heavy - tailed . furthermore , we analyze the exponential convergence of the current location of the supermarket model to its fixed point , and study the lipschitz condition in the kurtz theorem under general service times . based on these analysis , one can gain a new understanding how workload probing can help in load balancing jobs with general service times such as heavy - tailed service . 0.5 cm * keywords : * randomized load balancing , supermarket model , density dependent jump markov process , fixed point , doubly exponential solution , heavy - tailed distribution , exponential convergence , lipschitz condition .

0712.2140

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we have studied the passage from a local conformal quantum field theory defined on the halfspace @xmath4 of two - dimensional minkowski spacetime ( boundary cft , bcft ) to an associated local conformal quantum field defined on the full minkowski spacetime ( 2d cft ) . there are essentially two ways : the first is to consider bcft vacuum correlations of observables localized far away from the boundary . in the limit of infinite distance , these correlation factorize into chiral correlations ( conformal blocks ) of charged fields . we have traced this effect back to the cluster property of the underlying local chiral subtheory . the second method exploits the split property , i.e. , the existence of states of the underlying local chiral cft in which correlations between observables in two fixed intervals at a finite distance are suppressed . with the help of the split property one can algebraically identify a fixed local algebra of the bcft with a fixed local algebra of the 2d cft , and one can generate a unitary representation of the 2d mbius group in the gns hilbert space of a suitable `` extended split state '' of this algebra . its ground state is different from the bcft vacuum . then , by acting with the 2d mbius group , one can obtain _ all _ local algebras of the 2d cft in the same hilbert space . the converse question : can one consistently `` add '' a boundary in any 2d cft ( without affecting the algebraic structure away from the boundary ) , is not addressed here . however , there arises a necessary condition from the discussion in app . [ apphmi ] : the 2d partition function should be either modular invariant , or at least it should be intermediate between the vacuum partition function and some modular invariant partition function . we hope to return to this problem , and find also a sufficient condition . * acknowledgements : * khr thanks the dipartimento di matematica of the universit di roma `` tor vergata '' for hospitality and financial support , and m. weiner and i. runkel for discussions related to the subject .

dipartimento di matematica , + universit di roma `` tor vergata '' , via della ricerca scientifica 1 , 00133 roma , italy + institut fr theoretische physik , universitt gttingen , + friedrich - hund - platz 1 , d-37077 gttingen , germany _ dedicated to klaus fredenhagen on the occasion of his 60th birthday _

the relation between two - dimensional conformal quantum field theories with and without a timelike boundary is explored . dipartimento di matematica , + universit di roma `` tor vergata '' , via della ricerca scientifica 1 , 00133 roma , italy + institut fr theoretische physik , universitt gttingen , + friedrich - hund - platz 1 , d-37077 gttingen , germany _ dedicated to klaus fredenhagen on the occasion of his 60th birthday _

cond-mat0306278

i

the correlation - driven transition from a paramagnetic metal to a paramagnetic insulator ( mott - hubbard transition @xcite ) is one of the most interesting problems in condensed - matter physics . as a prime example for a quantum - phase transition , the mott - hubbard transition is important from the physical point of view but also for the development and test of general theoretical methods to treat correlated electron systems . the minimum model required to study the mott - hubbard transition is the single - band hubbard model . @xcite inherent to this model is the competition between the electrons kinetic energy which tends to delocalize the electrons and favors a metallic state and the on - site coulomb interaction which tends to localize the electrons to avoid double occupancies and thereby favors an insulating state at half filling . except for the one - dimensional case , @xcite however , exact results with regard to the nature of the transition and the critical interaction strength @xmath1 are not available even for this highly simplified model system . a direct numerical solution using exact - diagonalization or quantum monte - carlo methods @xcite suffers from the difficulty to access the thermodynamic limit or the low - temperature , low - energy regimes . considerable progress has been made in recent years due to the development of the dynamical mean - field theory ( dmft ) @xcite which focuses on the opposite limit of infinite spatial dimensions @xmath2 . @xcite within the dmft the problem is simplified by mapping the original lattice model onto an impurity model the parameters of which must be determined by a self - consistency condition . different techniques to solve the effective impurity model have been employed to study the mott transition within the dmft , iterative perturbation theory , @xcite exact diagonalization , @xcite renormalization - group methods , @xcite and quantum monte - carlo . @xcite one of the most important characteristic of the transition is the value of the critical interaction strength @xmath1 at zero temperature . roughly , the different techniques to solve the mean - field equations predict @xmath3 where @xmath4 is the width of the free density of states . recently , a self - energy - functional approach ( sfa ) has been put forward . @xcite the sfa is a general variational approach to correlated lattice models where the grand potential @xmath5 is considered as a functional of the self - energy @xmath6 . as this functional is constructed from an infinite series of renormalized skeleton diagrams , it is not known in an explicit form and the variational principle @xmath7 = 0 $ ] can not be exploited _ directly_. usually , one replaces the exact but unknown functional with an explicitly known but approximate one this is essentially the standard diagrammatic approach @xcite which leads to weak - coupling approximations in the end . @xcite opposed to this weak - coupling perturbational approach , the functional dependence @xmath8 $ ] is not approximated at all in the sfa . the key observation is that the functional , though unknown explicitly , can be evaluated on a restricted domain of trial self - energies @xmath9 . the evaluation of the functional is exact , while the approximation is due to the fact that the self - energy in the variational principle is no longer considered as arbitrary . in this way , depending on the choice for the space @xmath9 , some well - known but also some novel approximations can be realized . here we are interested in the single - band hubbard model with hamiltonian @xmath10 . as argued in ref . a useful trial self - energy has to be constructed as the exact self - energy of a different model ( `` reference system '' ) with hamiltonian @xmath11 . the reference system can be chosen arbitrarily it must , however , share the same interaction part with the original model @xmath10 . the variational parameters at one s disposal are therefore the one - particle parameters of the reference system @xmath12 . the trial self - energy is parameterized as @xmath13 , and the variational principle reads @xmath14 / \partial { \bm t } ' = 0 $ ] . to provide trial self - energies is the only purpose of the reference system @xmath11 . whenever one is able to compute @xmath6 for the reference system @xmath11 , an exact evaluation of @xmath15 $ ] is possible . choosing @xmath11 to be a system of decoupled sites , yields a hubbard - i - type approximation . an improved approximation is obtained when @xmath11 consists of decoupled clusters with a finite number of sites @xmath16 per cluster as has been considered in refs . . this approach not only recovers the so - called cluster - perturbation theory ( cpt ) @xcite but also gives a variational improvement ( v - cpt ) which e.g. allows to describe phases with spontaneously broken symmetry . @xcite another possibility is to take @xmath17 , which implies the trial self - energy to be local , but to include a coupling to a number of @xmath18 additional uncorrelated ( `` bath '' ) sites . in this case the reference system consists of a decoupled set of single - impurity anderson models ( siam ) with @xmath19 sites each . as has been shown in ref . , this approach not only recovers the dmft ( namely in the limit @xmath20 ) but also provides a new variant of the exact - diagonalization approach , namely for any finite @xmath18 . as compared to previous dmft - exact - diagonalization approaches , @xcite the construction gives a thermodynamically consistent approximation even for small @xmath18 . more complicated reference systems may be taken for the construction of consistent approximations , for example a system of decoupled clusters of size @xmath21 where each site in the cluster is coupled to @xmath18 additional bath sites . it has been shown @xcite that in the limit @xmath20 the cellular dmft ( c - dmft ) is obtained , @xcite while approximations with finite @xmath18 represent cluster approximations which `` interpolate '' between the cpt ( @xmath22 ) and the c - dmft ( @xmath23 ) . in the present paper the mott transition is studied within the most simple but non - trivial approximation : the variational principle @xmath7 = 0 $ ] is exploited using a local trial self - energy from a reference system with @xmath17 and a single additional bath site only , @xmath24 . as @xmath25 this approximation will be referred to as the two - site dynamical impurity approximation ( @xmath26-dia ) in the following . the paper is organized as follows : a brief review of the self - energy - functional approach will be given in the next section [ sec : sfa ] . the general aspects of the evaluation of the sfa are discussed in sec . [ sec : eval ] while sec . [ sec : local ] focuses on local approximations ( @xmath17 , @xmath27 arbitrary ) in particular . in sec . [ sec : twosite ] the further specialization to the case @xmath28 is considered . the @xmath26 dynamical - impurity approximation is motivated ( i ) by the fact that at the critical point for the mott transition the entire calculation can be done _ analytically _ , ( ii ) by the conceptual simplicity of the approach which rests on a _ single _ approximation only and ( iii ) by making contact with a linearized dmft ( l - dmft ) @xcite developed previously . this is discussed in detail in sec . [ sec : twosite ] while sec . [ sec : lin ] then presents the analytical calculation for the critical regime . the results are discussed in sec . [ sec : results ] . the complete phase diagram for @xmath0 and finite temperatures is addressed in sec . [ sec : temp ] and the conclusions are given in sec . [ sec : con ] .

the self - energy - functional approach proposed recently is applied to the single - band hubbard model at half - filling to study the mott - hubbard metal - insulator transition within the most simple but non - trivial approximation . this leads to a mean - field approach which is interesting conceptually : trial self - energies from a two - site single - impurity anderson model are used to evaluate an exact and general variational principle . while this restriction of the domain of the functional represents a strong approximation , the approach is still thermodynamically consistent by construction and represents a conceptual improvement of the `` linearized dmft '' which has been suggested previously as a handy approach to study the critical regime close to the transition . , the entire calculation can be done analytically . this calculation elucidates different general aspects of the self - energy - functional theory . furthermore , it is shown how to deal with a number of technical difficulties which appear when the self - energy functional is evaluated in practice .

the self - energy - functional approach proposed recently is applied to the single - band hubbard model at half - filling to study the mott - hubbard metal - insulator transition within the most simple but non - trivial approximation . this leads to a mean - field approach which is interesting conceptually : trial self - energies from a two - site single - impurity anderson model are used to evaluate an exact and general variational principle . while this restriction of the domain of the functional represents a strong approximation , the approach is still thermodynamically consistent by construction and represents a conceptual improvement of the `` linearized dmft '' which has been suggested previously as a handy approach to study the critical regime close to the transition . it turns out that the two - site approximation is able to reproduce the complete ( zero and finite - temperature ) phase diagram for the mott transition . for the critical point at , the entire calculation can be done analytically . this calculation elucidates different general aspects of the self - energy - functional theory . furthermore , it is shown how to deal with a number of technical difficulties which appear when the self - energy functional is evaluated in practice .

astro-ph0010643

r

in table 1 we show the ionization potentials and the ionization fractions @xmath19(x@xmath20 ) is the ratio of the radially integrated number density of ion x@xmath20 to the radially integrated total number density of the element x in all ionization stages , i.e. @xmath21 , the relative column density of the ion x@xmath20 . ] of the most important ions which are observed or can potentially be observed in dlas , as a function of the ionization parameter @xmath12 for two temperatures @xmath10 = 33000 k and 40000 k of ionizing radiation and the heavy element mass fraction @xmath22 = 0.1@xmath23 . on the first line we also show @xmath1(h@xmath18+h@xmath8 ) , the total hydrogen column density across the ionized slab . over the entire range of @xmath12 , except for the highest value shown here ( @xmath24 ) , @xmath1(h@xmath18+h@xmath8 ) remains significantly smaller than the column density of neutral hydrogen observed in damped ly@xmath0 system = 40000 k and the `` typical '' value of @xmath25 3.25 the column density is @xmath26 40 % of the lower limit which defines damped systems . the baryonic mass of low column density dlas could thus be underestimated by up to this amount . ] . for an ionization parameter @xmath12 @xmath26 10@xmath13 hydrogen is essentially neutral , while at @xmath12 @xmath2 10@xmath27 it is almostly ionized as it is evidenced by small neutral hydrogen fraction @xmath19(h@xmath18 ) ( table 1 ) . calculations for lower heavy element abundances show that the ionization fractions are not strongly changed . therefore , the data from table 1 can be used for objects with metallicity [ fe / h ] @xmath28 1 . the distribution of the ionic fractions @xmath19(x@xmath29 ) of selected ions as a function of ionization parameter @xmath12 is shown in figure 1 . while the ionization fractions of all neutral and singly ionized species decrease with increasing ionization parameter @xmath12 , the ionization fraction of al@xmath9 is increased . therefore , the ratio @xmath19(al@xmath9)/@xmath19(al@xmath8 ) = @xmath1(al iii ) / @xmath1(al ii ) is a very sensitive indicator of ionization conditions and can be used to determine @xmath12 . unfortunately , although line profiles of al ii and al iii in damped ly@xmath0 systems are essentially similar ( lu et al . 1996a ; prochaska & wolfe 1999 ) , in the many cases the al ii lines are saturated or marginally saturated . this circumstance complicates direct estimates of the ionization parameter @xmath12 . however , very often , unsaturated lines of si ii , fe ii and al iii are observed in the same spectra and they can be used to estimate @xmath12 . for this , we assume that the observed heavy element abundance patterns at low metallicities are similar to that observed in low - metallicity halo stars , i.e. [ si / fe ] @xmath26 0.3 , [ al / fe ] @xmath26 0.4 ( timmes et al . 1995 ; samland 1998 ) , and adopt that log ( al / si)@xmath30 @xmath7 log ( al / fe)@xmath30 @xmath7 1.0 ( anders & grevesse 1989 ) . then , the expected ratio of column densities is equal to @xmath31 @xmath32 the typical values of log [ @xmath1(al iii)/@xmath1(si ii ) ] and log [ @xmath1(al iii)/@xmath1(fe ii ) ] in damped ly@xmath0 systems are @xmath26 2.0 to 2.5 and @xmath26 1.5 to 2.0 , respectively , which translates to log [ @xmath19(al@xmath9)/@xmath19(si@xmath8 ) ] @xmath26 0.3 to 0.8 , [ @xmath19(al@xmath9)/@xmath19(fe@xmath8 ) ] @xmath26 0.1 to 0.6 , or log @xmath12 @xmath26 3 ( fig . this estimated value of ionization parameter is dependent on the uncertainties in abundance determination and those for the adopted photoionized model and possible depletion of elements into grains . in principle , other single ionized species , e.g. zn ii , can be used instead of si ii or fe ii . however , si ii and fe ii absorption features are more often seen and measured in the dlas , and the atomic data for these ions are known with better precision ( howk & sembach 1999 ) . the above estimate of @xmath12 is based on the assumption that heavy elements are not present in the neutral gas surrounding the region of ionized gas . if the neutral gas is significantly enriched in heavy elements then an additional contribution to the column densities of si ii and fe ii comes from neutral gas and the ionization parameter should be increased to account for observed @xmath1(al iii)/@xmath1(si ii ) and @xmath1(al iii)/@xmath1(fe ii ) ratios . before we proceed to discuss the implications of this model when applied to observations of damped ly@xmath0 systems it is useful to recall that some neutral species with ionization potentials below that of hydrogen can be present in ionized gas as well . for instance lu et al . ( 1996a ) have measured @xmath33(mg ii ) @xmath34 14.38 and @xmath33(mg i ) = 12.44@xmath350.04 in the @xmath36 = 0.8598 system toward q0454 + 0356 which are consistent with the predictions of our simplified models ( table 1 ) . their measurements for another @xmath36 = 1.2667 system toward q04491326 provide only lower limits @xmath33(mg ii ) @xmath34 14.1 and @xmath33(mg i ) @xmath34 12.62 , also not in contradiction with the ionization model . prochaska & wolfe ( 1999 ) have derived @xmath33(c ii ) @xmath34 14.6 and @xmath33(c i ) @xmath37 12.8 in the @xmath36 = 2.140 toward q0149 + 33 which are consistent with predictions of ionization models . hence , the presence of species like c i or mg i does not necessarily mean that they reside in neutral gas . a useful validity check of our model is the comparison of the predictions of photoionization models with the observed values of [ o i / si ii ] . in the case of the neutral gas model it is expected that [ o i / si ii ] @xmath26 0 , while in the case of our ionization models [ o i / si ii ] = 0.5 - 0.8 depending on @xmath10 and for the range log @xmath12 = 3.5 - 3.0 ( table 1 ) . in the majority of cases observations of dla systems give only lower limits of o i abundance because of saturation of the o i @xmath381302 absorption line . the available data in the literature shows that , in general , the lower limits of [ o i / si ii ] are consistent with values expected from the ionization models . however , in some dlas the lower limits of [ o i / si ii ] are larger than those expected from the ionization models . ( 1996b ) find [ o i / si ii ] @xmath34 0.27 for the @xmath39 = 4.38 absorber towards 12020275 , while prochaska & wolfe ( 1999 ) find [ o i / si ii ] = 0.17 in the absorber towards q095104 . these values seems difficult to reconcile with ionization models unless a low ionization parameter is appropriate . however , no measurements of al iii have been done for these absorbers which would allow to constrain the ionization parameter @xmath12 . recently molaro et al . ( 2000 ) have derived a high value of [ o i / si ii ] = 0.0 - 0.1 from the unsaturated o i and si ii lines in the @xmath39 = 3.39 absorber towards the qso 00002620 . for this absorber @xmath1(al iii ) / @xmath1(si ii ) = 2.4 is rather high , suggesting an ionization parameter @xmath25 3.0 to 3.5 . however , inspection of fig . 1 in prochaska & wolfe ( 1999 ) indicates different profiles of si ii @xmath381808 and al iii @xmath381854 in this absorber , at variance with other absorbers rendering the estimate of the ionization parameter @xmath12 rather uncertain . the above discussion suggests that large ionized regions and abundance discontinuities might be present in some dlas , while other dlas might be essentially neutral . it is likely that dlas may represent a mixed bag of systems with varying ionization conditions . while the ionization model does not pretend to explain abundance pattern in all damped ly@xmath0 systems , we conclude that in many cases the derived lower limits of [ o i / si ii ] do not rule out this model . however , we point out that better determinations of [ o i / h i ] are needed to test the importance of the ionization effects in the damped ly@xmath0 systems . a very extensive literature exists on the interpretation of the metallicity of dla as a function of redshift ( e.g. pettini et al . 1994 ; lu et al . 1996a ; lindner , fritze - von alvensleben & fricke 1999 ; prantzos & boissier 2000 ) . among the main issues discussed are the question of apparent evolution or non - evolution of metallicity with @xmath39 , the origin of the scatter , and possible observational biases affecting this relation . a detailed comparison with such studies is beyond the scope of the present paper . here , we shall only indicate the typical metallicity shift expected in the framework of our model and mention the main implication in terms of age - metallicity relations . pettini et al . ( 1994 , 1999 ) , lu et al . ( 1996a ) , prochaska & wolfe ( 2000 ) noted that the chemical enrichment processes in damped ly@xmath0 galaxies appear to be quite inhomogeneous . the [ zn / h ] and [ fe / h ] distributions show a scatter by a factor of @xmath26 20 with the mean value of [ zn / h ] which is 0.4 larger than that of [ fe / h ] for the dlas at @xmath39 @xmath7 2 ( prochaska & wolfe 2000 ) . furthermore , lu et al . ( 1996a ) and pettini et al . ( 1999 ) noted that the degree of chemical enrichment in the sample of damped ly@xmath0 galaxies is , on average , considerably lower than the milky way disk at any given time in the past . this lead them to conclude that the chemical enrichment of damped ly@xmath0 galaxies is different from that in the disk of milky way . a possible explanation for the difference in chemical enrichment is simply that dlas are in general not necessarily spiral galaxies ( le brun et al . 1997 ) . alternatively , if in the framework of our model the heavy element lines are produced only in the ionized region ( i.e. the neutral gas has a very low metal content ) , the real fe / h abundance in the ionized gas is several times higher than that derived from the @xmath1(fe ii)/@xmath1(h i ) ratio , because of the non negligible upward correction for iron ( table 1 ) . the upward correction for zinc is lower , and interestingly it nearly compensates the difference between [ fe / h ] and [ zn / h ] discussed by prochaska & wolfe ( 2000 ) . then , the age - metallicity relation for damped ly@xmath0 galaxies is more consistent with that for thick disk stars of our galaxy . the opposite situation is of course realised if the neutral gas has the same metallicity as the ionized gas . in this case the observed fe / h ratio is higher than real because in ionized gas @xmath19(fe@xmath8 ) @xmath34 @xmath19(h@xmath18 ) while in neutral gas @xmath19(fe@xmath8 ) = @xmath19(h@xmath18 ) = 1 . as we will show below , it is , however , difficult to adjust all observed heavy element abundance ratios in the frame of the model with similar metallicities of neutral and ionized gas . there is little doubt that some depletion of heavy elements by dust is present in dlas . however , the level of depletion in dlas is generally smaller than that in the disk and possibly in the halo of our galaxy . pettini et al . ( 2000 ) adopt the model of dla consisting only of neutral gas and propose for dlas with low level of depletion ( systems with typically [ zn / fe ] @xmath28 0.3 ) to correct abundances of refractory elements assuming constant depletion factors for all these elements . this approach obviously leaves the question open how to explain observed abundances in systems with more depletion . besides that , the similarity of the line profiles of singly ionized ions and al iii and the large @xmath1(al iii)/@xmath1(al ii ) ratio is not addressed . prochaska & wolfe ( 1999 ) have suggested that if the overabundance of si / fe relative to solar is indicative of dust depletion , then one might expect a correlation between [ si / fe ] and [ zn / fe ] with the most heavily depleted regions showing the largest si / fe and zn / fe ratios . indeed , they found such correlation and concluded that this appearance is consistent with that expected for dust depletion ( their fig . 23 ) . alternatively , as shown in fig . 2 , the regression between [ si / fe ] and [ zn / fe ] can be explained by ionization effects . dashed , solid and dotted lines in figure connect theoretical points [ @xmath19(si@xmath8)/@xmath19(fe@xmath8 ) , @xmath19(zn@xmath8)/@xmath19(fe@xmath8 ) ] in models with @xmath22 = 0.1 @xmath23 calculated for various @xmath12 values and for three values @xmath10 = 33000 k , 40000 k and 45000 k of the effective temperature characterising the hardness of the ionizing radiation . note that [ @xmath19(si@xmath8)/@xmath19(fe@xmath8)]@xmath40 and [ @xmath19(zn@xmath8)/@xmath19(fe@xmath8)]@xmath40 are the correction factors to convert respectively si@xmath8/fe@xmath8 to si / fe and zn@xmath8/fe@xmath8 to zn / fe and they are independent on the intrinsic abundances of si , fe and zn as far as these elements do not contribute significantly to the thermal balance of the ionized gas . however , the correction factors for the considered ions can depend on the helium and the total heavy element abundances which regulate the thermal balance and the ionization structure . as mentioned above , the values of the ionization fractions @xmath19 are essentially metallicity independent for heavy element mass fractions @xmath41 0.1 0.01 @xmath23 . we point out that the quantities commonly ( e.g. prochaska & wolfe 1999 ) denoted as [ si / fe ] and [ zn / fe ] are actually @xmath42 } = \log [ n{\rm ( si~ii)}/n{\rm ( fe~ii ) } ] - \log{\rm ( si / fe)}_\odot\ ] ] and @xmath43 } = \log [ n{\rm ( zn~ii)}/n{\rm ( fe~ii ) } ] - \log{\rm ( zn / fe)}_\odot,\ ] ] respectively . the total abundance ratios are then defined as @xmath42_{cor } } = { \rm [ si / fe ] } - \log[x({\rm si}^+)/x({\rm fe}^+)]\ ] ] and @xmath43_{cor } } = { \rm [ zn / fe ] } - \log[x({\rm zn}^+)/x({\rm fe}^+)].\ ] ] we find that both the observed range of @xmath19(al@xmath9 ) / @xmath19(si@xmath8 ) and [ zn / fe ] are consistent with same ionization parameter for the ionizing radiation with @xmath10 = 33000k and 40000k . figure 2 shows that if one applies the correction for ionization effects for the radiation effective temperature of 40000 k , assuming that after correction [ zn / fe]@xmath44 = 0 , the resulting [ si / fe]@xmath44 value remains on average above zero with a small spread of points ( see also fig . 4 ) , and no additional correction for dust depletion is required . however , models with harder radiation with @xmath10 = 45000 k do not reproduce the observed trend . if our approach is correct then we obtain important constraint on the hardness of the ionizing stellar radiation in dlas from figure 2 . note that with the hard intergalactic background radiation field considered by howk & sembach ( 1999 ) the observed [ zn / fe ] vs [ si / fe ] relation can not be reproduced because of their adopted boundary conditions . in this case ( see their fig . 1 ) the correction for ionization of [ zn / fe ] is positive , while that of [ si / fe ] is negative . even if an ionization bounded model with the hard intergalactic background radiation field is considered , the correction for ionization of [ zn / fe ] , though smaller , remains positive . in our case both corrections are negative . in summary , it is possible to reproduce the observed @xmath1(al iii)/@xmath1(si ii ) ratios and the trend seen in [ si / fe ] vs [ zn / fe ] diagram assuming ionization by a moderately hard stellar ionizing radiation field . in principle , no correction for dust depletion needs to be invoked , although it might be present in small amounts and can easily be taken into account in the ionization model without significant changing the main features of the [ si / fe ] vs [ zn / fe ] distribution . additional support of the ionization model comes from fig . 3 where we show the dependence of [ al iii / fe ii ] vs [ zn ii / fe ii ] . models with @xmath10 = 33000k ( dashed line ) and 40000k ( solid line ) fit quite well the observed points from prochaska & wolfe ( 1999 ) and lu et al . ( 1996a ) at the values of ionization parameter @xmath12 close to that obtained from fig . the above conclusion is broadly consistent with expectations for other heavy element abundance ratios . to illustrate this we apply a `` typical '' ionization correction factor to the observational data . to do so we adopt the characteristic correction factors of the model with gas ionized by the radiation with @xmath10 = 40000 k. we consider the metallicity @xmath22 = 0.1 @xmath23 as representative for the sample of dla systems and adopt log @xmath12 = 3.25 . then , our calculations yield the following mean ionization correction factors @xmath45 $ ] defined by @xmath46_{\rm corrected } = \log[{\rm x / h}]_{\rm observed } + \delta \log[{\rm x / h}]$ ] : @xmath47log[al / fe ] = 0.63 , @xmath47log[si / fe ] = 0.31 , @xmath47log[s / fe ] = 0.32 , @xmath47log[ti / fe ] = 0.12 , @xmath47log[cr / fe ] = + 0.16 , @xmath47log[mn / fe ] = 0.01 , @xmath47log[ni / fe ] = 0.38 , @xmath47log[zn / fe ] = 0.40 . note the small corrections for [ ti / fe ] and [ mn / fe ] which remain almost unchanged while the downward correction of [ zn / fe ] is high . interestingly , it is the same as the difference between mean [ fe / h ] and [ zn / h ] values for dlas at @xmath39 @xmath7 2 from prochaska & wolfe ( 2000 ) . the case of nitrogen is discussed separately below . the above `` typical '' correction factors have been applied to the sample of damped ly@xmath0 galaxies from lu et al . ( 1996a ) , prochaska & wolfe ( 1999 ) and pettini et al . ( 2000 ) . only galaxies with definitely derived column densities are included and we do not consider objects with lower or upper limits . the original ( open symbols ) and corrected ( filled symbols ) abundance ratios are shown in fig . 4 . as pointed out earlier , an upward correction of [ fe / h ] must also be applied because of the large column density of neutral hydrogen . however , this correction is uncertain and does not change the relative heavy element abundances . therefore , we simply use [ fe / h ] values derived by lu et al . ( 1996a ) , prochaska & wolfe ( 1999 ) and pettini et al . ( 2000 ) keeping in mind that correction might be up to of the order of + 1 dex . for 4 dlas of the sample the [ fe / h ] are not available . we adopt [ fe / h ] = [ cr / h ] for those systems . for [ ni / fe ] we have applied an additional upward correction which comes from the new measurements of oscillator strengths for ni ii from uv absorption lines ( fedchak & lawler 1999 ) ; older @xmath48-values were used by prochaska & wolfe ( 1999 ) and lu et al . ( 1996a ) . although the correction is different for different ni ii transitions , its mean value is @xmath26 0.3 dex , which we adopt for the sake of simplicity . we now discuss the behaviour of the element ratios of si , zn , s , mn , cr , ni , ti , and al with respect to fe . * silicon , zinc : * the case of si and zn has already been treated before ( sect . 3.3 ) . in short , it can be seen from fig . 4 that the corrected [ zn / fe ] values scatter around zero , while [ si / fe ] remains positive suggesting the production of this element in type ii supernovae . * sulphur : * [ s / fe ] shows the same snii like pattern as [ si / fe ] . we note that if the gas in dla galaxies is ionized by softer stellar radiation with @xmath10 = 33000 k , the downward correction of s / fe abundance ratio is 0.17 dex larger and in this case [ s / fe ] @xmath37 0 , in contradiction with the production of s in type ii supernovae . this difference in s correction factors also favours harder ionization radiation for the low - metallicity dlas as compared to that in the milky way . a new analysis of the s / zn abundance ratio in a sample of dlas was recently presented by centurin et al . they find [ s / zn ] @xmath37 0 in dlas with [ zn / h ] @xmath2 1.0 . both s and zn are not depleted into the dust grains and the correction for dust depletion does not change s / zn ratio . centurin et al . ( 2000 ) thus conclude that such unusual abundance ratios suggest that the dla galaxies are objects with low star formation rates such as low surface brightness galaxies or dwarf galaxies . based on our model , the correction for the ionization results in the increase of both [ s / zn ] ( table 1 ) and [ zn / h ] and in better agreement with [ s / fe ] for halo stars . if instead the model with the hard background intergalactic radiation is adopted , the correction of [ s / zn ] is negative and it increases the difference between [ s / zn ] in dlas and [ s / fe ] in halo stars . * manganese , chromium : * [ mn / fe ] remains nearly unchanged because of small correction factor for this ratio . the cr / fe ratio is overabundant by @xmath26 0.2 dex with respect to the solar value , which seems to be in contradiction with the stellar data . this may constitute a difficulty for our model . uncertainties in oscillator strengths for cr ii transitions are better than 10% ( bergeson & lawler ( 1993 ) . however uncertainties in the ionization and recombination cross - sections should be examined . adopting a higher effective temperature decreases the overabundance of cr relative to fe , as can be seen from table 1 . the mn / fe ratio remains underabundant supporting the origin of this odd - element in type ii supernovae . * nickel : * note that [ ni / fe ] calculated with the new oscillator strengths before the ionization correction ( open circles ) are already above zero . this poses a problem in the explanation of [ ni / fe ] when dust depletion is taken into account , since this correction shifts the points upward . although a large negative correction of 0.38 is predicted for [ ni / fe ] in the ionization model , it is almostly compensated by the upward shift of points introduced by the new oscillator strengths by fedchak & lawler ( 1999 ) . the points in [ ni / fe ] vs [ fe / h ] diagram scatter around the mean [ ni / fe ] value of 0.2 . * titanium : * prochaska & wolfe ( 1999 ) pointed out problems in explaining the ti / fe abundance ratio in the `` dust depletion '' model , since ti is expected to be more heavily incorporated into dust grains . hence , the correction for depletion shifts observed [ ti / fe ] to larger values . in our model , the correction of [ ti / fe ] for ionization effects is negative and small . therefore , its application to prochaska & wolfe ( 1999 ) data leaves ti moderately overabundant relative to iron ( filled squares in fig . 4 ) , in agreement with that observed in galactic halo stars . * aluminium : * our model predicts the largest downward correction factor of 0.63 dex for al / fe abundance ratio . in the prochaska & wolfe ( 1999 ) sample the [ al / fe ] scatter around zero value . this is likely at variance with what is observed in lowest - metallicity halo stars where [ al / fe ] scatters below zero with mean value of @xmath26 0.4 ( ryan et al . 1996 ; timmes et al . 1995 ; samland 1998 ) . our correction eliminates this difference and suggests that the odd - element al seen in damped ly@xmath0 galaxies is likely also produced by type ii supernovae . if instead the hard intergalactic ionization radiation is applied , the correction of [ al / fe ] is @xmath26 + 0.1 and shifts points upward in the direction opposite to the nucleosynthetic predictions . overall , we find that in the framework of our simplified model of photoionized gas and despite the uncertainties in the atomic data , the abundances in dla systems reproduce quite well observed halo star abundance patterns and lead to a consistent picture . several problems pertaining to neutral dla models are thus eliminated . in the new model , there is no need to take depletion of heavy elements into dust grains into account , although small depletion of heavy elements might be present . in the framework of the proposed model the abundance ratios of neutral and singly ionized species n i / o i , si ii/ s ii , mn ii / fe ii ( table 1 ) depend only weakly on ionization effects and can be used as a good measure of the total abundance ratios . we now turn to a discussion of the nitrogen abundance , which is of particular interest since it is one of the elements observable both in metal - poor hii regions and dlas , and because its primary and/or secondary origin remains debated ( see e.g. henry , edmunds & kppen 2000 ) . the heavy element abundance patterns seen in dla galaxies show several similarities with those found in local blue compact dwarf galaxies . izotov & thuan ( 1999 ) , based on the large sample of low - metallicity bcds , have demonstrated that all elements of @xmath0 process are overabundant relative to iron and hence they are produced in type ii supernovae . in this respect the n / o ratios seem , at first glance , to constitute the major difference . the n / o ratios in damped ly@xmath0 systems appear to be significantly lower than those measured in low - metallicity bcds ( cf . fig . 5 ) . for the most metal deficient of these objects with [ o / h ] @xmath28 1.3 thuan , izotov & lipovetsky ( 1995 ) and izotov & thuan ( 1999 ) have derived a mean value of log n / o = 1.60 with a very small dispersion . they argue that this value constitutes a lower limit to log n / o in bcds , which is set by primary n production in massive stars . pettini , lipman & hunstead ( 1995 ) have found an upper limit log n / o @xmath28 1.9 in one damped ly@xmath0 system , 0.3 dex below the value of izotov & thuan . however , within the errors the log n / o value derived by pettini et al . ( 1995 ) is still consistent with the mean value for bcds . furthermore , lu , sargent & barlow ( 1998 ) have compiled n / si abundance ratios in 15 damped ly@xmath0 galaxies , and have set upper limits for log n / o ranging from from 1.2 to 2.1 . whereas all these measurements constitute upper limits , an actual value of [ n / si ] = 1.70 has been derived in one system , 1946 + 7658 , by lu et al . ( 1998 ) . from these dla measurements of n / o and n / si , pettini et al . ( 1995 ) conclude that both primary and secondary nitrogen production are important over the whole range of metallicity measured in damped ly@xmath0 systems , while lu et al . ( 1998 ) favor the time - delayed primary nitrogen production by intermediate - mass stars . can these different scenarios be reconciled ? how well are these differences established , especially in view of the possible ionization corrections discussed above for other elements detected in dla systems ? indeed if our model holds , ionization effects are also important for the n / si abundance ratio . the inspection of table 1 and figure 1 shows that correction factors for the observed @xmath1(n@xmath18)/@xmath1(si@xmath8 ) ratio increase with increasing @xmath12 . for the typical value log @xmath12 = 3.25 adopted for the above analysis of other heavy element abundance ratios ( cf . 4 ) we find @xmath47log[@xmath19(n@xmath18)/@xmath19(si@xmath8 ) ] = 0.72.log[@xmath19(n@xmath18)/@xmath19(si@xmath8 ) ] is significantly larger ( 1.48 dex ) because of the assumption of density - bounded h ii region in their case . ] the observations of n / o in bcds ( izotov & thuan 1999 , filled circles ) and the dla data from lu et al . ( 1998 ) and outram et al . ( 1999 ) ( open circles ) assuming neutral systems are plotted in figure 5 . overplotted for illustration is the contribution of primary and secondary nitrogen production as well as the combined production by both mechanisms . the `` typical '' ionization correction for n / si and si / h is shown by the arrow in the lower left corner of figure 5 . taking into account such a correction , the vast majority of measurements for dlas are found at or above the n / o value from the bcds . this suggests that a significant part of the difference in [ n / si ] can be explained by ionization effects . the typical correction brings even the lowest value of [ n / si ] @xmath26 1.7 , measured in the @xmath36 = 2.8448 damped ly@xmath0 system toward q1946 + 7658 , to [ n / si ] @xmath26 0.98 after correction for ionization , fairly close to the [ n / o ] values for the bcds . the open square in fig . 5 shows the n / o abundance ratio derived recently by molaro et al . ( 2000 ) in a dla with @xmath49 = 3.3901 from the unsaturated o i and n i absorption lines . potentially , the n / o abundance ratio derived directly from n i and o i ( instead of using si as a proxy ) is the least model - dependent . also it has the advantage of being very little dependent on the correction for ionization ( see table 1 ) . most interestingly , the n / o value of molaro et al . ( 2000 ) is in very good agreement with n / o derived in the low - metallicity bcds . in any case , if the typical ionization corrections derived from our model apply , we have to conclude that the bulk of the present data does not show a significant difference in n / o abundance ratios between low - metallicity bcds and dla systems implying similar origin of these two elements . we shall now briefly summarise recent progress in stellar models regarding the nucleosynthetic origin of nitrogen . interestingly both intermediate - mass and massive stars are found to be potential producers of primary @xmath50n in the most recent stellar models . intermediate mass stars ( @xmath51 3.5 @xmath52 ) produce primary nitrogen when the cn cycle operates in their convective envelope during the agb phase ( e.g. renzini & voli 1981 ) . this production results from the combined effect of the 3rd dredge - up and envelope burning , and thus varies both with stellar mass and metallicity ( e.g. forestini & charbonnel ( 1997 ) and references therein ) . it is also highly dependent on the parameters which intervene in the description of agb stars . among them , the mixing length and the dredge - up parameters which are empirically calibrated to reproduce peculiar observed properties of different agb populations ( in particular the observed luminosity function of carbon stars in the lmc and smc ) , and which influence the efficiency of the burning inside the envelope . in addition , the mass loss prescription which remains uncertain ( e.g. vassiliadis & wood 1993 ) has a crucial impact on the theoretical nucleosynthesis by controlling the number of thermal pulses undergone by the agb star and the duration of the envelope burning . the most recent models find a @xmath50n production similar to that of renzini & voli ( 1981 , @xmath53 case with the largest n production ) at [ o / h ] @xmath26 0.7 but which decreases with increasing metallicity ( see marigo 1998 ; marigo et al . 1998 ; lattanzio , forestini & charbonnel 1999 ) . intermediate mass stars are thus potential primary @xmath50n producers . however , no calculations are yet available in the metallicity range of interest for our study . the behaviour at [ o / h ] @xmath37 0.7 remains to be investigated . regarding massive stars it is well known that standard stellar evolution models do not produce primary nitrogen ( e.g. woosley & weaver 1995 ) . however , considerable advances have been made recently to include rotation and its effects on the transport of elements and angular momentum in the description of stellar interiors and evolution ( see review of maeder & meynet 2000 ) . the corresponding new models for massive stars , which solve a number of difficulties encountered by `` standard '' models ( cf . maeder 1995 ) , also produce primary nitrogen ( maeder 1999 ; langer et al . in particular the models of maeder ( 1999 ) reproduce well the n excess in smc supergiants found by venn ( 1999 ) , and suggest that these stars could be responsible for primary n production at early epochs . increasing rotational velocities found at low o / h ( maeder , grebel & mermilliod 1999 ) could favor the primary n production in metal - poor environments . quantitative yields from these new stellar models have still to be awaited . last , but not least , such new yields from intermediate and massive stars will be included in chemical evolution models to fully exploit all the observational constraints regarding n and other elements . this should hopefully solve the question on the origin of primary n. independently of the outcome , the conclusion from our work is that in the light of possible ionization corrections for dlas one can not presently exclude the same primary origin of n in both dlas and nearby metal - poor galaxies .

we calculate photoionization equilibrium models for region 1 , and constrain the ionization parameter by the observed(al iii)/(si ii ) column density ratio . under these conditions . in particular we can not exclude the same primary n origin in both dlas and metal - poor galaxies . no depletion of heavy elements on dust grains needs to be invoked , although our models do not exclude the presence of little depletion .

the similarity between observed velocity structures of al iii and singly ionized species in damped ly systems ( dlas ) suggests the presence of ionized gas in the regions where most metal absorption lines are formed . a simplified model consisting of _ region 1 ) _ a plane - parallel ionization bounded region illuminated by an internal radiation field , and _ region 2 ) _ a neutral region with a negligible metal content is considered . we calculate photoionization equilibrium models for region 1 , and constrain the ionization parameter by the observed(al iii)/(si ii ) column density ratio . under these conditions we find that ionization effects are important . if these effects are taken into account , the element abundance ratios in dlas are quite consistent with those observed in milky way stars and in h ii regions of local low - metallicity blue compact dwarf galaxies . in particular we can not exclude the same primary n origin in both dlas and metal - poor galaxies . no depletion of heavy elements on dust grains needs to be invoked , although our models do not exclude the presence of little depletion . although highly simplified and relying on the strong assumption of a significantly lower metal content in region 2 , our model appears to be supported by recent data on a local dla and it is not in contradiction with the current knowledge on high redshift dlas . if correct , it offers a clear simplification in the understanding of heavy element abundance ratios in dlas and their comparison with the local universe . = cmr10 scaled 1000 _ accepted for publication in apj ( scheduled in march 10 , 2001 , issue ) _

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the above analysis shows the importance of consideration of the ionization effects in the dlas element abundance studies which was pointed out earlier by prochaska & wolfe ( 1999 ) , howk & sembach ( 1999 ) and izotov & thuan ( 1999 ) . however , at variance with many previous studies assuming that the heavy element absorption lines in dla galaxies are formed in the neutral gas , we consider the following simplified `` multi - component '' picture for dla systems : _ region 1 ) _ a plane - parallel ionization bounded region illuminated by an internal radiation field complemented by _ region 2 ) _ , a neutral region with a lower metal content . interestingly it appears that the structure of at least some dla systems might be similar to that observed in nearby low - metallicity blue compact dwarf galaxies . for example , the bcd galaxy sbs 0335052 showing supergiant h ii regions over a region of @xmath26 7 kpc with ongoing star formation embedded in much larger clouds of neutral gas with a column density @xmath1(h i ) as high as 7@xmath310@xmath54 @xmath5 , can be considered as a local damped ly@xmath0 system ( e.g. , thuan & izotov 1997 ) . another interesting parallel is the most metal - poor bcd galaxy i zw 18 , which shows a high hydrogen column density @xmath1(h i ) @xmath7 3.5@xmath310@xmath54 @xmath5 ( kunth et al . 1994 ) thus also qualifying as a local dla system , and for which recent _ fuse _ spectroscopic observations were obtained by vidal - madjar et al . in contrast with high - redshift dlas the structure of i zw 18 is known better . it consists of two central regions of active star formation ionizing the ambient gas . radio observations and the presence of strong ly@xmath0 absorption line indicate that the h ii region is embedded in the outer h i cloud . measurements of the column densities of n i , si ii , ar i and fe ii derived from the _ fuse _ spectrum of i zw 18 were kindly made available to us by alfred vidal - madjar ( 2000 , private communication ) . it is striking that the column density ratios given in table 2 ( column 2 ) are very different from those observed in the h ii regions ( nw and se components ) of i zw 18 and other low - metallicity bcds also given in the table 2 . we suspect that such large differences are due to ionization effects . to analyse the influence of the ionization on the observed column densities we consider a spherically - symmetric ionization - bounded h ii region model with the parameters derived from the observations ( see e.g. hunter & thronson 1995 ; de mello et al . 1998 ) . in particular , the heavy element mass fraction in h ii region is adopted to be 1/50 @xmath23 , while for the neutral gas we assume zero metallicity . the results of the calculations are shown in table 2 , where the observed ratio from _ fuse _ ( col . 2 ) and the ionization corrected column density ratio ( col . 3 ) are given . note the good agreement with the abundance ratios derived from the _ hst _ and ground - based observations of i zw 18 and other bcds , while solar ratios do not match corrected ratios . to obtain the total hydrogen column density a large amount of gas must now be added to that of the ionized gas ( cf . table 2 ) . however , since the heavy element ratios are already close to the observed values from the h ii regions in bcds , there is little room for additional metals in the neutral phase . hence , this analysis provides some support in favor of the basic assumption of our model that neutral gas in dlas systems might be more metal - poor as compared to the ionized gas . \1 . using the observed @xmath1(al iii)/@xmath1(si ii ) column density ratio to constrain the ionization parameter @xmath12 , one obtains almost complete ionization of hydrogen in regions with a column density @xmath1(h@xmath18+h@xmath8 ) @xmath26 10@xmath4 @xmath5 ( region 1 ) , several times smaller than the observed hi column in dla systems . in the ionized region fe is mainly in the fe@xmath9 form . both effects imply that the true fe / h abundance in the ionized gas must be larger ( by up to one order of magnitude ) than that derived from the @xmath1(fe ii)/@xmath1(h i ) ratio . compared to [ fe / h ] derived from a neutral dla model , such ionized systems have an age - metallicity relation in better agreement with that of the thick disk of the milky way . however , in general , due to the assumption of a significant metal - deficiency in the neutral region ( 2 ) , abundance ratios with respect to hydrogen are a priori not meaningful when the total absorbing column is taken into account . accounting for ionization effects improves the agreement between dlas and milky way stellar thick disk measurements . although not excluded , no significant depletion of elements by dust grains is required . the majority of heavy element abundance ratios are brought into agreement with those expected from the production by type ii supernovae . the apparent difference between [ n / o ] derived in local blue compact dwarf galaxies and [ n / si ] derived in dla systems can be fairly well explained by ionization effects in the latter . thus one can not currently exclude the same primary n origin in both dlas and metal - poor galaxies . the main sources of uncertainties potentially affecting our results are : poor atomic data ( oscillator strengths , recombination coefficients etc . for the photoionization models , affecting e.g. zn , cr , and ni ) , the unknown structure and geometry of the absorbing systems , the spatial distribution of ionizing sources and their radiation field , and uncertainties related to the measurement of column densities . future investigations should hopefully be able to improve on these issues and to assess the validity of our picture . for example , quantitative studies of the line profile structure of different ions , and detailed ionization properties of individual systems and large samples , should be extremely useful . it is the hope that the proposed simplified model reflects the main trends due to ionization effects in dlas . if correct , our picture of dla systems partly ionized by internal radiation offers a clear simplification in the understanding of heavy element abundance ratios in dlas and their comparison with the local universe . thanks the staff of the observatoire midi - pyrnes for their kind hospitality , and acknowledges an invitation by the universit paul sabatier in toulouse . alfred vidal - madjar kindly provided us with results of _ fuse _ observations . we thank richard f. green and an anonymous referee for useful comments on this paper . this international collaboration was possible thanks to the partial financial support of intas grant no . 97 - 0033 for which y.i.i . and d.s . are grateful . y.i.i . acknowledges the partial financial support of the joint research project between eastern europe and switzerland ( scope ) no . 7ukpj62178 . anders , s. , & grevesse , n. 1989 , geochim . acta , 53 , 197 bergeson , s. d. , & lawler , j. e. 1993 , , 408 , 382 centurin , m. , bonifacio , p. , molaro , p. , & vladilo , g. 2000 , , 536 , 540 de mello , d. f. , schaerer , d. , heldmann , j. , & leitherer , c. 1998 , , 507 , 199 fedchak , j. a. , & lawler , j. e. 1999 , , 523 , 734 ferland , g. j. 1996 , hazy , a brief introduction to cloudy 90 ( university of kentucky , department of physics and astronomy , internal report ) ferland , g. j. , korista , k. t. , verner , d. a. , ferguson , j. w. , kingdon , j. b. , & verner , e. m. 1998 , , 110 , 761 forestini , m. , & charbonnel , c. 1997 , , 123 , 241 henry , r. b. c. , edmunds , m. g. , & kppen , j. 2000 , , 541 , 660 howk , j. c. , & sembach , k. r. 1999 , , 523 , l141 howk , j. c. , savage , b. d. , & fabian , d. 1999 , , 525 , 253 hunter , d. a. , & thronson , h. a. , jr . 1995 , , 452 , 238 izotov , y. i. , chaffee , f. h. , foltz , c. b. , green , r. f. , guseva , n. g. , & thuan , t. x. 1999 , , 525 , 757 izotov , y. i. , & thuan , t. x. 1998 , , 500 , 188 . 1999 , , 511 , 639 jenkins , e. b. , oegerle , w. r. , gry , c. , vallerga , j. , sembach , k. r. , shelton , r. l. , ferlet , r. , vidal - madjar , a. , york , d. g. , linsky , j. l. , roth , k. c. , dupree , a. k. , & edelstein , j. 2000 , , 538 , l81 kunth , d. , lequeux , j. , sargent , w. l. w. , & viallefond , f. 1994 , , 282 , 709 kurucz , r. l. 1991 , in proc . workshop on precision photometry : astrophysics of the galaxy , ed . a. c. davis philip , a. r. upgren , & k. a. james ( schenectady : davis ) , 27 lanzetta , k. m. , wolfe , a. m. , & turnshek , d. a. 1995 , , 440 , 435 lattanzio , j. , forestini , m. , & charbonnel , c. , 1999 , in international workshop on `` the changes in abundances in agb stars '' , monteporzio , in press ( astro - ph/9912298 ) lauroesch , j. t. , truran , j. w. , welty , d. e. , & york , d. g. 1996 , , 108 , 641 le brun , v. , bergeron , g. , boiss , p. , & deharveng , j. m. 1997 , , 321 , 733 lindner , u. , fritze - von alvensleben , u. , & fricke , k. j. 1999 , , 341 , 709 lu , l. , sargent , w. l. w. , & barlow , t. a. 1998 , , 115 , 55 lu , l. , sargent , w. l. w. , barlow , t. a. , churchill , c. w. , & vogt , s. s. 1996a , , 107 , 475 lu , l. , sargent , w. l. w. , womble , d. s. , & barlow , t. a. 1996b , , 457 , l1 maeder , a. 1995 , in astrophysical applications of stellar pulsation , ed . stobie , p.a . whitelock , asp conf . series , 83 , 1 maeder , a. 1999 , in wolf - rayet phenomena in massive stars and starburst galaxies , ed . k. a. van der hucht , g. koenigsberger , & p. r. j. eenens ( sheridan books : michigan ) , 177 maeder , a. , & meynet , g. 2000 , , in press maeder , a. , grebel , e. k. , & mermilliod , j .- c . 1999 , , 346 , 459 marigo , p. 1998 , phd thesis , universita de padova marigo , p. , bressan , a. , & chiosi , c. 1998 , , 331 , 564 molaro , p. , bonifacio , p. , centurin , m. , dodorico , s. , vladilo , g. , santin , p. , & di marcantonio , p. 2000 , , 541 , 54 outram , p. j. , chaffee , f. h. , & carswell , r. f. 1999 , , 310 , 289 pettini , m. , ellison , s. l. , steidel , c. c. , & bowen , d. v. 1999 , , 510 , 576 pettini , m. , ellison , s. l. , steidel , c. c. , shapley , a. e. , & bowen , d. v. 2000 , , 532 , 65 pettini , m. , king , d. l. , smith , l. j. , & hunstead , r. w. 1997 , , 478 , 536 pettini , m. , lipman , k. , & hunstead , r. w. 1995 , , 451 , 100 pettini , m. , smith , l. j. , hunstead , r. w. , & king , d. l. 1994 , , 426 , 79 prantzos , n. , & boissier , s. 2000 , , 315 , 82 prochaska , j. , & wolfe , a. m. 1996 , , 470 , 403 . 1999 , , 121 , 369 . 2000 , , 533 , l5 renzini , a. , & voli , m. 1981 , , 94 , 175 ryan , s. g. , norris , j. e. , & beers , t. c. 1996 , , 471 , 254 samland , m. 1998 , , 496 , 155 sembach , k. r. , howk , j. c. , ryans , r. s. i. , & keenan , f. p. 2000 , , 528 , 310 stasiska , g. , & leitherer , c. 1996 , 107 , 661 thuan , t. x. , & izotov , y. i. 1997 , , 489 , 623 thuan , t. x. , izotov , y. i. , & lipovetsky , v. a. 1995 , , 445 , 108 timmes , f. x. , woosley , s. e. , & weaver , t. a. 1995 , , 98 , 617 vassiliadis , e. , & wood , p. r. 1993 , , 413 , 641 venn , k. a. 1999 , , 518 , 405 vidal - madjar , a. 2000 , private communication vidal - madjar , a. , kunth , d. , lecavelier des etangs , a. , lequeux , j. , andr , m. , benjaffel , l. , ferlet , r. , hbrard , g. , howk , j. c. , kruk , j. w. , lemoine , m. , moos , h. w. , roth , k. c. , sonneborn , g. , & york , d. g. 2000 , , 538 , l77 viegas , s. m. 1995 , , 276 , 268 vladilo , g. 1998 , , 493 , 583 wolfe , a. m. 1990 , in the interstellar medium in galaxies , ed . h. a. thronson & j. m. shull ( dordrecht : kluwer ) , 387 wolfe , a. m. , lanzetta , k. m. , foltz , c. b. , & chaffee , f. h. 1995 , , 454 , 698 wolfe , a. m. , & prochaska , j. x. 2000 , , in press ( preprint astro - ph/0009081 ) woosley , s. e. , & weaver , t. a. 1995 , , 101 , 181 lcccccc @xmath1(h ) , @xmath5 & 2.1@xmath310@xmath54&7.7@xmath310@xmath55&&&&@xmath56 , mpc & & 10&&&&log @xmath57 , s@xmath40 & & 51.6&&&&log @xmath58 , cm&&20.08&&&&@xmath10 , k&&50000&&&&@xmath1 , cm@xmath27&&100&&&&@xmath48&&0.1&&&&log n / si & 0.77&0.14&&0.09@xmath350.23&0.10@xmath350.06&@xmath60 log ar / si & 1.32&0.57&0.61@xmath350.22&0.74@xmath350.22&0.72@xmath350.09&@xmath61 log fe / si & 0.77&0.42&&0.32@xmath350.24&0.24@xmath350.12&@xmath62

the similarity between observed velocity structures of al iii and singly ionized species in damped ly systems ( dlas ) suggests the presence of ionized gas in the regions where most metal absorption lines are formed . a simplified model consisting of _ region 1 ) _ a plane - parallel ionization bounded region illuminated by an internal radiation field , and _ region 2 ) _ a neutral region with a negligible metal content is considered . we find that ionization effects are important . if these effects are taken into account , the element abundance ratios in dlas are quite consistent with those observed in milky way stars and in h ii regions of local low - metallicity blue compact dwarf galaxies although highly simplified and relying on the strong assumption of a significantly lower metal content in region 2 , our model appears to be supported by recent data on a local dla and it is not in contradiction with the current knowledge on high redshift dlas . if correct , it offers a clear simplification in the understanding of heavy element abundance ratios in dlas and their comparison with the local universe .

the similarity between observed velocity structures of al iii and singly ionized species in damped ly systems ( dlas ) suggests the presence of ionized gas in the regions where most metal absorption lines are formed . a simplified model consisting of _ region 1 ) _ a plane - parallel ionization bounded region illuminated by an internal radiation field , and _ region 2 ) _ a neutral region with a negligible metal content is considered . we calculate photoionization equilibrium models for region 1 , and constrain the ionization parameter by the observed(al iii)/(si ii ) column density ratio . under these conditions we find that ionization effects are important . if these effects are taken into account , the element abundance ratios in dlas are quite consistent with those observed in milky way stars and in h ii regions of local low - metallicity blue compact dwarf galaxies . in particular we can not exclude the same primary n origin in both dlas and metal - poor galaxies . no depletion of heavy elements on dust grains needs to be invoked , although our models do not exclude the presence of little depletion . although highly simplified and relying on the strong assumption of a significantly lower metal content in region 2 , our model appears to be supported by recent data on a local dla and it is not in contradiction with the current knowledge on high redshift dlas . if correct , it offers a clear simplification in the understanding of heavy element abundance ratios in dlas and their comparison with the local universe . = cmr10 scaled 1000 _ accepted for publication in apj ( scheduled in march 10 , 2001 , issue ) _

astro-ph0511283

c

the cbi observations of ldn 1622 resulted in the first cm - wave continuum image of a dark cloud , at frequencies where traditional emission from dust is not expected . the cbi data follow a tight correlation with the far - ir emission , confirming that the 31 ghz emission is nonetheless related to dust . under visual inspection the 31 ghz map is closer to the _ iras _ 12 @xmath1 m and _ iras _ 25 @xmath1 m maps than to the _ iras _ 100 @xmath1 m map . to quantify the ir radio similarities we calculate the cross - correlation of the 31 ghz images with each of the _ iras _ images . we find a trend for a decreasing cross - correlation with wavelength , such that the 31 ghz12 @xmath1 m comparison has the highest cross - correlation . the mid - ir cm - wave correlation in ldn 1622 indicates that the cm - wave continuum emission arises in a shell coincident with the pdr at the surface of ldn 1622 exposed to the ori ob 1b uv field . the closer match between the 31 ghz and 12 @xmath1 m images can be interpreted as support for spinning dust . alternatively the 31 ghz continuum may stem from a mechanism of molecular continuum emission at 31 ghz or a dense molecular forest spread over 2636 ghz . we suspect the reason why the mid - ir cm - wave correlation was not previously detected in other objects , or in the diffuse ism , is because the _ iras _ 12@xmath1 m maps are contaminated by many more point sources than the _ iras _ 100 @xmath1 m maps . the stellar emission at mid - ir wavelengths has no counterpart in cm - waves , as shown here in the case of ldn 1622 . the 10 cbi channels allow estimating a spectral index @xmath101 . combining all measurements we obtain @xmath129 . this article benefitted from the constructive comments of an anonymous referee that motivated sec . [ sec : sed ] , the discussion on unresolved radiosources , fig . [ fig : ysosed ] and its discussion in appendix c. s.c . acknowledges support from fondecyt grant 1030805 , and from the chilean center for astrophysics fondap 15010003 . we gratefully acknowledge the generous support of maxine and ronald linde , cecil and sally drinkward , barbara and stanely rawn , jr . , fred kavli , and rochus vogt . this work is supported by the national science foundation under grant ast 00 - 98734 . we acknowledge the use of nasa s _ skyview _ facility ( http://skyview.gsfc.nasa.gov ) located at nasa goddard space flight center .

ldn 1622 is conspicuous in the 31 ghz image we obtained with the cosmic background imager , which is the first cm - wave resolved image of a dark cloud . the mid - ir cm - wave correlation in ldn 1622 is evidence for very small grain ( vsg ) or continuum emission at 2636 ghz from a hot molecular phase . in dark clouds and their photon - dominated regions ( pdrs ) the mid - ir and cm - wave dust emissions arise in a limb - brightened shell coincident with the pdr of ldn 1622 , where the incident uv radiation from the ori ob 1b association heats and charges the grains , as required for spinning dust .

the spectral energy distribution of the dark cloud ldn 1622 , as measured by finkbeiner using _ wmap _ data , drops above 30 ghz and is suggestive of a boltzmann cutoff in grain rotation frequencies , characteristic of spinning dust emission . ldn 1622 is conspicuous in the 31 ghz image we obtained with the cosmic background imager , which is the first cm - wave resolved image of a dark cloud . the 31 ghz emission follows the emission traced by the four _ iras _ bands . the normalised cross - correlation of the 31 ghz image with the _ iras _ images is higher by 6.6 for the 12 m and 25 m bands than for the 60 m and 100 m bands : and . the mid - ir cm - wave correlation in ldn 1622 is evidence for very small grain ( vsg ) or continuum emission at 2636 ghz from a hot molecular phase . in dark clouds and their photon - dominated regions ( pdrs ) the 12 m and 25 m emission is attributed to stochastic heating of the vsgs . the mid - ir and cm - wave dust emissions arise in a limb - brightened shell coincident with the pdr of ldn 1622 , where the incident uv radiation from the ori ob 1b association heats and charges the grains , as required for spinning dust .

gr-qc0406038

i

stellar mass compact binaries consisting of double neutron stars ( ns ) , double black holes ( bh ) or a mixed binary consisting of a neutron star and a black hole , are the primary targets for a direct first detection of gravitational waves ( gw ) by interferometric detectors , ligo @xcite , virgo @xcite , geo600 @xcite , and tama @xcite . under radiation reaction the orbit of a binary slowly decays , emitting a signal whose amplitude and frequency increases with time and is termed a `` chirp '' signal . while it is believed that there is a greater population of ns - ns binaries @xcite , it is the bh - bh binaries that are the strongest candidates for detection since they can be seen from a greater volume , about two orders - of - magnitude greater than ns - ns binaries @xcite . in order to detect such sources one employs the method of matched filtering @xcite . briefly , the method works as follows : firstly , one creates a set of waveforms , or templates as they are called , that depend on a number of parameters of the source and its location and orientation relative to the detector . these templates are then cross - correlated with the detector output weighted by the inverse of the noise spectral density . if a signal , whose parameters are close to one of the template waveforms , is actually present in the detector output then the cross - correlation builds up , with the dominant contribution coming from frequencies where the noise spectral density is low . thus , in the presence of a sufficiently strong signal the correlation will be much larger than the rms correlation in the absence of any signal . how large should it be before we can be confident about the presence of a signal depends on the combination of the rate of inspiral events and the false alarm probability ( see e.g. ref . @xcite for a simple estimation ) . the effectiveness of matched filtering depends on how well the phase evolution of the waveform is known . even tiny instantaneous differences , as low as one part in @xmath10 in the phase of the true signal that might be present in the detector output and the template that is used to dig it out could lead to a cumulative difference of several radians since one integrates over several hundreds to several thousands of cycles . in view of improving the signal - to - noise ratio for inspiral events there has been a world - wide effort in accurately computing the dynamics of a compact binary and the waveform it emits or to use phenomenologically defined detection template families @xcite . there have been parallel efforts on using two different approximation schemes : on the one hand the post - newtonian ( pn ) expansion of einstein s equations has been used to treat the dynamics of two bodies of comparable masses with and without spin , in orbit around each other . this approximation is applicable when the velocities involved in the system are small but there is no restriction on the ratio of the masses @xcite . on the other hand , black hole perturbation theory has been used to compute the dynamics of a test particle in orbit around a spin - less or spinning black hole . black hole perturbation theory does not make any assumptions on the velocity of the components , but is valid only in the limit when the mass of one of the bodies is much less than the other @xcite . the post - newtonian approximation is a perturbative method which expands the equations of motion , binding energy and gw flux as a power series in @xmath11 , where @xmath12 is a typical velocity in the system and @xmath13 is the speed of light . in the early stages of an inspiral , the radiation reaction time - scale @xmath14 where @xmath15 is the angular velocity and @xmath16 its time - derivative , is much greater than the orbital time - scale @xmath17 . it is during this adiabatic regime that the post - newtonian approximation works best . at present , the pn expansion for the case of comparable - masses is known to order @xmath18 @xcite and @xmath19 @xcite , for the energy and flux functions , respectively . however , at this order an arbitrary parameter exists in the expression for the flux . in order to see how well pn theory performs , we can compare two different systems . if we assume a ns - ns binary of masses ( 1.4,1.4 ) @xmath20 and a lower frequency cutoff of the detector at 40 hz , then the orbital velocity " of the binary is small , @xmath21 , ] when it enters the detector bandwidth and the two stars are still largely separated , @xmath22 . the ratio of time - scales in the most sensitive regime of the detector is in the range @xmath23 . if on the other hand we take a bh - bh binary of masses ( 10,10)@xmath20 , the orbital velocity is quite large , @xmath24 and the separation is quite small , @xmath25 upon entering the detector bandwidth . this is very close to the regime , @xmath26 , @xmath27 , where the background curvature becomes strong and the motion relativistic . once again , comparing time - scales , we obtain @xmath28 , where the final value is taken at the last stable orbit at @xmath29 hz . it is known that pn theory becomes inaccurate at an orbital separation of @xmath30 @xcite . therefore , post - newtonian approximation becomes less valid for higher mass systems in the ligo band but well describes the early stages of the inspiral of a ns - ns system visible in ligo . as previously stated , black hole perturbation theory makes no assumptions about the orbital velocity of the components , but does restrict their masses . one assumes that a test particle of mass @xmath31 is in orbit about a central bh of mass @xmath32 such that @xmath33 . assuming this restriction is satisfied we have an analytical expression for the energy . however , no analytical expression has been worked out for the gravitational wave flux emitted by such a system . using black hole perturbation theory , a series approximation was initially calculated to @xmath34 by poisson for a test particle in circular orbit around a schwarzschild black hole @xcite . the series was extended numerically to @xmath35 by cutler et al . @xcite , and then to @xmath36 by tagoshi and nakamura @xcite and confirmed analytically by tagoshi and sasaki @xcite . the most recent progress is an extension of the series to @xmath37 by tagoshi , tanaka and sasaki @xcite . for a test particle in circular orbit about a kerr black hole , the initial progress was again made by poisson @xcite . the series approximation was improved from @xmath38 to @xmath35 , and subsequently to @xmath39 by tagoshi , tanaka , shibata and sasaki @xcite . several authors @xcite have shown that the convergence of both post - newtonian approximation and black hole perturbation theory is too slow to be useful in constructing accurate templates . more recently , damour , iyer and sathyaprakash ( hereafter dis ) showed for the case of a test - mass in orbit about a schwarzschild bh , that by using properly defined energy and flux functions that have better analytical properties , combined with pad techniques , it was possible to take the existing series expansion and improve its convergence properties @xcite . the new approximation in which pad approximants of new energy and flux functions are used to derive improved templates is called p - approximant . using a fiducially defined `` exact '' waveform , it was shown that the p - approximant templates were both more _ effectual _ ( i.e. larger overlaps with the exact waveform ) and _ faithful _ ( i.e. larger overlaps with the exact waveform and lower biases in the estimation of parameters ) than the corresponding post - newtonian ( hereafter t - approximant ) templates . while in general , more templates are needed for p - approximant templates to cover the same volume of parameter space @xcite , the extra computational cost is preferred for the increased performance in p - approximants . the failure of the pn expansion to converge sufficiently quickly in the case of a test particle orbiting a schwarzschild bh @xcite does not bode well for the modelling of even a test particle inspiralling into a kerr bh . another motivation for this work is that at present there is effort to use _ effective one body _ ( eob ) waveforms @xcite to detect the inspiral and merger signals from two comparable - mass kerr bhs in gw data . as the eob waveforms are based partially on p - approximants , any development and concretization of the benefits of p - approximant templates will boost our confidence in using these improved waveforms as detection templates . in this paper we will extend the p - approximant technique to the case of a test particle orbiting a kerr black hole . the reason for focusing on test - mass systems is that we can use the exact numerical fluxes @xcite from black hole perturbation theory with which to compare our results and thereby reliably demonstrate the usefulness of the technique . we begin in sec . [ sec : waveform ] with a summary of the matched filtering and the signal - to - noise ratio achieved by the first generation of geo , ligo and virgo interferometers for spinning black hole binaries . we then go on to discuss in sec . [ sec : energyandflux ] the current state - of - the - art in our understanding of the evolution of a test particle in orbit around a kerr black hole . in particular , we shall discuss the time - evolution of the orbital energy and gravitational wave flux as a function of the spin of the central black hole at various post - newtonian orders , and the locations of the last stable and unstable circular orbits . we shall see that the post - newtonian expansion of the flux does not show a regular behaviour as we move from low to high orders in the post - newtonian expansion , becoming worse for more rapidly spinning black holes . in order to improve the convergence properties of the flux function , in sec . [ sec : fluxmodel ] we shall introduce a modified form of the flux function and its pad approximant . we shall demonstrate in sec . [ sec : results ] the improved behaviour of the pad approximant , at first graphically and then by showing that the overlaps , of the inspiral waveform based on it with the exact waveform , are close to unity . we shall use a number of different test systems in our comparison : these will range from systems with dissimilar masses , such as a ns - bh binary , to comparable - mass systems , such as a bh - bh binary . to deal with the comparable mass systems , we shall introduce in the energy and flux functions a term dependent on the symmetric mass ratio @xmath40 while not being entirely consistent , because of the fact that no finite mass correction terms are included , it allows us to examine the performance of various templates as we move from the test - mass systems to comparable - mass systems . the emphasis of the current paper is also on the estimation of parameters . we have carried out a detailed study of how good t- and p - approximants are in measuring the parameters of the binary . we shall show in sec . [ sec : results ] that as a result of not being _ effectual _ representations of the exact signal , t - approximants also turn out not to be _ faithful _ representations either . in other words , the systematic error in the estimation of the parameters caused by the wrong phasing of the signal is much larger in the case of t - approximants than in the case of p - approximants . in summary , p - approximants are not only _ effectual _ but they are _ faithful _ too as in the case of non - spinning black hole binaries .

( i.e. larger overlaps with the exact signal ) , and _ faithfulness _ ( i.e. smaller biases while measuring the parameters of the signal ) with the exact ( numerical ) waveforms . the p - approximants achieve effectualness of for all spins up to the bias in the estimation of parameters is much lower in the case of p - approximants than t - approximants . we find that p - approximants are both effectual and faithful and should be more effective than t - approximants as a detection template family when for both t- and p - approximants perform equally well so that either of them could be used as a detection template family .

the standard post - newtonian approximation to gravitational waveforms , called t - approximants , from non - spinning black hole binaries are known not to be sufficiently accurate close to the last stable orbit of the system . a new approximation , called p - approximants , is believed to improve the accuracy of the waveforms rendering them applicable up to the last stable orbit . in this study we apply p - approximants to the case of a test - particle in equatorial orbit around a kerr black hole parameterized by a spin parameter that takes values between and in order to assess the performance of the two approximants we measure their _ effectualness _ ( i.e. larger overlaps with the exact signal ) , and _ faithfulness _ ( i.e. smaller biases while measuring the parameters of the signal ) with the exact ( numerical ) waveforms . we find that in the case of prograde orbits , that is orbits whose angular momentum is in the same sense as the spin angular momentum of the black hole , t - approximant templates obtain an effectualness of for spins for the effectualness drops to about 0.82 . the p - approximants achieve effectualness of for all spins up to the bias in the estimation of parameters is much lower in the case of p - approximants than t - approximants . we find that p - approximants are both effectual and faithful and should be more effective than t - approximants as a detection template family when for both t- and p - approximants perform equally well so that either of them could be used as a detection template family .

1110.0911

i

the notion of transmitting data over powerlines has posed an interesting challenge for information and coding theory . the noise characteristics of such a communication channel include permanent narrowband noise , impulse noise and white gaussian noise . communication over this channel also has an additional requirement that the power envelope be as close to constant as possible . vinck @xcite studied this channel and showed that @xmath0-ary frequency shift keying ( @xmath0-fsk ) modulation , in conjunction with the use of permutation codes , provides a constant power envelope , frequency spreading and redundancy to correct errors resulting from the harsh noise pattern . this has since resulted in research on frequency permutation arrays ( fpas ) and constant composition codes ( cccs ) which retain the property of a constant power envelope ( see @xcite , and @xcite for a survey ) . every codeword of an fpa or a ccc has the requirement that the frequency of each symbol is fixed by the parameters of the code . versfeld@xcite introduced the notion of the `` same - symbol weight '' of a code by relaxing the requirement that every symbol must occur a fixed number of times in any codeword . in every codeword of a same - symbol weight code , the frequency of any symbol is bounded . even with this relaxation it is possible to detect permanent narrowband noise . versfeld@xcite used reed - solomon codes to design codes with specified same - symbol weight . in this work we mostly study the asymptotic behavior of codes in the symbol weight space . we use the term _ bounded symbol weight _ ( as opposed to same - symbol weight @xcite ) to denote all words in the hamming space with bounded symbol weight , that is , any symbol in a codeword does not occur more than a fixed number of times , say @xmath1 this terminology is adopted in order to distinguish this space from the _ constant symbol weight space _ , in which every symbol in a word in the hamming space occurs at most @xmath2 times and there exists one symbol which occurs exactly @xmath2 times . the constant symbol weight space is clearly a subset of the bounded symbol weight space . we also use the term symbol weight space to refer to either the bounded symbol weight or constant symbol weight space . the actual space being referred to is made clear from the context and notation . as described in @xcite , the symbol weight determines whether the code can detect and correct narrowband noise in the powerline channel . an fpa or a ccc belongs to some constant symbol weight space . the constant symbol weight space also contains other compositions all of which have the same maximal part , that is , all such codes have the same fixed symbol weight . thus a code in the constant symbol weight space is larger than a ccc of a fixed composition , and is still relevant for correcting narrowband noise . the asymptotic behavior of fpas have been studied in @xcite . in contrast , there are relatively fewer results on the asymptotic behavior of cccs ( see @xcite ) . we consider familiar techniques used to derive classical bounds such as the gv bound , the johnson bound and the singleton bound , on codes in the symbol weight space . however , the derivation of these results are not immediate because of the lack of any reasonable structure in the symbol weight spaces . in particular , even the hamming balls of a fixed radius in these spaces depend on the center of the ball . in section [ sec : lower - bnd - sw ] , we also study non - asymptotic bounds on codes in the symbol weight spaces by expressing them in terms of different cccs . this also raises related combinatorial questions regarding the size and construction of optimal codes , which can be an interesting avenue of future research . in later sections we show that there exists codes , which are subsets of reed - solomon codes , with high rate and relative distance , which are a subset of the constant symbol weight space . throughout this work we are mostly concerned with codes that have positive rate and positive relative distance . hence we do not study codes with very large distances , in the plotkin region . we start with some basic definitions and notations in the following section . we devote section [ sec : asymp - sws ] to deriving the exact and asymptotic size of the symbol weight spaces . the results in section [ sec : asymp - sws ] allow us to determine which constant composition space contained within the symbol weight space contributes the most to the rate of a symbol weight space . these estimates are used in section [ sec : sw - asymp ] to determine upper and lower bounds on bounded symbol weight and constant symbol weight codes . in particular , it is clear that asymptotically some constant composition code determines the rate of a symbol weight code . an upper bound is readily obtained from either the singleton bound or the linear programming bound in the hamming space . in section [ sec : sw - asymp ] we also provide a johnson - type bound on codes in the constant symbol weight space , and use this bound to derive an asymptotic improvement of the singleton bound and the linear programming bound for certain ranges of the minimum distances and the symbol weight . in section [ sec : lower - bnd - sw ] we provide non - asymptotic lower bounds on symbol weight codes . we introduce a new metric on the space of compositions of an integer and use this metric to lower bound the size of symbol weight codes by a sum of sizes of cccs . finally , in section [ sec : constructions ] we provide other constructions of constant symbol weight codes , and in particular show that the asymptotic lower bound presented in section [ sec : asymp - sws ] is tight for certain parameters , for subcodes of reed - solomon codes .

various types of codes such as permutation codes , frequency permutation arrays , and constant composition codes have been proposed over the years . in this work we study a type of code called the bounded symbol weight codes which was first introduced by versfeld in 2005 , and a related family of codes that we term constant symbol weight codes . we provide new upper and lower bounds on the size of bounded symbol weight and constant symbol weight codes . we also give direct and recursive constructions of codes for certain parameters .

the study of codes for powerline communications has garnered much interest over the past decade . various types of codes such as permutation codes , frequency permutation arrays , and constant composition codes have been proposed over the years . in this work we study a type of code called the bounded symbol weight codes which was first introduced by versfeld in 2005 , and a related family of codes that we term constant symbol weight codes . we provide new upper and lower bounds on the size of bounded symbol weight and constant symbol weight codes . we also give direct and recursive constructions of codes for certain parameters . asymptotic bounds , constant composition codes , powerline communications , reed solomon codes , symbol weight codes .

1605.07017

i

quasi - two - dimensional organic charge transfer salts of bis - ethylenedithio - tetrathiafulvalene molecules , abbreviated bedt - ttf or et , have attracted much interest due to their rich phase diagrams @xcite . among these materials , the family of @xmath0-(et)@xmath3 salts , where @xmath0 refers to a specific arrangement of the et molecules and @xmath4 corresponds to a monovalent anion , stands out due to the realization of fascinating states of matter like mott insulator , unconventional superconductor or spin - liquid @xcite . especially the immediate vicinity of the superconducting phase to an antiferromagnetic mott insulator suggests a deeper connection between two - dimensional organics and high - temperature cuprate superconductors @xcite . although superconducting @xmath0-type charge transfer salts have been investigated , for instance , in studies of specific heat @xcite , surface impedance @xcite , thermal conductivity @xcite , millimeter - wave transmission @xcite , scanning tunneling spectroscopy ( sts ) @xcite and elastic constants @xcite , no consensus about the symmetry of the superconducting pairing has been reached so far . some of the experiments are in favor of @xmath5-wave symmetry @xcite , while other studies have proposed @xmath6-wave states with contradictory positions of the nodes in the superconducting order parameter @xcite . evidence for a mixed - symmetry order parameter was recently provided in refs . . notably , evidence for a phase separation between different @xmath6-wave states has recently been reported in ref . . in theoretical approaches , the @xmath0-(et)@xmath3 family of materials is often described by a half - filled hubbard model of ( et)@xmath7 dimers on the anisotropic triangular lattice @xcite , which is equivalent to a square lattice model with an additional coupling along one of the diagonals . many theoretical methods have been applied to the dimer based hubbard model , for instance , the fluctuation - exchange approximation ( flex ) @xcite , the path - integral renormalization group @xcite , cluster dynamical mean field theory @xcite , variational monte carlo @xcite and exact diagonalization @xcite . these studies do not agree entirely on all details of the phase diagram , especially whether superconductivity is realized in the model or not . those studies that do show superconductivity nevertheless agree , with the exception of ref . , that it is of @xmath8-type as in high - temperature cuprate superconductors @xcite . although the triangular lattice hubbard model has been remarkably successful in explaining the overall phase diagram @xcite and also some more subtle physics @xcite of @xmath0-(et)@xmath3 materials , the recent discovery of multiferroicity @xcite in antiferromagnetic @xmath9-(et)@xmath7cu[n(cn)@xmath7]cl and the still unresolved problem of superconducting pairing - symmetry @xcite call for alternative approaches . in particular , the dimer model on the anisotropic triangular lattice is only an approximation with _ a priori _ unclear range of applicability to the real lattice structure of @xmath0-(et)@xmath3 charge transfer salts . in a seminal paper @xcite kuroki _ _ investigated the superconducting pairing taking into account the realistic lattice structure and in fact found a phase transition between @xmath8- and @xmath2-symmetric states when lowering the degree of dimerization . other possible directions of future theoretical research beyond the dimer hubbard model are outlined in refs . . -(et)@xmath11 layer . individual et molecules are represented by white and dark grey ellipsoids . the four dominant hopping integrals are ( @xmath12,@xmath13,@xmath14,@xmath15 ) . note the pronounced asymmetry in magnitude between @xmath13 and @xmath15 , which is indicated here by different line thickness . ( b ) dimer approximated @xmath0-(et)@xmath11 layer . two molecules are contracted into one dimer site indicated by a bold shaded circle . the intra - dimer hopping integral @xmath12 is integrated out , while @xmath13 and @xmath15 are averaged . therefore , the dimer model is characterized by only two hopping parameters \{@xmath16,@xmath17}=\{@xmath18,@xmath19}. in both subfigures the unit cell considered in our work is indicated by a bold magenta colored line . ] in this work , building upon the idea by kuroki _ , we derive a set of realistic molecule - based low - energy models for superconducting @xmath0-(et)@xmath3 materials from _ ab initio _ density functional theory ( dft ) calculations . after identifying the parameter region relevant for the real materials , we investigate the symmetry of the superconducting pairing in this model within a random phase approximation ( rpa ) spin - fluctuation approach . our results show that the position of many materials in the phase diagram is close to a phase - transition line between states with extended @xmath20 and @xmath2 pairing symmetry . furthermore , we clarify that the customary dimer model not only fails in the limit of weak dimerization , but also when the in - plane anisotropy of hopping integrals becomes too large , which we find to be the case for all investigated materials . finally , we simulate tunneling spectra in the superconducting state for selected cases and compare our findings to relevant experiments .

we investigate the evolution of the superconducting pairing symmetry within this model and point out a phase - transition between extended and symmetry . our calculations show that many-type materials lie close to the phase transition line between the two pairing symmetry types found in our calculation , possibly explaining the multitude of contradictory experiments in this field .

the symmetry of the superconducting order parameter in quasi - two - dimensional bedt - ttf organic superconductors is a subject of ongoing debate . we report _ ab initio _ density functional theory calculations for a number of organic superconductors containing-type layers . using projective wannier functions we derive parameters of a common low - energy hamiltonian based on individual bedt - ttf molecular orbitals . in a random phase approximation spin - fluctuation approach we investigate the evolution of the superconducting pairing symmetry within this model and point out a phase - transition between extended and symmetry . we discuss the origin of the mixed order parameter and the relation between the realistic molecule description and the widely used dimer approximation . based on our _ ab initio _ calculations we position the investigated materials in the obtained molecule model phase diagram and simulate scanning tunneling spectroscopy experiments for selected cases . our calculations show that many-type materials lie close to the phase transition line between the two pairing symmetry types found in our calculation , possibly explaining the multitude of contradictory experiments in this field .

1605.07017

m

we use _ ab initio _ density functional theory ( dft ) calculations within an all - electron full - potential local orbital ( fplo)@xcite basis to calculate the electronic bandstructure . for the exchange - correlation functional we employ the generalized gradient approximation ( gga)@xcite . all calculations are converged on @xmath21 @xmath22-point grids . we use crystal structures from refs . . in the case of ref . , where crystal structures were measured for several temperatures , we use the data taken at 100 k. in contrast to the customary dimer approximation , we model the @xmath0-(et)@xmath11 layer taking into account each individual et molecule as a lattice site ( see fig . [ fig : lattice ] ) . tight - binding parameters are obtained from projective molecular orbital wannier functions as implemented in fplo@xcite . therefore , the number of bands in the tight - binding model is equal to the number of et molecules in the crystallographic unit cell . with the molecular wannier function method , almost perfect representations of the dft bandstructures can be obtained and ambiguities from fitting procedures are avoided . the latter is especially important for many - body calculations based on the obtained low - energy hamiltonians . in the following model investigation , we only keep the four largest in - plane hopping elements ( @xmath12,@xmath13,@xmath14,@xmath15 ) between et molecules [ see fig . [ fig : lattice](a ) ] . the resulting hopping structure is a generalization of the shastry - sutherland lattice @xcite , which is reached in the limit of @xmath23 and @xmath24 . in cases where the unit cell contains multiple @xmath0-type layers , we discard all but one of the layers after the wannierization procedure , because the interlayer coupling is negligible . in some of the investigated compounds , the crystal symmetry is lowered with respect to the high - symmetry orthorhombic space group _ pnma _ of @xmath9-(et)@xmath7cu[n(cn)@xmath7]br , which leads to a small additional splitting of the hoppings @xmath25 into @xmath26 and @xmath27 . for simplicity , this particular anisotropy is discarded in our study by averaging the hopping integrals as @xmath28 . as a result , we obtain the kinetic part of a four - band hamiltonian which is 3/4-filled and of the same form for all materials investigated . @xmath29 alternatively , because et molecules in @xmath0-type arrangement are quite strongly dimerized , it is popular to approximate the @xmath0-(et)@xmath11 layer by dimers on an anisotropic triangular lattice , integrating out the intra - dimer degrees of freedom . the parameters of this dimer model can be calculated directly from the molecule model using geometric formulas @xcite . @xmath30 [ eq : geometricformulas ] by convention the dimer approximation uses the crystallographic unit cell containing two dimers [ see fig . [ fig : lattice](b ) ] . therefore , the dimer - approximated hamiltonian consists of two bands , which are half - filled . note that based on the geometric formulas , any anisotropy between @xmath13 and @xmath15 of the molecule model is discarded when going from the molecule to the dimer model . with few exceptions @xcite , the dimer approximated model nevertheless reproduces well the low - energy part of the original bandstructure . it has recently been demonstrated that improved estimates for dimer model parameters can be obtained by a wannier function calculation @xcite . the two - band dimer model can be unfolded to a one - band model by transforming to a unit cell of half the size and rotated by 45 degrees . the so - obtained model is directly related to the square lattice hubbard model , but with an additional coupling along one of the diagonals . results obtained in the one - band model are therefore rotated by 45 degrees with respect to the physical brillouin zone of organic charge transfer salts , so that e.g. different @xmath6-wave order parameters exchange their designation when going from one to the other brillouin zone ( see fig . [ fig : brillouinzones ] ) . thus , the same physical order parameter which has @xmath2-symmetry in the realistic four molecule / two dimer unit cell [ fig . [ fig : brillouinzones](b ) ] has @xmath8-symmetry in the model one dimer / one band unit cell [ fig . [ fig : brillouinzones](c ) ] . in our study , we always work in the physical unit cell containing two dimers [ fig . [ fig : brillouinzones](b ) and ( d ) ] . we refer to the small backfolded part of the fermi surface close to the brillouin zone boundary as the _ elliptic _ part of the fermi surface , while we call those sheets running almost parallel to the @xmath31-direction _ quasi-1d_. an overview of unit cell and hopping paths for molecule and dimer model is shown in fig . [ fig : lattice ] . the resulting hamiltonians in orbital - space for all three cases are listed in appendix [ sec : kinhamil ] . -(et)@xmath3 material . the outer dashed lines show brillouin zone and fermi surface of the unfolded one - band dimer model . ( b ) d@xmath32 order parameter in the physical brillouin zone . nodes are located in the @xmath33- and @xmath34-directions . ( c ) d@xmath35 order parameter in the unfolded brillouin zone . nodes are located along the brillouin zone diagonals . the different designation is only due to a rotation of the coordinate axes by @xmath36 . ( d ) d@xmath35 order parameter in the physical brillouin zone . ( e ) d@xmath32 order parameter in the unfolded brillouin zone . ] in @xmath0-(et)@xmath3 materials there is strong evidence for antiferromagnetic spin - fluctuations @xcite . therefore , we investigate the superconducting state of these materials based on a random phase approximation ( rpa ) spin - fluctuation approach in the singlet channel @xcite . we have extended our implementation from single - site multi - orbital models @xcite to multi - site single - orbital models relevant for the materials discussed here . compared to the flex approximation used in ref . , our rpa method uses only states at the fermi level and neglects the electronic self - energy correction . while this approximation prevents us from making quantitative statements about the superconducting transition temperature @xmath37 , it reduces significantly the numerical cost compared to flex , so that we can calculate the momentum structure of the superconducting order parameter for numerous input parameter sets and with high angular resolution . competing magnetically ordered or paramagnetic mott insulating states are not investigated in our study . furthermore , we do not investigate possible time - reversal symmetry - breaking superconducting states or spin - triplet pairing . the low - energy hamiltonian is given by the kinetic part @xmath38 , derived with the wannier function method described above , and the intra - orbital hubbard interaction @xmath39 . @xmath40 here , @xmath41 represents the spin and @xmath42 . the sum over @xmath43 runs over all et sites in the unit cell . the interaction strength @xmath44 is treated as a parameter . note that the coulomb repulsion on a dimer and the coulomb repulsion on a molecule are not identical . especially the role of intermolecular coulomb repulsion is currently unclear . the investigation of interaction terms beyond on - site repulsion is left for future studies . we calculate the non - interacting static susceptibility @xmath45 , where matrix elements @xmath46 resulting from the diagonalization of the initial hamiltonian @xmath38 connect orbital and band space denoted by indices @xmath47 and @xmath48 respectively . the @xmath49 are the eigenvalues of @xmath38 and @xmath50 is the fermi function . @xmath51 is the number of sites in the unit cell . @xmath52 in our calculation both @xmath53 and @xmath54 run over uniform grids spanning the reciprocal unit cell . temperature enters the calculation through the fermi functions . the fraction in eq . [ eq : nonintsuscep ] becomes problematic in numerical calculations , when the band energies @xmath55 and @xmath49 become degenerate . however , the expression can be rectified using lhospital s rule , which we use in practice when the magnitude of the denominator falls below a certain threshold ( e.g. @xmath56 ) . here , @xmath57 denotes the inverse temperature @xmath58 . @xmath59 the static spin- and orbital - susceptibilities ( @xmath60 and @xmath61 ) are constructed in an rpa framework . since the interaction term defined in eq . [ eq : hamiltonian ] is local and we have only one orbital per lattice site , we can restrict the calculation to the diagonal elements of the susceptibility and use scalar equations for the rpa - enhanced susceptibilities . @xmath62 [ eq : rpasuscep ] here , @xmath63 with @xmath64 denotes the diagonal element of the susceptibility tensor associated with an et site indexed by @xmath47 . note that this formulation allows us to treat multiple inequivalent et sites in the unit cell , keeping the individual @xmath65-dependence of their associated susceptibilities . therefore , the symmetry of the susceptibility follows the symmetry of the et layer in the crystallographic unit cell , which is important for checking the simplified four - parameter model against _ ab initio _ hamiltonians , which can have monoclinic , as e.g. in @xmath0-(et)@xmath7cu(ncs)@xmath7 , or even triclinic symmetry , as in @xmath0-@xmath66-(et)@xmath7ag(cf@xmath67)@xmath68(tce ) . the total spin susceptibility is given by the sum over all site - resolved contributions : @xmath69 the pairing vertex in orbital space for the spin - singlet channel can be calculated using the fluctuation exchange approximation @xcite : @xmath70_{{l_1 } { l_2 } { l_3 } { l_4 } } \end{aligned } \label{eq : pairingvertexorbitalspace}\ ] ] in the pairing vertex , the momenta @xmath54 and @xmath71 are restricted to the fermi surface . as vectors @xmath72 do not necessarily lie on the grid used in the calculation of the susceptibility @xmath73 , we interpolate the grid data linearly . the pairing vertex in orbital space is transformed into band space using the matrix elements @xmath74 : @xmath75\\ \times & a_\nu^{l_2 } ( \vec k^\prime ) a_\nu^{l_3 } ( -\vec k^\prime ) \end{aligned } \label{eq : pairingvertexbandspace}\ ] ] finally , we solve the linearized gap equation by performing an eigendecomposition on the kernel and obtain the dimensionless pairing strength @xmath76 and the symmetry function @xmath77 . @xmath78 g_i ( \vec k^\prime ) = \lambda_i g_i ( \vec k ) \label{eq : gapequation}\ ] ] the integration runs over the discretized fermi surface and @xmath79 is the magnitude of the fermi velocity . for the computations presented in this paper , we evaluated the susceptibility @xmath73 using @xmath80 point grids for @xmath53 and the integrated - out variable @xmath54 ( see eq . [ eq : nonintsuscep ] ) . the inverse temperature in the susceptibility calculation is fixed to @xmath81 for the molecule model and @xmath82 for the dimer model . these values result in about the same effective temperature . the fermi surface is determined by inverting linear interpolants for the band energies on a fine grid . for the models considered here about @xmath83 points on the fermi surface are sufficient . the hubbard repulsion parameter @xmath44 is chosen in all calculations so that the leading eigenvalue in eq . [ eq : gapequation ] is @xmath84 . for most combinations of input parameters this leads to a clear separation of the leading and the first subleading eigenvalue . the pairing symmetries corresponding to the leading and sub - leading eigenvalues do not change as a function of @xmath44 . [ cols=">,<,>,>,>,>,>,>,>,>,>",options="header " , ] the central quantity measured in the scanning tunneling spectroscopy ( sts ) experiments on superconductors is the local density of states ( dos ) in the superconducting phase . here we start from the standard bardeen - cooper - schrieffer ( bcs ) theory for isotropic s - wave superconductors . a simple approximate extension allows us to treat realistic fermi surfaces and unconventional pairing symmetries derived from the _ ab initio _ calculations combined with rpa spin - fluctuation theory as presented above . to derive an approximation for the dos of a superconductor , we start with the hamiltonian for cooper pairs with vanishing total momentum @xcite . @xmath85 the interaction can be treated in mean field theory ( @xmath86 ) , where terms quadratic in @xmath87 are neglected . the resulting hamiltonian can be diagonalized using the bogoliubov - valatin transformation which introduces quasiparticle creation and annihilation operators @xmath88 and @xmath89 . the quasiparticle excitation energies are given as @xmath90 , where @xmath91 . the bcs hamiltonian can be rewritten in terms of the quasiparticle creation and annihilation operators : @xmath92 & - \sum_{k , k ' } u(k , k')\langle c_{k\uparrow}^\dagger c_{-k\downarrow}^\dagger\rangle \langle c_{-k'\downarrow } c_{k'\uparrow } \rangle \end{array } \label{eq : bcshamilqp}\ ] ] the excitation spectrum of the quasiparticles @xmath93 is gapped and defined only for positive energies . the density of states of quasiparticles in an isotropic s - wave superconductor can be calculated from the normal state density of states @xmath94 and the constant superconducting gap @xmath95 : @xmath96 = & \int d\epsilon \ , \rho_0(\epsilon ) \frac{\sqrt{\epsilon^2+\vert \delta\vert^2}}{\epsilon } \delta(\epsilon -\sqrt{e^2-\vert \delta\vert^2})\\[4pt ] = & \begin{cases } \rho_0(\sqrt{e^2-\vert \delta\vert^2 } ) \frac{e}{\sqrt{e^2-\vert \delta\vert^2 } } & e > \vert \delta\vert\\[4pt ] 0 & e < \vert \delta\vert \end{cases } \end{array } \label{eq : dosqpswave}\ ] ] the previous derivation assumed an isotropic gap and an energy dispersion of free electrons to identify the normal state dos @xmath97 . for realistic electronic structure and anisotropic gap @xmath98 this factorization of contributions is not easily possible due to the non - trivial momentum dependence of both functions : @xmath99 \neq&\int d\epsilon \ , \rho_n ( \epsilon ) \ , \delta(\vert e\vert -\sqrt{\epsilon^2+\vert \delta_k\vert^2 } ) \end{array } \label{eq : dosqpapprox}\ ] ] however , in a widely used ansatz @xcite the electrons with effective mass @xmath100 are considered to be free , i.e. the fermi surface is approximated by a concentric circle , and the gap only depends on the angle @xmath101 . @xmath102 we introduce in this expression a finite quasiparticle lifetime @xcite by adding an imaginary part @xmath103 to the quasiparticle excitation energies . this allows us to carry out calculations with finite angular resolution and facilitates comparison to experiment . furthermore , we improve upon the circular integration by replacing it with a summation over the discretized realistic fermi surface and drop the irrelevant prefactors to obtain the final expression for the quasiparticle dos in our study : @xmath104 in this form , the connection to the _ ab initio _ and rpa spin - fluctuation calculations is easily obtained : the vectors @xmath54 in eq . [ eq : dosqpfinal ] all lie on the fermi surface determined from the _ ab initio _ derived tight - binding model and the gap @xmath105 on the fermi surface can be substituted by the symmetry function @xmath77 extracted from rpa ( eq . [ eq : gapequation ] ) . note that the overall energy scale of the superconducting gap is not included in @xmath77 because our formalism neglects the electronic self - energy and lacks a self - consistency condition . we checked that our approximation agrees well with a direct calculation of the quasiparticle spectrum based on eq . [ eq : bcshamilqp ] , which is numerically more costly . the quasiparticle dos @xmath106 corresponds to the local density of states ( ldos ) measured in sts experiments . for a direct comparison , thermal smearing and additional effects such as electronic disorder might have to be taken into account @xcite

we report _ ab initio _ density functional theory calculations for a number of organic superconductors containing-type layers . using projective wannier functions we derive parameters of a common low - energy hamiltonian based on individual bedt - ttf molecular orbitals . in a random phase approximation spin - fluctuation approach we discuss the origin of the mixed order parameter and the relation between the realistic molecule description and the widely used dimer approximation . based on our _ ab initio _

the symmetry of the superconducting order parameter in quasi - two - dimensional bedt - ttf organic superconductors is a subject of ongoing debate . we report _ ab initio _ density functional theory calculations for a number of organic superconductors containing-type layers . using projective wannier functions we derive parameters of a common low - energy hamiltonian based on individual bedt - ttf molecular orbitals . in a random phase approximation spin - fluctuation approach we investigate the evolution of the superconducting pairing symmetry within this model and point out a phase - transition between extended and symmetry . we discuss the origin of the mixed order parameter and the relation between the realistic molecule description and the widely used dimer approximation . based on our _ ab initio _ calculations we position the investigated materials in the obtained molecule model phase diagram and simulate scanning tunneling spectroscopy experiments for selected cases . our calculations show that many-type materials lie close to the phase transition line between the two pairing symmetry types found in our calculation , possibly explaining the multitude of contradictory experiments in this field .

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neutron stars in mass - transferring binaries accrete hydrogen and helium rich material from their companions at rates ranging from @xmath9@xmath10 . this matter undergoes thermonuclear fusion within hours to days of reaching the neutron star surface , releasing @xmath11 per nucleon for solar abundances . the nuclear burning is thermally unstable on weakly magnetic neutron stars ( @xmath12 ) accreting at @xmath13 and produces energetic ( @xmath14 ) type i x - ray bursts when @xmath15 ( see lewin , van paradijs & taam 1995 and bildsten 1998b for recent reviews ; observationally , the nature of the time dependent burning in the regime @xmath16 is still not understood ) . the composition of the ashes from the unstable burning is still uncertain , but most certainly consists of heavy nuclei , potentially beyond the iron group ( hanawa , sugimoto & hashimoto 1983 ; wallace & woosley 1984 ; schatz et al . 1997 ; schatz et al . 1998 , koike et al . 1999 ) . in this paper , we calculate for the first time the mix of nuclei made during _ thermally stable _ hydrogen / helium burning in the upper atmosphere of an accreting neutron star . this is appropriate for most accreting x - ray pulsars , where the local accretion rate is high enough for stable burning on the magnetic polar cap ( joss & li 1980 ; bildsten & brown 1997 ) , and for the bright `` z '' sources of hasinger and van der klis ( 1989 ) that are not regular type i bursters and accrete globally at @xmath17 . whereas accurately calculating the ashes from unstable burning requires time - dependent , three - dimensional modelling of the ignition and propagation of the flame , stable burning is time - independent and therefore calculation of the ashes is much more straightforward . the ashes are forced by accretion into the neutron star ocean and crust , replacing what was there at birth . the ensuing electron captures , neutron emissions and pycnonuclear reactions release energy locally and drive the matter neutron - rich ( bisnovatyi - kogan & chechetkin 1979 ; sato 1979 ; haensel & zdunik 1990 ; blaes et . al . 1990 ; bildsten 1998a ; brown , bildsten & rutledge 1998 ) . thus the composition of an accreted or accreting neutron star ocean and crust is very different from the primordial one ( see pethick and ravenhall 1995 for a recent discussion of the primordial crust ) and depends critically on the range and type of nuclei made during the h / he burning in the upper atmosphere . previous studies of accreting neutron star crusts presumed that iron is the sole product of nuclear burning in the upper atmosphere and is the only nucleus entering the neutron star crust . we find that the hydrogen burning on these rapidly accreting neutron stars is mostly via the rp process of wallace and woosley ( 1981 ) , resulting in a complicated mix of elements , _ nearly all much heavier than iron . _ the thin outer crust of a neutron star ( before neutron drip at @xmath18@xmath19 ) is replaced by accretion of only @xmath20 of material . thus all of the neutron stars in low - mass x - ray binaries should have an accreted outer crust . indeed these objects accrete enough material to unambiguously replace their _ whole _ crust ( down to the crust / core interface ) , which is typically a few percent of the total stellar mass ( ravenhall & pethick 1994 ) . the x - ray pulsars typically accrete from the wind of a massive companion at a rate @xmath21@xmath22 ( see bildsten et al . 1997 for a recent overview ) and so are capable of replacing their outer crusts . a few of these objects ( smc x-1 , lmc x-4 , her x-1 ) are accreting at high enough rates or for long enough times ( as inferred by the @xmath23 mass companion to her x-1 ) to replace their whole crust . knowledge of the composition and thermal properties of an accreting neutron star s ocean and crust is important for many studies . for example , the temperature and composition of the crust affects the thermal conductivity and the ohmic diffusion time there ( see brown & bildsten 1998 for a recent application / overview of this problem ) . the crustal composition determines the amount of heat deposited directly in the crust ( haensel & zdunik 1990 ; miralda - escude et al . 1990 ) and the rate of neutrino emission from the crust ( haensel , kaminker & yakovlev 1996 ) , both of which are important for finding the equilibrium core temperature of an accreting neutron star ( fujimoto et al . 1984 ; brown & bildsten 1998 ) . the predicted frequencies of the so - far unobserved ocean g - modes depend directly on the average nuclear mass ( bildsten & cutler 1995 ; bildsten & cumming 1998 ) . we begin in 2 with an introduction to the basic equations we solve and a summary of the input microphysics . in 3 , we discuss the high accretion rate burning regime and explain why the burning is thermally stable at high accretion rates and why the helium ignites in a hydrogen - rich environment , thus providing an excellent site for the rp process . in 4 , we explain the overall thermal and compositional structure of the burning layer and provide convenient analytic expressions for the temperature and depth of the burning . section 5 contains an in - depth discussion of the nature of the rp process . we explain how the burning depends on the local accretion rate , with particular emphasis on the important role of the @xmath8p process in determining the final average mass of the nuclei . we conclude in 6 with a summary of our work and some speculations about how these results will impact studies of the neutron star crust and ocean . in the appendix , we describe how we calculate the radiative and conductive opacities for the complex mixtures produced by the hydrogen / helium burning .

the temperature and nuclear composition of the crust and ocean of an accreting neutron star depend on the mix of material ( the ashes ) that is produced at lower densities by fusion of the accreting hydrogen and helium . the hydrogen / helium burning is thermally stable at high accretion rates , a situation encountered in weakly magnetic ( ) neutron stars accreting at rates and in most accreting x - ray pulsars , where the focusing of matter onto the magnetic poles results in local accretion rates high enough for stable burning . for a neutron star accreting at these high rates , nuclear statistical equilibrium , leading to a composition of mostly iron , occurs only for very high local accretion rates in excess of 50 times the eddington rate . we briefly discuss the consequences of our results for the properties of the neutron star . this has repercussions for the thermal , electrical and structural properties of the neutron star crust .

the temperature and nuclear composition of the crust and ocean of an accreting neutron star depend on the mix of material ( the ashes ) that is produced at lower densities by fusion of the accreting hydrogen and helium . the hydrogen / helium burning is thermally stable at high accretion rates , a situation encountered in weakly magnetic ( ) neutron stars accreting at rates and in most accreting x - ray pulsars , where the focusing of matter onto the magnetic poles results in local accretion rates high enough for stable burning . for a neutron star accreting at these high rates , we calculate the steady state burning of hydrogen and helium in the upper atmosphere ( ) , where . since the breakout from the `` hot '' cno cycle occurs at a temperature comparable to that of stable helium burning ( ) , the hydrogen is always burned via the rapid proton capture ( rp ) process of wallace and woosley . the rp process makes nuclei far beyond the iron group , always leading to a mixture of elements with masses . the average nuclear mass of the ashes is set by the extent of helium burning via (,p ) reactions , and , because these reactions are temperature sensitive , depends on the local accretion rate . nuclear statistical equilibrium , leading to a composition of mostly iron , occurs only for very high local accretion rates in excess of 50 times the eddington rate . we briefly discuss the consequences of our results for the properties of the neutron star . the wide range of nuclei made at a fixed accretion rate and the sensitivity of the ash composition to the local accretion rate makes it inevitable that accreting neutron stars have an ocean and crust made up of a large variety of nuclei . this has repercussions for the thermal , electrical and structural properties of the neutron star crust . a crustal lattice as impure as implied by our results will have the conductivity throughout most of its mass set by impurity scattering , allowing for more rapid ohmic diffusion of magnetic fields than previously estimated for mono - nuclear mixes . * to appear in the astrophysical journal *

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we have fully explored the complicated nucleosynthesis from thermally stable mixed hydrogen / helium burning at high accretion rates on accreting neutron stars . our major finding is that the rp process produces a mixture of very heavy elements , the average mass of which depends on the local accretion rate . the important reaction sequences during the mixed hydrogen and helium burning are the 3@xmath8 reaction , the @xmath8p process and the rp process . for all accretion rates where the nuclear burning is in steady state , a breakout of the hot cno cycles into the rp process takes place . it is the endpoint of the rp process that determines the energy generation and final composition of the ashes . in contradiction to taam et al . ( 1996 ) , we find that no hydrogen survives the steady state burning and consequently deep hydrogen burning by electron capture does not take place ( the possibility still remains that there is substantial residual hydrogen from unstable burning in x - ray bursts ) . for @xmath123c the situation is similar : for accretion rates of a few times eddington , some @xmath123c survives the burning , but never enough to trigger carbon flashes via exposive burning in deeper layers of the atmosphere . the most important nuclear physics input parameters for our steady state burning calculations are 1 ) the 3@xmath8 reaction rate , which triggers the burning ; 2 ) the breakout reactions from the hot cno cycles @xmath72o(@xmath8,@xmath122)@xmath125ne and @xmath131ne(@xmath8,p)@xmath151na , as discussed in 5.1 ; 3 ) the ( @xmath8,p ) and ( p,@xmath122)- reaction rates on @xmath70o , @xmath132 mg , @xmath133si , and @xmath134s together with the proton separation energies and the proton capture rates of @xmath137al , @xmath235p , @xmath236cl , and @xmath237k ( these data affect the extent of helium burning and therefore the endpoint of the rp process ) ; 4 ) the proton capture rates on the waiting points @xmath203fe and @xmath159ni ; and 5 ) proton capture q - values and @xmath60-decay half lives of the even @xmath238 , @xmath173 and the even @xmath238 , @xmath239 nuclei between @xmath159ni and @xmath56sn as discussed in schatz et al . while the 3@xmath8 reaction is known with sufficient accuracy , most of the other data are completely or partially based on theoretical data , for which extrapolation to the very neutron deficient nuclei in the rp process is often doubtful ( see schatz et al . 1998 for a more detailed discussion ) . however , while these uncertainties may affect the detailed abundance pattern for a given local accretion rate , they have no influence on our general conclusions concerning the nature of steady state burning on accreting neutron stars ( see 5.1 ) . nevertheless , more experimental information on the nuclear data mentioned above would certainly be desirable . our calculations of the composition of the nuclear ashes in steady - state burning show that the ocean and crust of an accreting neutron star do not consist of pure iron , as assumed in previous work . instead , the final composition consists of a wide range of nuclei . this is characteristic of the rp process in which some fraction of nuclei is locked at a large number of waiting points with long lifetime . our results will have interesting consequences for studies of the crust of accreting neutron stars . for example , our discovery of the large range of nuclei present will directly impact estimates of the thermal and electrical conductivity of the crust . to illustrate this point , we have calculated the `` impurity parameter '' @xmath240 for our models , where @xmath241 are the nuclear abundances and the subscript max indicates the most abundant species . we find that @xmath242 is typical of the mixture from the ashes of steady state burning . even at very high accretion rates , ( @xmath243 ) when nuclear statistical equilibrium favors @xmath159ni as the sole product of nucleosynthesis , @xmath244 . brown & bildsten ( 1998 ) showed that for @xmath245 the thermal and electrical conductivity is dominated by impurity scattering , which is strongly composition dependent . in previous work which assumed a crust of pure iron ( before electron captures ) , impurity scattering was unimportant . thus in accreting neutron stars , the thermal and electrical crust conductivities will be in general much lower than previously assumed , leading to a different thermal structure and faster ohmic diffusion of magnetic fields in the crust . we thank ed brown and felix rembges for many discussions during this work . we are especially grateful to f .- k . thielemann and t. rauscher for providing the reaction network solver and many of the reaction rates . this research was supported by nasa via grants nag 5 - 2819 and nagw-4517 . l. b. was supported by the hellman family faculty fund award ( ucb ) and the alfred p. sloan foundation .

a crustal lattice as impure as implied by our results will have the conductivity throughout most of its mass set by impurity scattering , allowing for more rapid ohmic diffusion of magnetic fields than previously estimated for mono - nuclear mixes . * to appear in the astrophysical journal *

the temperature and nuclear composition of the crust and ocean of an accreting neutron star depend on the mix of material ( the ashes ) that is produced at lower densities by fusion of the accreting hydrogen and helium . the hydrogen / helium burning is thermally stable at high accretion rates , a situation encountered in weakly magnetic ( ) neutron stars accreting at rates and in most accreting x - ray pulsars , where the focusing of matter onto the magnetic poles results in local accretion rates high enough for stable burning . for a neutron star accreting at these high rates , we calculate the steady state burning of hydrogen and helium in the upper atmosphere ( ) , where . since the breakout from the `` hot '' cno cycle occurs at a temperature comparable to that of stable helium burning ( ) , the hydrogen is always burned via the rapid proton capture ( rp ) process of wallace and woosley . the rp process makes nuclei far beyond the iron group , always leading to a mixture of elements with masses . the average nuclear mass of the ashes is set by the extent of helium burning via (,p ) reactions , and , because these reactions are temperature sensitive , depends on the local accretion rate . nuclear statistical equilibrium , leading to a composition of mostly iron , occurs only for very high local accretion rates in excess of 50 times the eddington rate . we briefly discuss the consequences of our results for the properties of the neutron star . the wide range of nuclei made at a fixed accretion rate and the sensitivity of the ash composition to the local accretion rate makes it inevitable that accreting neutron stars have an ocean and crust made up of a large variety of nuclei . this has repercussions for the thermal , electrical and structural properties of the neutron star crust . a crustal lattice as impure as implied by our results will have the conductivity throughout most of its mass set by impurity scattering , allowing for more rapid ohmic diffusion of magnetic fields than previously estimated for mono - nuclear mixes . * to appear in the astrophysical journal *

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a small fraction of red giant stars have lithium abundances ( @xmath3(li ) ) exceeding the predictions of standard evolution models even though the majority of red giants ( rgs ) exhibit @xmath3(li ) orders of magnitude below standard model predictions @xcite . the low @xmath3(li ) demonstrates that non - convective mixing processes contribute significantly to li depletion , which makes the li - rich stars appear even more unusual . the most li - rich rgs have abundances exceeding the meteoritic abundances ( @xcite , @xcite , ) and require a nucleosynthetic origin for the li . @xcite described a pathway for li nucleosynthesis through the reactions @xmath6he(@xmath7,@xmath8)@xmath9be and @xmath9be(@xmath10,@xmath11)@xmath9li . this process requires high temperatures ( @xmath12 k ) for the first reaction to occur and fast mixing ( such as convection ) to transport the by - products to a cool region of the star ( @xmath13 k ) for lithium to be long - lived . these conditions are met at the base of the convection zones in luminous asymptotic giant branch ( agb ) stars . however , understanding li - rich stars(li ) meets or exceeds the commonly used threshold of 1.5 dex . ] found along the red giant branch ( rgb ) presents a problem because these stars convection zones are too cool to synthesize @xmath9be . thus , the @xmath6he reaction must occur below the convection zone , and a fast non - convective mixing mechanism is required to connect the convection zone to the deeper layers of the star in order to explain the enriched surface abundances . through a series of observations and advances in evolution modeling ( e.g. , , @xcite , @xcite ) , it has become largely accepted that red giants evolving through the luminosity bump stage of evolution likely experience a short - lived phase of enriched li . a number of deep mixing mechanisms for this stage of evolution have been proposed , including thermohaline mixing , magnetic buoyancy @xcite , and the hybrid magneto - thermohaline mixing @xcite . however , as the number of the relatively rare li - rich stars continues to grow , it has become clear that they are not restricted to just the luminosity bump and agb , but instead are found along the rgb . a new short - lived phase of li - richness was hypothesized by ( * ? ? ? * hereafter k11 ) , who suggested that li might be regenerated during the he - flash . this mechanism would account for the population of li - rich red giants with temperatures too warm to be luminosity bump stars and that fall in a narrow luminosity range that coincides with the red clump ( rc ) . this he - flash phenomenon would be relevant for stars in a narrow mass range of @xmath141.52.25 @xmath0 , the upper limit being defined by the maximum mass that experiences a he flash , and the lower limit by the stars that maintain a relatively large reservoir of @xmath6he . for the upper bound , showed that the transition occurs closer to 1.81.9 @xmath0 . at least one li - rich star is known to be in this mass range and is confirmed to be a he - burning star via asteroseismology @xcite . as a test of the hypothesis suggested by , we observed rc stars in four open clusters with ages and metallicities that place their rc stars in the mass range specified by . in three of the four clusters , we also observed rgs at other evolutionary stages to constrain the pre - he flash abundances . in addition to @xmath3(li ) , we also measure @xmath1c/@xmath2c . many of the li - rich field stars in have @xmath1c/@xmath2c that is much lower than predicted from standard evolution models , presumably a consequence of the same mixing that brought the synthesized li into the convection zone . although newly synthesized li can be destroyed if exposed to high enough temperatures , the altered @xmath1c/@xmath2c will persist as evidence of the past deep mixing . the selection and observation of the stars in this study are described in sections [ sec : clusters ] and [ sec : obs ] , respectively . in section [ sec : methods ] , we outline the measurement of li abundances and @xmath1c/@xmath2c . in section [ sec : discuss ] , we present the significance of our results , and we give our conclusions in section [ sec : end ] .

the temperature distribution of field li - rich red giants suggests the presence of a population of li - rich red clump ( rc ) stars . one proposed explanation for this population is that all stars with masses near 2 experience a short - lived phase of li - richness at the onset of core he - burning . many of these stars have lowc/c , a signature of deep mixing that is presumably associated with the li regeneration . to test this purported mechanism of li enrichment , we measured abundances in 38 rc stars and 6 red giant branch ( rgb ) stars in four open clusters selected to have rc masses near 2 . thus , if li synthesis during the he flash occurs , it is a rare , but potentially long - lived occurrence rather than a short - lived phase for all stars .

the temperature distribution of field li - rich red giants suggests the presence of a population of li - rich red clump ( rc ) stars . one proposed explanation for this population is that all stars with masses near 2 experience a short - lived phase of li - richness at the onset of core he - burning . many of these stars have lowc/c , a signature of deep mixing that is presumably associated with the li regeneration . to test this purported mechanism of li enrichment , we measured abundances in 38 rc stars and 6 red giant branch ( rgb ) stars in four open clusters selected to have rc masses near 2 . we find six li - rich stars ((li).50 dex ) of which only two may be rc stars . none of the rc stars have li exceeding the levels observed in the rgb stars , but given the brevity of the suggested li - rich phase and the modest sample size , it is probable that stars with larger li - enrichments were missed simply by chance . however , we find very few stars in our sample with lowc/c . such lowc/c , seen in many field li - rich stars , should persist even after lithium has returned to normal low levels . thus , if li synthesis during the he flash occurs , it is a rare , but potentially long - lived occurrence rather than a short - lived phase for all stars . we estimate a conservative upper limit of the fraction of stars going through a li - rich phase to be , based on stars that have lowc/c for their observed(li ) .

1608.01678

c

in figure [ fig : li_histo ] , we show the distribution of @xmath3(li)@xmath207 for the four clusters in this study , with histograms for both the full observed sample and the subset of rc candidate stars . the non - rc stars tend to fall at either extremes of the distributions , but are more commonly at the high extreme . for three of the clusters , the majority of the rc candidates fall into a single distribution that peaks around @xmath208 dex and is composed of mostly upper limit measurements . two of the those clusters ( collinder 110 and ngc 2204 ) have rc candidates in a second group or tail that extends into the li - rich regime . in contrast , the fourth cluster ( ngc 6583 , both the most - metal rich and youngest cluster in this study ) shows a peak in the distribution at much higher @xmath3(li ) with very few upper limit measurements . only a single rc star has significantly lower @xmath3(li ) . ( li ) for all stars observed in each cluster ( shaded gray histograms ) and the subset of candidate rc stars ( open blue histograms ) . the hatched regions denote stars with only upper limits on @xmath3(li ) in the full sample ( diagonal lines ) and the rc sample ( horizontal lines ) . [ fig : li_histo],scaledwidth=50.0% ] these bimodal - like lithium distributions are similar to three clusters with @xmath3(li ) dichotomies reported previously in the literature for ngc 752 , ngc 3680 , and ic 4651 ( @xcite , , ) . all three clusters have similar ages ( 1.51.9 gyr ) and are older than two of our clusters ( ngc 6583 and collinder 110 ) but younger than the other two ( ngc 2204 and ngc 2506 ) . the dichotomy of @xmath3(li ) in these three literature clusters has been interpreted as discriminating between first ascent rgs and rc stars in each cluster , with the higher @xmath3(li ) corresponding to the former , and lower @xmath3(li ) to the latter . this interpretation is also borne out in collinder 110 and ngc 2204 , where it is clear from figure [ fig : cmds2 ] that the highest li stars ( filled symbols ) are the ones that appear to be first ascent rgb stars and not rc stars . however , because rc should be more common than first ascent rgs , one would expect all of the clusters to have more low @xmath3(li ) stars than high @xmath3(li ) stars . this is not the case for ngc 3680 ( or ngc 6583 in this work ) , which led to suggest that the high @xmath3(li ) stars in ngc 3680 were in fact the rc stars . an expanded sample of giants in ngc 3680 by @xcite confirmed this li dichotomy . ngc 3680 is the oldest and most metal - poor ( [ fe / h]@xmath209 dex ) of those three literature clusters , but ngc 6583 is the youngest and most metal - rich of the clusters studied here . since we have previously estimated evolutionary stages for our cluster stars , we can explore the li distribution of each cluster in more detail . in figure [ fig : li_results ] , we show @xmath3(li ) as a function of @xmath210 magnitude and @xmath1c/@xmath2c . in general , the rgb stars ( identified as squares ) show the largest abundances , while the candidate rc stars ( triangles ) show depleted abundances . this is true even in ngc 6583 ; the rc stars have depleted @xmath3(li ) compared to the first ascent rgb stars , but the depletion in this cluster is less than that in the other three clusters . the apparent dichotomous @xmath3(li ) distribution in this cluster is in fact three different levels of @xmath3(li ) : rgb stars with the least li dilution , rc stars with moderate li dilution , and one rc star with significant dilution . our four cluster sample suggests that if li - replenishment is commonly occurring at the he flash , the subsequent destruction of li reduces the surface abundance below the rgb levels . a few outliers are worth noting . first , in ngc 6583 the most luminous star has @xmath3(li ) comparable to the other rgb star , whereas the most luminous star in ngc 2204 has severely depleted levels . this implies that the ngc 2204 luminous star is on the agb , not the rgb . in all of the clusters except ngc 2506 , there are one or more candidate rc stars with @xmath3(li ) more similar to the rgb star levels . rc stars are plotted as red circles in figures [ fig : cmds ] ( which was used to determine their rc candidacy ) and [ fig : cmds2 ] . we find that all but one of the candidate rc stars with high li are closer matches to the first ascent rgb in figure [ fig : cmds2 ] and were reclassified based on those positions . the exception is ngc 6583 72 , whose classification is ambiguous in figure [ fig : cmds2 ] . the second panel in figure [ fig : li_results ] shows @xmath3(li ) as a function of @xmath1c/@xmath2c . most of the stars fall along a trend of decreasing @xmath1c/@xmath2c with decreasing @xmath3(li ) . this behavior is expected since both quantities are altered by mixing in stars . the stars along the linear trend follow the same distribution as the open cluster stars studied by @xcite . there are again some exceptions . there is a grouping of eleven stars with low @xmath1c/@xmath2c but @xmath3(li)@xmath211 dex . seven of these have limits in one of the parameters such that they could fall along the trend . four stars , on the other hand , are still outliers . all of the stars are in the clusters that had the difficult telluric removal , so it is possible that the low @xmath1c/@xmath2c measurements are spurious . however , our confidence in the validity of the measurements are due to the facts that ( 1 ) the @xmath2cn feature is stronger ( more easily detectable ) for low @xmath1c/@xmath2c , and ( 2 ) owing to the blend of lines creating the @xmath2cn feature , the width of the line would be difficult to mimic with residuals from the telluric removal . this sample of stars was selected specifically to test the hypothesis that li is generated at the he flash . in the sample , all of the li - rich stars that have @xmath1c/@xmath2c available have @xmath3(li)@xmath212 dex . this minimum @xmath3(li ) in the sample is influenced by two factors . first , the newly discovered rgs in were pre - screened for the presence of the li line in low resolution spectra , leading to a temperature - dependent minimum @xmath3(li ) . second , the lowest @xmath3(li ) stars in both the new rg and literature rg samples in do not have @xmath1c/@xmath2c measurements . none of our stars have li abundances at this level , implying a low occurrence rate for li - rich stars . using the binomial statistics in @xcite , we can estimate the @xmath213 upper bound for the occurrence rate of rc clump stars more li - rich than @xmath214 dex to be @xmath215% . this result is the same if we use all 38 photometrically identified rc candidates or if we reduce the sample size to 35 to account for the ones that may be rgb stars . the lack of a li - rich star in our sample is still consistent with the field giant study , which estimated the incidence to be around 1% . if we factor @xmath1c/@xmath2c into our consideration , we can perform a more stringent test of the fraction of stars that go through a li - enriched phase early in the core he - burning stage . in figure [ fig : cratio_hist ] , we show the @xmath1c/@xmath2c distribution of the subset of the sample that overlaps our rc sample in parameter space . we remove stars from the paper that have @xmath216 and @xmath47@xmath217 k. the first cut removes four luminous rgs in that are outside of the mass range and are near the second dredge - up phase on the early - agb ( see ) . the second cut removes cooler rgs that are more likely to be at the luminosity bump . overlaid in figure [ fig : cratio_hist ] is the @xmath1c/@xmath2c distribution of our sample of 38 rc candidates . the distributions are very different . the majority of the li - rich stars have @xmath1c/@xmath2c@xmath218 . such a low @xmath1c/@xmath2c is a signature of deep mixing that dredges up material from the vicinity of the h - burning shell , where @xmath1c/@xmath2c is 3.5 @xcite . this implies that the mechanism responsible for the enhanced li requires ( or is accompanied by ) very deep mixing . because @xmath1c/@xmath2c of the stellar atmosphere can only be lowered by mixing , this signature of low @xmath1c/@xmath2c will persist even when the lithium levels return to normal low values . therefore , the @xmath1c/@xmath2c distribution of our rc sample is inconsistent with the hypothesis that most / all stars of 1.52.2 @xmath0 experience a brief li - rich stage . instead , the li - rich stage must only be experienced by a small fraction of stars . we can identify the subset of stars in our sample that likely went through a li - rich phase as the outlier group of low @xmath1c/@xmath2c stars we identified in figure [ fig : li_results ] . if the four stars that are clear outliers ( i.e. , no limit on either abundance measurement ) are the only true outliers , then only @xmath219 of the rc stars went through a li - rich phase . the fraction is larger if we include all 11 stars in the low @xmath1c/@xmath2c outlier group , which results in an occurrence rate of @xmath220 . the rc sample for these two calculations only use the rc candidates without strong evidence for reclassification ( i.e. , the ` reclassified ' rc candidates in collinder 110 and ngc 2204 are removed ) and only considers stars with @xmath1c/@xmath2c measurements . these constraints yield 29 rc stars . c/@xmath2c in the 38 rc candidates in this work ( open histogram ) and for the li - rich stars with @xmath221 and @xmath47@xmath222 k in ( filled histogram ) . the temperature and luminosity limits were imposed on the sample to restrict it to stars most similar to the rc stars in this work . [ fig : cratio_hist],scaledwidth=50.0% ] our interpretations may also be affected by the unknown rotational histories of the individual stars . the main sequence progenitors of the stars in the mass range we are studying have a large distribution of rotational velocities , with a typical value of 150 km@xmath19s@xmath20 . despite this large variation on the ms , @xcite showed that the red giant descendants of these stars are still almost uniformly slow rotators , a result that is reproduced here ( section [ sec : rot ] ) . this fact makes it difficult to discern which stars were faster or slower ms rotators . the initial ms rotation affects the depth of mixing and thus the observed surface @xmath3(li ) of rgs . furthermore , rotation extends the main sequence lifetime . in an effort to explain the extended ms turn - offs of clusters in the magellanic clouds , @xcite explored the differences of isochrone morphology of models including large initial rotation compared to non - rotating models . they found that the isochrones made with fast rotating models were nearly indistinguishable from the slow rotating models . the implication to this work is that some of the rgs may be both more massive than we expect and may have experienced extensive rotational mixing . these stars would be difficult to distinguish from the stars that conform to the non - rotating model assumptions . among intermediate age milky way open clusters , some show extended rc morphologies that are inconsistent with simple single stellar population models . some of this extension is due to the fact that the ages of these clusters are such that the rc stars span the mass range that delineates the transition from quiescent to he flash core burning , resulting in a primary and secondary rc @xcite . however , this can not explain all of the spread in the msto , nor can it be explained with an age spread . the authors note that variations in the mass loss rate on the rgb or in the core overshoot efficiencies on the ms ( which affects the mass transition for the different types of he core burning onset ) could be responsible . if these factors are at play in the clusters of this work , they may also influence the variation of @xmath3(li ) observed in our clusters .

we find six li - rich stars ((li).50 dex ) of which only two may be rc stars . none of the rc stars have li exceeding the levels observed in the rgb stars , but given the brevity of the suggested li - rich phase and the modest sample size , it is probable that stars with larger li - enrichments were missed simply by chance . such lowc/c , seen in many field li - rich stars , should persist even after lithium has returned to normal low levels . we estimate a conservative upper limit of the fraction of stars going through a li - rich phase to be , based on stars that have lowc/c for their observed(li ) .

the temperature distribution of field li - rich red giants suggests the presence of a population of li - rich red clump ( rc ) stars . one proposed explanation for this population is that all stars with masses near 2 experience a short - lived phase of li - richness at the onset of core he - burning . many of these stars have lowc/c , a signature of deep mixing that is presumably associated with the li regeneration . to test this purported mechanism of li enrichment , we measured abundances in 38 rc stars and 6 red giant branch ( rgb ) stars in four open clusters selected to have rc masses near 2 . we find six li - rich stars ((li).50 dex ) of which only two may be rc stars . none of the rc stars have li exceeding the levels observed in the rgb stars , but given the brevity of the suggested li - rich phase and the modest sample size , it is probable that stars with larger li - enrichments were missed simply by chance . however , we find very few stars in our sample with lowc/c . such lowc/c , seen in many field li - rich stars , should persist even after lithium has returned to normal low levels . thus , if li synthesis during the he flash occurs , it is a rare , but potentially long - lived occurrence rather than a short - lived phase for all stars . we estimate a conservative upper limit of the fraction of stars going through a li - rich phase to be , based on stars that have lowc/c for their observed(li ) .

cond-mat9710330

i

the effects of the coulomb interaction of electrons in metals can only be described approximately @xcite . with the progress in producing artificial low dimensional structures the theoretical work on _ one - dimensional _ interacting fermions has gained importance @xcite . special features of the spectrum of low energy excitations in one dimension allow _ exact _ solutions of models of _ interacting _ fermions . the main idea can already be understood by working with noninteracting fermions , which have the same spectrum of excitations as a harmonic chain . this `` fermion - boson - transmutation '' ( fbt ) was discussed in a recent publication on different levels of sophistication @xcite . in the following this paper is referred to as i. the basic idea can be understood on the level of elementary quantum statistical mechanics . only in chapter v. of i the method of second quantization was introduced to calculate the momentum distribution of _ noninteracting _ fermions in the _ canonical _ ensemble . it was pointed out that the technique presented can also be used in the description of _ interacting fermions_. from the response we obtained to i it is clear that many readers would have liked to see more explicitly the application to this problem . the purpose of this paper is to fill this gap on a level which requires only a basic knowledge of the method of second quantization but none of relativistic quantum field theory . the exact solution to the `` tomonaga - luttinger ( tl- ) model '' is presented starting with tomonaga s model of spinless interacting nonrelativistic fermions on a ring @xcite . in section ii the momentum distribution in the interacting ground state is calculated in leading order perturbation theory . this already demonstrates one of the important ideas towards the exact solution and on the quantitative level shows a sign of the infrared singularities later found in the exact solution . tomonaga s concept of `` right '' and `` left '' moving electrons later extended by luttinger @xcite is introduced and the commutation relations of the fourier components of the operator of the particle density are derived . in order to avoid mathematical subtleties we work with _ two _ cut - offs one for the number of momentum states ( `` band cut - off '' ) and one for the inverse range of the two - body interaction ( `` interaction cut - off '' ) . this allows to smoothly go from tomanaga s original model to the model discussed by luttinger . in section iii the exact low energy eigenvalues of the tl - model are obtained using the bosonization technique . as the most important `` luttinger - liquid '' ( ll ) feature the momentum distribution in the ground state is calculated . its derivative at the fermi points diverges in a power law fashion determined by the important constant called `` anomalous dimension '' . one effort to experimentally verify ll - properties is photoemission from quasi - one dimensional conductors @xcite . as the theoretical description of photoemission involves spectral functions they are discussed in section iv . the model including spin is introduced in section v. after the definition of `` charge '' and `` spin '' bosons the hamiltonian of the model can be written as a sum of two _ commuting _ terms of the spinless type leading to the phenomenon of `` spin - charge - separation '' . in section vi . the general ll - concept is presented and it is shortly discussed how the ll parameters which completely determine the low energy physics also for more complicated @xmath0 lattice models can be extracted from finite size numerical data . in appendix a the proof of the kronig - identity which provides the bosonization of the kinetic energy is given . the bosonization of the field operator is discussed in appendix b. a novel straightforward approach is presented to determine the particle number changing contribution . we put @xmath1 in this paper .

this fermion - boson transmutation allows to describe interacting fermions as a system of coupled oscillators . tomonaga s model of interacting nonrelativistic fermions on a ring is presented and first discussed in low order perturbation theory . after introducing the concept of two independent species of right and left moving fermions the exact solution of the tomonaga - luttinger model is discussed in detail . the general luttinger liquid phenomenology is shortly discussed .

the theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low energy spectrum of noninteracting fermions is identical to the one for a harmonic chain . this fermion - boson transmutation allows to describe interacting fermions as a system of coupled oscillators . tomonaga s model of interacting nonrelativistic fermions on a ring is presented and first discussed in low order perturbation theory . after introducing the concept of two independent species of right and left moving fermions the exact solution of the tomonaga - luttinger model is discussed in detail . the momentum distribution and spectral functions are calculated using the method of the bosonization of the field operator . the general luttinger liquid phenomenology is shortly discussed .

1310.0841

i

the goal of these lectures is to discuss the theory of relativistic real fluids under the excuse of its application to the description of relativistic heavy ion collisions @xcite . more concretely , our goal is to discuss , in the simplest possible terms , why the `` einstein elevator '' concept is not useful in the development of this theory . namely , we can not build a theory of relativistic real fluids by just asking that it reduces to its nonrelativistic counterpart , namely the navier - stokes equations , in an inertial frame where the fluid is at rest . for this reason we shall begin with a `` derivation '' of the nonrelativistic theory of ideal fluids ( those which flow with no entropy production ) from thermodynamics @xcite . for ideal fluids , the relativistic theory may be found as the covariant extension of the nonrelativistic theory enforced in the rest frame . we shall then show that already in this simple framework we may obtain a working picture of how a relativistic heavy ion collision works , yielding remarkably accurate predictions regarding several concrete observables . among these observables there is the so - called elliptic flow , namely the anisotropy of the particle yield in the transverse plane to the beam direction . if the matter deposited in the collision region behaves as a nearly ideal fluid , then elliptic flow arises as the simple transduction of pressure gradients in the original configuration into velocities in the asymptotic expanding state . this is an obvious prediction of the euler equations which is surprisingly hard to reproduce in non - hydrodynamic models . the success in predicting that there must be an elliptic flow is one of the most compelling reasons to believe that matter in the collision region , from some very early time after the actual collision up to the break up in the individual hadrons which are eventually detected , behaves as a fluid . however , ideal hydrodynamics overestimates the amount of elliptic flow @xcite . this suggests there must be a mechanism that tends to isotropize flow , and indeed viscosity acts in precisely that direction . therefore , the next natural step is to consider hydrodynamic models based on real fluid hydrodynamics . at this point we return to the formal theory , and generalize our previous `` thermodynamic '' derivation to the case of real fluids . the resulting non relativistic theory is given by the navier - stokes equations , which is satisfactory , but the relativistic theory emerging from the `` einstein elevator '' is essentially flawed - if covariance is enforced , then the theory has no stable solutions @xcite . how to get out of this cul de sac is the subject of the rest of the lectures . since the `` thermodynamic '' approach led us nowhere , we shall begin anew from a more fundamental point of view , that provided by relativistic kinetic theory . in this case , there is an agreed upon relativistic formulation to build on @xcite . the problem is how to reduce it to the hydrodynamic level . in the nonrelativistic case , the method of choice is the so - called chapman - enskog expansion , which leads to the navier - stokes equations @xcite . in the relativistic case , it works likewise , and so it must be rejected . however , a second well known technique , the grad expansion , is successful in building a relativistic hydrodynamics where linear perturbations of an equilibrium state evolve causally . however , the application to relativistic heavy ion collisions forces us to face the relationship between kinetic and hydro descriptions a second time , because what is actually measured are individual hadrons . this means that there must be some space time `` break up '' or `` freeze out '' surface ( or region ) where the fluid nucleates into individual particles that fly away to the detectors ( a process that is by no means simple , but does not belong to these lectures ) . we must be able to read the one particle distribution function of these particles out of the hydrodynamic state of the fluid just before break up . if we simple invert the grad expansion , we are led to a one particle distribution function which is not nonnegative throughout phase space , a defect that contaminates the predictions of the theory regarding observables which are sensitive to high momenta . this drawback of the grad approach , and also the need to include nonlinear corrections to the linearized equations of motion without spoiling stability and covariance , prompted us to suggest that the grad approach may be just the linear approximation to a more comprehensive view of the kinetic - hydro relationship @xcite . the basic insight is that any realistic kinetic theory displays a whole hierarchy of relaxation times , from the relaxation times characteristic of large scale inhomogeneities to the much shorter relaxation times of hard modes . fluctuations in the hydrodynamic modes relax on the longer time scales , and are perceived by the harder modes as externally imposed thermodynamic forces which prevent their relaxation to true equilibrium . in other words , the truly kinetic modes relax not to equilibrium but to a nonequilibrium steady state constrained by the instantaneous configuration of the hydrodynamic modes . it has been known from long ago that such steady states are the solutions to variational problems @xcite . prigogine among others has proposed that they are the extrema of the entropy _ production _ , as opposed to the extrema of the entropy itself , which are the true equilibria @xcite . known proofs of the so - called `` prigogine theorem '' are restricted to linear irreversible thermodynamics @xcite ; we shall appeal to it on a heuristic rather than formal basis - the idea is that most kinetic modes are in the linear regime most of the time anyway , so a theory which is good in the linear regime is good enough to compute global observables such as stress tensor components , but we shall not attempt to formulate this insight in any rigorous way @xcite . we shall therefore conclude these lectures with a brief presentation of this `` entropy production variational method '' , its relationship to positivity of the one particle distribution function , and its nonlinear generalization . the lectures are organized as follows . in next section we present the theory of relativistic ideal fluids , as derived from thermodynamics , and its application to the description of relativistic heavy ion collisions ( rhics ) . the main success of the theory , namely the prediction of elliptic flow , is also its fatal drawback , because experimental data show that ideal hydrodynamics overestimates the flow anisotropy @xcite . we are therefore motivated to extend the theory to include viscosity , whereby we hit on the stability problem @xcite . we present the theory of real fluids in section iii ; since the thermodynamic derivation fails , we base our discussion on relativistic kinetic theory . we must confront the _ closure _ problem , that is , to relate the one particle distribution function in the kinetic description to the hydrodynamic degrees of freedom . we present the chapman - enskog solution ( which reproduces the results from the thermodynamic analysis , and therefore is unsuitable ) and the grad solution , and finally identify the grad solution of the closure problem as the linearized approximation to an approach based on the entropy production variational method ( epvm ) . we conclude with some brief final remarks . if relativistic hydrodynamics may be founded on kinetic theory , kinetic theory itself comes from quantum field theory , the main subject matter of this school . we show the main lines of the derivation of kinetic theory from quantum field theory in the appendix , which relies heavily on ref .

the theory of real relativistic fluids is in the rather unique situation that there is a natural relativistic extension of the nonrelativistic theory , but it is physically untenable . on the other hand , mounting evidence that matter created in relativistic heavy ion collisions behaves as a relativistic fluid with small but finite viscosity has given the quest for an alternative a definite goal . we shall review different approaches to relativistic real fluids , their link to relativistic kinetic theory , and their application to the analysis of heavy ion collisions

the theory of real relativistic fluids is in the rather unique situation that there is a natural relativistic extension of the nonrelativistic theory , but it is physically untenable . on the other hand , mounting evidence that matter created in relativistic heavy ion collisions behaves as a relativistic fluid with small but finite viscosity has given the quest for an alternative a definite goal . we shall review different approaches to relativistic real fluids , their link to relativistic kinetic theory , and their application to the analysis of heavy ion collisions

hep-ph9908320

i

recently the magnetic catalysis of dynamical chiral symmetry breaking has been established as a universal phenomenon in 2 + 1 and 3 + 1 dimensions : a constant magnetic field leads to the generation of a fermion dynamical mass even at the weakest attractive interaction between fermions @xcite . the essence of this effect is the dimensional reduction @xmath0 in the dynamics of fermion pairing in a magnetic field : at weak coupling , this dynamics is dominated by the lowest landau level ( lll ) which is essentially ( @xmath1)-dimensional @xcite . the effect may have interesting applications in condensed matter physics @xcite and cosmology @xcite . in particular , this phenomenon was considered in 3 + 1 dimensional qed @xcite . since the dynamics of the lll is long - range ( infrared ) , and the qed coupling constant is weak in the infrared region , one may think that the rainbow ( ladder ) approximation is reliable in this problem . as was shown in refs . @xcite , in all the covariant gauges , the dynamical mass of fermions in this approximation is @xmath2 , \label{m_dyn}\ ] ] where @xmath3 is a magnetic field , the constant @xmath4 is of order one and @xmath5 is the renormalized coupling constant related to the scale @xmath6 . are higher order contributions indeed suppressed in this problem ? the answer is no " . as was shown in refs . @xcite , because of the ( 1 + 1)-dimensional form of the fermion propagator of the lll fermions , there are relevant higher order contributions . in particular , considering this problem in the improved rainbow approximation ( with the bare vertex in the schwinger - dyson equations for both the fermion propagator and the polarization operator ) , it was shown that , in all the covariant gauges , the fermion mass @xmath7 is given by eq . ( [ m_dyn ] ) but with @xmath8 @xcite . as we wrote in the paper @xcite , it is a challenge to define the class of all those diagrams in qed in a magnetic field that give a relevant contribution in this problem " . in this paper , we will solve the problem . ( a brief outline of our results was given in ref . we will show that there exists a ( non - covariant ) gauge in which the schwinger - dyson equations written in the improved rainbow approximation are reliable : in other words , in that gauge , there exists a consistent truncation of the schwinger - dyson equations for this _ non - perturbative _ problem . the expression for @xmath7 takes the following form , @xmath9 , \label{m}\ ] ] where @xmath10 is the number of fermion flavors,@xmath11 , @xmath12 and the constant @xmath13 is of order one . this expression for @xmath7 is essentially different from that in the rainbow approximation ( [ m_dyn ] ) . as we will see , this reflects rather rich and sophisticated dynamics in this problem . the paper is organized as follows . in section [ secii ] the schwinger - dyson equations in qed in a magnetic field are discussed . in section [ seciii ] we define a ( non - covariant ) gauge in which the improved rainbow approximation for these equations is reliable . in section [ seciv ] the loop expansion for the schwinger - dyson equations is considered and it is confirmed that the improved rainbow approximation is indeed reliable in the gauge introduced in section [ seciii ] . in section [ secv ] the schwinger - dyson equations in this approximation are solved both analytically and numerically . in section [ secvi ] we summarize the main results of the paper . the details of our analysis and some useful formulas and relations are presented in appendices [ seca ] , [ secb ] and [ secc ] .

an approximation for the schwinger - dyson equations describing reliably this phenomenon is established , _ i.e. _ , it is shown that there exists a consistent truncation of those equations in this problem . epsf.sty * keywords : * quantum electrodynamics , chiral symmetry , magnetic field .

the theory of the magnetic catalysis of chiral symmetry breaking in qed is developed . an approximation for the schwinger - dyson equations describing reliably this phenomenon is established , _ i.e. _ , it is shown that there exists a consistent truncation of those equations in this problem . the equations are solved both analytically and numerically , and the dynamical mass of fermions is determined . epsf.sty * keywords : * quantum electrodynamics , chiral symmetry , magnetic field .

cond-mat0107007

m

the goal of the unitary correlation operator method ( ucom ) is to describe short - range interaction - induced correlations by a unitary transformation of an uncorrelated many - body state with @xmath4 particles . the unitary operator @xmath5 associated with this transformation can be written as an exponential of a hermitian generator @xmath6 @xmath7 .\ ] ] the generator is chosen to be an irreducible two - body operator @xmath8 which describes genuine two - body correlations only . in principle we could add a three - body part to account for genuine three - body correlations . for the moment we omit this step to develop the basic formalism on a simple level . the particular structure of the unitary transformation which should reflect the properties of the short - range correlations is described by the two - body generator @xmath9 . the repulsive core of the interaction leads to a suppression of the probability density within the range @xmath10 of the core . uncorrelated many - body states that are symmetrized products of single - particle states lead , however , to a two - body density that does not show any depletion for relative distances @xmath11 between the pair of particles . therefore the unitary transformation should shift those particles that are in the forbidden region of the repulsion to larger distances . this is done by means of a distance - dependent radial shift in the relative coordinate of two - particles . the hermitian generator of this shift in two - body space reads @xmath12 , \ ] ] where @xmath13 is the operator of the relative momentum , @xmath14 is the relative coordinate , and @xmath15 is the associated unit vector . the function @xmath16 describes the size of the shift as function of the distance of the particles . first we want to apply the unitary correlation operator @xmath5 to an uncorrelated many - body state @xmath17 out of a low - momentum model space . the correlated many - body state @xmath18 is defined by @xmath19 here and in the following all correlated quantities are marked by a tilde . in order to demonstrate the generic effect of the correlation operator we discuss first a two - body system with an uncorrelated two - body state @xmath20 . using the definition of the correlation operator @xmath5 and the generator @xmath9 we can evaluate the correlated two - body wave function in coordinate representation explicitly @xcite @xmath21 the respective transformation with the hermitian adjoint correlation operator @xmath22 leads to @xmath23 the correlation operator acts in the relative coordinate @xmath24 of the two - body system only , the center of mass coordinate @xmath25 is invariant . according to the construction of the the generator the unitary transformation corresponds to a radial shift in the relative two - body coordinate @xmath26 the transformed relative distances are given by the correlation functions @xmath27 and @xmath28 , respectively . due the unitarity of the correlation operator @xmath29 the correlation functions @xmath27 and @xmath28 are inverse to each other @xmath30 = r .\ ] ] the conservation of the norm of the correlated two - body wave function is guaranteed by the metric factor @xmath31 in and @xmath32 where @xmath33 denotes the derivative of @xmath34 . it corresponds to the square root of the jacobi determinant associated with the transformation of the normalization integral . the correlation functions @xmath34 that describe the coordinate transformation are connected to the function @xmath16 , which enters in the generator , by the integral equation @xmath35 for small shift distances the approximate relation @xmath36 holds . since all correlated quantities can be expressed directly in terms of the correlation functions @xmath27 and @xmath28 we will use one of these as basic quantity to describe the detailed structure of the short - range correlations . the shift function @xmath16 is only used for formal considerations and never specified explicitly . complementary to the definition of a correlated state we can use the correlation operator to define correlated operators . for an arbitrary observable @xmath37 the correlated operator @xmath38 is given by the similarity transformation @xmath39 it is evident that the formulations in terms of correlated states and correlated operators are equivalent when expectation values or matrix elements are calculated @xmath40 thus we can choose the formulation that is technically or intuitively better suited for the specific application under consideration . in most cases the formulation in terms of correlated operators is easier to apply in the many - body system . moreover it provides a systematic approximation scheme that will be discussed in section [ sec : ucom_clusterexp ] . as for the correlated wave function we first discuss specific correlated operators for a two - body system . the generalization to many - body systems will be done in the following sections . the simplest operator of interest is the local two - body potential @xmath41 that depends on the relative distance @xmath42 only . to evaluate the correlated potential we use the results on the correlated two - body wave function to determine a general two - body matrix element of the form @xmath43 & \quad= \int\!\!{\ensuremath{\mathrm{d}}}^3r\,{\ensuremath{\mathrm{d}}}^3\!x\;{\ensuremath { \big < { \psi } \big| \,{{\ensuremath{{\ensuremath{{{{\ensuremath{\bm{c}}}}}^{\dag}}}}}}\ , \big| { { \ensuremath{\vec{x}}},{\ensuremath{\vec{r } } } } \big > } } \,v(r)\ , { \ensuremath { \big < { { \ensuremath{\vec{x}}},{\ensuremath{\vec{r } } } } \big| \,{{\ensuremath{{\ensuremath{\bm{c}}}}}}\ , \big| { \psi ' } \big > } } \\[-2pt ] & \quad= \int\!\!{\ensuremath{\mathrm{d}}}^3r\,{\ensuremath{\mathrm{d}}}^3\!x\;{\ensuremath { \big < { \psi } \big| { { \ensuremath{\vec{x}}},{\ensuremath{\vec{r } } } } \big > } } \;v[{\ensuremath{r_+}}(r)]\ ; { \ensuremath { \big < { { \ensuremath{\vec{x}}},{\ensuremath{\vec{r } } } } \big| { \psi ' } \big > } } \\[2pt ] & \quad= { \ensuremath { \big < { \psi } \big| \,{v[{\ensuremath{r_+}}({\ensuremath{{\ensuremath{\bm{r}}}}})]}\ , \big| { \psi ' } \big > } } . \end{split}\ ] ] in going from the second to the third line we use equations and and substitute the integration variable @xmath24 by @xmath44 . since the two - body states are arbitrary this relation is valid on the operator level @xmath45 .\ ] ] thus the correlated two - body potential @xmath46 is given by the original potential with transformed radial coordinate @xmath47 . the correlated operator of the kinetic energy in the two - body system is slightly more complicated due to its momentum dependence . first we decompose the operator of the two - body kinetic energy @xmath48 in a center of mass contribution @xmath49 and an relative part @xmath50 @xmath51 the operator of the center of mass momentum @xmath52 commutes with the correlation operator , i.e. , the operator of the center of mass kinetic energy is invariant under the unitary transformation . the correlation operator acts on the relative part @xmath50 of the kinetic energy only . a similar calculation as for the local potential leads to the following structure of the correlated relative kinetic energy @xcite @xmath53 besides @xmath50 an additional momentum dependent term appears in the correlated relative kinetic energy , which can be formulated in terms of a tensorial effective mass correction . it is conveniently split into a correction for the radial part @xmath54 and a different correction for the angular component @xmath55 @xmath56 where @xmath57 is the operator of the relative two - body angular momentum . the distance dependent effective mass corrections @xmath58 and @xmath59 depend on the correlation function @xmath28 only @xmath60 in addition to these momentum dependent terms a local contribution @xmath61 appears in @xmath62 . \end{split}\ ] ] this additional two - body potential is also determined by the correlation function @xmath28 and its derivatives . in the preceding section we evaluated correlated operators explicitly in the two - body system . however , correlated operators in the many - body system contain additional terms . the unitary transformation of an operator , e.g. , an one - body operator like the kinetic energy or a two - body operator like the potential , generates a correlated operator , which contains irreducible contributions to all particle numbers @xmath63 } + { \ensuremath{\tilde{{\ensuremath{{\ensuremath{\bm{o}}}}}}}}^{[2 ] } + { \ensuremath{\tilde{{\ensuremath{{\ensuremath{\bm{o}}}}}}}}^{[3 ] } + \dots . \end{split}\ ] ] we use the notation @xmath64}$ ] for the irreducible @xmath65-body part of the correlated operator @xmath38 . this decomposition according to irreducible particle number is called cluster expansion @xcite . the cluster expansion gains physical meaning by the so called cluster decomposition principle @xcite : two localized subsystems , which are separated beyond the range of interactions , are independent of each other . therefore the state of the total system decouples into a direct product of the states of the two subsystems . this implies an analogous decomposition property of the correlation operator and of correlated operators . because of the cluster decomposition principle the cluster expansion is a natural starting point for approximations of the correlated operators . for a selected particle there will be a certain number of other particles within the range of the correlation depending on the density . the number of particles in this cluster gives the maximum order of the cluster expansion that contributes . we can truncate the cluster expansion at low orders if the range of the correlations is sufficiently small compared to the average distance of the particles . the simplest nontrivial approximation results from the truncation of the cluster expansion beyond two - body order . the correlated operator in two - body approximation reads @xmath66 } + { \ensuremath{\tilde{{\ensuremath{{\ensuremath{\bm{o}}}}}}}}^{[2 ] } .\ ] ] this approximation requires that the system is sufficiently dilute such that contributions of the three - body order of the cluster expansion are small . or in other words , the probability for three and more particles to be in the range of the repulsive core simultaneously has to be small . the technical advantage of the two - body approximation is that closed analytic expressions for the correlated operators can be deduced by just considering the two - body system . the correlated hamiltonian in two - body approximation is of the form @xmath67 } + { \ensuremath{\tilde{{\ensuremath{{\ensuremath{\bm{t}}}}}}}}^{[2 ] } + { \ensuremath{\tilde{{\ensuremath{{\ensuremath{\bm{v}}}}}}}}^{[2 ] } \\ & = \sum_i^n { \ensuremath{\tilde{{\ensuremath{{\ensuremath{\bm{t}}}}}}}}^{[1]}_i + \sum_{i < j}^n { \ensuremath{\tilde{{\ensuremath{{\ensuremath{\bm{t}}}}}}}}^{[2]}_{ij } + \sum_{i < j}^n { \ensuremath{\tilde{{\ensuremath{{\ensuremath{\bm{v}}}}}}}}^{[2]}_{ij } . \end{split}\ ] ] the one - body part of the correlated kinetic energy is simply the uncorrelated kinetic energy operator . the two - body part consists of the effective mass corrections and the additional local potential as determined in the previous section @xmath68 } & = { \ensuremath{{\ensuremath{\bm{t}}}}}\\ { \ensuremath{\tilde{{\ensuremath{{\ensuremath{\bm{t}}}}}}}}^{[2 ] } & = { \ensuremath{\tilde{{\ensuremath{{\ensuremath{\bm{t}}}}}}}}_{\omega } + { \ensuremath{\tilde{{\ensuremath{{\ensuremath{\bm{t}}}}}}}}_r + { \ensuremath{\tilde{u}}}({\ensuremath{{\ensuremath{\bm{r } } } } } ) . \end{split}\ ] ] the correlated potential has only a two - body contribution that is given by @xmath69 } = { \ensuremath{\tilde{v}}}({\ensuremath{{\ensuremath{\bm{r } } } } } ) .\ ] ] in order to get a rough measure for the validity of the two - body approximation we define a smallness parameter @xmath70 as a product of the density @xmath71 of the system and a typical volume in which the correlations between a pair of particles change their relative wave function . the correlation volume @xmath72 is defined by the norm of the defect wave function , i.e. , the difference between the uncorrelated uniform wave function @xmath73 and its correlated companion @xmath74 ^ 2 = \int\!\!{\ensuremath{\mathrm{d}}}^3r\ ; [ { \ensuremath{\mathcal{r}_+}}(r)-1]^2 .\ ] ] the smallness parameter @xmath75 is a measure for the probability to find a third particle within the volume where the correlations between two particles change their relative wave function significantly . the two - body approximation is valid only if this probability is small such that three - body correlations are negligible . we have shown for different physical systems @xcite that the relative contribution of the three - body order to the energy exceeds 10% if the smallness parameter reaches a value of typically @xmath76 . if the two - body approximation is not sufficient one can include higher orders of the cluster expansion successively . however , already the calculation of a three - body correlated wave function starting from the many - body correlation operator in analogy to section [ sec : ucom_wavefct ] is not practicable . therefore we reverse the procedure and start from a general many - body coordinate transformation in analogy to the correlation function @xmath34 and determine correlated many - body wave functions and operators . in a second step we connect the explicit structure of the coordinate transformation with the many - body correlation operator , at least in an approximate way . consider a @xmath4-body system with a collective coordinate vector @xmath77 . the short - range correlations are described by a @xmath4-body coordinate transformation @xmath78 the transformation function @xmath79 corresponds to the correlation function @xmath27 in the two - body case . similar to @xmath28 we define an inverse transformation function @xmath80 by @xmath81 = x .\ ] ] the correlated @xmath4-body wave function @xmath82 is defined via the coordinate transformation @xmath83 with a metric factor @xmath84 that ensures norm conservation . the metric factor is given by the square root of the jacobi determinant of the transformation @xmath85 with the matrix elements @xmath86_{ij } = { \ensuremath{\frac{\partial{x'_i}}{\partial{x_j } } } } = { \ensuremath{\frac{\partial{[{\ensuremath{\mathcal{x}_-}}(x)]_i}}{\partial{x_j } } } } .\ ] ] formally we can construct a unitary many - body correlation operator @xmath5 that generates this particular coordinate transformation @xmath87 the check of the unitarity relation @xmath88 with this definition is straightforward . using this formulation we can evaluate many - body correlated operators in the same way as shown in section [ sec : ucom_operator ] for the two - body approximation . we will only present selected results that are needed for the following investigations . the full formalism is discussed in @xcite . a general local potential @xmath89 , which depends on the coordinates @xmath77 of all @xmath4 particles , is transformed as in the two - body case @xmath90 , \ ] ] i.e. , the correlated potential is given by the original potential with transformed coordinate dependence . the expression for the @xmath4-body correlated kinetic energy operator @xmath91 is more involved @xmath92_{jk } \ ; { \ensuremath{{\ensuremath{\bm{p}}}}}_k + { \ensuremath{\tilde{u}}}({\ensuremath{{\ensuremath{\bm{x } } } } } ) , \ ] ] where @xmath93 denotes the collective momentum vectors of all @xmath4 particles . as in the two - body case the correlated kinetic energy contains an effective mass tensor and an additional local potential . the effective mass tensor is given by the square of the jacobi matrix @xmath94_{jk } = \frac{1}{2 m } \sum_{i=1}^{3n } [ j_-(x)]_{ji}\ , [ j_-(x)]_{ik } .\ ] ] the additional local potential @xmath95 given by @xmath96_{x ' = { \ensuremath{\mathcal{x}_+}}(x ) } .\ ] ] with these expressions it is in principle possible to calculate expectation values of the correlated hamiltonian up to arbitrary order in the cluster expansion . in practice all extensions beyond two - body approximation are very costly , thus only the three - body order will be considered . we will use the general formulation of the many - body coordinate transformation to estimate the contribution of the three - body order of the cluster expansion . since we can not derive the many - body coordinate transformation directly from the correlation operator we will construct the transformation by generalization of the known one in the two - body system . it is useful to reformulate the two - body coordinate transformation discussed in section [ sec : ucom_wavefct ] in terms of the general transformation function @xmath97 , where the upper index indicates the number of particles involved . the transformation of the relative coordinate with the correlation function @xmath34 is equivalent to the following transformation of the single - particle coordinates @xmath98 with a shift vector @xmath99\ , { \ensuremath{\hat{r}}}.\ ] ] this notation reveals the intuitive picture behind the description of short - range correlations by means of a coordinate transformation . as a consequence of the short - range repulsion the particles are displaced along their connecting axis by the shift vector @xmath100 . the two - body transformation can be readily generalized to describe three - body correlations . the corresponding three - body coordinate transformation @xmath101 is given by @xmath102 thus the coordinate of the first particle is transformed with respect to the second and the third particle simultaneously . as a necessary prerequisite this transformation obeys the cluster decomposition principle . if one of the three particles is separated beyond the range of the correlations , i.e. , to distances where @xmath100 vanishes , then the transformation reduces to the two - body transformation for the remaining pair . we will use this three - body transformation to calculate the local three - body contributions of the correlated hamiltonian , i.e. , the correlated potential and the local part of the correlated kinetic energy . the irreducible three - body part @xmath103}$ ] of the correlated potential is given by @xmath104 } & = { \ensuremath{{\ensuremath{{{{\ensuremath{\bm{c}}}}}^{\dag}}}}}({\ensuremath{{\ensuremath{\bm{v}}}}}_{12 } + { \ensuremath{{\ensuremath{\bm{v}}}}}_{13 } + { \ensuremath{{\ensuremath{\bm{v}}}}}_{23})\ , { \ensuremath{{\ensuremath{\bm{c}}}}}\\ & - ( { \ensuremath{\tilde{{\ensuremath{{\ensuremath{\bm{v}}}}}}}}^{[2]}_{12 } + { \ensuremath{\tilde{{\ensuremath{{\ensuremath{\bm{v}}}}}}}}^{[2]}_{13 } + { \ensuremath{\tilde{{\ensuremath{{\ensuremath{\bm{v}}}}}}}}^{[2]}_{23 } ) , \end{split}\ ] ] where @xmath105 is the uncorrelated two - body potential and @xmath106}_{ij}$ ] is the two - body part of the correlated potential . the first term describes the fully correlated two - body potential in a three - body system , which is given by a three - body coordinate transformation according to . the second term is the sum of the two - body correlated potentials . an analogous expression results for the local three - body part of the correlated kinetic energy @xmath107}$ ] , which involves and .

the unitary correlation operator method ( ucom ) is employed to treat short - range correlations in both , homogeneous liquid and small droplets of bosoniche atoms . the dominating short - range correlations in these systems are described by an unitary transformation in the two - body relative coordinate , applied either to the many - body state or to the hamiltonian and other operators . it is shown that the two - body correlated interaction can describe the binding energy of clusters of up to 6 atoms very well , the numerical effort consisting only in calculating one two - body matrix element with gaussian single - particle states . only one adjusted parameter the binding energies and radii of larger droplets and the equation of state of the homogeneoushe liquid can be described quantitatively in a physically intuitive and numerically simple way .

the unitary correlation operator method ( ucom ) is employed to treat short - range correlations in both , homogeneous liquid and small droplets of bosoniche atoms . the dominating short - range correlations in these systems are described by an unitary transformation in the two - body relative coordinate , applied either to the many - body state or to the hamiltonian and other operators . it is shown that the two - body correlated interaction can describe the binding energy of clusters of up to 6 atoms very well , the numerical effort consisting only in calculating one two - body matrix element with gaussian single - particle states . the increasing density of bigger droplets requires the inclusion of correlation effects beyond the two - body order , which are successfully implemented by a density - dependent two - body correlator . with only one adjusted parameter the binding energies and radii of larger droplets and the equation of state of the homogeneoushe liquid can be described quantitatively in a physically intuitive and numerically simple way .

astro-ph0002490

i

we have used the vla radio telescope to image a contiguous @xmath36 area to a ( mean ) limiting ( @xmath1 ) sensitivity of @xmath200 mjy . from a total of 62 detections , the results of optical and near - infrared photometry are reported for 43 sources . our optical photometry is more sensitive than previous optical follow - up studies of radio surveys of similar depth . our main findings are : \(1 ) we have used a robust , likelihood - ratio method for determining optical identifications and their reliability . this method is seldom used in identification studies and is insensitive to assumptions concerning fluctuations in background source density and gaussian error distributions . we assigned optical candidates to 26 radio sources with reliability @xmath8 . nine radio sources are uncertain and/or ambiguous , and eight are empty fields . near - infrared photometry from the _ 2mass _ database was reported for 7 sources . \(2 ) the eight optical empty field sources all display compact and symmetric radio morphologies and most probably represent compact starbursts at @xmath136 strongly obscured by dust . they may require at least 4 magnitudes optical extinction to account for their large radio to optical flux ratio compared to the identified population . our conclusion for them being ` compact starbursts ' is very tentative as it is purely based on starburst versus agn number statistics expected from sub - mjy radio surveys . further deep infrared / optical imaging and spectroscopy will be necessary . \(3 ) consistent with previous studies , our deep ( @xmath3 ) optical imaging shows that the optical appearence can be divided into two classes according to radio flux - density : elliptical - like morphologies for @xmath132 mjy , and peculiar or disturbed for @xmath201 mjy . \(4 ) using a stellar synthesis model which includes radio emission and dust reddening , we find that the near - infrared to optical emission in a small , bright sub - sample is reddened by ` optically thin ' dust with @xmath9 mag , regardless of morphological type . this appears consistent with other more direct determinations . consistent with previous studies , the radio emission from early - type systems seems to be powered by agn rather than star - formation to account for their anomalously large radio to optical(near - infrared ) ratios . despite the lack of spectroscopic information , our study of a homogeneous population of faint radio sources has stressed the importance of dust on studies of intrinsic galaxy properties and their evolution at optical wavelengths . a future goal would be to obtain spectra , or multi - color optical / near - infrared photometry to better explore these sources and the validity of the simple stellar synthesis models presented in this paper . the ever improving resolution ( and sensitivity ) capabilities of optical / near - ir detectors over those feasible at ( the longest ) radio wavelengths requires robust identification techniques to better ascertain their properties . likelihood - ratios provide one such technique . the present study complements other deep optical studies of faint radio sources to constitute a statistically significant sample for inferring their nature and importance to galaxy evolution . fjm thanks glenn morrison and joann olinger for valuable assistance with the data reduction and rosalie ewald for assistance with radio / optical image overlays . we thank the staff at palomar observatory for technical assistance during the observing run . this publication makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation . the national radio astronomy observatory is operated by associated universities , inc . , under cooperative agreement with the national science foundation . this research has made use of the nasa / ipac extragalactic database ( ned ) which is operated by the jet propulsion laboratory , caltech , under contract with the national aeronautics and space administration . fjm acknowledges support from a jpl / nasa postdoctoral fellowship grant . benn , c. r. , rowan - robinson , m. , mcmahon , r. g. , broadhurst , t. j. , & lawrence , a. , 1993 , , 263 , 98 blain , a. w. , smail , i. , ivison , r. j. , & kneib , i. -p . , 1999 , , 302 , 632 bruzual , a. g. , & charlot , s. , 1993 , , 405 , 538 bryant , p. , 1996 , in _ co observations of luminous infrared galaxies _ , phd thesis , california institute of technology calzetti , d. kinney , a. l. , & storchi - bergmann , t. , 1994 , , 429 , 582 calzetti , d. kinney , a. l. , & storchi - bergmann , t. , 1996 , , 458 , 132 calzetti , d. , armus , l. , bohlin , r. c. , kinney , a. l. , koornneef , j. , storchi - bergmann , t. , 2000 , , 533 , 682 ciliegi , p. , mcmahon , r. g. , miley , g. , gruppioni , c. , rowan - robinson , m. et al . , 1999 , , 302 , 222 condon , j. j. , 1989 , , 338 , 13 condon , j. j. , & yin , q. f. , 1990 , , 357 , 97 condon , j. j. , 1992 , , 30 , 575 condon , j. j. , 1997 , , 109 , 166 condon , j. j. , cotton , w. d. , greison , e. w. , yin , q. f. , perley , r. a. , taylor , g. b. , & broderick , j. j. , 1998 , , 115 , 1693 cram , l. e. , 1998 , , 506 , l85 cram , l. e. , hopkins , a. m. , mobasher , b. , & rowan - robinson , m. , 1998 , , 507 , 155 cutri et al . , 2000 , explanatory supplement to the 2mass second incremental data release , http://www.ipac.caltech.edu/2mass/releases/second/doc/explsup.html danese , l. , de zotti , g. , franceschini , a. , & toffolatti , l. , 1987 , , 318 , l15 de ruiter , h. r. , willis , a. g. , & arp , h. c. , 1977 , , 28 , 211 devriendt , j. e. , guiderdoni , b. , & sadat , r. , 1999 , , 350 , 381 downes , a. j. b. , peacock , j. a. , savage , a. , carrie , d. r. , 1986 , , 218 , 31 fanaroff , b. l. , & riley , j. m. , 1974 , , 167 , 31 gavazzi , g. , & scodeggio , m. , 1996 , , 312 , l29 georgakakis , a. , mobasher , b. , cram , l. , hopkins , a. , & lidman , c. , 1999 , , 306 , 708 genzel , r. , lutz , d. , sturm , e. , egami , e. , kunze , d. , moorwood , a. f. m. , rigopoulou , d. , spoon , h. w. w. , sternberg , a. , tacconi - garman , l. e. , tacconi , l. , and thatte , n. , 1998 , , 498 , 579 goudfrooij , p. , & de jong , t. , 1995 , , 298 , 784 gruppioni , c. , mignoli , m. , & zamorani , g. , 1998 , , 304 , 199 haarsma , d. b. , partridge , r. b. , waddington , i. , & windhorst , r. a. , 1999 , 19th texas symposium on relativistic astrophysics and cosmology , paris 1998 , ed . j. paul , t. montmerle , & e. aubourg ( cea sarclay ) , 600 haarsma , d. b. , partridge , r. b. , windhorst , r. a. , & richards , e. a. , 2000 , astro - ph/0007315 , to appear in hammer , f. , crampton , d. , lilly , s. j. , le fvre , o. , & kenet , t. , 1995 , , 276 , 1085 helou , g. , soifer , b. t. , & rowan - robinson , m. , 1985 , , 298 , l7 hopkins , a. m. , mobasher , b. , cram , l. , & rowan - robinson , m. , 1998 , , 296 , 839 kells , w. , dressler , a. , sivaramakrishnan , a. , carr , d. , koch , e. , epps , h. , hilyard , d. , & pardeilhan , g. , 1998 , , 110 , 1487 kron , r. g. , koo , d. c. , & windhorst , r. a. , 1985 , , 146 , 38 lonsdale , c. j. , conrow , t. , evans , t. , fullmer , l. , moshir , m. , chester , t. , yentis , d. , wolstencroft , r. , macgillivray , h. , & egret , d. , 1998 , new horizons from multi - wavelength sky surveys , proc . iau colloquium 179 , johns hopkins university , ed . b. mclean , d. golombek , j. hayes , & h. payne , kluwer academic publishers , p. 450 lutz , d. , spoon , h. w. w. , rigopoulou , d. , moorwood , a. f. m. , genzel , r. , 1998 , , 505 , l103 madau , p. , ferguson , h. c. , dickinson , m. e. , giavalisco , m. , steidel , c. c. , & fruchter a. , 1996 , , 283 , 1388 madau , p. , pozetti , l. , dickinson , m. , 1998 , , 498 , 106 maddox , s. j. , sutherland , w. j. , efstathiou , g. , loveday , j. , 1990 , , 243 , 692 metcalfe , n. , shanks , t. , fong , r. , jones , l. r. , 1991 , , 249 , 498 meurer , g. , heckman , t. m. , lehnert , m. d. , leitherer , c. , & lowenthal , j. , 1997 , , 114 , 54 mitchell , k. j. & condon , j. j. , 1985 , , 90 , 1957 mobasher , b. , cram , l. , georgakakis , a. , & hopkins , a. , 1999 , , 308 , 45 nakata , f. , shimasaku , k. , doi , m. , kashikawa , n. , kawasaki , w. et al . , 1999 , , 309 , l25 norris , r. p. , allen , d. a. , & roche , p. f. , 1988 , , 234 , 773 okumura , s. k. , kawabe , r. , ishiguro , m. , kasuga , t. , morita , k. i. , ishizuki , s. , 1991 , in _ dynamics of galaxies and their molecular cloud distributions _ f. combes , f. casoli , p. 425 , dordrecht : reidel oort , m. j. a. , 1987 , s , 71 , 221 pei , y. c. , 1992 , , 395 , 130 prestage , r. m. , & peacock , j. a. , 1983 , , 204 , 355 richards , e. a. , fomalont , e. b. , kellermann , k. i. , windhorst , r. a. , partridge , r. b. , cowie , l. l. , barger , a. j. , 1999 , , 526 , l73 richards , e. a. , 2000 , astro - 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this optical follow - up is much deeper than that of existing larger area radio surveys of similar radio sensitivity . , we optically identified 26 radio sources with probabilities , nine are uncertain / ambiguous detections , and eight are empty fields . comparisons with a stellar synthesis model that includes radio emission and dust reddening suggests that the near - infrared to optical emission in a small , bright sub - sample is reddened by ` optically thin ' dust with absorption mag , regardless of morphological type . this is consistent with other , more direct determinations of absorption .

the very large array ( vla ) has been used in c - configuration to map an area at 1.4 ghz with sensitivities of 0.305 , 0.325 , 0.380 and 0.450 mjy beam over four equal subareas . radio properties are presented for 62 detected sources . deep optical imaging to gunn mag using the hale 5-m telescope covering is reported for a subset of 43 sources . this optical follow - up is much deeper than that of existing larger area radio surveys of similar radio sensitivity . archival , and-band photometry from the two - micron all sky survey ( 2mass ) is also presented . using a robust likelihood - ratio technique , we optically identified 26 radio sources with probabilities , nine are uncertain / ambiguous detections , and eight are empty fields . comparisons with a stellar synthesis model that includes radio emission and dust reddening suggests that the near - infrared to optical emission in a small , bright sub - sample is reddened by ` optically thin ' dust with absorption mag , regardless of morphological type . this is consistent with other , more direct determinations of absorption . the radio to optical(near - infrared ) flux ratios of early - type galaxies require significant contamination in the radio by an active galactic nucleus ( agn ) , consistent with the current paradigm . using our simple modeling approach , we also discuss a potential diagnostic for selecting ultraluminous infrared galaxies ( uligs ) to from microjansky radio surveys .

1503.02963

c

this survey for gcs in the lg has identified 5 new gcs in the halo of m31 ( see table 1 ) . their properties do not appear to be exceptional , and their discovery suggests that the census of gcs in m31 may be still incomplete . the searches of the sdss galaxy catalogue for gcs described here and in papers i & ii have yielded a total of 22 new gcs near m31 ( see table 2 ) . these clusters span a wide range of @xmath14 ( 10 - 137 kpc ) , but even the most remote ones are likely to be members of m31 s halo . it is possible that measurements of their radial velocities and 3-d distances from m31 could reveal that some are not bound to it and are igcs . of all the objects that passed our 5 selection criteria for gcs and our visual inspection , only 12 are so far from m31 that they may be igcs in the lg ( see table 3 ) . while they resemble gcs in the sdss imaging ( see fig . 7 ) , there is still the possibility that they are galaxies , and we consider them to be only gc candidates . these objects need to be investigated in more detail to see if they are truly gcs . this sample of candidate igcs in the lg is clearly incomplete because our survey has covered only about one - third of the sky ( see fig . 8) , and we intend to expand the search in the southern sky . moreover , some igcs could have escaped our detection because they are hidden by obscuration near the galactic plane , blended with other objects , or fainter than our magnitude limit , which at the outer reaches of the lg excludes gcs with @xmath106 ( see fig . 2 ) . also , as mentioned previously , about 15% of the known gcs fail our selection criteria . even with these caveats , our survey suggests that the lg does not appear to have a large population of igcs , independently of their possible origin . we gratefully acknowledge the technical support provided by gabriele zinn throughout this project , which greatly facilitated its completion . this research has been supported by nsf grant ast-1108948 to yale university . this project would not have been possible without the public release of the data from the sloan digital sky survey iii and the very useful tools that the sdss has provided for accessing and examining the publically released data . funding for sdss - iii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , and the u.s . department of energy office of science . the sdss - iii web site is http://www.sdss3.org/. sdss - iii is managed by the astrophysical research consortium for the participating institutions of the sdss - iii collaboration including the university of arizona , the brazilian participation group , brookhaven national laboratory , university of cambridge , carnegie mellon university , university of florida , the french participation group , the german participation group , harvard university , the instituto de astrofisica de canarias , the michigan state / notre dame / jina participation group , johns hopkins university , lawrence berkeley national laboratory , max planck institute for astrophysics , max planck institute for extraterrestrial physics , new mexico state university , new york university , ohio state university , pennsylvania state university , university of portsmouth , princeton university , the spanish participation group , university of tokyo , university of utah , vanderbilt university , university of virginia , university of washington , and yale university . this publication makes use of data products from the wide - field infrared survey explorer , which is a joint project of the university of california , los angeles , and the jet propulsion laboratory / california institute of technology , funded by the national aeronautics and space administration . it also used observations made by the galaxy evolution explorer satellite , which were obtained through the galexview website . dtzz-06 & 9.48287 & 41.30932 & 18.82@xmath1070.03 & 2.62@xmath1070.08 & 0.72@xmath1070.06 & 1.11@xmath1070.15 & 3.63 & 0.043@xmath1070.032 + dtzz-08 & 9.63313 & 39.86855 & 18.22@xmath1070.01 & 4.69@xmath1070.27 & 1.01@xmath1070.02 & 1.59@xmath1070.06 & 3.28 & 0.088@xmath1070.051 + dtzz-09 & 9.75310 & 41.23024 & 17.89@xmath1070.01 & 3.89@xmath1070.07 & 0.81@xmath1070.03 & 1.04@xmath1070.08 & 3.54 & 0.119@xmath1070.046 + dtzz-13 & 11.43322 & 42.65674 & 18.90@xmath1070.02 & 3.84@xmath1070.16 & 1.04@xmath1070.03 & 2.02@xmath1070.07 & 3.79 & 0.050@xmath1070.019 + dtzz-14 & 11.59881 & 42.60960 & 18.92@xmath1070.02 & & 1.02@xmath1070.04 & 1.05@xmath1070.14 & 3.62 & 0.078@xmath1070.034 & + dtzz-01 & a & 5.14119 & 36.65953 & 17.44 & 0.82 & -7.0 & 8.5 & 86 & b.c + dtzz-02 & b & 6.71750 & 38.74947 & 15.99 & 0.69 & -8.5 & 4.2 & 54 & b , c + dtzz-03 & c & 7.86467 & 39.53942 & 17.33 & 0.68 & -7.1 & 4.1 & 38 & b , c + dtzz-04 & sdss1 & 9.00774 & 40.49723 & 17.36 & 1.08 & -7.1 & 10.5 & 20 & b , c + dtzz-05 & d & 9.03580 & 39.29165 & 17.24 & 0.73 & -7.2 & 4.1 & 32 & b + dtzz-06 & & 9.48287 & 41.30932 & 18.82 & 0.72 & -5.6 & 9.7 & 12 & b + dtzz-07 & e & 9.61483 & 40.65835 & 18.26 & 1.01 & -6.2 & 5.6 & 14 & b + dtzz-08 & & 9.63313 & 39.86855 & 18.22 & 1.01 & -6.2 & 5.1 & 22 & b + dtzz-09 & & 9.75310 & 41.23024 & 17.89 & 0.81 & -6.6 & 6.3 & 10 & b + dtzz-10 & sdss3 & 9.80443 & 41.70220 & 18.25 & 1.08 & -6.2 & 5.9 & 11 & b , c + dtzz-11 & sdss4 & 10.32496 & 42.77124 & 17.71 & 1.14 & -6.8 & 7.2 & 21 & b , c + dtzz-12 & sdss6 & 10.61489 & 39.92444 & 18.51 & 0.93 & -6.0 & 7.1 & 18 & b , c + dtzz-13 & & 11.43322 & 42.65674 & 18.90 & 1.04 & -5.6 & 4.7 & 20 & b + dtzz-14 & & 11.59881 & 42.60960 & 18.92 & 1.02 & -5.5 & 6.3 & 21 & b + dtzz-15 & sdss8 & 12.65142 & 42.53047 & 18.57 & 1.10 & -5.9 & 9.1 & 26 & b , c + dtzz-16 & sdss9 & 13.41490 & 42.58747 & 17.20 & 0.66 & -7.3 & 7.2 & 33 & b , c + dtzz-17 & sdss11 & 14.73495 & 42.46061 & 15.61 & 0.70 & -8.9 & 4.0 & 44 & b , c + dtzz-18 & sdss12 & 18.19590 & 42.42356 & 16.88 & 0.74 & -7.6 & 5.0 & 78 & b , c + dtzz-19 & sdss15 & 20.76470 & 41.91971 & 16.77 & 0.70 & -7.7 & 4.0 & 103 & b , c + dtzz-20 & c62 & 21.94838 & 40.67996 & 18.71 & 0.76 & -5.8 & 11.3 & 116 & b , c + dtzz-21 & g & 22.20478 & 47.07277 & 16.98 & 0.81 & -7.5 & 6.1 & 137 & b , d + dtzz-22 & sdss16 & 22.25898 & 40.78570 & 18.25 & 0.83 & -6.2 & 6.6 & 119 & b , c + dtzz - c01 & 13.61358 & 4.18373 & 18.72@xmath1070.08 & 1.68@xmath1070.06 & 0.31@xmath1070.12 & 1.46@xmath1070.17 & 2.78 & 0.041@xmath1070.025 & 2.7 + dtzz - c02 & 17.34474 & -5.91597 & 18.08@xmath1070.04 & & 0.73@xmath1070.04 & 1.67@xmath1070.06 & 2.82 & 0.072@xmath1070.075 & 3.4 + dtzz - c03 & 31.37672 & 6.77809 & 17.84@xmath1070.01 & 1.98@xmath1070.14@xmath107 & 0.46@xmath1070.02 & 1.31@xmath1070.06 & 3.30 & 0.034@xmath1070.010 & 2.1 + dtzz - c04 & 37.649609 & 46.31996 & 17.25@xmath1070.01 & 2.29@xmath1070.20 & 0.85@xmath1070.02 & 1.22@xmath1070.05 & 3.02@xmath1070.33 & 0.071@xmath1070.041 & 3.2 + dtzz - c05 & 102.15198 & -18.38880 & 17.71@xmath1070.04 & & 0.69@xmath1070.07 & 1.19@xmath1070.10 & 3.84 & 0.100@xmath1070.057 & 2.7 : + dtzz - c06 & 120.87215 & 13.07730 & 18.20@xmath1070.01 & & 0.85@xmath1070.03 & 1.70@xmath1070.07 & 3.95 & 0.067@xmath1070.029 & 2.2 + dtzz - c07 & 152.40421 & 61.26622 & 18.53@xmath1070.03 & 2.01@xmath1070.07 & 0.60@xmath1070.05 & 0.19@xmath1070.20 & 3.57 & 0.047@xmath1070.037 & 2.1 + dtzz - c08 & 238.65523 & 12.92038 & 18.00@xmath1070.01 & 1.47@xmath1070.10 & 0.37@xmath1070.03 & 0.91@xmath1070.11 & 3.94 & 0.035@xmath1070.019 & 2.1 + dtzz - c09 & 250.07475 & 54.96822 & 17.66@xmath1070.01 & 3.78@xmath1070.45 & 0.93@xmath1070.01 & 1.41@xmath1070.03 & 2.30 & 0.074@xmath1070.036 & 2.4 + dtzz - c10 & 255.93616 & 38.79727 & 18.02@xmath1070.01 & 2.89@xmath1070.08 & 0.93@xmath1070.02 & 1.90@xmath1070.04 & 2.58@xmath1070.39 & 0.068@xmath1070.028 & 1.2 + dtzz - c11 & 313.82498 & 54.71283 & 15.51@xmath1070.01 & & 0.85@xmath1070.02 & 1.56@xmath1070.03 & 1.14 & 0.079@xmath1070.051 & 1.3 + dtzz - c12 & 343.69748 & 17.43929 & 18.08@xmath1070.02 & & 0.63@xmath1070.03 & 1.36@xmath1070.08 & 3.90 & 0.067@xmath1070.016 & 2.8 + m81-c1 & 148.10805 & 68.80711 & 19.22@xmath1070.02 & 1.84@xmath1070.03 & 0.54@xmath1070.03 & 1.89@xmath1070.10 & 3.99 & 0.049@xmath1070.014 & 24 + m81-c2 & 148.57085 & 68.92275 & 17.37@xmath1070.02 & 3.24@xmath1070.03 & 0.76@xmath1070.01 & 1.46@xmath1070.04 & 2.24 & 0.046@xmath1070.024 & 12 + m81-c3 & 149.52321 & 69.57946 & 18.46@xmath1070.01 & 3.20@xmath1070.04 & 0.68@xmath1070.02 & 1.57@xmath1070.08 & 3.96 & 0.041@xmath1070.026 & 36 + m81-c4 & 151.32164 & 68.77572 & 18.51@xmath1070.01 & 3.82@xmath1070.32 & 0.84@xmath1070.02 & 1.08@xmath1070.11 & 3.61 & 0.073@xmath1070.031 & 58 + m81-c5 & 158.17458 & 65.70965 & 17.99@xmath1070.01 & 2.92@xmath1070.10 & 0.79@xmath1070.01 & 1.74@xmath1070.04 & 3.11 & 0.060@xmath1070.020 & 309 + gc-1 & 148.35931 & 69.52164 & 18.26@xmath1070.01 & 3.36@xmath1070.05 & 0.76@xmath1070.02 & 1.14@xmath1070.09 & 3.75 & 0.037@xmath1070.021 & 31 + gc-2 & 148.33411 & 69.65462 & 17.31@xmath1070.01 & 3.29@xmath1070.03 & 0.81@xmath1070.01 & 1.23@xmath1070.05 & 2.45 & 0.067@xmath1070.030 & 39 +

even though this search covers only one - third of the sky and some gcs could have been missed , it suggests that the lg does not contain a large population of igcs more luminous than . in the direction of the m81 group , the search yielded five candidate gcs , probable members of that group

the whole sloan digital sky survey ( sdss , ) has been searched for intergalactic globular clusters ( igcs ) in the local group ( lg ) . using optical , infrared , and ultraviolet photometric selection criteria and photometric redshifts , the of objects in the sdss galaxy catalogue were reduced to only 183,791 brighter than that might be gcs . visual examination of their sdss images recovered 84% of the confirmed gcs in m31 and m33 and yielded 17 new gc candidates , 5 of them of high confidence , which we could confirm as gcs in megaprime images from the canada , france , hawaii telescope . these 5 gcs are within m31 s halo , but the other 12 candidates are not close to lg galaxies or galaxies within 3 mpc of the lg . even though this search covers only one - third of the sky and some gcs could have been missed , it suggests that the lg does not contain a large population of igcs more luminous than . in the direction of the m81 group , the search yielded five candidate gcs , probable members of that group

cond-mat0212321

c

taking a one - dimensional @xmath1-function bose gas as a typical example of integrable systems , we have derived the @xmath0-particle partition function . a method in this paper , referred to as the direct method , is an exact analysis of the partition function only based on the periodic boundary condition . using the explicit expression of the partition function , we have calculated the @xmath0-particle cluster integral , and proved a perfect agreement between the results of this direct method and the thermal bethe ansatz ( tba ) method . the extensions and applications of the direct method to integrable and non - integrable systems may clarify mathematical structures of the tba method . those problems are left for future studies .

the-particle partition function of a one - dimensional-function bose gas is calculated explicitly using only the periodic boundary condition ( the bethe ansatz equation ) . the-particles cluster integrals are shown to be the same as those by the thermal bethe ansatz method . + + keywords : thermal bethe ansatz method ,-function bose gas , integrable system , partition function , cluster expansion

the-particle partition function of a one - dimensional-function bose gas is calculated explicitly using only the periodic boundary condition ( the bethe ansatz equation ) . the-particles cluster integrals are shown to be the same as those by the thermal bethe ansatz method . + + keywords : thermal bethe ansatz method ,-function bose gas , integrable system , partition function , cluster expansion

cond-mat0701020

i

kagome antiferromagnets are among the most extreme examples of frustrated spin systems realized with nearest - neighbor interactions . both the frustration in each triangular unit and the rather loose `` corner - sharing '' aggregation of these units into the kagome lattice suppress the tendency to magnetically order . on the classical level , kagome spin systems are known to exhibit rather special properties : nearest - neighbor ising and xy models remain disordered even in the zero - temperature limit , while the @xmath2 system undergoes order - by - disorder into a coplanar spin structure.@xcite quantum kagome antiferromagnets , which are much less understood , provide a fascinating arena for the possible realization of spin liquids . early exact diagonalization and series expansion studies@xcite as well as further exhaustive numerical works , @xcite provide strong evidence for the absence of any magnetic order or other symmetry breaking in the nearest neighbor spin-1/2 system . moreover , a plethora of low energy singlet excitations is found , below a small ( if non - zero ) spin gap . but the precise nature of the putative spin liquid phase in this model has remained elusive . on the experimental front , several quasi - two dimensional materials with magnetic moments in a kagome arrangement have been studied , including srcr@xmath3ga@xmath4o@xmath5 with cr@xmath6 ( @xmath7 ) moments@xcite , jarosites km@xmath8(oh)@xmath9(so@xmath10)@xmath11 with m@xmath12cr@xmath6 or fe@xmath6 ( @xmath13 ) moments@xcite , and volborthite cu@xmath8v@xmath14o@xmath15(oh)@xmath16 2h@xmath14o with cu@xmath17 ( @xmath18 ) moments@xcite . recently , herbertsmithite zncu@xmath8(oh)@xmath9cl@xmath14 which also has cu@xmath17 moments on a kagome lattice was synthesized for which no magnetic order is observed down to 50 mk despite the estimated exchange constant of 300 k. @xcite the second layer of @xmath19he absorbed on graphoile is also believed to realize the kagome magnet.@xcite the suppression of long - range spin correlations or other signs of symmetry breaking down to temperatures much lower than the characteristic exchange energy scale is manifest in all of these materials , consistent with expectations . moreover , there is evidence for low energy excitations , both spin carrying and singlets . but the ultimate zero - temperature spin liquid state is often masked in these systems by magnetic ordering or glassy behavior at the lowest temperatures , perhaps due to additional interactions or impurities , rendering the experimental study of the spin liquid properties problematic . new materials and other experimental developments are changing this situation , and the question of the quantum spin liquid ground state of the kagome antiferromagnet is becoming more prominent . there are two broad classes of spin liquids which have been explored theoretically , both in general terms and for the kagome antiferromagnet in particular . the first class comprise the `` topological '' spin liquids , which have a gap to all excitations and have particle - like excitations with fractional quantum numbers above the gap . arguably , the simplest topological liquids are the so - called @xmath20 spin liquids , which support a vortex like excitation - a vison - in addition to the spin one - half spinon . for the kagome antiferromagnet , sachdev @xcite and more recently wang and vishwanath @xcite have employed a schwinger boson approach to systematically access several different @xmath20 spin liquids . for a kagome antiferromagnet with easy axis anisotropy and further neighbor interactions , balents@xcite unambiguously established the presence of a @xmath20 spin liquid , obtaining an exact ground state wavefunction in a particular limit . quantum dimer models on the kagome lattice can also support a @xmath20 topological phase@xcite . spin liquids with topological order and time reversal symmetry breaking , the chiral spin liquids which are closely analogous to fractional quantum hall states , have been found on the kagome lattice@xcite within a fermionic representation of the spins . but all of these topological liquids are gapped , and can not account for the presence of many low excitations found in the exact diagonalization studies and suggested by the experiments . a second class of spin liquids - the `` critical '' or `` algebraic spin liquids '' ( asl ) - have gapless singlet and spin carrying excitations . although these spin liquids share many properties with quantum critical points such as correlation functions falling off as power laws with non - trivial exponents , they are believed to be stable quantum phases of matter . within a fermionic representation of the spins , hastings@xcite explored an algebraic spin liquid on the kagome lattice , and more recently ran@xcite have extended his analysis in an attempt to explain the observed properties of herbertsmithite zncu@xmath0(oh)@xmath21cl@xmath11 . in this paper , motivated by the experiments on the kagome materials and the numerical studies , we pursue yet a different approach to the possible spin liquid state of the kagome antiferromagnet . as detailed below , for a kagome antiferromagnet with easy - plane anisotropy we find evidence for a new critical spin liquid , an `` algebraic vortex liquid '' ( avl ) phase . earlier we had introduced and explored the avl in the context of the triangular xxz antiferromagnet in refs . . compared to the slave particle techniques for studying frustrated quantum antiferromagnets , the avl approach is less microscopically faithful to a specific spin hamiltonian , but has the virtue of being unbiased . our approach requires the presence of an easy - plane anisotropy , which for a spin one - half system can come from the dzyaloshinskii - moriya interaction , although this is usually quite small . but for higher half - integer spin systems , spin - orbit coupling allows for a single ion anisotropy @xmath22 which can be appreciable . with @xmath23 this leads to an easy - plane spin character , and from a symmetry stand point our analysis should be relevant . moreover , a very interesting unpublished exact diagonalization study by sindzingre @xcite suggests that an unusual spin liquid phase is also realized for the nearest - neighbor quantum xy antiferromagnet . he finds a small gap to @xmath24 excitations , but below this gap there is a plethora of @xmath25 states , which is reminiscent of the many singlet excitations below the triplet gap in the heisenberg su(2 ) spin model.@xcite thus , based on the exact diagonalization studies , the easy plane anisotropy does not appear to gap out the putative critical spin liquid of the heisenberg model , although it will presumably modify its detailed character . our approach to easy - plane frustrated quantum antiferromagnets focuses on vortex defects in the spin configurations , rather than the spins themselves . in this picture , the magnetically ordered phases do not have vortices present in the ground state . but there will be gapped vortices , and these can lead to important effects on the spectrum . for example , vortex - antivortex ( i.e. roton ) excitations can lead to minima in the structure factor at particular wavevectors in the brillouin zone , @xcite in analogy to superfluid he-4 . as we demonstrated for the triangular antiferromagnet and explore below for the kagome lattice , our approach predicts specific locations in the brillouin zone for the roton minima , which could perhaps be checked by high order spin wave expansion techniques . on the other hand , the presence of mobile vortex defects in the ground state can destroy magnetic order , giving access to various quantum paramagnets . if the vortices themselves condense , the usual result is the breaking of lattice symmetries , such as in a spin peierls state . but if the vortices remain gapless one can access a critical spin liquid phase . for frustrated spin models the usual duality transformation to vortex degrees of freedom does not resolve the geometric frustration since the vortices are at finite density . however , by binding @xmath26-flux to each vortex converting them into fermions coupled to a chern - simons gauge field followed by a simple flux - smearing mean - field treatment gives a simple way to describe the vortices . the long - range interaction of vortices actually works to our advantage here since it suppresses their density fluctuations and leads essentially to incompressibility of the vortex fluid . as demonstrated in the easy - plane quantum antiferromagnet on the triangular lattice,@xcite including fluctuations about the flux - smeared mean field enables one to access a critical spin liquid with gapless vortices . the theory has the structure of a ( 2 + 1)-dimensional [ ( 2 + 1)d ] quantum electrodynamics ( qed@xmath0 ) , with relativistic fermionic vortices minimally coupled to a non - compact u(1 ) gauge field . the resulting algebraic vortex liquid ( avl ) phase is a novel critical spin liquid phase that exhibits neither magnetic nor any other symmetry - breaking order . this approach also allows one to study many competing orders in the vicinity of the gapless phase . when applied to the spin-1/2 easy - plane antiferromagnet on the kagome lattice , the duality transformation combined with fermionization and flux smearing also leads to a low - energy effective qed@xmath0 theory with 8 flavors of dirac fermions with an emergent @xmath1 flavor symmetry . amusingly , avl s with @xmath27 @xcite , @xmath28 @xcite and @xmath29 @xcite emergent symmetries were obtained previously for quantum xy antiferromagnets on the triangular lattice , with integer spin , half - integer spin and half - integer spin in an applied magnetic field , respectively . qed@xmath30 theory with @xmath31 flavors of dirac fermions is known to realize a stable critical phase for sufficiently large @xmath32 . while numerical attempts to determine @xmath33 are so far inconclusive,@xcite an estimate from the large-@xmath31 expansion suggests @xmath34.@xcite it seems very likely that @xmath35 is large enough , implying the presence of a stable critical spin liquid ground state for the easy - plane spin-1/2 quantum antiferromagnet on the kagome lattice . although the algebraic vortex liquid and the algebraic spin liquid@xcite obtained for the kagome lattice are accessed in rather different ways , they share a number of commonalities , both theoretically and with regard to their experimental implications . both approaches end with a qed@xmath0 theory , the former a non - compact gauge field theory with fermionic vortices carrying an emergent su(8 ) symmetry , and the latter a compact gauge theory with fermionic spinons with su(4 ) symmetry . the non - compact nature of the gauge field in the avl follows from the fact that the @xmath36 component of spin appears as the gauge flux in the dualized theory . hence the states with zero flux and @xmath26 flux are physically distinct ; moreover , it follows that since the total @xmath36 is conserved , so also is the total gauge flux . this should be contrasted with the slave particle approach , where a compact gauge theory arises on the lattice and there is no such conservation law . physically , this means that dynamical monopole operators , which could potentially destabilize the spin liquid and open a gap in the excitation spectrum , are not allowed in our low - energy theory for the avl , while they are allowed in a low - energy description of spin liquids obtained using a slave particle framework . with regard to experimentally accessible quantities , both theories predict a power law specific heat @xmath37 at low temperatures , which follows from the linear dispersion of the fermions , and which would dominate the phonon contribution to the specific heat for magnets with exchange interactions significantly smaller that the debye frequency . @xcite because the spinons couple directly to magnetic fields , one would expect the specific heat in the asl to be more sensitive to an external applied magnetic field than the avl phase . both theories predict a thermal conductivity which vanishes as @xmath38 , @xcite which is an interesting experimental signature reflecting the dynamical mobility of the gapless excitations . the momentum resolved dynamical spin structure factor which can be extracted from inelastic neutron experiments can in principle give very detailed information about the spin dynamics . following the framework developed on the triangular lattice,@xcite for the kagome avl we can extract the wavevectors in the magnetic brillouin zone which have gapless spin carrying excitations , and find 12 of them as shown in fig . [ fig : enhbilin.eps ] . in contrast , the kagome asl phase is predicted to have gapless spin excitations at only 4 of these 12 momenta . the momentum space location of the gapless excitations is perhaps the best way to try and distinguish experimentally between these two ( and any other ) critical spin liquids . the rest of the paper is organized as follows . we start by introducing our model in sec . [ sec : model ] . the low - energy effective field theory is then developed in sec . [ sec : fermionized vortex description ] . in sec . [ sec : properties of the avl phase ] , the properties of the critical spin liquid phase ( avl phase ) are discussed , especially , the spin excitation ( roton spectrum ) ( fig . [ fig : spinwaves ] ) , the @xmath36 dynamical structure factor ( eq . [ eq : sz structure factor ] ) , and the in - plane dynamical structure factor ( eq . [ eq : s^+- structure factor ] ) . we conclude in sec . [ sec : conclusion ] . some details of the analysis are presented in three appendices .

there is growing evidence from both experiment and numerical studies that low half - odd integer quantum spins on a kagome lattice with predominant antiferromagnetic near neighbor interactions do not order magnetically or break lattice symmetries even at temperatures much lower than the exchange interaction strength . moreover , there appear to be a plethora of low energy excitations , predominantly singlets but also spin carrying , which suggest that the putative underlying quantum spin liquid is a gapless `` critical spin liquid '' rather than a gapped spin liquid with topological order . here , we develop an effective field theory approach for the spin-1/2 heisenberg model with easy - plane anisotropy on the kagome lattice . by employing a vortex duality transformation , followed by a fermionization and flux - smearing , we obtain access to a gapless yet stable critical spin liquid phase , which is described by ( 2 + 1)-dimensional quantum electrodynamics ( qed ) with an emergent flavor symmetry . the specific heat , thermal conductivity , and dynamical structure factor are extracted from the effective field theory , and contrasted with other theoretical approaches to the kagome antiferromagnet .

there is growing evidence from both experiment and numerical studies that low half - odd integer quantum spins on a kagome lattice with predominant antiferromagnetic near neighbor interactions do not order magnetically or break lattice symmetries even at temperatures much lower than the exchange interaction strength . moreover , there appear to be a plethora of low energy excitations , predominantly singlets but also spin carrying , which suggest that the putative underlying quantum spin liquid is a gapless `` critical spin liquid '' rather than a gapped spin liquid with topological order . here , we develop an effective field theory approach for the spin-1/2 heisenberg model with easy - plane anisotropy on the kagome lattice . by employing a vortex duality transformation , followed by a fermionization and flux - smearing , we obtain access to a gapless yet stable critical spin liquid phase , which is described by ( 2 + 1)-dimensional quantum electrodynamics ( qed ) with an emergent flavor symmetry . the specific heat , thermal conductivity , and dynamical structure factor are extracted from the effective field theory , and contrasted with other theoretical approaches to the kagome antiferromagnet .

1111.6595

i

it is well - known that late - type stars show magnetic activity similar to the activity of our sun , but the physics of ` stellar ' activity is not yet well understood . in addition , the activity level manifested by late - type stars is much higher than that observed for the sun . fr cnc (= bd+16 1753 = mcc 527 = 1es 0829 + 15.9 = 1rxs j083230.9 + 154940 = hip 41889 ) was first mentioned as a probable active star when it was identified as the optical counterpart of a soft x - ray source 1es 0829 + 15.9 in the _ einstein slew survey_. it has @xmath12 mag , spectral type k8v , the x - ray flux of @xmath13 ( @xcite @xcite ; @xcite @xcite ) . lately , this object was rediscovered as an x - ray source 1rxs j083230.9 + 154940 in the _ rosat _ all - sky survey ( rass ) with lower x - ray flux at the level of @xmath14 ( @xcite @xcite ) . the x - ray luminosity of @xmath15 and the ratio of x - ray to bolometric luminosity @xmath16 of @xmath17 ( @xcite @xcite ) indicates that this object has an active corona ( @xcite @xcite ) . in the _ hipparcos _ catalogue this star was mentioned as an unsolved variable star with the identifier hip 41889 and @xmath18 mag amplitude of variability ( @xcite @xcite ) . it was classified as by dra type star ( i.e. its variability caused by rotational modulation of starspots ) and given the name fr cnc by @xcite . for analysis of _ hipparcos _ observations see @xcite . fr cnc ( @xmath19 and @xmath20 ) has @xmath21 marcsec parallax ( @xcite @xcite ) that implies a distance of @xmath22 pc and an absolute magnitude of @xmath23 . the kinematics of fr cnc suggests that it is a very young ( 3555 myr ) main - sequence star and a possible member of the ic 2391 supercluster , as it was shown by @xcite . @xcite concluded that fr cnc is not a binary system , based on two measurements of the rv . the presence of ca ii h & k and h@xmath24 emission lines in the spectra indicates high chromospheric activity in fr cnc ( @xcite @xcite ; @xcite @xcite ) . in quiescent state this object manifests optical variability with the dominant period @xmath25 d due to the presence of starspots and axial rotation ( @xcite @xcite ) . in addition , photometry obtained in 2005 february april with kilodegree extremely little telescope indicates fr cnc optical variability with @xmath26 d period ( @xcite @xcite ) when monitoring the praesepe open cluster for transiting exoplanets . the first ever - detected optical flare of this object was observed during ccd photometry of fr cnc on 2006 november 23 at crimean astrophysical observatory ( ukraine ) with 38-cm cassegrain telescope and described by @xcite . the flare was observed in @xmath27-bands ( see fig . [ ibvs ] ) . the amplitude reached even 1 mag in the @xmath28-band and was decreasing towards the @xmath29-band . the flare energy output in the @xmath28-band was about @xmath30 and flare to quiescent flux ratio was 38.63 per cent .

we present the study of fr cnc , a young , active and spotted star . polarimetric observations indicate the probable presence of a supplementary source of polarization . [ firstpage ] stars : activity stars : flare stars : rotation stars : individual : fr cnc .

this is a part of a multiwavelength study aimed at use of complementary photometric , polarimetric and spectroscopic data to achieve an understanding of the activity process in late - type stars . here we present the study of fr cnc , a young , active and spotted star . we performed analysis of ( the all sky automated survey ) data for the years 20022008 and amended the value of the rotational period to be 0.826518 d. the amplitude of photometric variations decreased abruptly in the year 2005 , while the mean brightness remained the same , which was interpreted as a quick redistribution of spots . and broad band photometric calibration was performed for 166 stars in fr cnc vicinity . the photometry at terskol observatory shows two brightening episodes , one of which occurred at the same phase as the flare of 2006 november 23 . polarimetric observations indicate the probable presence of a supplementary source of polarization . we monitored fr cnc spectroscopically during the years 20042008 . we concluded that the rv changes can not be explained by the binary nature of fr cnc . we determined the spectral type of fr cnc as k7v . calculated galactic space - velocity components ( ) indicate that fr cnc belongs to the young disc population and might also belong to the ic 2391 moving group . based on li i .8 measurement , we estimated the age of fr cnc to be between 10120 myr . doppler tomography was applied to create a starspot image of fr cnc . we optimized the goodness of fit to the deconvolved profiles for axial inclination , equivalent width and sin , finding sin = km s and . we also generated a synthetic-band lightcurve based on doppler imaging that makes simultaneous use of spectroscopic and photometric data . this synthetic lightcurve displays the same morphology and amplitude as the observed one . the starspot distribution of fr cnc is also of interest since it is one of the latest spectral types to have been imaged . no polar spot was detected on fr cnc . [ firstpage ] stars : activity stars : flare stars : rotation stars : individual : fr cnc .

1111.6595

i

we have carried out a photometric , polarimetric and spectroscopic study of fr cnc . optical @xmath28-band photometry was carried out during 2007 march 2008 february at terskol branch of the astronomy institute ( russia ) . there are no peculiar features in the 2008 light curve , while in the 2007 photometry two brightening episodes were detected . one of them occurred at the same phase as the flare of november 23 , 2006 ( phase = @xmath130 ) and probably indicates that both of these events ( i.e. the flare on november 23 , 2006 and the photometric brightening episode ) originated from the same long - living active region on fr cnc . the non - detection of any other flares in our photometry except 2006 november 23 implies that fr cnc has a low frequency of flares . we analysed _ photometry obtained in 20022008 in @xmath11-band . no evidence of flares in _ _ data were found . the profiles of variability are different from season to season . the mean magnitude in @xmath11-band remained the same ( @xmath131 mag ) during 20022008 , while the amplitude decreased abruptly in 2005 . the proposed interpretation is a redistribution of spots / spot groups over the surface of the star , while the total percentage of the spotted area was assumed to be constant within the error limits . a detailed periodogram study of the _ asas-3 _ photometric data enabled us to derive a more accurate value for the period of fr cnc . we find that @xmath132 d. in addition , we also presented @xmath133 photometric calibration of 166 stars in fr cnc vicinity , whose @xmath11-magnitude is in the range of @xmath134@xmath135 mag . the @xmath3 broad - band polarimetric observations of fr cnc have been obtained at aries in nainital ( india ) at manora peak . the observed polarization in @xmath28-band is well matched with the theoretical values expected for zeeman polarization model . however , the observed polarization in @xmath11 and @xmath136 bands slightly exceeds the theoretical values and thompson and rayleigh scattering from inhomogeneous regions are not enough to explain the observed polarization excess . therefore the excess of linear polarization should come from an additional source of polarization . taking into account that we conclude that fr cnc is not a binary , the mechanism which can produce additional linear polarization is probably scattering in circumstellar material distributed in an asymmetric geometry ( e.g. see @xcite , @xcite ) . a total of 58 spectra of fr cnc , which have been obtained in 20042008 , were analysed in this work . based on our spectroscopic observations , fr cnc was classified as k7v star . rv analysis supports the single nature of fr cnc . anticorrelation between bis and rv also indicates that the rv variations are due to stellar activity variations and not due to a secondary companion . the kinematics study , based on obtained galactic space - velocity components ( @xmath4 ) of fr cnc , shows that this star clearly lies in the young disc population velocity space and might also belong to ic 2391 moving group , although the eggen kinematic criteria shows that fr cnc may not be a member of any mg in the young disc area . the li i @xmath56707.8 averaged @xmath106 measured is 34 m , giving the spectral type of fr cnc , it is in agreement with being a young object between 10120 myr . the h@xmath24 line was always observed above the continuum in all the obtained spectra . measuring the @xmath106 of this line , we found that the h@xmath24 emission @xmath106 average in every season is quite different . in 2004 , as with the photometry , spectroscopic indicators of chromospheric activity show a high level of activity which decreased in 2005 . the ca ii ( irt ) is included in our echelle spectra . from the ratio of excess emission @xmath106 we found that in fr cnc , ca ii emission comes from plage - like regions . we noticed that fr cnc can show an activity cycle of 4 - 5 years , although further follow up will confirm this periodicity . since fr cnc is a rapid rotator , we generated an indirect starspot map using the doppler tomography of stars imaging code . from it we derive @xmath6 sin @xmath7 = @xmath137 km s@xmath9 and @xmath138 . fr cnc belongs to one of the latest spectral types to have been imaged with the doppler tomography . we independently estimated a rotational velocity of fr cnc during our observations using queloz method ( sect . 5.3 ) and by the d.i . fits ( sect . although they are differences in the results of the two methods , they are consistent . in table [ tab : par ] we have put as the rotational velocity of fr cnc , the value obtained in the d.i . as it is likely more accurate . despite the short rotation period and its late spectral type , fr cnc shows very few flare events . it shows high level of activity as it is a young star , but an unusually short variability due to the redistribution of activity features on the stellar surface . while this variability is reflected in the changes of the amplitude of brightness , the mean brightness permanently is nearly constant , indicating that the percentage of stellar surface covered by spots is also constant . the spots location is also unusual , not showing a polar spot like other f k stars do but a distribution more resembling those seen in m1m2 dwarfs . although this may be indicative of a distributed dynamo , the mid - high latitude spot locations are more suggestive of an interface dynamo under the action of rapid rotation . we can only speculate as to whether fr cnc is representative of a regime in which a convective - shell - type dynamo gives way to a fully convective dynamo . polarimetric observations of the magnetic field by @xcite ( @xcite ) and @xcite ( @xcite ) for example suggest that this occurs at a later spectral type of m4 , whereas other chromospheric indicators show no obvious changes until later m spectral types ( e.g. @xcite @xcite ) . further spectroscopy with a higher cadence would enable more detailed maps to be derived , with multiple epochs enabling the evolution of starspots to be investigated .

the photometry at terskol observatory shows two brightening episodes , one of which occurred at the same phase as the flare of 2006 november 23 . calculated galactic space - velocity components ( ) indicate that fr cnc belongs to the young disc population and might also belong to the ic 2391 moving group . based on li i .8 measurement , we estimated the age of fr cnc to be between 10120 myr .

this is a part of a multiwavelength study aimed at use of complementary photometric , polarimetric and spectroscopic data to achieve an understanding of the activity process in late - type stars . here we present the study of fr cnc , a young , active and spotted star . we performed analysis of ( the all sky automated survey ) data for the years 20022008 and amended the value of the rotational period to be 0.826518 d. the amplitude of photometric variations decreased abruptly in the year 2005 , while the mean brightness remained the same , which was interpreted as a quick redistribution of spots . and broad band photometric calibration was performed for 166 stars in fr cnc vicinity . the photometry at terskol observatory shows two brightening episodes , one of which occurred at the same phase as the flare of 2006 november 23 . polarimetric observations indicate the probable presence of a supplementary source of polarization . we monitored fr cnc spectroscopically during the years 20042008 . we concluded that the rv changes can not be explained by the binary nature of fr cnc . we determined the spectral type of fr cnc as k7v . calculated galactic space - velocity components ( ) indicate that fr cnc belongs to the young disc population and might also belong to the ic 2391 moving group . based on li i .8 measurement , we estimated the age of fr cnc to be between 10120 myr . doppler tomography was applied to create a starspot image of fr cnc . we optimized the goodness of fit to the deconvolved profiles for axial inclination , equivalent width and sin , finding sin = km s and . we also generated a synthetic-band lightcurve based on doppler imaging that makes simultaneous use of spectroscopic and photometric data . this synthetic lightcurve displays the same morphology and amplitude as the observed one . the starspot distribution of fr cnc is also of interest since it is one of the latest spectral types to have been imaged . no polar spot was detected on fr cnc . [ firstpage ] stars : activity stars : flare stars : rotation stars : individual : fr cnc .

1609.02174

i

cooperative control of multi - robot / agent systems ( mrs / mas ) has generated wide interest for researchers in control and robotics communities . compared with a single robot , multiple robots can cooperatively accomplish complicated tasks with the advantages of high efficiency and robustness to the link failures . over the last decade , mrs have wide applications in implementing a large number of tasks ranging from coverage , deployment , rescue , to surveillance and reconnaissance . among these tasks , a basic one is to reach synchronization , i.e. , all robots reach the same state , which actually has close connection with many important engineering applications , such as rendezvous problem @xcite , agreement problem @xcite , distributed optimization @xcite and formation control @xcite . recently , the synchronization problem of mas has been extensively studied in the literature where the neighbor relations are typically modeled as graphs or networks . for example , and , respectively , studied the first - order discrete - time mas with undirected graphs and directed graphs . studied the mas with first - order continuous - time dynamics . the nonholonomic unicycle mrs are investigated by and . mas with nonlinear dynamics , time delays , and measurement noises are also considered @xcite . in almost all existing results , the neighbor graphs are required to satisfy certain connectivity assumptions for synchronization . how to verify or guarantee such conditions has been a challenging issue . in order to maintain connectivity of dynamical communication graphs , potential function methods are commonly used when designing the distributed control laws @xcite . for a real world mrs , it is more practical that the dynamics of the system are modeled in a continuous - time manner whereas the control laws are designed based on the sampled - data information . the sampled - data technique is of interest in many situations , such as unreliable information channels , limited bandwidth , transport delay . the synchronization of mas with sampled - data control laws has been studied @xcite , where the neighbor graphs are also required to satisfy certain connectivity assumptions . it is clear that the potential function techniques are not applicable for the analysis of mas with continuous - time dynamics and sampled - data control , because connectivity of the networks might be lost between sampling instants . how to analyze the synchronization behavior of such kind of systems becomes more challenging . in this paper , we first present a distributed sampled - data algorithm for a group of nonholonomic unicycle robots with continuous - time dynamics , and provide a comprehensive analysis for the synchronization of the closed - loop hybrid system . in our model , each robot has limited sensing and communication range , and the neighbor relations are described by proximity networks . a dwell time is assumed when updating information from neighbors , implying that the control signals are kept constant between the sampled instants and only updated at discrete - time instants . with such sampled - data information , our design of distributed control laws based on nearest - neighbor rules will clearly result in a hybrid closed - loop system , which is different from the case of discrete - time mas studied by and , and is also different from the previous results given by where the control law for the rotational speed is designed using the continuous - time information . for a multi - agent system , we may design a distributed algorithm to guarantee synchronization of the system , but the synchronization state is inherently determined by the initial states and model parameters . in many practical applications , we expect that the system achieves a desired synchronization state and we can treat that state as a reference signal . the agents that have access to the reference signal are referred to as leaders , and they can help steer the mrs to the desired state . although a large number of theoretical analysis and results for the leader - follower model have been provided , further theoretical investigation is still needed due to some limitations in the existing theory : i ) similar to the leaderless case , the neighbor graphs are required to be connected or contain spanning trees to guarantee that the followers track the reference signal @xcite , but there are few results to address how to verify such conditions . ii ) in order to guide all agents to accomplish complicated tasks , such as tracking time - varying signals and the containment control problem , a number of ( not only one ) leaders need to be introduced into the system @xcite . however , quantitative theoretical results for the number of leaders needed are still lack . hence , this paper considers also a multi - unicycle system with multiple leaders and presents some new quantitative results . the sampled - data information is used to design the control laws for the followers and leaders . for the case of the constant reference signal , we analyze the mrs with heterogeneous agents where the leaders and followers have different dynamics since the reference signal is only obtained by the leaders , and quantitatively provide the proportion of leaders needed to track the reference signal . in addition , we investigate the case where the reference signal is dynamic but piecewise constant , and provide quantitative results for the proportion of leaders needed to track a slowly time - varying signal by analyzing the hybrid dynamics at each stage . the main contributions of this paper are summarized into the following three aspects . ( i ) for the leaderless case , we establish a sufficient condition , imposed on the neighborhood radius , the dwell time and the maximum moving speed , to guarantee synchronization of the nonholonomic unicycles , which overcomes the difficulty of requiring _ a prior _ connectivity assumption on neighbor graphs used in most of the existing results . ( ii ) for the leader - follower model , we provide the proportion of leaders needed to guide all robots to track a reference signal which can be constant or slowly time - varying . these quantitative results illustrate that adding leaders is a feasible approach to guide mrs to accomplish some complicated tasks . ( iii ) for both the leaderless case and leader - following case , we provide comprehensive analysis for nonlinear hybrid closed - loop systems . different from the work of and , we need to estimate the synchronization rate of the continuous - time variables ( i.e. , speed and orientation ) . here the speed and orientation are determined by the corresponding values at sampling time instants and they are updated according to the states of relevant neighbors , and the neighbors are defined via the positions of all robots . hence , the positions , orientations and moving speeds of all robots are coupled . we deal with the coupled relationships by combining the dynamical trajectories of the robots at discrete - time instants with the analysis of continuous - time dynamics in sampling intervals . the rest of this paper is organized as follows . in section [ leaderless ] , we present the problem formulation for a leaderless model and provide the main result for synchronization . in section [ leader ] , we first investigate the leader - following problem where the leaders have constant reference signal , and quantitatively provide the ratio of the number of leaders to the number of followers needed to track the signal . we then extend our result to the dynamical tracking where the leaders have time - varying reference signal , and present some simulations to illustrate our theoretical results . concluding remarks are presented in section [ concluding ] . notations : for a vector @xmath0 , @xmath1 denotes the transpose of @xmath2 , and @xmath3 denotes the 2-norm , i.e. , @xmath4 . for a square matrix @xmath5 , @xmath6 denotes the 2-norm of @xmath7 , i.e. , @xmath8 . for any two positive sequences @xmath9 and @xmath10 , @xmath11 means that there exists a positive constant @xmath12 independent of @xmath13 , such that @xmath14 for any @xmath15 ; @xmath16 ( or ( @xmath17 ) ) means that @xmath18 ; @xmath19 , if there exist two positive constants @xmath20 and @xmath21 , such that @xmath22 .

this paper considers the distributed sampled - data control problem of a group of mobile robots connected via distance - induced proximity networks . a dwell time is assumed in order to avoid chattering in the neighbor relations that may be caused by abrupt changes of positions when updating information from neighbors . distributed sampled - data control laws are designed based on nearest neighbor rules , which in conjunction with continuous - time dynamics results in hybrid closed - loop systems . for uniformly and independently initial states , all these conditions depend only on the neighborhood radius , the maximum initial moving speed and the dwell time , without assuming _ a prior _ properties of the neighbor graphs as are used in most of the existing literature . , , , , distributed control , unicycle , synchronization , sampled - data , hybrid system , leader - follower model

this paper considers the distributed sampled - data control problem of a group of mobile robots connected via distance - induced proximity networks . a dwell time is assumed in order to avoid chattering in the neighbor relations that may be caused by abrupt changes of positions when updating information from neighbors . distributed sampled - data control laws are designed based on nearest neighbor rules , which in conjunction with continuous - time dynamics results in hybrid closed - loop systems . for uniformly and independently initial states , a sufficient condition is provided to guarantee synchronization for the system without leaders . in order to steer all robots to move with the desired orientation and speed , we then introduce a number of leaders into the system , and quantitatively establish the proportion of leaders needed to track either constant or time - varying signals . all these conditions depend only on the neighborhood radius , the maximum initial moving speed and the dwell time , without assuming _ a prior _ properties of the neighbor graphs as are used in most of the existing literature . , , , , distributed control , unicycle , synchronization , sampled - data , hybrid system , leader - follower model

1609.02174

c

in this paper , we proposed a sampled - data distributed control law for a group of nonholonomic unicycle robots , and established sufficient conditions for synchronization for the leaderless case without relying on dynamical properties of the neighbor graphs . in order to steer the system to a desired state , we then introduced leaders with constant or time - varying signals into the system , and provided the proportion of the leaders needed to track the static or dynamic signals . in our model , the robots are connected via distance - induced graphs , and a dwell time is assumed for the feasibility of information sensing and processing which as a consequence avoids issues such as chattering caused by abrupt changes of the neighbor relations . some interesting problems deserve to be further investigated , for example , how to design the control law based on the information of relative orientations and relative positions , how to design the sampled - data control law to avoid collisions , and how to design the observer - based control laws for the case where the relative speed and relative orientation can not be directly measured .

a sufficient condition is provided to guarantee synchronization for the system without leaders . in order to steer all robots to move with the desired orientation and speed , we then introduce a number of leaders into the system , and quantitatively establish the proportion of leaders needed to track either constant or time - varying signals .

this paper considers the distributed sampled - data control problem of a group of mobile robots connected via distance - induced proximity networks . a dwell time is assumed in order to avoid chattering in the neighbor relations that may be caused by abrupt changes of positions when updating information from neighbors . distributed sampled - data control laws are designed based on nearest neighbor rules , which in conjunction with continuous - time dynamics results in hybrid closed - loop systems . for uniformly and independently initial states , a sufficient condition is provided to guarantee synchronization for the system without leaders . in order to steer all robots to move with the desired orientation and speed , we then introduce a number of leaders into the system , and quantitatively establish the proportion of leaders needed to track either constant or time - varying signals . all these conditions depend only on the neighborhood radius , the maximum initial moving speed and the dwell time , without assuming _ a prior _ properties of the neighbor graphs as are used in most of the existing literature . , , , , distributed control , unicycle , synchronization , sampled - data , hybrid system , leader - follower model

1301.6901

i

this paper focuses on subnormality for toeplitz operators with matrix - valued symbols and more precisely , the case of toeplitz operators with matrix - valued bounded type symbols . in this paper we give an appropriate generalization of abrahamse s theorem to the case of matrix - valued symbols and apply this generalization to solve a subnormal toeplitz completion problem . to describe our results in more detail , we first need to review a few essential facts about ( block ) toeplitz operators , and for that we will use @xcite , @xcite , @xcite , @xcite , @xcite and @xcite . let @xmath9 be a complex hilbert space and let @xmath10 be the algebra of bounded linear operators acting on @xmath9 . an operator @xmath11 is said to be _ hyponormal _ if its self - commutator @xmath12:= t^*t - tt^*$ ] is positive ( semi - definite ) , and _ subnormal _ if there exists a normal operator @xmath13 on some hilbert space @xmath14 such that @xmath15 is invariant under @xmath13 and @xmath16 . let @xmath17 be the unit circle in the complex plane . let @xmath18 be the set of all square - integrable measurable functions on @xmath19 and let @xmath20 be the corresponding hardy space . let @xmath21 , that is , @xmath22 is the set of bounded analytic functions on @xmath23 . given @xmath0 , the toeplitz operator @xmath3 and the hankel operator @xmath24 are defined by @xmath25 where @xmath26 and @xmath27 denote the orthogonal projections that map from @xmath28 onto @xmath29 and @xmath30 , respectively , and where @xmath31 denotes the unitary operator on @xmath28 defined by @xmath32 . in 1988 , the hyponormality of @xmath3 was completely characterized in terms of its symbol via cowen s theorem @xcite . * cowen s theorem . * ( @xcite , @xcite ) _ for each @xmath0 , let @xmath33 then @xmath3 is hyponormal if and only if @xmath34 is nonempty . _ this elegant and useful theorem has been used in @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite and @xcite , which have been devoted to the study of hyponormality for toeplitz operators on @xmath29 . when one studies the hyponormality ( also , normality and subnormality ) of the toeplitz operator @xmath3 one may , without loss of generality , assume that @xmath35 ; this is because hyponormality is invariant under translation by scalars . we now recall that a function @xmath0 is said to be of _ bounded type _ ( or in the nevanlinna class ) if there are analytic functions @xmath36 such that @xmath37 if @xmath0 , we write @xmath38 let @xmath39 denote the set of functions of bounded mean oscillation in @xmath40 . then @xmath41 . it is well - known that if @xmath42 , then @xmath43 is bounded on @xmath29 whenever @xmath44 ( cf . @xcite ) . if @xmath0 , then @xmath45 , so that @xmath46 and @xmath47 are well understood . it is well known ( * ? ? ? * lemma 3 ) that if @xmath0 then @xmath48 assume now that both @xmath1 and @xmath2 are of bounded type . since @xmath49 for all @xmath50 , it follows from beurling s theorem that @xmath51 and @xmath52 for some inner functions @xmath53 . we thus have @xmath54 , and hence we can write @xmath55 in the factorization ( [ 1.1 - 1 ] ) , we will always assume that @xmath56 and @xmath57 are coprime and @xmath58 and @xmath59 are coprime . in particular , if @xmath3 is hyponormal and @xmath60 , and since @xmath61=h_{\overline\varphi}^ * h_{\overline\varphi}-h_\varphi^ * h_\varphi= h_{\overline{\varphi_+}}^ * h_{\overline{\varphi_+}}-h_{\overline{\varphi_-}}^ * h_{\overline{\varphi_-}},\ ] ] it follows that @xmath62 which implies that @xmath56 divides @xmath58 , i.e. , @xmath63 for some inner function @xmath64 . we write , for an inner function @xmath65 , @xmath66 note that if @xmath67 , then @xmath68 if and only if @xmath69 ; in particular , if @xmath70 then @xmath71 . thus , if @xmath72 is such that @xmath1 and @xmath2 are of bounded type and @xmath3 is hyponormal , then we can write @xmath73 in this case , @xmath74 and @xmath75 are called _ coprime factorizations _ of @xmath76 and @xmath77 , respectively . by kronecker s lemma @xcite , if @xmath78 then @xmath79 is a rational function if and only if @xmath80 , which implies that @xmath81 we now introduce the notion of block toeplitz operators . for a hilbert space @xmath82 , let @xmath83 be the hilbert space of @xmath84-valued norm square - integrable measurable functions on @xmath19 and let @xmath85 be the corresponding hardy space . we observe that @xmath86 and @xmath87 . if @xmath88 is a matrix - valued function in @xmath89 ( @xmath90 ) then @xmath91 denotes the block toeplitz operator with symbol @xmath88 defined by @xmath92 where @xmath93 is the orthogonal projection of @xmath94 onto @xmath95 . a block hankel operator with symbol @xmath96 is the operator @xmath97 defined by @xmath98 where @xmath99 is the orthogonal projection of @xmath94 onto @xmath100 , @xmath101 denotes the unitary operator on @xmath94 given by @xmath102 for @xmath103 , and where @xmath104 is the @xmath105 identity matrix . for @xmath96 , we write @xmath106 for @xmath96 , we also write @xmath107 thus we can write @xmath108 . however , it will be often convenient to permit the constant term for @xmath109 . hence , if there is no confusion we may assume that @xmath109 shares the constant term with @xmath110 : in this case , @xmath111 . a matrix - valued function @xmath112 ( @xmath113 ) is called _ inner _ if @xmath114 for almost all @xmath115 . the following basic relations can be easily derived : @xmath116 for a matrix - valued function @xmath117\in l^\infty_{m_n}$ ] , we say that @xmath88 is of _ bounded type _ if each entry @xmath118 is of bounded type and that @xmath88 is _ rational _ if each entry @xmath118 is a rational function . in 2006 , gu , hendricks and rutherford @xcite characterized the hyponormality of block toeplitz operators in terms of their symbols . in particular they showed that if @xmath119 is a hyponormal block toeplitz operator on @xmath95 , then @xmath88 is normal , i.e. , @xmath120 . their characterization for hyponormality of block toeplitz operators resembles cowen s theorem except for an additional condition the normality condition of the symbol . [ lem1.2](*hyponormality of block toeplitz operators * ) ( gu - hendricks - rutherford @xcite ) for each @xmath121 , let @xmath122 then @xmath119 is hyponormal if and only if @xmath88 is normal and @xmath123 is nonempty . in @xcite , the normality of block toeplitz operator @xmath119 was also characterized in terms of the symbol @xmath88 , under a determinant " assumption on the symbol @xmath88 . [ lem1.3](*normality of block toeplitz operators * ) ( gu - hendricks - rutherford @xcite ) let @xmath124 be normal . if @xmath125 is not identically zero then @xmath126 on the other hand , m. abrahamse ( * ? ? * lemma 6 ) showed that if @xmath3 is hyponormal , if @xmath60 , and if @xmath1 or @xmath127 is of bounded type then both @xmath1 and @xmath127 are of bounded type . however , by contrast to the scalar case , @xmath128 may not be of bounded type even though @xmath119 is hyponormal , @xmath129 and @xmath88 is of bounded type . but we have a one - way implication ( see ( * ? ? ? * corollary 3.5 and remark 3.6 ) ) : @xmath130 for a matrix - valued function @xmath131 , we say that @xmath132 is a _ left inner divisor _ of @xmath88 if @xmath133 is an inner matrix function such that @xmath134 for some @xmath135 ( @xmath136 ) . we also say that two matrix functions @xmath131 and @xmath137 are _ left coprime _ if the only common left inner divisor of both @xmath88 and @xmath138 is a unitary constant and that @xmath131 and @xmath139 are _ right coprime _ if @xmath140 and @xmath141 are left coprime . two matrix functions @xmath88 and @xmath138 in @xmath142 are said to be _ coprime _ if they are both left and right coprime . we remark that if @xmath143 is such that @xmath144 is not identically zero then any left inner divisor @xmath133 of @xmath88 is square , i.e. , @xmath145 . if @xmath143 is such that @xmath144 is not identically zero then we say that @xmath146 is a _ right inner divisor _ of @xmath88 if @xmath147 is a left inner divisor of @xmath148 . the following lemma will be useful in the sequel . [ lem1.1](@xcite)for @xmath96 , the following statements are equivalent : \(i ) @xmath88 is of bounded type ; \(ii ) @xmath149 for some square inner matrix function @xmath150 ; \(iii ) @xmath151 , where @xmath152 and @xmath5 and @xmath150 are right coprime . for an inner matrix function @xmath153 , write @xmath154 suppose @xmath155 \in l^\infty_{m_n}$ ] is such that @xmath128 is of bounded type . then we may write @xmath156 , where @xmath157 is an inner function and @xmath157 and @xmath158 are coprime . thus if @xmath65 is the least common multiple of @xmath157 s ( i.e. , the @xmath157 divide @xmath65 and if they divide an inner function @xmath159 then @xmath65 in turn divides @xmath159 ) , then we can write @xmath160=[\theta_{ij}\overline{b}_{ij}]=[\theta \overline{a}_{ij}]= \theta a^ * \quad ( \theta=\theta i_n,\ a \in h^{2}_{m_n}).\ ] ] we note that the representation ( [ 1.9 ] ) is minimal , " in the sense that if @xmath161 ( @xmath162 is inner ) is a common inner divisor of @xmath150 and @xmath5 , then @xmath162 is constant . let @xmath163 be such that @xmath88 and @xmath128 are of bounded type . then in view of ( [ 1.9 ] ) we can write @xmath164 where @xmath165 with an inner function @xmath166 for @xmath167 and @xmath168 . in particular , if @xmath121 is rational then the @xmath166 are chosen as finite blaschke products as we observed in ( [ 1.4 ] ) . in this paper we consider the subnormality of block toeplitz operators and in particular , the matrix - valued version of halmos s problem 5 : which subnormal toeplitz operators with matrix - valued symbols are either normal or analytic ? in 1976 , m. abrahamse showed that if @xmath0 is such that @xmath1 or @xmath169 is of bounded type , if @xmath3 is hyponormal , and if @xmath170 $ ] is invariant under @xmath3 then @xmath3 is either normal or analytic . the purpose of this paper is to establish a matrix - valued version of abrahamse s theorem and then apply this result to solve a toeplitz completion problem . in section 2 we make a brief sketch on halmos s problem 5 and the earlier results . section 3 is devoted to get an abrahamse s theorem for matrix - valued symbols . in section 4 , using our extension of abrahamse s theorem for matrix - valued symbols , we solve the following toeplitz completion " problem : find the unspecified toeplitz entries of the partial block toeplitz matrix @xmath4 so that @xmath5 becomes subnormal , where @xmath6 is a blaschke factor of the form @xmath7 ( @xmath8 ) .

this paper deals with subnormality of toeplitz operators with matrix - valued symbols and , in particular , with an appropriate reformulation of halmos s problem 5 : which subnormal toeplitz operators with matrix - valued symbols are either normal or analytic ? in 1976 , m. abrahamse showed that if is such that or is of bounded type and if is subnormal , then is either normal or analytic . in this paper we establish a matrix - valued version of abrahamse s theorem and then apply this result to solve the following toeplitz completion problem : find the unspecified toeplitz entries of the partial block toeplitz matrix so that becomes subnormal , where is a blaschke factor of the form ( ) .

this paper deals with subnormality of toeplitz operators with matrix - valued symbols and , in particular , with an appropriate reformulation of halmos s problem 5 : which subnormal toeplitz operators with matrix - valued symbols are either normal or analytic ? in 1976 , m. abrahamse showed that if is such that or is of bounded type and if is subnormal , then is either normal or analytic . in this paper we establish a matrix - valued version of abrahamse s theorem and then apply this result to solve the following toeplitz completion problem : find the unspecified toeplitz entries of the partial block toeplitz matrix so that becomes subnormal , where is a blaschke factor of the form ( ) .

1210.5837

i

this paper develops and analyzes interior penalty discontinuous galerkin ( ipdg ) methods for the following time harmonic maxwell problem : @xmath4 where @xmath5 is a bounded domain with lipschitz continuous boundary @xmath6 and of diameter @xmath7 . @xmath8 denotes the unit outward normal to @xmath9 , @xmath10 , the imaginary unit , and @xmath11 , the _ tangential component _ of the electric field @xmath12 . @xmath1 , called _ wave number _ , is a positive constant and @xmath13 is known as the impedance constant . is the standard impedance boundary condition . assume that @xmath14 , hence , @xmath15 . problem is a prototypical problem in electromagnetic scattering ( cf . @xcite and the references therein ) and has been used extensively as a model ( and benchmark ) problem to develop various numerical discretization methods including finite element methods @xcite and discontinuous galerkin methods @xcite , and to develop fast solvers ( cf . @xcite and the references therein ) . the above maxwell problem with large wave number @xmath1 is numerically difficult to solve mainly because of the following two reasons . first , the large wave number @xmath1 implies the small wave length @xmath16 , that is , the wave is a short wave and very oscillatory . it is well known that , in every coordinate direction , one must put some minimal number of grid points in each wave length in order to resolve the wave . using such a fine mesh evidently results in a huge algebraic problem to solve regardless what discretization method is used . practically , the rule of thumb " is to use @xmath17 grid points per wave length , which means that the mesh size @xmath0 must satisfy the constraint @xmath18 . to the best of our knowledge , no numerical method in the literature has been proved to be uniquely solvable and to have an error bound under the mesh constraint @xmath18 for the above maxwell problem . moreover , numerical experiments have shown that under the mesh condition @xmath18 the errors of all existing numerical methods grow as the wave number @xmath1 increases . this means that the error is not completely controlled by the product @xmath19 and it provides strong evidences of the existence of so - called pollution " in the error bounds . it is known now @xcite that the existence of pollution is related to the loss of stability of numerical methods with large wave numbers for the scalar wave equation , which is also expected to be the case for the vector wave equations . second , for large wave number @xmath1 , the maxwell operator is strongly indefinite . such a strong indefiniteness certainly passes onto any discretization of the maxwell problem . in other words , the stiffness matrix of the discrete problem is not only very large but also strongly indefinite . solving such a large , strongly indefinite , and ill - conditioned algebraic problem is proved to be very challenging and all the well - known iterative methods were proved numerically to be either ineffective or divergent for indefinite wave problems in the case of large wave number ( cf . @xcite and the references therein ) . this paper is an attempt to address the first difficulty mentioned above for the maxwell equations . in particular , our goal is to design and analyze discretization methods which have superior stability properties and give optimal rates of convergence for the maxwell problem . motivated by our previous experiences with the helmholtz equation @xcite , we again try to accomplish the goal by developing some interior penalty discontinuous galerkin method for problem . the focus of the paper is to establish the rigorous stability and error analysis for the proposed ipdg method , in particular , in the preasymptotic regime ( i.e. , when @xmath20 ) . for the ease of presentation and to better present ideas , we confine ourselves to only consider the linear element in this paper and will discuss its high order extensions in a forthcoming paper . the remainder of this paper is organized as follows . section [ sec-2 ] is devoted to the study of the coercivity of the maxwell operator and the wave - number explicit estimates for the solution of . we show that the sesquilinear form associated with the maxwell problem satisfies a generalized weak coercivity ( i.e. , inf - sup condition ) . this coercivity in turn readily infers the wave - number explicit solution estimates which were proved in @xcite . we note that the proofs of both results given in this paper are of independent interest and refer the reader to @xcite for further discussions in the direction . section [ sec-3 ] presents the construction of our ipdg method and some simple properties of the proposed discrete sesquilinear form . section [ sec-4 ] studies the coercivity of the discrete sesquilinear form and derives stability estimates for the ipdg solutions . it is proved that the discrete sesquilinear form satisfies a coercivity for all mesh size @xmath21 and all wave number @xmath22 and for general domains including non - star - shaped ones , which is stronger than the generalized weak coercivity satisfied by its continuous counterpart . all these are possible because of the special design of the discrete sesquilinear form and the special property @xmath23 ( element - wise ) for all piecewise linear functions @xmath24 . this coercivity in turn readily infers the well - posedness and stability estimates for the discrete problem without imposing any mesh constraint . section [ sec-5 ] devotes to the error analysis for the proposed ipdg method . by using the discrete stability estimates and adapting a nonstandard error estimate technique of @xcite , we derive both the energy - norm and the @xmath2-norm error estimates for the ipdg method in all mesh parameter regimes including pre - asymptotic regime ( i.e. , @xmath3 ) . finally , we present some numerical experiment results in section [ sec-6 ] to gauge the theoretical results and to numerically examine the pollution effect ( with respect to @xmath1 ) in the error bounds .

this paper develops and analyzes an interior penalty discontinuous galerkin ( ipdg ) method using piecewise linear polynomials for the indefinite time harmonic maxwell equations with the impedance boundary condition in the three dimensional space . for the differential problem , we prove that the sesquilinear form associated with the maxwell problem satisfies a generalized weak stability ( i.e. , inf - sup condition ) for star - shaped domains . such a generalized weak stability readily infers wave - number explicit a priori estimates for the solution of the maxwell problem , which plays an important role in the error analysis for the ipdg method . for the proposed ipdg method , we show that the discrete sesquilinear form satisfies a coercivity for all positive mesh size and wave number and for general domains including non - star - shaped ones . in turn , the coercivity easily yields the well - posedness and stability estimates ( i.e. , a priori estimates ) for the discrete problem without imposing any mesh constraint . based on these discrete stability estimates , by adapting a nonstandard error estimate technique of , we derive both the energy - norm and the-norm error estimates for the ipdg method in all mesh parameter regimes including pre - asymptotic regime ( i.e. , ) . numerical experiments are also presented to gauge the theoretical results and to numerically examine the pollution effect ( with respect to ) in the error bounds . time harmonic maxwell equations , impedance boundary condition , interior penalty discontinuous galerkin methods , absolute stability , error estimates 65n12 , 65n15 , 65n30 , 78a40

this paper develops and analyzes an interior penalty discontinuous galerkin ( ipdg ) method using piecewise linear polynomials for the indefinite time harmonic maxwell equations with the impedance boundary condition in the three dimensional space . the main novelties of the proposed ipdg method include the following : first , the method penalizes not only the jumps of the tangential component of the electric field across the element faces but also the jumps of the tangential component of its vorticity field ; second , the penalty parameters are taken as complex numbers of negative imaginary parts . for the differential problem , we prove that the sesquilinear form associated with the maxwell problem satisfies a generalized weak stability ( i.e. , inf - sup condition ) for star - shaped domains . such a generalized weak stability readily infers wave - number explicit a priori estimates for the solution of the maxwell problem , which plays an important role in the error analysis for the ipdg method . for the proposed ipdg method , we show that the discrete sesquilinear form satisfies a coercivity for all positive mesh size and wave number and for general domains including non - star - shaped ones . in turn , the coercivity easily yields the well - posedness and stability estimates ( i.e. , a priori estimates ) for the discrete problem without imposing any mesh constraint . based on these discrete stability estimates , by adapting a nonstandard error estimate technique of , we derive both the energy - norm and the-norm error estimates for the ipdg method in all mesh parameter regimes including pre - asymptotic regime ( i.e. , ) . numerical experiments are also presented to gauge the theoretical results and to numerically examine the pollution effect ( with respect to ) in the error bounds . time harmonic maxwell equations , impedance boundary condition , interior penalty discontinuous galerkin methods , absolute stability , error estimates 65n12 , 65n15 , 65n30 , 78a40

1210.5837

m

to formulate our ipdg methods , we first need to introduce some notation . let @xmath126 be a family of partitions ( into tetrahedrons and/or parallelepipeds ) of the domain @xmath49 parameterized by @xmath21 . for any element " @xmath127 , we define @xmath128 . similarly , for each face @xmath129 of @xmath127 , define @xmath130 . we assume that the elements of @xmath131 satisfy the minimal angle condition . let @xmath132 we define the jump @xmath133 and average @xmath134 of @xmath135 on an interior face @xmath136 as @xmath137 if @xmath138 , set @xmath139 and @xmath140 . for every @xmath141 , let @xmath142 be the unit outward normal to the face @xmath129 of the element @xmath143 if the global label of @xmath143 is bigger and of the element @xmath144 if the other way around . for every @xmath138 , let @xmath145 the unit outward normal to @xmath146 . to formulate our ipdg methods , we recall the following ( local ) integration by parts formula : @xmath147 where @xmath148 . next , multiplying equation by a test function @xmath149 , integrating over @xmath127 , using the integration by parts formula , and summing the resulted equation over all @xmath127 we get @xmath150 to deal with the boundary terms in the big sum , we appeal to the following algebraic identity . for each interior face @xmath151 there holds @xmath152 substituting identity into after dropping the first term on the right - hand side of ( because @xmath153 if @xmath12 is sufficiently regular ) yields @xmath154 utilizing the boundary condition in the third term on the left - hand side and adding a symmetrization " term then lead to the following equation : @xmath155 where @xmath156 . the most important and tricky issue for designing an ipdg method is how to introduce suitable _ interior penalty _ term(s ) on the left - hand side of . obviously , different interior penalty terms will result in different numerical methods . as it was proved in @xcite , using the standard interior penalty terms will lead to ipdg methods which require a restrictive mesh constraint to ensure the stability and accuracy in the case of large wave number @xmath1 . inspired by our previous work @xcite on ipdg methods for the helmholtz equation and guided by our stability analysis ( see section [ sec-4 ] ) , here we introduce some non - standard interior penalty terms into , which we shall describe below , and the ipdg method so constructed will be proved to be absolutely stable ( with respect to wave number @xmath1 and mesh size @xmath0 ) in the next section . to define our ipdg methods , we first introduce the energy " space @xmath157 and the sesquilinear form @xmath158 on @xmath159 as follows . @xmath160 @xmath161}\\ { \mathcal{j}}_0({\mathbf{u}},{\mathbf{v}}):=&\sum_{{\mathcal{f}}\in{\mathcal{e}}_h^i}\frac{{\gamma}_{0,{\mathcal{f}}}}{h_{\mathcal{f}}}\ , \bigl\langle \jump{{\mathbf{u}}_t},\jump{{\mathbf{v}}_t}\bigr\rangle_{\mathcal{f}},\label{e3.6}{\displaybreak[0]}\\ { \mathcal{j}}_1({\mathbf{u}},{\mathbf{v}}):=&\sum_{{\mathcal{f}}\in{\mathcal{e}}_h^i } { \gamma}_{1,{\mathcal{f } } } h_{\mathcal{f}}\bigl\langle\jump{\operatorname{\mathbf{curl}}{\mathbf{u}}\times{\mathbf{n}}_{\mathcal{f}}},\jump{\operatorname{\mathbf{curl}}{\mathbf{v}}\times{\mathbf{n}}_{\mathcal{f } } } \bigr\rangle_{\mathcal{f } } , \label{cj1}\end{aligned}\ ] ] where @xmath162 and @xmath163 are nonnegative numbers to be specified later . \(a ) clearly , @xmath158 is a consistent discretization for @xmath164 since @xmath165 for all @xmath166 and @xmath167 with @xmath168 . \(b ) the terms in @xmath169 are called penalty terms . the penalty parameters @xmath170 and @xmath171 are pure imaginary numbers with _ negative _ imaginary parts . our analysis still applies if they are taken as complex numbers of negative imaginary parts . \(c ) the @xmath172 term penalizes the jumps of the vector field @xmath102 and the @xmath173 term penalizes the jumps of the tangential component of the vector field @xmath174 . which , to the best of our knowledge , has not been used before in the context of ipdg methods for the maxwell equations . they play a vital role for our ipdg methods being absolutely stable , see section [ sec-4 ] . \(d ) @xmath175 correspond to the nonsymmetric , incomplete , and symmetric ipdg methods for the poisson problem . in the remainder of this paper , we shall only consider the symmetric case @xmath176 and set @xmath177 for notation brevity . with the help of the sesquilinear form @xmath178 we now introduce the following weak formulation for : find @xmath179 such that @xmath180 where @xmath181 from , it is clear that , if @xmath182 is the solution of , then holds for all @xmath183 . for any @xmath127 , let @xmath184 denote the set of all complex - valued polynomials whose degrees in all variables ( total degrees ) do not exceed @xmath185 . we define our ipdg approximation space @xmath186 as @xmath187 clearly , @xmath188 . but @xmath189 . we are now ready to define our ipdg methods based on the weak formulation : find @xmath190 such that for all @xmath191 @xmath192 we note that defines a family of ipdg methods for @xmath193 . for the ease of presentation and to better present ideas , in the rest of this paper we only consider the case @xmath194 , the linear element case . in the next two sections , we shall study the stability and error estimates for the above ipdg method with @xmath194 . especially , we are interested in knowing how the stability constants and error constants depend on the wave number @xmath1 ( and mesh size @xmath0 , of course ) and what are the optimal " relationship between mesh size @xmath0 and the wave number @xmath1 . we remark that the ipdg method with @xmath194 uses piecewise linear polynomials even for cartesian meshes . by contrast , for the corresponding linear conforming edge element method on cartesian meshes , the trial functions have to be chosen as piecewise trilinear polynomials . we also note that the linear system resulted from is ill - conditioned and strongly indefinite because the coefficient matrix has many eigenvalues with very large negative real parts . solving such a large linear system is another challenging problem associated with time harmonic maxwell problems , which will be addressed in a future work . for further analysis we introduce the following semi - norms / norms on @xmath157 : @xmath195}\\ { \left\vert{\mathbf{v}}\right\vert}_{dg}^2 : = & \|\operatorname{\mathbf{curl}}{\mathbf{v}}\|_{{\mathbf{l}}^2({\mathcal{t}}_h)}^2 + { \vert{\mathbf{v}}\vert_{{\mathbf{l}}^2({\omega})}}^2 \label{e3.12 } \\ & + \sum_{{\mathcal{f}}\in{\mathcal{e}}_h^i } \bigl ( \frac{{\gamma}_{0,{\mathcal{f}}}}{h_{\mathcal{f } } } { \vert{\left[{\mathbf{v}}_t\right]}\vert_{{\mathbf{l}}^2({\mathcal{f}})}}^2 + { \gamma}_{1,{\mathcal{f } } } h_{\mathcal{f}}{\vert{\left[\operatorname{\mathbf{curl}}{\mathbf{v}}\times { \boldsymbol{\nu}}_{\mathcal{f}}\right]}\vert_{{\mathbf{l}}^2({\mathcal{f}})}}^2 \bigr ) \nonumber{\displaybreak[0]}\\ = & \|\operatorname{\mathbf{curl}}{\mathbf{v}}\|_{{\mathbf{l}}^2({\mathcal{t}}_h)}^2 + { \vert{\mathbf{v}}\vert_{{\mathbf{l}}^2({\omega})}}^2+{\mathcal{j}}_0({\mathbf{v}},{\mathbf{v } } ) + { \mathcal{j}}_1({\mathbf{v}},{\mathbf{v } } ) , { \nonumber}{\displaybreak[0]}\\ { \vert{\hskip -1.3pt}\vert { \mathbf{v}}\vert{\hskip -1.3pt}\vert_{dg}}^2 : = & { \left\vert{\mathbf{v}}\right\vert}_{dg}^2 + \sum_{{\mathcal{f}}\in{\mathcal{e}}_h^i } \frac{h_{\mathcal{f}}}{{\gamma}_{0,{\mathcal{f}}}}{\vert{\left\{\operatorname{\mathbf{curl}}{\mathbf{v}}\times { \boldsymbol{\nu}}_{\mathcal{f}}\right\}}\vert_{{\mathbf{l}}^2({\mathcal{f}})}}^2 . \label{e3.13}\end{aligned}\ ] ] clearly , the sesquilinear form @xmath178 satisfies : for any @xmath167 @xmath196

the main novelties of the proposed ipdg method include the following : first , the method penalizes not only the jumps of the tangential component of the electric field across the element faces but also the jumps of the tangential component of its vorticity field ; second , the penalty parameters are taken as complex numbers of negative imaginary parts .

this paper develops and analyzes an interior penalty discontinuous galerkin ( ipdg ) method using piecewise linear polynomials for the indefinite time harmonic maxwell equations with the impedance boundary condition in the three dimensional space . the main novelties of the proposed ipdg method include the following : first , the method penalizes not only the jumps of the tangential component of the electric field across the element faces but also the jumps of the tangential component of its vorticity field ; second , the penalty parameters are taken as complex numbers of negative imaginary parts . for the differential problem , we prove that the sesquilinear form associated with the maxwell problem satisfies a generalized weak stability ( i.e. , inf - sup condition ) for star - shaped domains . such a generalized weak stability readily infers wave - number explicit a priori estimates for the solution of the maxwell problem , which plays an important role in the error analysis for the ipdg method . for the proposed ipdg method , we show that the discrete sesquilinear form satisfies a coercivity for all positive mesh size and wave number and for general domains including non - star - shaped ones . in turn , the coercivity easily yields the well - posedness and stability estimates ( i.e. , a priori estimates ) for the discrete problem without imposing any mesh constraint . based on these discrete stability estimates , by adapting a nonstandard error estimate technique of , we derive both the energy - norm and the-norm error estimates for the ipdg method in all mesh parameter regimes including pre - asymptotic regime ( i.e. , ) . numerical experiments are also presented to gauge the theoretical results and to numerically examine the pollution effect ( with respect to ) in the error bounds . time harmonic maxwell equations , impedance boundary condition , interior penalty discontinuous galerkin methods , absolute stability , error estimates 65n12 , 65n15 , 65n30 , 78a40

1112.5850

i

an arbitrage operation involves buying some good or asset for a lower price than that for which it can be sold , taking advantage of any imbalance in the quoted prices . the `` law of one price '' is a statement of a key implication of the absence of arbitrage opportunities . in turn arbitrage is often the process invoked to explain why goods or assets that are in some sense `` identical '' should have a common price . a study of commodity prices since 1273 concluded that `` despite the steady decline in transportation costs over the past 700 years , the repeated intrusion of wars and disease , and the changing fashions of commercial policy , the volatility and persistence of deviations in the law of one price have remained quite stable '' @xcite . the present paper investigates a relatively neglected complication regarding arbitrage operations , namely the order in which information about arbitrage opportunities is presented , illustrating this in relation to arbitrage chains involving four currencies . the key finding is that arbitrage operations can be periodic in nature , rather than involving a smooth convergence to a law of one price . the early literature on the law of one price is coeval with the purchasing power parity explanation of foreign exchange rates . the terminology was coined in @xcite , involving arbitrage between relatively homogeneous goods priced in different currencies @xcite . empirical tests suggest that arbitrage operations in goods do not exert a strong influence on exchange rates until the price index deviations involved exceed about 25% @xcite . innovations that were expected to reduce price dispersion , such as the european single market legislation coming into effect in 1992 , and the economic and monetary union project beginning in 1999 , have had little effect on price level disparities @xcite . the degree of price level dispersion between us cities has displayed no marked trend over time @xcite . a study of the prices charged for identical products in ikea stores in twenty - five countries revealed typical price divergences of 2050% , differences that could not be attributed to just country or location - specific factors @xcite . among the most cited reasons for deviations from the law of one price are transaction costs , taxes , transport costs , trade barriers , the costs of searching for price differences , nominal price rigidities , customer market pricing , nominal exchange rate rigidities and differences in market power @xcite . in relation to assets , an early application of the law of one price was to the interest rate parity theory of the forward exchange rate , whereby the ratio of the forward to spot exchange rate between two currencies is equal to the ratio of the interest rates in the two currencies over the forward period in question @xcite . an arbitrage opportunity in relation to assets can be defined as `` an investment strategy that guarantees a positive payoff in some contingency with no possibility of a negative payoff and with no net investment '' ( * ? ? ? * online ) . the absence of such arbitrage opportunities has been seen as the unifying concept underlying mainstream theories in finance , no - arbitrage principles being applied in the modigliani miller theorem of corporate capital structure , in the black scholes model of option pricing and in the arbitrage pricing model of asset prices @xcite . actual arbitrage operations in relation to assets often involve net investment and risk and/or uncertainty , in addition to the complications arising in relation to arbitrage in goods . notable deviations from the law of one price in financial markets have been documented in relation to comparable circumstances applying to closed - end country funds , american depository receipts , twin shares , dual share classes and corporate spin - offs @xcite . among the limits to arbitrage in financial markets are those arising from transactions costs @xcite , and those involving the capital requirements of conducting arbitrage operations @xcite . a spectacular illustration of the capital limits to arbitrage was provided by the demise of the long - term capital management ( ltcm ) hedge funds . the arbitrage discrepancies being exploited in ltcm s `` convergence trades '' widened in 1998 . ltcm attempted unsuccessfully to raise new capital to finance its arbitrage positions . to avoid a major financial collapse the new york federal reserve board organised a bail - out by creditors @xcite . in what follows we focus on the limits to arbitrage arising from the order in which information is disseminated to arbitrage traders . the illustration used is for a foreign exchange ( fx ) market with four fx traders and four currencies , see sections [ s-3currencies ] and [ s-4currencies ] . an arbiter , the metaphorical equivalent of an unpaid auctioneer in a walrasian system , knows all the actual exchange rates . the individual fx traders , however , initially know only the exchange rates involving their own , domestic currencies . justification for the assumptions used in our model is provided in section [ s - structfx ] . so the us fx trader knows the exchange rates for the dollar against the euro , sterling and yen , but not the cross exchange rates for the non - dollar currencies . there are no transactions costs , no net capital requirements and no risks involved in the arbitrage operations . instead we focus on the information dissemination problem , and show that the order in which information about cross exchange rate discrepancies , and hence arbitrage opportunities , is presented makes an important difference to the sequences of arbitrage operations conducted . a general discussion of arbitrage dynamics is given in section [ s - arbitrages ] . an unexpected feature of the processes considered in this paper is that , _ rather than there being a smooth convergence to an ensemble of exchange rates with no arbitrage opportunities , the arbitrage operations may display periodicity and no necessary convergence on a cross exchange rate law of one price_. see proposition [ 32 ] in section [ mrss ] for a rigorous explanation . a further unexpected feature is that , _ starting at an ensemble of exchange rates which is not balanced , and using special periodic sequences of arbitrages , the arbiter can achieve balanced ( satisfying the law of one price ) exchange rate ensemble_. see , in particular , theorem [ arbh ] in section [ mrss ] and theorem [ irratbc ] in section [ s - gencase ] . these counter - intuitive results are new , as far as we are aware . in line with the renowned `` impossibility theorem '' of @xcite these results suggest an `` arbitrage impossibility theorem '' . proofs are relegated to section [ s - proofs ] . the mathematical approach taken in this paper to the analysis of arbitrage operation chains may be understood as a typical example of the asynchronous interactions that are important in systems theory and in control theory , see the monographs @xcite and the surveys @xcite . the arbitrage chains are particularly relevant to desynchronised systems theory , see @xcite . presence of an asynchronous interaction often leads to a dramatic complication of the related mathematical problems . @xcite proved that many asynchronous problems can not be solved algorithmically , and also @xcite and @xcite demonstrated that , even in the cases when the problem is algorithmically solvable , it is typically as hard to solve numerically as the famous `` travelling salesman problem , '' see @xcite ( that is , in the mathematical language , the problem is np - hard which is an abbreviation for `` non - deterministic polynomial - time hard '' which means in the theory of algorithms that a problem is very hard , if possible , to solve , see @xcite ) . in this context the fact that the principal questions that arise in analysis of arbitrage operation chains admit straightforward combinatorial analysis came to the authors as a pleasant surprise . our construction uses a geometrical approach to visualisation of arbitrage chains presented in sections [ simpleass][s - proofs ] , which may be useful in relation to other problems in mathematical economics . the periodicity results in this paper have implications for several strands of literature . one is that dealing with the disequilibrium foundations of equilibrium economics . the stability analysis of fisher poses the question : `` can one expect to prove that an economy with rational agents conscious of disequilibrium and taking advantage of arbitrage opportunities is driven ( asymptotically ) to any equilibrium , walrasian or constrained ? '' fisher uses the assumption of `` no favorable surprise '' as a means of demonstrating that a cessation of exogenous shocks can lead to convergence to equilibrium . the results in this paper suggest that there can be endogenous reasons , arising from the cyclical response of arbitrage sequences to an exogenous shock that gives rise to an arbitrage opportunity , why convergence to equilibrium may not take place . another strand of literature to which our results relate is that on market segmentation and arbitrage networks . goods and assets are not traded on a single exchange . instead there are various trading posts , such as commodity and stock exchanges . other trades , including a sizeable proportion of foreign exchange deals , are conducted `` over the counter '' in direct transactions that bypass formal exchanges . `` as a result , various clienteles trade on different exchanges , and very few retail clients trade on more than one exchange , let alone on all of them simultaneously '' @xcite . a key aspect of segmentation in the foreign exchange `` market '' is that dealing rooms tend to specialise in domestic currency trades . this provides a rationale for the specification in this paper that foreign exchange dealers initially are aware of only the exchange rates involving their domestic currencies . we restrict our analysis to the case of 4 currencies , with 6 principal exchange rates . the financial times gives daily quotes for 52 currencies . the 1,326 principal exchange rates involved suggest richer potential opportunities for arbitrage than in the four currency case studied in the present paper . bank for international settlements ( bis ) data indicate that , in 2010 , transactions in these four currencies counted for 155.9% of global fx market turnover , the currency components being us dollars ( 84.9% ) , euros ( 39.1% ) , japanese yen ( 19.0% ) and pound sterling ( 12.9% ) . because two currencies are involved in each transaction , the % shares sum to 200% ( * ? ? ? * table b.4 ) .

this paper investigates arbitrage chains involving four currencies and four foreign exchange trader - arbitrageurs . the goal of this article is to understand some interesting features of sequences of arbitrage operations , features which might well be relevant in other contexts in finance and economics . limits to arbitrage , four currencies , recurrent sequences , asynchronous systems _ jel classification _ : c60 , f31 , d82

this paper investigates arbitrage chains involving four currencies and four foreign exchange trader - arbitrageurs . in contrast with the three - currency case , we find that arbitrage operations when four currencies are present may appear periodic in nature , and not involve smooth convergence to a `` balanced '' ensemble of exchange rates in which the law of one price holds . the goal of this article is to understand some interesting features of sequences of arbitrage operations , features which might well be relevant in other contexts in finance and economics . limits to arbitrage , four currencies , recurrent sequences , asynchronous systems _ jel classification _ : c60 , f31 , d82

0911.1413

i

there have been many papers written recently on noncommutative versions of soliton equations , such as the kp equation , the kdv equation , the hirota - miwa equation and the two - dimensional toda lattice equation @xcite . it has been shown that noncommutative integrable systems often have solutions expressed in terms of quasideterminants @xcite . in @xcite for example , two families of solutions of the noncommutative kp equation were presented which were termed quasiwronskians and quasigrammians . the origin of these solutions was explained by darboux and binary darboux transformations . the quasideterminant solutions were then verified directly using formulae for derivatives of quasideterminants ( see also @xcite ) . supersymmetric integrable systems are a particular noncommutative extension of integrable systems , and have attracted much attention because of their applications in physics . some well - known example are supersymmetric versions of the kdv , kp , sine - gordon , nonlinear schrdinger equation , akns and harry dym equations @xcite . among these , the manin - radul super kdv equation is perhaps the best known and has been studied extensively and a number of interesting properties have been established . we mention here the existence of an infinite number of conservation laws , a bi - hamiltonian structure @xcite , a bilinear form @xcite and darboux transformations @xcite . partly motivated by the properties of superderivatives , which we describe in section 2 , we consider a generalized derivation which has regular derivations , difference operators , @xmath3-difference operators and superderivatives as some of its special cases . we call this a twisted derivation , following the terminology used in @xcite . we show that one can formulate darboux transformations for such twisted derivations and the iteration formulae are expressed in terms of quasideterminants in which one simply replaces the derivative with the twisted derivation . a special case of this result can be used to construct solutions to supersymmetric equations in terms of quasideterminants . in @xcite , solutions for the manin - radul super kdv equation were constructed by iterating darboux transformations by considering the cases of an even number and an odd number of iterations separately . all but one of the formulae obtained by the authors expressed the solutions in terms of superdeterminants . in this paper , we use an alternative approach to the darboux transformations using quasideterminants . this is successful in obtaining unified formulae for the solutions , not depending on the parity of the number of iterations . from these quasideterminant solutions , we are not only able to recover superdeterminant solutions given in @xcite but also get the superdeterminant representation in the one case they did not . the paper is organized as follows . in section 2 , we give a brief review on superdeterminants , quasideterminants and the relationship between them . in section 3 , we define a twisted derivation and related darboux transformation . we obtain a formula for iteration of this twisted darboux transformation in terms of quasideterminants . section 4 gives applications of both darboux and binary darboux transformations to the manin - radul super kdv system . in this section we obtain two general solution formulae in terms of quasideterminants , obtained using iterated darboux and binary darboux transformations respectively , and then show how these can be expressed in terms of superdeterminants . on the other hand , we present quasideterminant solutions constructed from its binary darboux transformations to the mrskdv system . in section 5 we present conclusions .

remarkably , the formulae for the iteration of darboux transformations are identical with those in the standard case of a regular derivation and are expressed in terms of quasideterminants . as an example , we revisit the darboux transformations for the manin - radul super kdv equation , studied in q.p . finally , we obtain another type of quasideterminant solutions to the main - radul super kdv equation constructed from its binary darboux transformations . these can also be expressed as ratios of superdeterminants and are a substantial generalization of the solutions constructed using binary darboux transformations in earlier work on this topic .

this paper is concerned with a generalized type of darboux transformations defined in terms of a twisted derivation satisfying where is a homomorphism . such twisted derivations include regular derivations , difference and-difference operators and superderivatives as special cases . remarkably , the formulae for the iteration of darboux transformations are identical with those in the standard case of a regular derivation and are expressed in terms of quasideterminants . as an example , we revisit the darboux transformations for the manin - radul super kdv equation , studied in q.p . liu and m. maas , physics letters b * 396 * 133140 , ( 1997 ) . the new approach we take enables us to derive a unified expression for solution formulae in terms of quasideterminants , covering all cases at once , rather than using several subcases . then , by using a known relationship between quasideterminants and superdeterminants , we obtain expressions for these solutions as ratios of superdeterminants . this coincides with the results of liu and maas in all the cases they considered but also deals with the one subcase in which they did not obtain such an expression . finally , we obtain another type of quasideterminant solutions to the main - radul super kdv equation constructed from its binary darboux transformations . these can also be expressed as ratios of superdeterminants and are a substantial generalization of the solutions constructed using binary darboux transformations in earlier work on this topic .

0911.1413

c

in this paper , we have considered a twisted derivation which includes normal derivative , forward difference operator , q - difference operator and superderivatives as special cases . we showed that a darboux transformation defined in terms of such a twisted derivation has an iteration formula written in terms of a quasideterminant . this results opens the opportunity for an unified approach to darboux transformations for differential , superdifferential difference and @xmath3-difference operators . in this paper we showed how this was achieved for one example , the manin - radul super kdv equation . in the darboux transformation approach to this equation given in @xcite , the authors were forced to consider two different cases , for an odd and an even number of iterations , in order to obtain solutions expressed in terms of superdeterminants . using the same darboux transformation , we have obtained quasideterminant solutions in a unified manner , irrespective of the parity of the number of iterations , and then we were able in all cases to reexpress the solutions in terms of superdeterminants using the known relationship between quasideterminants and superdeterminants . this illustrates the advantage of using quasideterminants over using superdeterminants from the start and comes about because quasideterminants need no assumption about the nature of the noncommutativity whereas for superdeterminants restrictive assumptions about parity of matrix elements are required . the same advantage holds in connection with iterated binary darboux transformations . in this case we were able to construct a much more general types of solution as well . in earlier work @xcite only solutions expressed in terms of determinants were found . however , it is to be expected that for a supersymmetric integrable system the most general solutions have expressions in terms of superdeterminants rather than determinants . this deficiency was remedied in this paper and we have obtained a much wider class of solutions expressed in terms of both quasideterminants and superdeterminants .

this paper is concerned with a generalized type of darboux transformations defined in terms of a twisted derivation satisfying where is a homomorphism . such twisted derivations include regular derivations , difference and-difference operators and superderivatives as special cases . the new approach we take enables us to derive a unified expression for solution formulae in terms of quasideterminants , covering all cases at once , rather than using several subcases .

this paper is concerned with a generalized type of darboux transformations defined in terms of a twisted derivation satisfying where is a homomorphism . such twisted derivations include regular derivations , difference and-difference operators and superderivatives as special cases . remarkably , the formulae for the iteration of darboux transformations are identical with those in the standard case of a regular derivation and are expressed in terms of quasideterminants . as an example , we revisit the darboux transformations for the manin - radul super kdv equation , studied in q.p . liu and m. maas , physics letters b * 396 * 133140 , ( 1997 ) . the new approach we take enables us to derive a unified expression for solution formulae in terms of quasideterminants , covering all cases at once , rather than using several subcases . then , by using a known relationship between quasideterminants and superdeterminants , we obtain expressions for these solutions as ratios of superdeterminants . this coincides with the results of liu and maas in all the cases they considered but also deals with the one subcase in which they did not obtain such an expression . finally , we obtain another type of quasideterminant solutions to the main - radul super kdv equation constructed from its binary darboux transformations . these can also be expressed as ratios of superdeterminants and are a substantial generalization of the solutions constructed using binary darboux transformations in earlier work on this topic .

0801.4372

i

we have studied the long - term evolution of the magnetic field and the densities of neutrons and charged particles ( protons and electrons in the interior of a neutron star , using a multi - fluid model with a simplified geometry in which the magnetic field points in one cartesian direction and varies along an orthogonal direction . we found a set of three non - linear partial differential equations of first order in time describing this evolution , and we analyzed them in three different ways : ( i ) estimating evolutionary timescales directly from the equations , guided by physical intuition ; ( ii ) a normal - mode analysis of the equations in the limit of a nearly uniform system ; and ( iii ) a finite - difference numerical integration of the equations . in this section , we summarize the main results of each one of these approaches and present the main conclusions of this work . the three partial differential equations of our model constitute a dynamical system of three independent variables ( magnetic - field , charged - particle , and neutron density perturbations ) . we identified three characteristic evolutionary timescales on which the system approaches successive quasi - equilibrium states . in the following , we summarize the basic physical processes governing the evolution and the estimates of each timescale . during the early stages of a neutron star s life , the lorentz force moves the bulk stellar fluid , inducing perturbations in its pressure . in this short time , all particles move together as a single fluid with the same bulk velocity . there is also not enough time for weak interactions between particles ( beta decays ) to operate , so the composition is frozen . the system evolves until it reaches a magnetohydrodystatic quasi - equilibrium state , in which the lorentz and the fluid forces are close to balancing . neutron stars with no rotation or convection reach this quasi - equilibrium state in a short time , not much longer than the alfvn time , which for typical magnetar core parameters scales as @xmath317 where @xmath178 denotes the radius of the star in units of @xmath318 and @xmath180 the magnetic field in units of @xmath319 on timescales far longer than the alfvn time , relative movements between the different species of particles in the star as well as weak interactions between them become relevant ( gr-92 ) . therefore , a description of the system during these stages requires a multi - fluid theory . in this paper , we develop a model to study the decay of the magnetic field induced by these long - term mechanisms . the alfvn time is far shorter than the timescales of these long - term processes ( see sects . [ conc12 ] and [ conc13 ] ) , which are of the order of years or much more . a numerical code simulating the evolution during the alfvn timescale would require a time step many orders of magnitude shorter than that required to simulate the long - term evolution in a computational time not prohibitively long . in our model , we overcome this difficulty by replacing the short - term dynamics by a ficticious friction force term acting on the neutrons ( the most abundant species ) . its strength is controlled by an artificial parameter @xmath25 , chosen so that the timescale to reach magnetohydrostatic quasi - equilibrium is long enough for the numerical code to be able to deal with it ( and therefore much longer than the alfvn time ) , but shorter than the timescales of the long - term processes that we are interested in modeling . on timescales far longer than required to reach magnetohydrostatic quasi - equilibrium , the neutrons and charged particles move relative to each other with different velocities and are affected by collisional drag . also , weak interactions ( beta decays ) convert particles from one species into another , erasing departures from chemical quasi - equilibrium among neutrons , protons , and electrons caused by the induced particle density perturbations . both processes contribute to the evolution of the particle densities . in estimating the timescale for this evolution , it is useful to distinguish the regimes in which each one of these processes is dominant . if the collisions between the charged particles and the neutrons are rare and the weak interactions are slow , the charged particles move easily relative to the neutrons ( ambipolar diffusion ) allowing the particles to reach a diffusive quasi - equilibrium state ( in which gravitational , electromagnetic , and pressure forces are closely balanced ) but staying avoid chemical quasi - equilibrium . the diffusive quasi - equilibrium is reached in a timescale controlled by the collision rate between neutrons and charged particles given by @xmath320 where @xmath185 and @xmath186 in the opposite regime , when the collisions between charged particles and neutrons are frequent , and the weak interaction rate is high , the relative diffusion of particles will be impeded by the collisional drag , but the system reaches the chemical quasi - equilibrium in a timescale controlled by weak interactions of magnitude ( assuming modified urca reactions ) @xmath321 the ohmic dissipation promotes the decay of the magnetic field in a timescale @xmath322 this extremely long time implies that ohmic dissipation is not very effective in producing magnetic - field decay in neutron stars . a more rapid decay of the magnetic field can occur through ambipolar diffusion , i.e. , a joint drift of the magnetic field and the charged particles relative to the neutrons , in which magnetic energy becomes dissipated by collisions . this diffusion process induces local density perturbations that deviate from chemical quasi - equilibrium . weak interactions tend to erase the chemical imbalance by converting particles of one species into the other . during these conversions , neutrinos , and antineutrinos remove part of the magnetic energy . in estimating the timescale of magnetic field decay induced by these processes , it is useful to distinguish between the two regimes we discussed above . if ambipolar diffusion occurs far more rapidly than the weak interaction process , i.e. , @xmath323 diffusive quasi - equilibrium is quickly reached , but chemical quasi - equilibrium is not . thus , the rate at which chemical quasi - equilibrium is restored by weak interactions determines the characteristic timescale over which the magnetic field evolves , @xmath324 this timescale is the corresponding one to reach chemical quasi - equilibrium @xmath210 but amplified by a factor of the order of the ratio of the charged fluid pressure to the magnetic pressure . this is expected since the lorentz force drives the ambipolar diffusion that prevents weak interactions from restoring chemical quasi - equilibrium . in the opposite regime , collisions are frequent and weak interactions are fast , i.e. @xmath325 so the system reaches chemical quasi - equilibrium long before diffusive quasi - equilibrium . therefore , the evolution of the magnetic field is limited by the collisions that control the ambipolar diffusion , on a timescale of @xmath326 since the magnetic field sustains the diffusive imbalance and drives the diffusion , the timescale given in eq . ( [ tbb2 ] ) is similar to that taken by particles to achieve diffusive quasi - equilibrium but , as above , amplified by a factor that depends on the magnetic field strength . in the limit of non - interacting protons and neutrons studied by gr-92 , eqs . ( [ tbb1 ] ) and ( [ tbb2 ] ) correspond to the estimate of the timescale for magnetic field evolution due to the ambipolar diffusion process of eq . ( 35 ) in gr-92 . we note that gr-92 considered the neutrons to be a static species in diffusive quasi - equilibrium . from this correspondence , we confirm that the motion of the neutrons , which was included in our model , plays no important role in the one - dimensional evolution . in the spirit of finding an analytical solution to the set of non - linear partial differential equations that describes the evolution of the system , we completed a linear perturbation analysis of the equations in the limit of a nearly uniform system and tried a normal mode solution ( sect . [ normmodes ] ) . we found three exponentially - decaying modes that could be interpreted as the episodes of successive relaxation to the quasi - equilibrium states identified in the previous physical analysis ( see sects . [ carsca ] and [ conc1 ] ) . we found analytical and numerical solutions for the decay times of these modes ( see appendix [ apa ] ) that agree with the estimated formulae for the evolutionary timescales of the general non - linear system ( see sects . [ carsca ] , [ conc1 ] and figs . [ t1],[t2 ] , and [ t3 ] ) . we constructed a finite - difference numerical code to solve the full system of non - linear partial differential equations . this was tested against the normal - mode solutions ( fig . [ linen ] ) and by verifying the known conservation laws of magnetic flux and baryon number in highly non - linear situations ( fig . [ gauss ] ) . applying this numerical code , we propose to consider , in the future , conditions in which the background is non - homogeneous , as well as non - linear situations . we have established a general multifluid formalism in which it is possible to study the magnetic field decay processes in neutron stars identified by gr-92 , which are likely to represent the basis of the magnetar phenomenon . as a first step , we have focused on a simplified geometry in which the magnetic field points in one cartesian direction and varies in an orthogonal direction to it . we estimated the timescales of the relevant processes , and using numerical simulations we followed the temporal evolution of some simple magnetic - field configurations . the present work is far from exhausting the possibilities of this formalism , which should be applied to more realistic situations , including neutron stars with spherical symmetry , non - uniform background density and three - dimensional magnetic fields with components that depend on two or three spatial coordinates . further steps might consider convective motions and additional species of particles as well as the effects of superfluidity and superconductivity .

this approximation leads to three nonlinear partial - differential equations describing the evolution of the magnetic field , as well as the movement of two fluids : the charged particles ( protons and electrons ) and the neutrons . we study the evolution of the system in three different ways : ( i ) estimating timescales directly from the equations , guided by physical intuition ; ( ii ) a normal - mode analysis in the limit of a nearly uniform system ; and ( iii ) a finite - difference numerical integration of the full set of nonlinear partial - differential equations . depending on parameter values , the magnetic field can evolve by ohmic diffusion or by ambipolar diffusion , the latter being limited either by interparticle collisions or by relaxation to chemical quasi - equilibrium through beta decays . the numerical simulations are further validated by verifying that they satisfy the known conservation laws in highly nonlinear situations .

this paper is the first in a series that aims to understand the long - term evolution of neutron star magnetic fields . we model the stellar matter as an electrically neutral and lightly - ionized plasma composed of three moving particle species : neutrons , protons , and electrons ; these species can be converted into each other by weak interactions ( beta decays ) , suffer binary collisions , and be affected by each other s macroscopic electromagnetic fields . since the evolution of the magnetic field occurs over thousands of years or more , compared to dynamical timescales ( sound and alfvn ) of milliseconds to seconds , we use a slow - motion approximation in which we neglect the inertial terms in the equations of motion for the particles . this approximation leads to three nonlinear partial - differential equations describing the evolution of the magnetic field , as well as the movement of two fluids : the charged particles ( protons and electrons ) and the neutrons . these equations are first rather than second order in time ( involving the velocities of the three species but not their accelerations ) . in this paper , we restrict ourselves to a one - dimensional geometry in which the magnetic field points in one cartesian direction , but varies only along an orthogonal direction . we study the evolution of the system in three different ways : ( i ) estimating timescales directly from the equations , guided by physical intuition ; ( ii ) a normal - mode analysis in the limit of a nearly uniform system ; and ( iii ) a finite - difference numerical integration of the full set of nonlinear partial - differential equations . we find good agreement between our analytical normal - mode solutions and the numerical simulations . we show that the magnetic field and the particles evolve through successive quasi - equilibrium states , on timescales that can be understood by physical arguments . depending on parameter values , the magnetic field can evolve by ohmic diffusion or by ambipolar diffusion , the latter being limited either by interparticle collisions or by relaxation to chemical quasi - equilibrium through beta decays . the numerical simulations are further validated by verifying that they satisfy the known conservation laws in highly nonlinear situations .

1103.1913

c

in this paper we present spectral analysis and emission line images from deep _ chandra _ observation of ngc 4151 , aiming to resolve and characterise the x - ray emission in the nlr . the findings are summarized as follows : * the soft x - ray emission line images of ngc 4151 ( ovii , oviii , and neix ) are clearly extended and show remarkable morphological coincidence with the biconical nlr mapped by the [ oiii ] emission , which supports a common emission mechanism for the hot- and cool - phase of the nlr gas . * extended emission in the x - ray image is detected along the nw se sectors , which is the direction of a putative torus . this may explain the faint rogue clouds identified in previous hst studies that require ionization in this direction , indicating leakage of nuclear ionization instead of full blocking by a continuous obscuring torus . * spectral models involving smooth continua ( a bremsstrahlung plus a power law ) with emission lines provide good descriptions of the spectra . the emission lines can not be uniquely identified with the present spectral resolution , but are consistent with the brighter lines seen in the _ chandra _ hetgs and xmm - newton rgs spectra below 2 kev . the absorption corrected x - ray luminosity of the extended emission between @xmath183 pc and @xmath184 kpc is @xmath42 erg s@xmath1 . * photoionization models successfully reproduce the soft x - ray emission , supporting the dominant role of nuclear photoionization . there are considerable variations in ionization states across the circum - nuclear region . a high ionization ( @xmath185 ) component is present in most regions . a low ionization ( @xmath92 ) component is present along the bicone direction ( ne sw ) , whereas a lower ionization ( @xmath125 ) component is found in the nw se direction , which is consistent with filtered nuclear emission by warm absorbers instead of a continuous absorbing torus . the lowest ionization component ( @xmath127 ) appears to be associated with the dense gas in the host plane . a thermal component may still be present at @xmath86 of the total soft emission , perhaps related to hot ism in the galactic disk or shocks associated with the outflow . * the measured ratios of [ oiii]/soft x - ray flux are consistent with a constant ratio of @xmath515 for the 1.5 kpc radius spanned by these measurements . this suggests a similar relative contributions from the low- and high - ionization gas phases at different radii . if the [ oiii ] and x - ray emission arise from a single photoionized medium , this further implies an outflow with a wind - like density profile ( @xmath186 ) . * the estimated mass outflow rate in ngc 4151 is @xmath52@xmath6 yr@xmath1 at 130 pc and the kinematic power of the ionized outflow is @xmath187 erg s@xmath1 , 0.3% @xmath181 . this value is significantly lower than the expected efficiency in the majority of quasar feedback models , but comparable to the two - stage model described in @xcite . placing all our findings in the context of previous studies , we obtain a comprehensive view of the ngc 4151 circum - nuclear region at various spatial scales , from the inner - most @xmath188 pc ( as illustrated in the schematic drawing in figure [ cartoon]a ) to as far as @xmath189 kpc ( figure [ cartoon]b ) . the key points are recapped here . photoionization by the nucleus is important at all scales . in the nuclear region , except for a few clouds that show interaction with the radio jet ( wang et al . 2009 , 2011b ) , most of the x - ray nlr clouds are consistent with being part of a photoionized biconical outflow , with a @xmath190 density profile expected for a nuclear wind . in the enlr of ngc 4151 , photoionization is still the dominant ionization mechanism for the observed x - ray emission ( e.g. , ogle et al . 2000 ; kraemer et al . 2005 ) , but a wide range of ionization states is present . this is likely related to the nature of the enlr . the bi - cone geometry indicates that one side of the conical outflow exits the galactic plane at a small angle , partly intersecting the host disk ( e.g. , crenshaw et al . 2000 ; das et al . 2005 ; storchi - bergmann et al . 2010 ) . optical studies ( e.g. , robinson et al . 1994 ; kaiser et al . 2000 ) have identified such a boundary between nlr and enlr at @xmath191 ( sw ) , and the ionized gas kinematics become consistent with the rotation velocity of the galactic disk at @xmath192 . thus the origin of the enlr is best explained as the inhomogeneous ism in the galactic plane ionized by the agn . part of the high density nuclear spirals illuminated in the path of the bicone can produce the curvy shape of x - ray enhancement and the associated low ionization . the presence of ionized emission perpendicular to the bicone indicates leaked nuclear emission along the putative torus direction , likely filtered nuclear emission by warm absorbers . in the large 3 kpc - scale cavity of the h i material , we find faint soft diffuse x - ray emission that provides evidence for agn host interaction in ngc 4151 ( wang et al . 2010a ) , originated from either hot gas heated by the nuclear outflow or photoionized gas from a recent nuclear outburst . as a concluding remark , our findings in ngc 4151 demonstrate that abundant information can be extracted from x - ray spectral imaging studies when supplemented with multiwavelength data . many valuable new radio , optical and ir observations and modeling of other nearby seyfert galaxies are emerging ( crenshaw et al . 2010 ; riffel et al . 2010 ; fisher et al . 2011 , schnorr mller et al . 2011 ) , and progress in the x - rays are being made to further our understanding of agn feeding and feedback processes in these galaxies . we thank the anonymous referees for providing us with detailed and constructive comments that have improved the clarity of this manuscript . this work is supported by nasa grant go8 - 9101x and go1 - 12009x . we acknowledge support from the cxc , which is operated by the smithsonian astrophysical observatory ( sao ) for and on behalf of nasa under contract nas8 - 03060 . cgm acknowledges financial support from the royal society and research councils u.k . gd was supported by dfg grants sch 536/4 - 1 and sch 536/4 - 2 as part of spp 1177 . j. w. thanks t. kallman , g. ferland , s. bianchi , a. marinucci , and s. chakravorty for advice on photoionization modeling . this research has made use of data obtained from the _ chandra _ data archive , and software provided by the cxc in the application packages ciao and sherpa . some of the data presented in this paper were obtained from the multimission archive at the space telescope science institute ( mast ) . stsci is operated by the association of universities for research in astronomy , inc . , under nasa contract nas5 - 26555 . cccccc ovii & & 0.57 & ... & @xmath193 & 13% + ... & ovii f & 0.5617 & 0.5611 & @xmath194 & + ... & ovii i & 0.5691 & 0.5687 & @xmath195 & + ... & ovii r & 0.5745 & 0.5740 & @xmath196 & + + oviii & & 0.66 & ... & @xmath197 & 13% + ... & oviii ly@xmath31 & 0.6541 & 0.6537 & @xmath198 & + ... & nvii rrc & 0.67 & ... & @xmath199 & + + ovii & & 0.73 & ... & @xmath200 & 12% + ... & ovii rrc & 0.74 & ... & @xmath201 & + ... & oviii ly@xmath202 & 0.7749 & 0.7747 & @xmath203 & + + oviii & & 0.82 & ... & @xmath204 & 2% + ... & oviii ly@xmath205 & 0.8175 & 0.8171 & @xmath206 & + ... & oviii rrc & 0.86 & ... & @xmath206 & + + neix & & 0.91 & ... & @xmath207 & 21% + ... & neix f & 0.9064 & 0.9052 & @xmath208 & + ... & neix i & 0.9172 & 0.9151 & @xmath209 & + ... & neix r & 0.9229 & 0.9221 & @xmath210 & + + nex & & 1.03 & ... & @xmath204 & 17% + ... & nex ly@xmath31 & 1.0224 & 1.0219 & @xmath210 & + ... & neix @xmath211 & 1.0749 & 1.0738 & @xmath212 & + + nex & & 1.20 & ... & @xmath213 & 12% + ... & neix rrc & 1.20 & ... & @xmath214 & + ... & nex ly@xmath202 & 1.2118 & 1.2110 & @xmath215 & + + mgxi & & 1.30 & ... & @xmath213 & 9% + ... & mgxi f & 1.3542 & 1.3313 & @xmath216 & + ... & mgxi r & 1.3525 & 1.3524 & @xmath214 & + + sii & & 1.75 & ... & @xmath217 & 9% + ... & sii k@xmath31 & 1.7413 & 1.7391 & @xmath207 & + ... & mgxii ly@xmath202 & 1.7472 & 1.7450 & @xmath218 & + ne 1 & 2432 & 0.04@xmath219 & 0.86 & 19.7 & -0.22 & 19.7 & @xmath220 & 63/65 & @xmath221 + .... 2 & 1814 & 0.07@xmath222 & 1.05 & 19.8 & 0.06 & 20.1 & @xmath223 & 60/53 & @xmath224 + .... 3 & 913 & 0.03@xmath225 & 0.49 & 19.9 & -1.87 & 23.5 & @xmath226 & 26/29 & @xmath227 + sw 1 & 2096 & 0.02 & 0.83 & 20.0 & -0.38 & 19.4 & @xmath228 & 60/57 & @xmath229 + .... 2 & 1667 & 0.02 & 1.06 & 20.0 & -0.42 & 19.8 & @xmath230 & 58/45 & @xmath231 + .... 3 & 1560 & 0.02 & 1.00 & 19.6 & -0.50 & 19.6 & @xmath232 & 54/46 & @xmath233 + .... 4 & 966 & 0.02 & 0.34 & 19.0 & -1.28 & 23.5 & @xmath234 & 34/30 & @xmath235 + nw & 1050 & 0.22@xmath219 & 1.03 & 19.2 & -0.98 & 19.5 & @xmath236 & 35/35 & @xmath237 + se & 1081 & 0.16@xmath238 & 1.26 & 20.3 & -1.16 & 19.9 & @xmath239 & 28/33 & @xmath240 + ovii - rich & 2626 & 0.02@xmath219 & 0.14 & 20.3 & -1.22 & 20.3 & @xmath223 & 60/56 & @xmath241 + neix - rich & 2141 & 0.07@xmath219 & 0.6 & 19.6 & -0.21 & 20.4 & @xmath242 & 50/56 & @xmath243 + cccccc 1 & 2.6 & 169 & 29.8@xmath244 & 25.7@xmath245 & 11.6 + 2 & 2.7 & 175 & 21.1@xmath246 & 15.2@xmath247 & 13.8 + 3 & 3.2 & 208 & 2.6@xmath248 & 2.4@xmath249 & 10.7 + 4 & 4.8 & 312 & 7.9@xmath250 & 5.4@xmath251 & 14.5 + 5 & 3.5 & 228 & 1.2@xmath248 & 1.6@xmath252 & 7.5 + 6 & 4.7 & 306 & 1.9@xmath253 & 4.7@xmath254 & 4.1 + 7 & 6.1 & 397 & 10.2@xmath255 & 6.6@xmath256 & 15.2 + 8 & 10.7 & 696 & 3.9@xmath257 & 4.2@xmath258 & 9.6 + 9 & 17.9 & 1164 & 0.9@xmath259 & 0.2@xmath260 & 43.4 + 10 & 17.7 & 1151 & 1.8@xmath259 & 0.9@xmath261 & 20.3 +

this paper is the third in a series in which we present deep chandra acis - s imaging spectroscopy of the seyfert 1 galaxy ngc 4151 , devoted to study its complex circum - nuclear x - ray emission . emission features in the soft x - ray spectrum of the bright extended emission ( erg s ) at pc ( 2 ) are consistent with blended brighter ovii , oviii , and neix lines seen in the _ chandra _ hetgs and xmm - newton rgs spectra below 2 kev . we construct emission line images of these features and find good morphological correlations with the narrow line region clouds mapped in [ oiii] . self - consistent photoionization models provide good descriptions of the spectra of the large scale emission , as well as resolved structures , supporting the dominant role of nuclear photoionization , although displacement of optical and x - ray features implies a more complex medium . presence of both low and high ionization spectral components and extended emission in the x - ray image perpendicular to the bicone indicates leakage of nuclear ionization , likely filtered through warm absorbers , instead of being blocked by a continuous obscuring torus . the ratios of [ oiii]/soft x - ray flux are approximately constant ( ) for the 1.5 kpc radius spanned by these measurements , indicating similar relative contributions from the low- and high - ionization gas phases at different radial distances from the nucleus . if the [ oiii ] and x - ray emission arise from a single photoionized medium , this further implies an outflow with a wind - like density profile . using spatially resolved x - ray features , we estimate that the mass outflow rate in ngc 4151 is yr at 130 pc and the kinematic power of the ionized outflow is erg s , approximately of the bolometric luminosity of the active nucleus in ngc 4151 .

this paper is the third in a series in which we present deep chandra acis - s imaging spectroscopy of the seyfert 1 galaxy ngc 4151 , devoted to study its complex circum - nuclear x - ray emission . emission features in the soft x - ray spectrum of the bright extended emission ( erg s ) at pc ( 2 ) are consistent with blended brighter ovii , oviii , and neix lines seen in the _ chandra _ hetgs and xmm - newton rgs spectra below 2 kev . we construct emission line images of these features and find good morphological correlations with the narrow line region clouds mapped in [ oiii] . self - consistent photoionization models provide good descriptions of the spectra of the large scale emission , as well as resolved structures , supporting the dominant role of nuclear photoionization , although displacement of optical and x - ray features implies a more complex medium . collisionally ionized emission is estimated to be% of the extended emission . presence of both low and high ionization spectral components and extended emission in the x - ray image perpendicular to the bicone indicates leakage of nuclear ionization , likely filtered through warm absorbers , instead of being blocked by a continuous obscuring torus . the ratios of [ oiii]/soft x - ray flux are approximately constant ( ) for the 1.5 kpc radius spanned by these measurements , indicating similar relative contributions from the low- and high - ionization gas phases at different radial distances from the nucleus . if the [ oiii ] and x - ray emission arise from a single photoionized medium , this further implies an outflow with a wind - like density profile . using spatially resolved x - ray features , we estimate that the mass outflow rate in ngc 4151 is yr at 130 pc and the kinematic power of the ionized outflow is erg s , approximately of the bolometric luminosity of the active nucleus in ngc 4151 .

0910.3699

i

the behavior of ultracold superfluid fermi gases continues to attract attention from the experimental and theoretical communities . through a feshbach resonance @xcite which tunes the strength of the attractive interaction , these trapped gases can exhibit a crossover from bcs to bose einstein condensation ( bec ) . unlike the bose superfluids , at the time of their discovery , the fermi superfluids are not associated with any ready - made theory ( such as gross pitaevskii , or bogoliubov theory for bosons ) . this provides an opportunity for theorists to work hand in hand with experimentalists to arrive at the same level of understanding of the fermionic as was reached for the bosonic superfluids . while the fermi systems are harder to address than the bose counterparts , the payoff for progress is great . moreover , there is a general belief that these systems may lead to important insights into high temperature superconductor ( htscs ) , in part because the htscs exhibit an anomalously short coherence length which suggests that they may be mid - way between bcs and bec @xcite . there is , as yet , no clear consensus about the theory which underlies bcs - bec crossover although there are three rather well studied analytic many body theories which have emerged . the goal of the present paper is to present a comparison and assessment of these approaches with a particular focus on the two of the three , which seem most reliable . in addition to assessing the theoretical approaches , we address physical consequences and how the theories may be differentiated through the behavior of the centrally important spectral function and related density of states . we do this in the context of radio - frequency-(rf ) based probes . what is among the most interesting features of bcs - bec crossover is the fact that the normal state ( out of which superfluidity forms ) is different from the normal state ( fermi liquid ) associated with strict bcs theory . the normal state of , for example , a unitary gas consists of pre - formed pairs which persist below @xmath2 in the form of non - condensed pair excitations of the condensate . this excitation branch is in addition to the usual gapped fermionic excitations . the normal state is often said to exhibit a pseudogap " which has features in common with the exotic normal state of the high temperature superconductors . this pseudogap @xcite reflects the formation of quasi - bound pairs which in turn require an energy input ( called @xmath3 ) in order to break the pairs and create fermionic excitations . physically , what differs from one crossover theory to another @xcite is the nature of these non - condensed or pre - formed pairs which , respectively , appear below and above @xmath2 . unlike the pair fluctuations of traditional superconductors ( which are associated with low dimensionality and impurity effects ) these pairs are present because of a stronger - than - bcs attractive interaction . as a consequence , the pairing gap @xmath3 persists to temperatures which can be several times @xmath2 for the case of the unitary gases . in this paper we address the temperature dependence of the spectral function particularly in the normal state . the density of states ( dos ) , which can be obtained from the spectral function , will also be presented . we compare with experiments in the context of rf spectra of both unpolarized and polarized fermi gases . quantum monte carlo simulations @xcite provide useful information such as the superfluid transition temperature @xmath2 , entropy , condensate fraction , etc . and recently reveal evidence of non - condensed pairs @xcite along with a pseudogap @xcite in the normal phase . our focus is on two different finite - temperature bcs - bec crossover theories and we present a detailed comparison of the results obtained from the two theories as well as an assessment of other bcs - bec crossover theories . a fair amount of controversy @xcite has surfaced in the literature regarding the three alternative analytic pairing fluctuation schemes . in this paper we address some of these issues and clarify misleading claims . at this early stage of understanding we do not believe it is suitable to invoke ( possibly fortuitous ) fits to particular experimental or monte - carlo derived numbers to establish which of these theories is best " . rather in line with the goal of this paper , one has to look at the differences at a more general level . one has , furthermore , to subject these theories to careful consistency tests . each of the three many body approaches is associated with a different ground state . thus far , only one of these can be written down analytically . in this context we note that one can trace the historical origin of the bcs - bec literature to the observation that the simplest bcs - like wavefunction @xmath4 is much more general than originally presumed @xcite . to implement this generalization , all that is required is that one solve for the two variational parameters @xmath5 and @xmath6 in concert with a self consistent condition on the fermionic chemical potential @xmath7 . as the attraction is increased , @xmath7 becomes different from the fermi energy @xmath8 , and in particular , in the bec regime , @xmath7 is negative . this ground state is often called the bcs - leggett " state and the two variational parameters @xmath5 and @xmath6 can be converted to two more physically accessible parameters associated with the zero temperature gap ( or equivalently order parameter ) and @xmath7 . the three theories currently of interest can be related to a t - matrix scheme . within a given t - matrix scheme one treats the fermionic self energy and the pair - propagator using a coupled equation scheme , but drops the contributions from higher order green s functions . this t - matrix is called @xmath9 , where @xmath10 is a four - vector and @xmath11 denotes the boson matsubara frequency ; it characterizes the non - condensed pairs which are described physically and formally in different ways in the different theories . here the subscript @xmath12 is associated with the pseudogap ( pg ) whose presence is dependent on the non - condensed or pre - formed pairs . quite generally we can write the t - matrix in a ladder - diagram series as @xmath13 where @xmath14 is the pair susceptibility and @xmath15 denotes the attractive coupling constant . the nozires - schmitt - rink ( nsr ) theory @xcite is associated with a pair susceptibility @xmath14 which is a product of two bare green s functions . the fluctuation exchange or flex approach is associated with two dressed green s functions and has been discussed by haussmann @xcite , zwerger and their collaborators in the context of the cold gases , and even earlier in the context of the cuprates @xcite . it is also called the luttinger - ward formalism @xcite , or galitskii - feynman theory @xcite . finally , it is well known @xcite that bcs theory ( and now its bcs - bec generalization ) is associated with one bare and one dressed green s function in the pair susceptibility . these differences would seem to be rather innocuous and technical but they have led to significant qualitative differences and concurrently strong claims by various proponents . we stress that while there are several variants , as we discuss below , the version of the nsr scheme which seems to us most free of concerns is that discussed in references @xcite which introduced a more physical treatment of the number equation . this revision of strict nsr theory was , in part , an answer to j. serene @xcite who raised a question about a central approximation in the theory in which the number equation ( @xmath16 , where @xmath17 is the single particle green s function ) is approximated by @xmath18 , where the thermodynamical potential @xmath19 is approximated by a ladder - diagram series . it was shown that this amounts to taking the leading order in a dyson series for @xmath17 . the present paper concentrates on the normal state behavior , although all three classes of theories have been extended below @xmath2 . what is essential about these extensions is that the non - condensed pair excitations associated with @xmath20 are gapless , as in boson theories . indeed , it is in these @xmath21 extensions that a number of concerns have been raised . in particular , in the leading order extended nsr theory ( or so called bogoliubov level " approach ) , @xcite , the gap equation ( which is assumed to take the usual bcs form , rather than derived , for example , variationally ) does not contain explicit pairing fluctuation contributions ; these enter indirectly only via the fermion chemical potential @xmath7 . at this level , the number equation is the only way in which explicit pairing fluctuations are incorporated . at the so called popov level " calculation , the gap equation is presumed to contain pair fluctuations @xcite but there is some complexity in ensuring the concomitant gaplessness of the pair excitations . similar issues arise with the flex or luttinger - ward approach in which ( @xcite and references therein ) gapless sound modes must be imposed somewhat artificially . while the order of the transition at @xmath2 is second order in the bcs - leggett scheme it is first order @xcite in nsr based approaches ( as well as for the fully renormalized pair susceptibility scheme . this leads to unwanted features in the density profiles @xcite and @xmath0 dependent superfluid density @xcite , @xmath22 . despite these unphysical aspects , the nsr - based scheme captures the physics of bogoliubov theory of weakly interacting bosons @xcite and should , in principle , be the quantitatively better low @xmath0 state , particularly in the bec limit . nevertheless some issues have been identified @xcite which suggest the breakdown of true quasi - particles associated with bogoliubov - like theories for paired fermions . this , in turn , derives from the self consistent treatment of coupling between the non - condensed pairs and the sound modes . further analysis will be required to establish if this is compatible with experimental or theoretical constraints . a very early concern about the so - called gg " or flex approach was raised in a paper by kadanoff and martin @xcite in 1961 : the similarity [ to a bethe - salpeter equation ] has led several people to surmise that the symmetrical equation [ involving fully dressed g s everywhere ] solved in the same approximation would be more accurate . this surmise is not correct . the green s functions resulting from that equation can be rejected in favor of those used by bcs by means of a variational principle . " importantly this approach does not have a true pseudogap . despite claims by the zwerger group @xcite that theirs is a more fully consistent " theory , and in this context appealing to ref . @xcite , the authors of ref . @xcite instead say : we thus conclude that ... approaches such as flex are unreliable in the absence of a migdal theorem and that there is indeed a pseudogap . " similar observations have appeared elsewhere in the literature @xcite . as noted in ref . vertex corrections to the self energy , which are discarded in the previous studies [ of flex ] are crucially important for the pseudogap " . additional concerns have been noted recently @xcite that in the flex ( or @xmath23 t - matrix ) theory the propagator @xmath24 does not display quasiparticle poles associated with the gap . `` this is because the dyson equation , @xmath25 , excludes identical poles of @xmath24 and @xmath26 while the linear relation demands them '' . in recent work below @xmath2 @xcite a non - variational gap equation was used to derive an additional term in the number equation related to @xmath27 . here @xmath28 is the order parameter and , here , again , @xmath19 is the thermodynamical potential . this extra term means there is no variational free energy functional , such as required by landau - ginsburg theory . of concern are arguments that by including @xmath29 , it is possible to capture the results of petrov et al @xcite for the inter - boson scattering length . we see no physical connection between the exact four - fermion calculations and the non - variational component of the many body gap equation . it should , moreover , be stressed that all other t - matrix schemes have reported an effective pair - pair scattering length given by @xmath30 which is larger than the value @xmath31 obtained from a four - body problem @xcite . here @xmath32 is the @xmath33-wave scattering length of fermions . indeed , our past work @xcite and that of reference @xcite have shown that one needs to go beyond the simple t - matrix theory to accommodate these four - fermion processes . additional concerns arise from the fact that an nsr - based scheme has difficulty @xcite accommodating polarization effects in the unitary regime . as stated by the co - workers in reference @xcite : unfortunately , in a region around the unitary limit we find that the nsr approach generally leads to a negative population imbalance at a positive chemical potential difference implying an unphysical compressibility . " . the central weakness of the bcs - leggett approach ( and its finite-@xmath0 extension ) appears to be the fact it focuses principally on the pairing channel and is not readily able to incorporate hartree effects . the evident simplicity of this ground state has raised concern as well . clearly , this is by no means the only ground state to consider but , among all alternatives , it has been the most widely applied by the cold gas community including the following notable papers @xcite . the central strengths of the finite-@xmath0 extended bcs - leggett approach in comparison with others are that ( i ) there are no spurious first order transitions and ( ii ) the entire range of temperatures is accessible . ( iii ) moreover , polarization effects may be readily included @xcite , ( iv ) as may inhomogeneities which are generally treated using bogoliubov degennes theory @xcite , based on this ground state . the above analysis leaves us with two theoretical schemes which we wish to further explore : the nsr approach ( which in the normal phase follows directly from the original paper @xcite ) and the bcs - leggett - based scheme , as extended away from zero temperature , and in particular above @xmath2 . as t - matrix approaches to many body theory , these are similar in spirit , but different in implementation . it is clearest below @xmath2 , that the two theories focus on different physics . nsr approaches view the dominant processes as the coupling of the order parameter collective modes to the non - condensed pairs and the bcs - leggett scheme focuses on the steady state equilibrium between the gapped fermions and the non - condensed pairs . thus nsr focuses more fully on the bosonic degrees of freedom and bcs - leggett focuses on the fermionic degrees of freedom . above @xmath2 , because the nsr scheme involves only bare green s functions , it is simpler . thus , it has been studied at a numerical level in a more systematic fashion . in the literature , the bcs - leggett approach at @xmath34 , has been addressed numerically @xcite , assessed more theoretically @xcite , as well as applied to different physical contexts @xcite . in this paper we apply an approximation based on prior numerical work @xcite to simplify the calculations . a central way of characterizing these different bcs - bec crossover theories is through the behavior of the fermionic spectral function , @xmath35 . for the most part , here , we restrict our consideration to the normal state where @xmath35 should indicate the presence or not of a pseudogap . a momentum integrated form of the spectral function is reflected in radio frequency studies both tomographic @xcite or effectively homogeneous and trap averaged @xcite . one of the principal observations of this paper is that these momentum integrated probes are not , in general , sufficiently sensitive to pick up more than gross differences between the three crossover theories . however , there are now momentum resolved rf studies @xcite which probe the spectral function more directly , in a fashion similar to angle - resolved photoemission spectroscopy ( arpes ) probes of condensed matter . a central aim of this paper is to show how these studies in future will be able to differentiate more clearly between the different crossover schools . here we confine our attention to homogeneous systems , although experiments are necessarily done for the trapped case . in addition to rf spectroscopy , it was proposed @xcite that the spectral function can also be measured in raman spectroscopy . we note that for the htscs , arpes studies have been centrally important in revealing information about the superconducting as well as the pseudogap phases @xcite . indeed , the close relation between arpes and radio frequency probes has been discussed in our recent review @xcite . it was shown in ref . @xcite that the spectral function of htscs in the pseudogap phase appears to exhibit dispersion features similar to those in the superconducting phase . this spectral function is modeled @xcite by a broadened bcs form with a self energy @xmath36 here @xmath37 is the ( @xmath33 or @xmath1-wave ) excitation gap of the normal phase and @xmath38 is a phenomenological damping . frequently , one adds an additional , structureless imaginary damping term @xmath39 , as well . high temperature superconductor experiments at temperatures as high as @xmath40 have reported that in the regions of the brillouin zone ( where the pseudogap is well established ) , the dispersion of the fermionic excitations behaves like @xmath41 importantly eq . ( [ eq:3a ] ) has also been used in the cold gas studies @xcite in the region near and above @xmath2 and implemented phenomenologically below @xmath2 @xcite . this both demonstrates the presence of pairing and ultimately provides information about the size of the pairing gap . it has been shown that eq . ( [ eq:2a ] ) is reasonably robust in the extended bcs - leggett state above @xmath2 , at least up to temperatures @xcite of the order of @xmath42 . by contrast this approximate self energy is not generally suitable to nsr theory @xcite , although for @xmath43 a fit to eq . ( [ eq:3a ] ) has been obtained . in a similar context we note that in the flex approach , the spectral function and associated self energy is not of the broadened bcs form . mathematically , this bcs - like structure in the self energy and fermionic dispersion ( which is numerically obtained ) comes from the facts that the effective pair chemical potential @xmath44 at and below @xmath2 , and that by having one bare and one dressed green s function in @xmath14 there is a gap in the pair excitation spectrum so that the pairs are long lived ; in this way @xmath38 ( which scales with the inverse pair lifetime ) is small . physically , we can say that this behavior reflects the stability of low momentum pairs near @xmath2 and below . these differences between the three different crossover theories become less apparent for the momentum integrated rf signals . in the bcs - leggett approach at low temperatures the dominant structure comes from pair breaking of the condensate ( which would be associated with the negative root in eq . ( [ eq:3a ] ) ) . despite the fact that their fermionic dispersions are different , both other theories yield a very similar positive detuning branch " in the rf spectrum @xcite . however , at higher temperatures , both for polarized and unpolarized gases , there is theoretical evidence of the negative detuning branch " arising from the positive root in eq . ( [ eq:3a ] ) in the bcs - leggett based approach @xcite . this is absent in the two other schemes , at least within the normal state . it also appears to be difficult to see experimentally in the unpolarized case , although it is clearly evident once even a small polarization @xcite is present @xcite . this paper is organized as follows . sections [ sec : nsrtheory ] and [ sec : g0gtheory ] briefly review nsr theory and bcs - leggett theory as extended to non - zero @xmath0 . section [ sec : spectral ] addresses a comparison of the spectral function at unitarity and on the bec side obtained from the two theories . in subsections [ sec : dos ] we plot a comparison of the related density of states at unitarity and in [ sec : rf ] we address a comparison of rf spectra in the two theories for an unpolarized fermi gas which also addresses experimental data . also included is a prediction of rf spectra on the bec side of resonance . the remaining sections ( section [ sec : rftc ] and section [ sec : rfpol ] ) do not focus on comparisons because the issues discussed pertain to questions which only bcs - leggett theory has been able to address . here we propose a subtle signature of the superfluid transition in section [ sec : rftc ] which could be addressed in future and in section [ sec : rfpol ] we address the theoretical rf spectrum of polarized fermi gases at unitarity and its comparison with experimental data . section [ sec : conclusion ] concludes this paper . we remark that in this paper we study @xmath33-wave pairing in three spatial dimensions which is more relevant to ultra - cold fermi gases while htscs should be modeled as @xmath1-wave pairing in quasi - two dimensions . however , as one will see , there are many interesting common features in these two systems .

this paper presents a comparison of two finite - temperature bcs - bose einstein condensation ( bec ) crossover theories above the transition temperature : nozieres schmitt - rink ( nsr ) theory and finite-extended bcs - leggett theory . both theories include pair fluctuations and exhibit pseudogap effects , although the nature of this pseudogap is very different . the fermionic quasi - particle dispersion is different in nsr theory and the damping is considerably larger . we argue that the two theories are appropriate in different temperature regimes with the bcs - leggett approach more suitable nearer to condensation . there should , in effect , be little difference at higher as the pseudogap becomes weaker and where the simplifying approximations used in the bcs - leggett approach break down . a full comparison for polarized gases is not possible since there is claimed to be inconsistencies in the nsr approach ( not found in the bcs - leggett scheme ) .

this paper presents a comparison of two finite - temperature bcs - bose einstein condensation ( bec ) crossover theories above the transition temperature : nozieres schmitt - rink ( nsr ) theory and finite-extended bcs - leggett theory . the comparison is cast in the form of numerical studies of the behavior of the fermionic spectral function both theoretically and as constrained by ( primarily ) radio frequency ( rf ) experiments . both theories include pair fluctuations and exhibit pseudogap effects , although the nature of this pseudogap is very different . the pseudogap in finite-extended bcs - leggett theory is found to follow a bcs - like dispersion which , in turn , is associated with a broadened bcs - like self energy , rather more similar to what is observed in high temperature superconductors ( albeit , for a-wave case ) . the fermionic quasi - particle dispersion is different in nsr theory and the damping is considerably larger . we argue that the two theories are appropriate in different temperature regimes with the bcs - leggett approach more suitable nearer to condensation . there should , in effect , be little difference at higher as the pseudogap becomes weaker and where the simplifying approximations used in the bcs - leggett approach break down . on the basis of momentum - integrated radio frequency studies of unpolarized gases , it would be difficult to distinguish which theory is the better . a full comparison for polarized gases is not possible since there is claimed to be inconsistencies in the nsr approach ( not found in the bcs - leggett scheme ) . future experiments along the lines of momentum resolved experiments look to be very promising in distinguishing the two theories .

0910.3699

c

the goal of this paper is to communicate that bcs - bec crossover theories are very exciting . they are currently being clarified and developed hand in hand with experiment . for the fermi superfluids , unlike their bose counterparts , we have no ready - made theory . in this paper we confine our attention to the normal phase , although we have presented a discussion of some of the controversial issues which have surface in the literature below @xmath2 . we view the principal value of this paper is the presentation of comparisons of two different crossover theories and the identification of ( mostly future ) experiments which can help distinguish them . the two theories we consider are the extended bcs - leggett theory and that of nozieres and schmitt - rink . we chose not to discuss the flex or luttinger - ward scheme in any detail because it is discussed elsewhere @xcite , and because there are concerns that , by ignoring vertex corrections , this approach has omitted the important physics associated with the pseudogap . these concerns are longstanding @xcite . here we have argued that the extended bcs - leggett theory is the one theory which preserves ( broadened ) bcs features into the normal state over a significant range of temperatures . even above @xmath2 one finds that the fermionic excitations have an ( albeit , smeared out ) dispersion of the form @xmath211 in the normal state . we find that nsr theory does not have this dispersion , although it has a pseudogap by all other measures . interestingly high @xmath2 superconductors have been shown to have this dispersion in their normal state @xcite and it is generally believed @xcite that their fermionic self energy can be fit to a broadened ( @xmath1-wave ) bcs form @xmath212 . in this paper we show that one can identify both physically and mathematically the difference between the two normal states of the different crossover theories . mathematically because bcs theory involves one dressed green s function in the pair susceptibility , it leads to a low frequency gap in the t - matrix or pair propagator ( at low @xmath157 ) . physically this serves to stabilize low momentum pairs . this helps us to understand that the pseudogap of nsr theory does not incorporate primarily low momentum pairs , but rather pairs of all momentum and that it should be better further from condensation . indeed , this is reenforced by our observation that at higher @xmath0 , feedback effects which distinguish the two theories becomes less and less important and the bcs - leggett pair susceptibility , @xmath125 , crosses over to something closer to @xmath152 as in nsr theory . our simplest approximation for the self energy in eq . ( [ eq:2a ] ) is no longer suitable once temperature exceeds , say @xmath213 . indeed this is reenforced by earlier numerical observations @xcite . as a result , we believe that both theories are right but in different temperature regimes . moreover , this serves to elucidate another concern about nsr theory ( and flex theory) that they are associated with an unphysical first order transition . both theories change discontinuously in going from above to below @xmath2 . in the superfluid phase the coupling which is included in all other theories is between the non - condensed pairs and the collective modes of the condensate , even though in the normal state one couples the fermions and the non - condensed pairs . in the extended bcs - leggett theory , ( as seems reasonable , in the vicinity of @xmath2 both above and below ) , the dominant coupling is , indeed , between non - condensed pairs and fermions . these ( effectively , pseudogap ) effects will behave smoothly across @xmath2 . the goldstone modes which turn on at @xmath2 are highly damped in its vicinity , where the condensate is weak . only at lower @xmath0 should their coupling become the more important . in summary , a central conclusion of this study of the spectral functions of the extended bcs - leggett theory and nsr theory is that one may expect that the former is suitable near @xmath2 due to its similarity to bcs theory while the latter better describes the normal phase at much higher @xmath0 as the system approaches a fermi liquid , and concomitantly , the pseudogap begins to disappear . in the course of this work we have found that the theoretical rf spectra from both theories agree ( only semi - quantitatively ) to about the same extent with experimental data at unitarity . the bcs - leggett approach has the advantage that it can address the rf spectrum of generally polarized fermi gases without the problems which have been noted @xcite for the nsr approach . however , momentum resolved experiments @xcite may be the ultimate way of distinguishing experimentally between different theories .

the comparison is cast in the form of numerical studies of the behavior of the fermionic spectral function both theoretically and as constrained by ( primarily ) radio frequency ( rf ) experiments . on the basis of momentum - integrated radio frequency studies of unpolarized gases , it would be difficult to distinguish which theory is the better .

this paper presents a comparison of two finite - temperature bcs - bose einstein condensation ( bec ) crossover theories above the transition temperature : nozieres schmitt - rink ( nsr ) theory and finite-extended bcs - leggett theory . the comparison is cast in the form of numerical studies of the behavior of the fermionic spectral function both theoretically and as constrained by ( primarily ) radio frequency ( rf ) experiments . both theories include pair fluctuations and exhibit pseudogap effects , although the nature of this pseudogap is very different . the pseudogap in finite-extended bcs - leggett theory is found to follow a bcs - like dispersion which , in turn , is associated with a broadened bcs - like self energy , rather more similar to what is observed in high temperature superconductors ( albeit , for a-wave case ) . the fermionic quasi - particle dispersion is different in nsr theory and the damping is considerably larger . we argue that the two theories are appropriate in different temperature regimes with the bcs - leggett approach more suitable nearer to condensation . there should , in effect , be little difference at higher as the pseudogap becomes weaker and where the simplifying approximations used in the bcs - leggett approach break down . on the basis of momentum - integrated radio frequency studies of unpolarized gases , it would be difficult to distinguish which theory is the better . a full comparison for polarized gases is not possible since there is claimed to be inconsistencies in the nsr approach ( not found in the bcs - leggett scheme ) . future experiments along the lines of momentum resolved experiments look to be very promising in distinguishing the two theories .

1403.7720

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storage is a new paradigm of storing data . it allows users to access data anywhere and anytime . companies such as google and apple are providing this service through their data centers , which are network - connected . such an architecture is called the distributed storage system ( dss ) . storage nodes in a dss are generally unreliable and subject to failure . when a failure occurs , a newcomer needs to _ repair _ the lost data by retrieving data from surviving storage nodes , called helper nodes , so as to maintain the _ reliability _ of the dss . besides , the dss should be able to provide data _ availability _ , which allows users to access their data anywhere and with low delay . to provide reliability and availability , erasure codes such as replication or reed - solomon ( rs ) code are commonly used . while replication requires less network bandwidth during node repair , rs code is more efficient in terms of storage space . in 2007 , dimakis et al . showed that there is a fundamental tradeoff between storage space and repair bandwidth @xcite . points on the tradeoff curve can be achieved by a class of codes called _ regenerating codes _ , which is based on the concept of network coding . in their formulation , a newcomer is able to recover the lost data by connecting to any @xmath0 surviving storage nodes , and a data collector is able to retrieve the data object by downloading data from any @xmath1 out of the @xmath2 storage nodes . we call this distributed storage model the _ regular _ model . since then , many codes that achieve points on the tradeoff curve have been constructed ( e.g. @xcite ) . the design rationale of regenerating codes is to minimize repair bandwidth . these codes , however , generally incur high disk i / o access during repair , since helper nodes need to read its stored data and linearly combine them to form packets to be sent to a newcomer . the stored data that needs to be read is often much more than the data to be sent to the newcomer . the disk access bandwidth thus becomes the bottleneck . in @xcite , the repair problem is considered in a different way . it aims to minimize the amount of information to be accessed when the number of node failures is smaller than the erasure correcting capability of an mds code . another approach is considered in @xcite . it proposes a new code formed by concatenating an outer mds code with an inner fractional repetition ( fr ) code . we call it mds - fr code . this code is a minimum bandwidth regenerating ( mbr ) code , which means that it minimizes the repair bandwidth of the system . furthermore , it has the nice _ uncoded repair _ property : a helper node only needs to read the exact amount of data that it needs to forward to the newcomer without any processing . in other words , it minimizes both repair bandwidth and disk access bandwidth at the same time . while the original construction of the fr code in @xcite is based on regular graph and steiner system , other constructions exist , which are based on bipartite graph @xcite , randomized algorithm @xcite , resolvable designs @xcite , and incidence matrix @xcite . note that the above mentioned works do not strictly follow the regular model , as they have different design considerations in mind . another notable example is the locally repairable code @xcite , which aims at reducing the number of nodes that need to be contacted during repair . in this paper , we focus on heterogeneous distributed storage systems . examples include heterogenous data centers , peer - to - peer cloud storage systems ( e.g. space monkey ) @xcite , peer - assisted cloud storage systems , and some wired or wireless caching systems @xcite . in these applications , the storage nodes and the network links are _ heterogeneous _ , meaning that the storage capacities and costs associated with different storage nodes may not be the same , and the communication links between each pair of storage nodes may have different characteristics in terms of bandwidth , communication cost , and transmission rate . furthermore , it is also possible that some storage nodes are not directly connected . in such an environment , new issues arise . the storage allocation problem , which focuses on how to allocate a given storage budget over the storage nodes such that the probability of successful recovery is maximized , is studied in @xcite . a distributed storage system in which the storage nodes have different download costs is considered in @xcite . in a distributed storage system with storage cost , how to allocate storage capacities among the storage nodes so as to minimize the total storage cost is investigated in @xcite . in @xcite , the bandwidth heterogeneity is taken into account to demonstrate that the tree - structured regeneration topology is an efficient topology to reduce the regeneration time . under functional repair model , the link costs and the impact of network topology are jointly considered in @xcite , and an information - theoretic study is performed in @xcite . to address the design issues of heterogenous cloud storage systems , we set up a flexible model , called the _ irregular _ model , in which the underlying network topology can be arbitrary , the storage capacities and costs of different storage nodes are allowed to be different , and the bandwidth and costs of communication links need not be the same . we relax the constraints of data repair and data retrieval in the regular model by introducing the concepts of repair overlay and retrieval sets . we use the term repair overlay to refer to the structure of an overlay network for data repairing . note that it is called repair table in @xcite . in the work of @xcite , for single failure case , the repair overlay is restricted to be a regular graph with each vertex having degree @xmath0 , and the graph is randomly generated . in this paper , we do not restrict the repair overlay to be a regular graph . for the general case of multiple failures , the repair overlay in @xcite is a steiner system . however , the existence of a steiner system requires the system parameters to satisfy some specific conditions , which makes the system design inflexible . in this paper , hypergraph is used to model the repair overlay , which exists for arbitrary system parameters and can be constructed easily compared with steiner system . recall that the code used in @xcite is a concatenation of an outer mds code and an inner fr code . we call this construction the mds - fr code . we extend the idea and propose the use of the _ irregular fractional repetition _ ( ifr ) code as the inner code . while it preserves the desirable uncoded repair property , it further allows more flexibility in system design . when the distributed storage system and the underlying network is heterogeneous , the ifr code can be constructed and adapted to the given environment by solving an optimization problem , thus further reducing repair bandwidth . in our formulation , we minimize the system repair cost by properly choosing the mds - ifr code . the problem is shown to be an integer linear programming ( ilp ) problem . when the number of storage nodes is small , the optimal solution can be found in a reasonable time . for larger networks , we decompose the problem into subproblems and propose a heuristic solution . for small network sizes , our heuristic is shown to be nearly optimal by comparing it with the optimal ilp method . the rest of the paper is organized as follows . a motivating example is given in section [ sec : motivation ] . section [ sec : model ] states our irregular model for distributed storage systems . in section [ sec : code ] , we describe the construction of mds - ifr code and its relationship with the concept of relay overlay . in section [ sec : formulation ] , we formulate the repair cost minimization problem as an integer linear problem ( ilp ) . in section [ sec : tradeoff ] , we describe how the storage - repair tradeoff of our code can be found . in section [ sec : heuristic ] , we design heuristic algorithms to find suboptimal repair overlay and retrieval sets . section [ sec : simulation ] provides our simulation results . we conclude the paper in section [ sec : conclusion ] .

this paper presents a flexible irregular model for heterogeneous cloud storage systems and investigates how the cost of repairing failed nodes can be minimized . the fractional repetition code , originally designed for minimizing repair bandwidth for homogeneous storage systems , is generalized to the irregular fractional repetition code , which is adaptable to heterogeneous environments . the code structure and the associated storage allocation can be obtained by solving an integer linear programming problem . for moderate sized networks , a heuristic algorithm is proposed and shown to be near - optimal by computer simulations .

this paper presents a flexible irregular model for heterogeneous cloud storage systems and investigates how the cost of repairing failed nodes can be minimized . the fractional repetition code , originally designed for minimizing repair bandwidth for homogeneous storage systems , is generalized to the irregular fractional repetition code , which is adaptable to heterogeneous environments . the code structure and the associated storage allocation can be obtained by solving an integer linear programming problem . for moderate sized networks , a heuristic algorithm is proposed and shown to be near - optimal by computer simulations . cloud storage , distributed storage systems , irregular fractional repetition code , regenerating code

1003.4438

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we have calculated specific contributions to jet pseudorapidity and transverse momentum distributions for the standard model higgs plus high-@xmath1 jet production cross section at the lhc and the tevatron . the remaining scale uncertainty of the nlo qcd prediction ( in the large top - mass limit ) for this higgs production mode via light quark parton processes is at the level of 10% @xcite . motivated by this , we discussed here the contributions of electroweak loops and of bottom - quark parton processes ( in the five - flavour scheme ) to cross section predictions for the tevatron and the large hadron collider with @xmath2 collision energy . for higgs bosons with a mass of @xmath3 , @xmath4 and @xmath5 , we find the maximal effects of the electroweak contributions to the total higgs plus jet @xmath1 and @xmath0 distribution to be @xmath6 and @xmath7 , respectively , for the tevatron , and @xmath8 and @xmath9 , respectively , for the lhc . for the maximal contribution of bottom - quark parton processes to the @xmath1 and @xmath0 distribution , we find @xmath10 and @xmath11 , respectively , for the tevatron , and @xmath12 and @xmath10 , respectively , for the lhc . those contributions are smaller but still comparable in size to the numerical impact of including bottom quarks of non - zero mass in quark - loop mediated contributions to the higgs plus jet cross section prediction . for both colliders , the magnitude of the electroweak contribution rises with higgs mass , while the bottom parton contribution falls with higgs mass . a separate study of the higgs + @xmath13-jet cross section demonstrates that a calculational approach which respects the hierarchies of yukawa couplings yields a leading order cross section prediction which is more accurate in the high-@xmath1 regime than conventional approaches . i thank frank petriello for the efficient comparison of our numerical results . i thank stefan dittmaier , alberto guffanti , karl jakobs and christian schwinn for valuable comments and useful discussions . this work was supported by the helmholtz alliance ha-101 physics at the terascale and in part by the european community s marie - curie research training network under contract mrtn - ct-2006 - 035505 ` tools and precision calculations for physics discoveries at colliders ' ( heptools ) . g. arnison _ et al . _ [ ua1 collaboration ] , phys . b * 122 * ( 1983 ) 103 ; 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s. catani , d. de florian , m. grazzini and p. nason , jhep * 0307 * ( 2003 ) 028 . d. de florian , m. grazzini and z. kunszt , phys . rev . lett . * 82 * ( 1999 ) 5209 ; v. ravindran , j. smith and w. l. van neerven , nucl . b * 634 * ( 2002 ) 247 ; c. j. glosser and c. r. schmidt , jhep * 0212 * ( 2002 ) 016 . j. campbell , r. k. ellis , f. maltoni and s. willenbrock , phys . d * 67 * ( 2003 ) 095002 ; s. dittmaier , m. krmer and m. spira , phys . d * 70 * ( 2004 ) 074010 . s. dawson , c. b. jackson , l. reina and d. wackeroth , phys . * 94 * ( 2005 ) 031802 and mod . phys . lett . a * 21 * ( 2006 ) 89 . s. dawson and p. jaiswal , arxiv:1002.2672 [ hep - ph ] . w. y. keung and f. j. petriello , phys . d * 80 * ( 2009 ) 013007 . j. m. campbell _ et al . _ , arxiv : hep - ph/0405302 ; k. a. assamagan _ et al . _ [ higgs working group collaboration ] , arxiv : hep - ph/0406152 ; c. buttar _ [ standard model and higgs working group ] , arxiv : hep - ph/0604120 . d. rainwater , m. spira and d. zeppenfeld , hep - ph/0203187 ; t. plehn , phys . rev . d * 67 * ( 2003 ) 014018 ; f. maltoni , z. sullivan and s. willenbrock , phys . rev . d * 67 * ( 2003 ) 093005 ; e. boos and t. plehn , phys . rev . d * 69 * ( 2004 ) 094005 ; r. v. harlander and w. b. kilgore , phys . d * 68 * ( 2003 ) 013001 . a. d. martin , w. j. stirling , r. s. thorne and g. watt , arxiv:0901.0002 [ hep - ph ] . w. m. yao _ et al . _ [ particle data group ] , j. phys . g * 33 * ( 2006 ) 1 . j. kblbeck , m. bhm , a. denner , comput . * 60 * ( 1990 ) 165 ; h. eck , ph.d . thesis , university of wrzburg ( 1995 ) ; t. hahn and m. perez - victoria , comput . phys . commun . * 118 * ( 1999 ) 153 ; t. hahn , comput . * 140 * ( 2001 ) 418 . m. r. whalley , d. bourilkov and r. c. group , arxiv : hep - ph/0508110 ; + http://hepforge.cedar.ac.uk/lhapdf/ qcd contributions to the scattering amplitudes of the partonic subprocesses ( a ) @xmath182 , ( b ) @xmath183 , ( c ) @xmath138 ( @xmath184 ) and ( d ) @xmath22 at leading order . the shaded blob represents a quark loop ( only top- and bottom loops contribute significantly ) . the symbol below each graph indicates to which coefficient in the mathematical expressions for the amplitudes ( eqs . ( [ gg - amp ] ) and ( [ q - amp ] ) ) this graph contributes . ] electroweak loop contributions to the @xmath185 scattering amplitude at leading order , assuming no up - quark higgs yukawa coupling . the depicted graphs contribute all to the coefficient @xmath186 in the mathematical expression for the amplitude ( eq . ( [ q - amp ] ) ) . the contributions look similar for the scattering of other quark flavours . ] electroweak loop contributions to the @xmath18 scattering amplitude at leading order which do not vanish for @xmath53 . the symbol below each graph indicates to which coefficient in the mathematical expression for the amplitude ( eq . ( [ b - amp ] ) ) this graph contributes . ] relative contributions of different parts of the squared matrix element @xmath187 ( see eq . ( [ b - amp - sq ] ) ) to the integrated partonic cross section of @xmath188 as a function of centre - of - mass energy @xmath82 for @xmath80 and a cut on the scattering angle @xmath81 . ] @xmath1 distribution for quark - gluon scattering at the tevatron : ( a ) quark parton processes with and without the @xmath13 quark contributions , with and without electroweak contributions ; ( b ) relative differences to the left panel ; ( c ) contributions to the @xmath13 quark parton processes . the depicted approximations are described in the main text . ] @xmath0 distribution for quark - gluon scattering at the tevatron : ( a ) quark parton processes with and without the @xmath13 quark contributions , with and without electroweak contributions ; ( b ) relative differences to the left panel ; ( c ) contributions to the @xmath13 quark parton processes . the depicted approximations are described in the main text . ] @xmath1 distribution for quark anti - quark annihilation at the tevatron : ( a ) quark parton processes with and without the @xmath13 quark contributions , with and without electroweak contributions ; ( b),(c ) relative differences to the left panel ; ( d ) contributions to the @xmath13 quark parton processes . the depicted approximations are described in the main text . ] @xmath0 distribution for quark anti - quark annihilation at the tevatron : ( a ) quark parton processes with and without the @xmath13 quark contributions , with and without electroweak contributions ; ( b ) relative differences to the left panel ; ( c ) contributions to the @xmath13 quark parton processes . the depicted approximations are described in the main text . ] relative size of the effects of including @xmath13-quark parton processes ( black lines ) and electroweak contributions ( green lines ) on the tevatron ( @xmath189 ) differential distributions for higgs + jet production : ( a ) @xmath1 distribution and ( b ) @xmath0 distribution of the recoiling jet . ] @xmath1 distribution for quark - gluon scattering at the lhc ( @xmath190 ) : ( a ) quark parton processes with and without the @xmath13 quark contributions , with and without electroweak contributions ; ( b ) relative differences to the left panel ; ( c ) contributions to the @xmath13 quark parton processes . the depicted approximations are described in the main text . ] @xmath0 distribution for quark - gluon scattering at the lhc ( @xmath190 ) : ( a ) quark parton processes with and without the @xmath13 quark contributions , with and without electroweak contributions ; ( b ) relative differences to the left panel ; ( c ) contributions to the @xmath13 quark parton processes . the depicted approximations are described in the main text . ] @xmath1 distribution for quark anti - quark annihilation at the lhc ( @xmath190 ) : ( a ) quark parton processes with and without the @xmath13 quark contributions , with and without electroweak contributions ; ( b ) relative differences to the left panel ; ( c ) contributions to the @xmath13 quark parton processes . the depicted approximations are described in the main text . ] @xmath0 distribution for quark anti - quark annihilation at the lhc ( @xmath190 ) : ( a ) quark parton processes with and without the @xmath13 quark contributions , with and without electroweak contributions ; ( b ) relative differences to the left panel ; ( c ) contributions to the @xmath13 quark parton processes . the depicted approximations are described in the main text . ] relative size of the effects of including @xmath13-quark parton processes ( black lines ) and electroweak contributions ( green lines ) on the lhc ( @xmath190 ) differential distributions for higgs + jet production : ( a ) @xmath1 distribution and ( b ) @xmath0 distribution of the recoiling jet . ]

this paper presents predictions for jet pseudorapidity ( ) and transverse momentum ( ) distributions for the production of the standard model higgs boson in association with a high- hadronic jet . we discuss the contributions of electroweak loops and of bottom - quark parton processes to the cross section . predictions for the tevatron and the large hadron collider with collision energy are presented . for higgs boson masses of , and , we find the maximal effects of the electroweak contributions to the higgs plus jet and distribution to be and , respectively , for the tevatron , and and , respectively , for the lhc . for the maximal contribution of bottom - quark parton processes to the and distribution , we find and , respectively , for the tevatron , and and , respectively , for the lhc . a separate study of the higgs +-jet cross section demonstrates that a calculational approach which respects the hierarchies of yukawa couplings yields a leading order cross section prediction which is more accurate in the high- regime than conventional approaches . fr - pheno-2010 - 016 * electroweak and bottom quark contributions + to higgs boson plus jet production + * + _ physikalisches

this paper presents predictions for jet pseudorapidity ( ) and transverse momentum ( ) distributions for the production of the standard model higgs boson in association with a high- hadronic jet . we discuss the contributions of electroweak loops and of bottom - quark parton processes to the cross section . the latter arise in the five - flavour scheme . predictions for the tevatron and the large hadron collider with collision energy are presented . for higgs boson masses of , and , we find the maximal effects of the electroweak contributions to the higgs plus jet and distribution to be and , respectively , for the tevatron , and and , respectively , for the lhc . for the maximal contribution of bottom - quark parton processes to the and distribution , we find and , respectively , for the tevatron , and and , respectively , for the lhc . a separate study of the higgs +-jet cross section demonstrates that a calculational approach which respects the hierarchies of yukawa couplings yields a leading order cross section prediction which is more accurate in the high- regime than conventional approaches . fr - pheno-2010 - 016 * electroweak and bottom quark contributions + to higgs boson plus jet production + * + _ physikalisches institut , albert - ludwigs - universitt freiburg + hermann - herder - str . 3 , d-79104 freiburg i m breisgau , germany + oliver.brein@physik.uni-freiburg.de_ +

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first observation of co cameron and @xmath4 uv doublet emissions in the martian dayglow were made by the mariner 6 and 7 flybys in 19691970 @xcite . these observations provided an opportunity to study the martian upper atmosphere in a greater detail . the co cameron band ( @xmath5 ; 180 260 nm ) system arises due to the transition from the excited triplet a@xmath1 state , which is the lowest of triplet states , to the ground state x@xmath6 of co. doublet transition ( @xmath7 ) from excited @xmath4 ( b@xmath8 ) to the ground state @xmath4 ( x@xmath9 ) gives emission in ultraviolet wavelengths at 288.3 and 288.6 nm . apart from these emissions , fox - duffenback - berger band of @xmath4 ( a@xmath10 x@xmath11 ) , fourth positive band of co , first negative band of co@xmath12 ( b x ) , and several atomic line emissions of carbon and oxygen atoms were also recorded by mariner 6 , 7 , and 9 @xcite . with the help of theoretical calculations and laboratory measurements , @xcite proposed possible mechanisms for the dayglow emission observed in the martian atmosphere . maximum intensity of co cameron band and uv doublet observed by mariner 6 and 7 were 600 kr at @xmath13131 km and 35 kr at 148 km , respectively . emissions from cameron band and @xmath4 uv doublet bands were also observed in 19711972 by mariner 9 , the first spacecraft to orbit mars . @xcite observed a reduction in the intensity of cameron band by a factor of 2.5 compared to mariner 6 and 7 observations . they attributed this difference to the reduction in the solar activity and better calibration of mariner 9 instrument . the observed maximum slant intensities of co cameron band were between 200 and 300 kr and averaged topside scale height for the same band was 17.5 km . @xcite also observed a good correlation between co cameron band intensity and solar f10.7 flux , which suggest that these emissions are controlled by the incident solar photon flux . since the mariner 6 , 7 , and 9 uv observations , spicam ( spectroscopy for the investigation of the characteristics of the atmosphere of mars ) on - board mars express ( mex ) is the first instrument dedicated for the aeronomical studies of mars . spicam has broaden our understanding about the martian dayglow . emissions observed by spicam in uv dayglow are h lyman-@xmath14 emission at 121.6 nm , the atomic oxygen emissions at 130.4 and 297.2 nm , the cameron band ( @xmath15 ) and fourth positive band ( @xmath16 ) of co , and ultraviolet doublet band ( @xmath17 ) emissions of @xmath4 ( cf . * ; * ? ? ? these emission features are similar to those observed by mariner 6 , 7 , and 9 but with better sensitivity , and spatial and temporal coverage . spicam has observed these dayglow emissions on mars throughout the martian year and showed the effect of solar zenith angle ( sza ) , seasonal variation , and martian dust storms on the dayglow emissions @xcite . spicam also provided first observation of @xmath18 uv emissions in martian dayglow @xcite . @xmath18 vegard - kaplan vk ( 0 , 5 ) and ( 0 , 6 ) band emissions at 260.4 nm and 276.2 nm , respectively , have been observed ; @xmath18 vk ( 0 , 7 ) emission at 293.7 nm has also been reported , but it has large uncertainty @xcite . the detailed model of @xmath18 dayglow emissions on mars is presented elsewhere @xcite . several theoretical studies have been made for the dayglow emissions on mars @xcite . first detailed calculation of dayglow emission on mars was carried out by @xcite . calculated overhead intensities of co cameron and @xmath4 uv doublet bands were 49 kr and 12 kr , respectively , for the low solar activity condition similar to viking landing @xcite . @xcite used trans - mars model to calculate limb intensities of cameron and @xmath4 uv doublet emissions for low solar activity condition ( similar to viking landing ) and compared them with spicam - observations . their calculated intensities are higher by @xmath225% than the observation . @xcite had to reduce the viking @xmath19 density in the model atmosphere by a factor of 3 to bring the altitude of peak emission in agreement with the observation . seasonal effects on intensities of cameron and uv doublet bands have been observed by spicam @xcite . @xcite have presented a statistical analysis of cameron band and uv doublet emissions , peak altitude of emissions , and ratios between uv doublet and cameron band . averaged peak emission brightness ( altitude of peak emission ) observed by @xcite for co cameron and uv doublet bands are 118 @xmath20 33 kr ( 121 @xmath20 6.5 km ) and 21.6 @xmath21 7.2 kr ( 119.1 @xmath20 7.0 km ) , respectively . they also presented observations for one particular season , solar longitude ( ls ) = 90 to 180@xmath22 , and compared observational data with model calculations based on monte carlo code , which has been used also by @xcite for the martian dayglow studies . modelling of co cameron and @xmath4 uv doublet dayglow emissions requires a sophisticated input solar euv ( @xmath1350 to 1000 ) flux , which is a fundamental parameter to model physics , chemistry and dynamics of the upper atmosphere of planets . since observations of solar euv irradiance are not frequent and generally not available simultaneously with the observation for the upper atmospheric studies , the solar euv flux model become important for modelling of aeronomical quantities in planetary atmospheres . generally , solar euv flux models are bin - averaged into numbers of wavelength bands and important solar emission lines appropriate for the calculation of photoionization and photoelectron impact production rates . characterisation of the solar euv flux for use in aeronomical and ionospheric studies were developed during the seventies based on the atmospheric explorer - e ( ae - e ) data @xcite . two ae - e reference spectra sc#21ref and f79050n have been published by @xcite at 37 wavelength bins for solar minimum and maximum conditions , respectively . later , based on the measured photoelectron flux , the short wavelength fluxes were increased by @xcite , and they incorporated modified f74113 solar euv flux in their euvac model . detailed discussion on the development of solar euv flux models is beyond the scope of this study ; @xcite , @xcite , and @xcite have provided reviews on solar euv flux models . for a given solar activity there are significant differences between the euv fluxes reproduced by different solar flux models . these models are based on the different input parameters and proxies , e.g. , solar 10.7 cm radio flux ( henceforth referred to as solar f10.7 ) is used as the measure of solar activity , and used for parametrization of solar euv flux models @xcite . euvac model of @xcite is based on solar f10.7 and its 81-day average and also on the f74113 solar flux ( in the euvac model , the f74113 flux below 250 , and below 150 , are doubled and tripled , respectively ) . solar2000 model of @xcite is based on measured solar flux irradiance and various proxies and provides solar flux from x - rays to infrared wavelengths , i.e. , 11000000 . different solar euv flux models have been used to study the solar radiation interaction with upper atmosphere of mars . presently , solar2000 ( s2k ) model of @xcite and euvac model of @xcite are commonly used solar euv flux models in aeronomical studies of mars ; _ e.g. _ , @xcite and @xcite have used euvac model , while @xcite and @xcite have used s2k model for the dayglow calculations on mars . @xcite have studied the effect of different solar euv flux models on calculated electron densities for low and high solar activity conditions . they have used 85315 and 79050 solar fluxes of @xcite and sc#21ref and f79050n ae - e reference solar spectra of hinteregger @xcite for low and high solar activity conditions , respectively . @xcite found that due to smaller fluxes at short wavelength range ( 18200 ) in hinteregger spectra , lower peak in electron density profile is significantly reduced ( 3035% ) compared to that calculated using solar fluxes of @xcite . @xcite calculated ionospheric electron density using euvac model of @xcite and euv94x solar flux model of @xcite . they found that photoionization rate in f2 region calculated by using euv94x model is larger than that calculated using euvac model due to the large euv fluxes in 3001050 wavelength range in euv94x solar flux model . recently , @xcite have studied the effect of solar euv flux models on @xmath18 vk band intensities in martian dayglow and showed that euv flux models does affect the @xmath18 dayglow emissions . similar conclusion have been drawn for @xmath18 dayglow emission on venus @xcite the aim of the present study is to calculate the impact of solar euv flux models on co cameron band and @xmath4 uv doublet band intensities in martian dayglow . we have used 37 bin euvac model of @xcite and s2k version 2.36 of @xcite as the solar euv fluxes . in these models , bins consist of band of 50 width each and few prominent solar euv lines , and are sufficient for the modelling of photoionization and photoelectron flux calculations @xcite . photoelectron flux , volume excitation rates and overhead intensities are calculated using both the solar euv flux models for low , moderate , and high solar activity conditions . line of sight intensities for cameron band and uv doublet emissions are calculated and compared with the latest observations by spicam instrument .

this study is aimed at making a calculation about the impact of the two most commonly used solar euv flux models solar2000 ( s2k ) of and euvac model of on photoelectron fluxes , volume emission rates , ion densities and co cameron and co uv doublet band dayglow emissions on mars in three solar activity conditions : minimum , moderate , and maximum . ( ays ) approach has been used to calculate photoelectron fluxes in martian upper atmosphere .

this study is aimed at making a calculation about the impact of the two most commonly used solar euv flux models solar2000 ( s2k ) of and euvac model of on photoelectron fluxes , volume emission rates , ion densities and co cameron and co uv doublet band dayglow emissions on mars in three solar activity conditions : minimum , moderate , and maximum . calculated limb intensities profiles are compared with spicam / mars express and mariner observations . analytical yield spectrum ( ays ) approach has been used to calculate photoelectron fluxes in martian upper atmosphere . densities of prominent ions and co molecule in excited triplet a state are calculated using major ion - neutral reactions . volume emission rates of co cameron and co uv doublet bands have been calculated for different observations ( viking condition , mariner and mars express spicam observations ) on mars . for the low solar activity condition , dayglow intensities calculated using the s2k model are% higher than those calculated using the euvac model . during high solar activity , due to the higher euv fluxes at wavelengths below 250 in the euvac model , intensities calculated using euvac model are slightly higher (% ) than those calculated using s2k model . irrespective of the solar activity condition , production of cameron band due to photodissociative excitation of co is around 50% higher when s2k model is used . altitude of peak limb brightness of co cameron and co uv doublet band is found to be independent of solar euv flux models . calculated limb intensities of co cameron and co uv doublet bands are on an average a factor of and.5 , respectively , higher than the spicam mars express observation , while they are consistent with the mariner observations . 2

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we run the model for low solar activity condition ( similar to viking landing ) , and calculated results are compared with those of @xcite by taking the similar model atmosphere . model atmosphere is based on density data derived from viking 1 @xcite . the sun - mars distance d@xmath40 = 1.64 au and solar zenith angle is taken as 45@xmath22 . [ fig : ionden ] shows the calculated densities of @xmath4 and o@xmath41 in the martian upper atmosphere . the density of @xmath4 around peak and above calculated using s2k model is @xmath230% higher than that calculated using euvac , which is due to higher production rate of @xmath4 when s2k model is used . below 120 km , ion densities calculated by using euvac model are higher due to the higher photoelectron fluxes above 70 ev ( cf . [ fig : pef ] ) . there is a small discontinuity in the density of o@xmath41 ion around 180 km , which is due to the sudden change in the electron temperature at 180 km ( see fig . 2 of * ? our calculated ion densities are consistent with calculations of @xcite . fig . [ fig : ver - viking ] ( upper panel ) shows the profiles of production mechanisms of co(a@xmath1 ) calculated using euvac and s2k solar euv flux models . around the peak of co(a@xmath1 ) production , the major source is photoelectron impact dissociation of @xmath19 , while at higher altitudes photodissociation excitation of @xmath19 takes over . dissociative recombination is about 13% , while photoelectron excitation of co contribute about 3% to the total cameron band excitation at the peak . the shape of volume excitation rate ( ver ) profiles and the altitude at the peak remain the same for all processes for the two solar flux models . however , the magnitude of vers calculated using s2k model are about 40% higher than those calculated using euvac model . contribution of electron impact dissociation of @xmath19 producing co(a@xmath1 ) is higher in our studies than that in @xcite . this is due to the higher value of co(a@xmath1 ) production cross section in e-@xmath19 collision used in the present study ( having the value of @xmath42 @xmath43 at 27 ev ) ; @xcite used the cross section derived from @xcite ( having the value of @xmath44 @xmath43 at 27 ev ) . due to larger photon flux at longer ( 7001050 ) wavelengths ( region where photodissociation of @xmath19 becomes important ) in s2k model compared to euvac model ( cf . [ fig : solar - flx ] ) , co(a@xmath1 ) production due to photodissociative excitation is higher by @xmath250% when s2k model is used . production rates of co cameron band for different processes calculated at the peak along with the peak altitude are given in table [ tab : ver ] . it is also clear from upper panel of fig . [ fig : ver - viking ] that the altitude where the photodissociation of @xmath19 takes over electron impact dissociation of @xmath19 in co(a@xmath1 ) formation is slightly higher when euvac model is used ( 167 km for euvac and 160 km for s2k solar flux model ) . in our model calculations , as well as in the work of @xcite , photodissociation process becomes the major source at higher altitudes ( @xmath45 160 km ) and is a factor of 2 higher than the electron impact dissociation of @xmath19 . for the @xmath4 uv doublet band , we have considered only photoionization and electron impact ionization of @xmath19 producing @xmath4 in the b@xmath46 state . contribution of solar fluorescent scattering is very small , less than 10% ( cf . * ? ? ? * ) , and hence it is not taken into account in the present study . while calculating the emission from @xmath4 uv doublet , we have assumed 50% crossover from @xmath29 to @xmath47 state @xcite . [ fig : ver - viking ] ( bottom panel ) shows the production rates for @xmath4 in @xmath29 state . production of co@xmath30 due to photoionization of @xmath19is about a factor of 34 higher than due to photoelectron impact ionization . here also we find that production rates calculated using s2k are higher than those calculated using euvac flux by about 50% , but peak altitude remains the same in both cases . production rates calculated at peak along with peak altitude for @xmath4 uv doublet band are given in table [ tab : ver ] . volume emission rates are height - integrated to calculate overhead intensities , which are presented in table [ tab : oi - cmp ] for co cameron and uv doublet bands . for cameron band , contribution of e-@xmath19 process is maximum ( 64% ) followed by photodissociation of @xmath19 ( 21% ) . contributions of dissociative recombination and e - co process are around 10% and 3% , respectively . for uv doublet band , the major contribution is coming from photoionization of @xmath19 ( 80% ) , the rest is due to electron impact ionization of @xmath19 . to compare the model output with observed emissions we have integrated volume emission rates along the line of sight . limb intensity at each tangent point is calculated as @xmath48 where @xmath49 is abscissa along the horizontal line of sight , and v(r ) is the volume emission rate ( in @xmath50 s@xmath51 ) at a particular emission point @xmath52 . the factor of 2 multiplication comes due to symmetry along the line of sight with respect to the tangent point . while calculating limb intensity we assumed that the emission rate is constant along local longitude / latitude . for emissions considered in the present study the effect of absorption in the atmosphere is found to be negligible . [ fig : int - viking ] shows the calculated limb profiles of the co cameron and @xmath4 uv doublet bands along with the spicam - observed limb intensity taken from @xcite . observed values are averaged over for the orbits close to viking 1 condition ( ls@xmath2100140@xmath22 ) , low solar activity , and for sza=45@xmath22 . below 100 km there is a sudden increase in the observed intensity of @xmath4 uv doublet band , which , according to @xcite , is due to the very significant solar contamination below 100 km . limb intensities calculated using s2k flux are @xmath24050% higher than those calculated using euvac : clearly showing the effect of input solar euv flux on the calculated intensities . magnitude of the calculated limb intensity of uv doublet band is in agreement with the observation , but for co cameron band calculated intensity is higher than the observed profile . for both bands , the calculated intensity profile peaks at higher ( @xmath25 km ) altitude in comparison with the observation indicating a denser neutral atmosphere in our model . the dashed curves in fig . [ fig : int - viking ] show intensities calculated after reducing the @xmath19 density by a factor of 1.5 ; a good agreement in the altitude of peak emission is seen between calculated and observed limb profiles . though the reduction in @xmath19density shifted the altitude of peak emission downwards , the magnitude of calculated cameron band intensity is still larger than the intensity measured by spicam . as pointed out in section [ sec : model ] , the e-@xmath19 cross sections producing cameron band are uncertain by a factor of @xmath22 . the calculated limb intensity profile for reduced e-@xmath19 cross section by a factor of 2 is also shown in fig . [ fig : int - viking ] . cameron band intensities obtained after reducing the density and cross section are in relatively close agreement with the observed values . in the model calculations of @xcite also the cameron band intensity and its peak emission altitude were higher than the spicam observed values . they have to reduced the density of @xmath19 by a factor of 3 and e-@xmath19 cameron production cross section by a factor of 2 to bring their calculated intensity profile in agreement with the spicam observation . @xcite have presented detailed analysis of spicam data during the period october 2004 to march 2005 , spanning the solar longitude ( ls ) from 101@xmath22 to 171@xmath22 . they divided the total data set in two periods of solar longitude : first , ls = 101@xmath22 to 130@xmath22 , and second , ls = 139@xmath22 to 171@xmath22(cf . table 2 of * ? ? ? @xcite found that the altitude of peak emission for @xmath4 uv doublet and co cameron bands is around 10 km higher for ls @xmath45 138@xmath22 ( 122.5 km and 132.5 km for uv doublet and cameron bands , respectively ) compared to ls @xmath32 130@xmath22 ( 112.5 km and 117.5 km , for the same emissions ) . @xcite could not provide the reason for the higher altitude of peak emission for ls @xmath45 130@xmath22 observations . later , @xcite derived neutral densities in martian upper atmosphere using the spicam instrument in stellar occultation mode for the same observation period . @xcite found that their is a sudden increase in the @xmath19 density in the martian upper atmosphere for ls @xmath2 130@xmath22140@xmath22 , which they attributed to a dust storm . dust storm can heat the lower atmosphere and thus increase the densities at higher altitudes , which could explain the higher altitude for peak emission observed by the spicam for ls @xmath53 130@xmath22 observations . increase in the altitude of peak intensity of dayglow emissions clearly shows the effect of dust storms on martian dayglow emissions . comparisons of spicam observations with model calculated dayglow emissions have been performed by @xcite , @xcite , and @xcite . @xcite have used one dimensional trans - mars model with euvac solar flux model , whereas @xcite and @xcite have used monte carlo model with s2k solar flux . in the present study , we have taken both euvac and s2k models and have calculated the cameron band and uv doublet band emissions using the analytical yield spectrum method ; the results are compared with the spicam observations . to model the spicam observations for ls @xmath54 130@xmath22 the model atmosphere is based on mtgcm of @xcite ( taken from * ? ? ? calculations are made for mex orbit no . 983 ( 24 oct . 2004 ) when d@xmath40 = 1.64 au , f10.7 = 87.7 ( f10.7a = 107.3 ) . [ fig : ver - cam - shem ] ( upper panel ) shows the volume excitation rate of co(a@xmath1 ) . the total ver calculated using s2k flux is only slightly higher than that obtained using euvac flux . however , the production rate due to photodissociative excitation of @xmath19 is around 50% higher when s2k model is used . another interesting feature is the dissociative recombination ( dr ) process , whose contribution is @xmath1318% in the total intensity , roughly equal to the photodissociative excitation process ( dr contribution is even higher than photodissociative excitation around production peak when euvac model is used ) , and it is significantly higher than compared to the dr process in viking condition case ( see table [ tab : oi - cmp ] ) . this is due to the higher density of @xmath4 ion compared to viking condition ( see fig . [ fig : ionden ] ) . @xcite mentioned that higher values of @xmath4 can contribute up to 30% to the cameron band production depending on the solar zenith angle . to account for dr in cameron band production , @xcite and @xcite have taken @xmath4 and electron densities from @xcite for low solar activity condition . since spicam observations are made during moderate solar activity condition , the contribution of dr in cameron band production would be lower in their calculations . [ fig : ver - cam - shem ] ( bottom panel ) shows the production rates of @xmath4 uv doublet band . total rate calculated using both solar flux models is peaking at same altitude ( @xmath2125 km ) , but total production rate calculated using s2k model is higher ( around 10% ) than that calculated using euvac model . table [ tab : oi - cmp ] shows the overhead intensities of co cameron and @xmath4 uv doublet bands calculated using both euvac and s2k solar flux models . contribution of different processes in cameron band production is slightly different than that in the low solar activity condition . contribution from @xmath19 photodissociation is slightly reduced ( 17% , 21% when s2k model is used ) , while dissociative recombination contribution is increased ( @xmath218% ) . contribution of e-@xmath19 and e - co processes remains almost same ; 61 ( 64% ) and 4 ( 4% ) , respectively , when calculated using euvac ( s2k ) model . for uv doublet band photoionization of @xmath19 remains the dominant process contributing around 80% to the total overhead intensity . we have also calculated overhead intensities of major vibrational bands of cameron system , which have been observed in martian dayglow , using frank - condon factors from @xcite and branching ratio from @xcite . table [ tab : vib - oi ] shows the calculated overhead intensities of major vibrational bands of co cameron band system . contribution of major vibrational bands to the total overhead cameron band intensity is around 10 , 10 , 16 , and 8% for ( 0 , 0 ) , ( 0 , 1 ) , ( 1 , 0 ) , and ( 2 , 0 ) bands , respectively . [ fig : int - min ] shows the limb intensity profiles of cameron and @xmath4 uv doublet bands . spicam - observed intensities of cameron and uv doublet bands averaged over ls = 100130@xmath22 observations @xcite are also shown in the fig . [ fig : int - min ] . limb intensities of @xmath4 uv doublet and cameron bands calculated by using s2k model are @xmath26% and @xmath215% , respectively , higher compared to those obtained using euvac model . calculated intensities for both solar flux models are higher than the spicam - observed values . in analogy to the viking case , we reduced the e-@xmath19 cross sections producing cameron band . the resulting intensity profile ( also shown in fig . [ fig : int - min ] ) is still higher than the observation around emission peak . calculated intensity of @xmath4 uv doublet band is also higher near the peak emission than the observed intensity . altitude of the calculated intensity for both co cameron and uv doublet bands peaks @xmath132 to 3 km higher than the observations , which is well within the observational uncertainties . line of sight intensity of different vibrational transitions of cameron band at the altitude of peak emission , which is @xmath13120 km for first case , are shown in table [ tab : vib - oi ] . [ fig : ratio - min ] shows the calculated intensity ratio of uv doublet to cameron band along with the observed ratio derived from spicam observations @xcite . at lower altitudes calculated ratio is in agreement with observation ( @xmath130.18 ) . the ratio remains almost constant up to @xmath2120 km ( where cameron band and uv doublet emission peaks ) , starts gradually decreasing with altitude and becomes almost constant after 150 km . the observed ratio decreases almost monotonically from 100 km all the way to 180 km . @xcite have not found any dependence of sza on the uv doublet to cameron band intensity ratios , though they have observed a weak dependence of this intensity ratio on the solar activity . from the observed intensity ratio profile it is clear that in upper atmosphere cameron band intensity is increasing steadily compare to uv doublet band , which indicates a difference in the source of production of cameron band and uv doublet band . that source could be the dissociative recombination process which is sensitive to the density of @xmath4 ion ( as shown in the fig . [ fig : ionden ] ) . loss of @xmath4 ions at higher altitudes ( @xmath45 200 ) can reduce the intensity of uv doublet and hence decreases the intensity ratio value . as discussed earlier , due to dust storm during spicam observations for ls greater than 130@xmath22 , atmospheric densities were higher resulting in altitude of peak emission shifting to higher altitudes ( @xmath2132.5 km for cameron band emission ) . for mariner 6 and 7 observations the intensity of co cameron band peaked at altitude of @xmath2133 km . mariner observations were carried out during solar maximum condition ( f10.7 @xmath2 180 ) , whereas spicam observations are made during moderate solar activity condition . to model dayglow emissions for ls @xmath53 130@xmath22 , we have made calculation for mex orbit 1426 ( 26 feb . 2005 ) , taking model atmosphere from @xcite for high solar activity condition . sun - mars distance is 1.5 au , f10.7 = 98 ( f10.7a = 97 ) . the euv flux at 1 au calculated using euvac model remains the same for first ( ls @xmath32 130@xmath22 ) and second ( ls @xmath45130@xmath22 ) cases . this is because in the euvac model average of f10.7 and f10.7a ( 81-day average ) is used to scale the solar flux , and on both days average of f10.7 and f10.7a does not change ( it is 97.5 on both days ) , although the f10.7 flux increased by 10 unit . s2k model does not depend on the f10.7 alone , but on other proxies also @xcite , hence flux calculated using s2k model is different on the two days . [ fig : ver - cam-138 ] ( upper panel ) shows the ver of co(a@xmath1)calculated using s2k and euvac models . total ver calculated using s2k is about 17% higher than that calculated using euvac model . major differences are in the co(a@xmath1)production due to dissociative excitation of @xmath19 by photon and electron impact , which are more than 50% and 10% higher , respectively , when s2k model is used . total production rate of cameron band ( calculated using euvac model ) maximises at an altitude of 134 km with a value of about 3328 @xmath50 s@xmath51 , which is around 10 km higher than that in the first case ( ls @xmath32 130@xmath22 ) . although production rate ( 3528 @xmath50 s@xmath51 ) at peak altitude is higher in the first case , but at higher altitudes rate increases faster in the second ( ls @xmath45 130@xmath22 ) case , e.g. , at 200 km , cameron band production rate is 61 @xmath50 s@xmath51 in second case , whereas in first case it is only 3 @xmath50 s@xmath51 . in both , first and second cases , for euvac model , the altitude where photodissociation of @xmath19 takes over electron impact dissociation of @xmath19 is around 30% higher than that for s2k model . bottom panel of fig . [ fig : ver - cam-138 ] shows production rates of @xmath4 uv doublet band . total excitation rate calculated using the s2k model is about 12% higher than that calculated using euvac model . similar to the cameron band , @xmath4 uv doublet production rate at peak is lower than that in the first case , but at higher altitudes uv doublet production rate becomes higher in the second case . table [ tab : oi - cmp ] shows the overhead intensities of cameron and @xmath4 uv doublet bands . contribution of photodissociation of @xmath19 , e-@xmath19 , dr , and e - co processes to the total cameron band production is 16 ( 22% ) , 62 ( 57% ) , 11 ( 11% ) , and 9 ( 8% ) , respectively , when euvac ( s2k ) model is used . [ fig : int - max ] shows the calculated limb intensity of uv doublet and cameron band along with spicam - observed intensities of cameron band and @xmath4 doublet band for mex orbit 1426 on 26 feb . 2005 @xcite . intensities calculated using s2k model are higher by @xmath131218% than those calculated using euvac model . altitude of peak emission of calculated and observed intensity profiles is in good agreement with each other ( e.g. , @xmath2128 km for cameron band ) within the uncertainties of observations and model calculations . however , intensities calculated using both solar flux models are higher than the observations . calculated intensities of co cameron band after reducing the e-@xmath19 cross section by a factor of 2 are also shown in fig . [ fig : int - max ] , which is in good agreement with the observed values . however , the calculated intensity of uv doublet band is 2030% higher than the spicam - observed values . uncertainties in photoionization cross sections for the production of co@xmath30 can also be one of reasons for the differences between observed and calculated intensity of co@xmath30 uv doublet emission . in our calculation ( using euvac model and reduced e-@xmath19 cross section for cameron band production ) , peak brightness of cameron band is 249 ( 255 ) kr with peak located at 120 ( 128 ) km in first ( second ) case . for @xmath4 uv doublet band , peak brightness is 31 ( 33 ) kr with peak located at 119 ( 127 ) km in first ( second ) case . altitude of peak brightness remains the same when s2k model is used but intensities of cameron and @xmath4 uv doublet bands for first ( second ) case are about a factor of 1.1 ( 1.18 ) and 1.07 ( 1.11 ) , respectively , higher than that calculated using euvac model . first dayglow measurements on mars were carried out by mariner series of spacecraft . mariner 6 and 7 observations were taken during the solar maximum conditions ( july - august , 1969 ; f10.7 = 186 at 1 au ) , and are the only martian dayglow observations so far taken during the solar maximum condition . mars was also at perihelion ( distance between sun and mars was around 1.42 au ) during mariner observations . we run our model for the condition similar to the mariner observation . model atmosphere for solar maximum condition is taken from @xcite . [ fig : solar - flx ] ( bottom panel ) shows the solar euv flux during mariner observations ( 2 aug . 1969 , f10.7 = 180 ) from euvac and s2k models . as discussed in section [ sec : model ] , overall the solar euv flux is higher in s2k model , except at wavelengths below 250 where euvac flux is larger . [ fig : pef ] ( bottom panel ) shows photoelectron fluxes calculated at different heights in solar maximum condition using both solar flux models . unlike in the solar minimum condition , the ratio of photoelectron flux calculated using s2k to that of euvac is less than 1 at most of the energies . at electron energies below 30 ev , fluxes calculated using s2k and euvac models are almost equal at altitudes of 130 and 160 km . above 30 ev , photoelectron fluxes calculated using euvac model are higher than those calculated using s2k model . the higher photon fluxes in euvac model at shorter wavelengths below 250 [ cf . [ fig : solar - flx ] ] produce higher energy photoelectrons that can produce more secondary electron through ionization , and hence compensates for the higher solar euv flux above 250 in the s2k model . table [ tab : oi - cmp ] shows the calculated overhead intensities of cameron band and uv doublet band using euvac and s2k models . cameron band production due to electron impact dissociation of @xmath19 is higher when euvac model is used , which is due to the higher photoelectron fluxes . contribution of photodissociation excitation calculated using s2k model is higher , due to higher euv flux at longer wavelengths ( specially flux in the 10001050 bin ) . [ fig : ver - cam - max ] ( upper panel ) shows the ver of co(a@xmath1 ) for higher solar activity condition , calculated using euvac and s2k solar flux models . due to the higher photoelectron flux , co(a@xmath1 ) production due to e-@xmath19 , e - co , and dissociative recombination are higher when euvac model is used . photodissociative excitation of @xmath19 producing cameron band for s2k model is still higher by @xmath250% than for euvac model , which is due to the higher euv fluxes at longer wavelengths in the s2k model . similar to that in the previous cases , the cross over point between photodissociation and electron impact dissociation of @xmath19 forming co(a@xmath1 ) occurs at higher altitude when euvac model is used . bottom panel of fig . [ fig : ver - cam - max ] shows the production rates of @xmath4 uv doublet band . here also calculated values using euvac model is slightly higher than that calculated using s2k model . during solar minimum condition total volume production rate of cameron and uv doublet bands calculated using s2k model is higher than that calculated using euvac model , whereas in solar maximum it is vice - versa . except photodissociation excitation process producing cameron band , production rates due to other processes calculated by using euvac model are higher than that calculated by using s2k model . in both , solar minimum and maximum conditions , cameron band production due to photodissociative excitation is about 50% higher , when s2k model is used . [ fig : int - mariner ] shows model intensities of cameron band and @xmath4(b x ) ultraviolet doublet band calculated using both euvac and s2k models at sza = 45@xmath22 along with intensities observed by mariner 6 and 7 . limb intensities measured by mariner 6 and 7 on mars are at sza = 27@xmath22and 0@xmath22 , and at sza = 44@xmath22 and 0@xmath22 , respectively . calculated limb intensities using euvac model at sza = 0@xmath22 are also shown in the fig . [ fig : int - mariner ] . limb intensities calculated using euvac model are only slightly higher than those calculated using s2k model . there were no observations at emission peak for both cameron band and @xmath4(b x ) band . below the emission peak , there are few observations for cameron band , but ultraviolet doublet observations were not available . solar zenith angle effect is clearly visible at altitudes below 150 km , where intensity is larger and emission peak shift deeper in the atmosphere for lower sza . calculated intensities of cameron and uv doublet bands are lower than the observed values . unlike previous cases , calculated intensities of cameron and uv doublet band emissions at the altitude of peak emission are slightly lower than the observation . @xcite has pointed out that due to calibration problem in mariner 6 and 7 instrument the observed values can be higher . as in the previous cases a reduction in e-@xmath19 cross section is required to get an agreement between observed and calculated intensity . calculated intensity of cameron band after reducing the e-@xmath19 cross section by a factor of 2 is also shown in figure [ fig : int - mariner ] for sza=0@xmath22 . density of co(a@xmath1 ) is calculated under photochemical equilibrium condition . radiative decay is the dominant loss process of co(a@xmath1 ) , the contribution from other processes are negligible ( cf . * ? ? ? [ fig : ionden ] shows the density of co(a@xmath1 ) calculated using euvac and s2k euv flux models for low solar activity condition . the calculated column density of co(a@xmath1)molecule is @xmath55 ( @xmath56 ) @xmath57 for the solar minimum condition using euvac ( s2k ) solar euv flux model . except in the solar maximum condition , density of co(a@xmath1 ) molecule calculated using s2k model is higher than that calculated using euvac model . during solar maximum condition , co(a@xmath1 ) density calculated using euvac model is slightly higher at peak ( around 5% ) , but at altitudes above 140 km , density calculated using s2k model becomes higher ( @xmath210% at 200 km ) . the shape of the density of co(a@xmath1 ) is similar to that of its production rate ( cf . [ fig : ver - viking ] ) since the main loss mechanism of co(a@xmath1 ) is radiative decay whose value is independent of altitude . hence , the density of co(a@xmath1 ) in the martian atmosphere can be represented by @xmath58 = \frac{\mathrm{[co_2]\,(k_1 + k_2 ) + [ co_2^+]\,[n_e]\ , k_3}}{\mathrm{k_4 } } \label{eq : coa - den}\ ] ] where @xmath59 , @xmath60 , @xmath61 , and @xmath62 are as described in table [ tab : rate - cameron ] . @xmath59 and @xmath60 are photodissociation rate and electron impact dissociation rate of @xmath19 , respectively , @xmath61 is dissociative recombination , @xmath62 is radiative decay loss , and @xmath63 is the electron density . the values of @xmath59 ( photodissociation rate ) in units of s@xmath51 at the top of atmosphere in case of euvac ( s2k ) model are @xmath64 ( @xmath65 ) , @xmath66 ( @xmath67 ) , @xmath68 ( @xmath69 ) , and @xmath70 ( @xmath71 ) in the solar minimum , first case , second case , and solar maximum , respectively .

irrespective of the solar activity condition , production of cameron band due to photodissociative excitation of co is around 50% higher when s2k model is used . limb intensities of co cameron and co uv doublet bands are on an average a factor of and.5 , respectively , higher than the spicam mars express observation , while they are consistent with the mariner observations . 2

this study is aimed at making a calculation about the impact of the two most commonly used solar euv flux models solar2000 ( s2k ) of and euvac model of on photoelectron fluxes , volume emission rates , ion densities and co cameron and co uv doublet band dayglow emissions on mars in three solar activity conditions : minimum , moderate , and maximum . calculated limb intensities profiles are compared with spicam / mars express and mariner observations . analytical yield spectrum ( ays ) approach has been used to calculate photoelectron fluxes in martian upper atmosphere . densities of prominent ions and co molecule in excited triplet a state are calculated using major ion - neutral reactions . volume emission rates of co cameron and co uv doublet bands have been calculated for different observations ( viking condition , mariner and mars express spicam observations ) on mars . for the low solar activity condition , dayglow intensities calculated using the s2k model are% higher than those calculated using the euvac model . during high solar activity , due to the higher euv fluxes at wavelengths below 250 in the euvac model , intensities calculated using euvac model are slightly higher (% ) than those calculated using s2k model . irrespective of the solar activity condition , production of cameron band due to photodissociative excitation of co is around 50% higher when s2k model is used . altitude of peak limb brightness of co cameron and co uv doublet band is found to be independent of solar euv flux models . calculated limb intensities of co cameron and co uv doublet bands are on an average a factor of and.5 , respectively , higher than the spicam mars express observation , while they are consistent with the mariner observations . 2