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it is shown that the quadratic algebra of the model has a four - dimensional representation provided that some constraints on the microscopic reaction rates are fulfilled . the dynamics of a product shock measure with two shock fronts , generated by the hamiltonian of this model , is also studied . it turns out that the shock fronts move on the lattice as two simple random walkers which repel each other provided that the same constraints on the microscopic reaction rates are satisfied .

i

0804.2524

the steady - state of a generalized coagulation - decoagulation model on a one - dimensional lattice with reflecting boundaries is studied using a matrix - product approach . it is shown that the quadratic algebra of the model has a four - dimensional representation provided that some constraints on the microscopic reaction rates are fulfilled . the dynamics of a product shock measure with two shock fronts , generated by the hamiltonian of this model , is also studied . it turns out that the shock fronts move on the lattice as two simple random walkers which repel each other provided that the same constraints on the microscopic reaction rates are satisfied .

the study of microscopic structure and dynamics of traveling wave solutions in multi - species one - dimensional stochastic systems has attracted people s attention in this field considerably in recent years @xcite-@xcite . for instance , the microscopic dynamics of shocks are studied for three families of single - species one - dimensional reaction - diffusion systems with open boundaries and nearest - neighbors interactions which include the partially asymmetric simple exclusion process ( pasep ) , the branching - coalescing random walk ( bcrw ) and the asymmetric kawasaki - glauber process ( akgp ) @xcite . it has been shown that in all three systems the time evolution of a product shock measure with a single shock front is equivalent to that of a simple random walker on a finite lattice with homogeneous hopping rates in the bulk and special reflection rates at the boundaries , provided that some constraints on the microscopic reaction rates are fulfilled . the steady - states of these three systems can be essentially written as a linear superposition of such product shock measures . on the other hand , the steady - states of these systems can be obtained using the matrix - product formulation @xcite in which the steady - state weights are written in terms of the product of non - commuting operators which satisfy a quadratic algebra ( for a recent review of this approach see @xcite ) . surprisingly , it has been found that the conditions under which these operators have two - dimensional matrix representations are exactly those for a product shock measure to have a simple random walk dynamics in these systems @xcite . + it has been shown in @xcite that the existence of a two - dimensional representation for the quadratic algebra of a multi - species one - dimensional reaction - diffusion system with open boundaries and nearest - neighbors interactions implies that the steady - state of the system can be written in terms of a linear superposition of product shock measures . it seems that the same is true for the systems whose quadratic algebras have higher - dimensional matrix representations . for instance , for the totally asymmetric simple exclusion process with open boundaries it is known that the quadratic algebra has an infinite - dimensional matrix representation . it has been shown that this is associated with the fact that the steady - state of this system can be written as a linear superposition of product shock measures with infinite number of shocks @xcite . + the microscopic dynamics of shock fronts has also been studied in driven - diffusive systems with more than a single species of particles and also in these systems with next - nearest - neighbor interactions @xcite-@xcite . + despite of these efforts it is still generally unclear whether the existence of a finite - dimensional matrix representation of the quadratic algebra is related to the fact that the steady - state can be expressed as a superposition of product shock measures . in this paper we consider a generalized one - dimensional single - species coagulation - decoagulation model with reflecting boundaries as a new example . we believe that the study of this exactly solvable model provides us with another piece of evidence for the existence of such relation and definitely sheds more light on the unknown aspects of this problem . we will show that a product shock measure with two shock fronts which have simple random walk dynamics can evolve in this system provided that the microscopic reaction rates satisfy some constraints . this will enable us to construct the steady - state of the system simply by considering a linear superposition of such measures ; however , we will not follow this approach here . instead we will show that under the _ same constraints _ the quadratic algebra of this model has a four - dimensional representation . + our paper is organized as follows : in section ( 2 ) we will explain the mathematical preliminaries and introduce the model . in section ( 3 ) we will study the dynamics of a product shock measure with two shock fronts and investigate the conditions ( by imposing some constraints on the microscopic reaction rates of the model ) under which it has a simple time evolution similar to that of two random walkers moving on a one - dimensional lattice while reflecting from the boundaries . the fourth section will be devoted to the investigation of whether a finite - dimensional representation exists for the quadratic algebra of the model under the same conditions . in the last section we will discuss the summery of results .

the structure of the nucleon and the first radial excitation of the nucleon , the roper , @xmath0 , is studied within the formalism of light - front holography . the @xmath1 transition form factors are then calculated without any adjustable parameters . the model compares well with the @xmath1 transition form factor data , suggesting that meson cloud effects are not large , except in the region @xmath3 gev@xmath4 . in particular , the meson cloud contributions for the pauli form factor are small .

i

1703.03819

the structure of the nucleon and the first radial excitation of the nucleon , the roper , @xmath0 , is studied within the formalism of light - front holography . the nucleon elastic form factors and @xmath1 transition form factors are calculated under the assumption of the dominance of the valence quark degrees of freedom . contrary to the previous studies , the bare parameters of the model associated with the valence quark are fixed by the empirical data for large momentum transfer ( @xmath2 ) assuming that the corrections to the three - quark picture ( meson cloud contributions ) are suppressed . the @xmath1 transition form factors are then calculated without any adjustable parameters . our estimates are compared with results from models based on valence quarks and others . the model compares well with the @xmath1 transition form factor data , suggesting that meson cloud effects are not large , except in the region @xmath3 gev@xmath4 . in particular , the meson cloud contributions for the pauli form factor are small .

within the nucleon excited states ( @xmath5 ) the @xmath0 resonance , also known as roper , plays a special role . contrarily to the @xmath6 and other nucleon excitations , the roper was not identified as a bump in a reaction cross - section but was instead found in the analysis of phase - shifts @xcite . nowadays there is evidence that the roper should be identified as the first radial excitation of the nucleon quark core , although meson excitations are also important for the internal structure . calculations based on valence quark degrees of freedom are consistent with the @xmath1 transition form factors for large @xmath2 ( @xmath7 gev@xmath4 ) @xcite . however , estimates based exclusively on quark degrees of freedom fail to describe the small @xmath2 data ( @xmath8 gev@xmath4 ) @xcite . the gap between valence quark models and the data at low @xmath2 has been interpreted as the manifestation of the meson cloud effects @xcite . when the meson cloud contributions are included in quark models the estimates approach the data @xcite . besides , the calculations based on dynamical coupled - channel reaction models , where the baryon excitations are described as baryon - meson states with extended baryon cores @xcite , corroborates the importance of the meson cloud effects . in those models the mass associated with the roper bare core is about 1.7 gev . only when the meson cloud dressing is considered the roper mass is reduced to the experimental value @xcite . the interpretation of the roper as a radial excitation of the nucleon combined with a dynamical meson cloud dressing solves the long standing problem of the roper mass in the context of a quark model @xcite . the roper decay widths into @xmath9 , @xmath10 and @xmath11 are large comparative to other @xmath5 decays . those decay widths are also difficult to explain in the context of a quark model . the meson cloud dressing helps to explain the @xmath12 width , where the contributions associated with baryon - meson - meson states play an important role @xcite . overall the recent developments in the study of the roper electromagnetic structure point to the picture of a radial excitation of the nucleon surrounded by a cloud of mesons @xcite . there is therefore a strong motivation to study the roper internal structure and to disentangle the effects of the valence quark component from the meson cloud component . in particular , one can use the knowledge of the baryon core structure to infer the contribution due to the meson cloud . this procedure was used in previous works based on different frameworks for the baryon core @xcite . in the case of the nucleon the valence quark degrees of freedom produce the dominant effect in the elastic form factors . the meson cloud contribution to the nucleon wave function is estimated to be of the order of a few percent @xcite . as for the roper , the meson cloud seems to play a more prominent role . we conclude at the end that the valence quark degrees of freedom provide a very good description of the data , but the meson cloud contribution are important below 1.5 gev@xmath4 , particularly for the dirac form factor . in the present work we propose a new framework to analyze the role of the valence quarks and the meson cloud in the roper . we use llight - front holography to estimate the leading order ( lowest fock state ) contribution to the @xmath1 transition form factors . since the leading order calculation includes only pure valence quark effects in the baryon wave functions ( @xmath13 contributions ) , there is no contribution from the meson cloud . in those conditions the gap between the calculations and the data must be essentially the consequence of the meson cloud effects . the light - front ( lf ) formalism is particularly appropriate to study hadron systems , ruled by qcd , and to describe the hadronic structure in terms of the constituents @xcite . the lf wave functions ( lfwf ) are relativistic and frame independent @xcite . the connection between lf quantization of qcd and anti - de - sitter conformal field theory ( ads / cft ) leads to light - front holography @xcite . lf holography have been used to study the structure of hadron properties , such as the hadron mass spectrum , parton distribution functions , meson and baryon form factors etc . in particular , the formalism was recently applied to the study of the nucleon @xcite and roper @xcite electromagnetic structure . an important advantage of the lf formalism applied to hadronic physics is the systematic expansion of the wave functions into fock states with different number of constituents @xcite . in the case of the baryons the leading order contributions is restricted to the three - valence quark configuration . although the restriction to the lowest order fock state ( three valence - quark system ) may look as a rough simulation of the real world , it may provide an excellent first approximation when the confinement is included in the lfwf , defined at the light - front time @xcite . in those conditions non - perturbative physics is effectively taken into account by lf holography @xcite . under the assumption that lf holography can describe accurately the large-@xmath2 region dominated by valence quark degrees of freedom , we calibrate the free parameters of the model by the available data above a given threshold @xmath14 ( @xmath152.5 gev@xmath4 ) . this procedure differs from the previous studies where the free parameters , associated with the nucleon anomalous magnetic moments were fixed at @xmath16 , where the meson cloud contamination is expected to be stronger . once the free parameters are fixed by the nucleon data , one uses the model to calculate the @xmath1 transition form factors . since no parameter is adjusted by the roper data , our calculations are true predictions for the @xmath1 transition form factors . this article is organized as follows : in sec . [ secholography ] we discuss lf holography . in the following section ( sec . [ secnucleon ] ) , we review the results for the nucleon form factors and fix the parameters by the nucleon data . our results for the valence quark contribution to the @xmath1 transition form factors and their discussion are presented in sec . [ secroper ] . the outlook and conclusions are presented in sec . [ secconclusions ] .

the study of conformal restriction properties in two - dimensions has been initiated by lawler , schramm and werner in @xcite who focused on the natural and important chordal case : they characterized and constructed all random subsets of a given simply connected domain that join two marked boundary points and that satisfy the additional restriction property . the radial case ( sets joining an inside point to a boundary point ) has then been investigated by wu in @xcite . in the present paper , we study the third natural instance of such restriction properties , namely the `` trichordal case '' , where one looks at random sets that join three marked boundary points . this case involves somewhat more technicalities than the other two , as the construction of this family of random sets relies on special variants of sle@xmath0 processes with a drift term in the driving function that involves hypergeometric functions . it turns out that such a random set can not be a simple curve simultaneously in the neighborhood of all three marked points , and that the exponent @xmath1 shows up in the description of the law of the skinniest possible symmetric random set with this trichordal restriction property .

i

1602.03416

the study of conformal restriction properties in two - dimensions has been initiated by lawler , schramm and werner in @xcite who focused on the natural and important chordal case : they characterized and constructed all random subsets of a given simply connected domain that join two marked boundary points and that satisfy the additional restriction property . the radial case ( sets joining an inside point to a boundary point ) has then been investigated by wu in @xcite . in the present paper , we study the third natural instance of such restriction properties , namely the `` trichordal case '' , where one looks at random sets that join three marked boundary points . this case involves somewhat more technicalities than the other two , as the construction of this family of random sets relies on special variants of sle@xmath0 processes with a drift term in the driving function that involves hypergeometric functions . it turns out that such a random set can not be a simple curve simultaneously in the neighborhood of all three marked points , and that the exponent @xmath1 shows up in the description of the law of the skinniest possible symmetric random set with this trichordal restriction property .

in the present paper we further study random two - dimensional sets that satisfy the conformal invariance property combined with the restriction property , following the work of lawler , schramm and werner in @xcite and the paper of wu in @xcite . measures that satisfy conformal restriction property were introduced and first studied by lawler , schramm and werner in @xcite : for a simply connected domain @xmath2 with two marked boundary points @xmath3 and @xmath4 ( we will say `` boundary points '' instead of prime ends in the present introduction ) , they studied a class of random simply connected and relatively closed sets @xmath5 such that @xmath6 intersects @xmath7 only at @xmath3 and @xmath4 . such a set ( or rather , its distribution ) is said to satisfy _ chordal conformal restriction property _ if the following two conditions hold : * ( conformal invariance ) the law of @xmath6 is invariant under any conformal map from @xmath8 onto itself that leave the boundary points @xmath3 and @xmath4 invariant . * ( restriction ) for any simply connected subset @xmath9 of @xmath8 such that @xmath10 , the conditional distribution of @xmath6 given @xmath11 is equal to the image of the law of @xmath6 under @xmath12 , where @xmath12 is any conformal map from @xmath8 onto @xmath9 that leaves the points @xmath13 invariant ( property ( i ) actually ensures that if this holds for one such map @xmath12 , then it holds also for any other such map ) . see figure [ fig : two - point - restriction ] . and @xmath14 is a conformal map from @xmath15 onto @xmath8 that leaves @xmath13 invariant . the conditional law of @xmath16 given @xmath17 is equal to the ( unconditional ) law of @xmath6 . , scaledwidth=78.0% ] it is straightforward to check that if a random set @xmath6 satisfies this chordal conformal restriction property in one simply connected domain @xmath8 with boundary points @xmath3 and @xmath4 , then if we map @xmath8 conformally to another simply connected domain @xmath18 via some fixed deterministic map @xmath19 , then @xmath20 satisfies chordal conformal restriction in @xmath21 with boundary points @xmath22 and @xmath23 ( and property ( i ) ensures that the image law depends only on the triplet @xmath24 , and not on the particular instance of @xmath19 ) . hence , it is sufficient to study this property in one particular given domain @xmath8 , such as the unit disc or the upper half - plane . recall that conformal invariance is believed to hold in the scaling limit for a large class of two - dimensional models from statistical physics . a chordal restriction property can be interpreted as follows : on a lattice , one can associate to each set @xmath6 an energy , and the restriction property means that this energy of @xmath6 is `` intrinsic '' in the sense that it does not depend on the domain in which it lives but only on @xmath6 ( and the extremal points @xmath3 and @xmath4 ) itself . for example , for a simple random walk on a square lattice in a discretized domain @xmath8 , which is conditioned to go from one boundary point @xmath3 to another boundary point @xmath4 , the probability of a given path @xmath25 will be proportional to @xmath26 where @xmath27 is the number of steps of @xmath25 . this weight @xmath26 is then intrinsic because it only depends on the path @xmath25 itself but not on the domain @xmath8 . as a consequence , if we condition such a random walk excursion from @xmath3 to @xmath4 in @xmath8 to stay in a subdomain @xmath9 of @xmath8 which still has @xmath3 and @xmath4 on its boundary , then one gets exactly a random walk excursion from @xmath3 to @xmath4 in this smaller domain @xmath9 . in the continuous limit , the brownian excursion from @xmath3 to @xmath4 in @xmath8 ( or rather its `` filling '' in order to get a simply connected set ) does indeed satisfy chordal conformal restriction . chordal restriction measures therefore describe the natural conformally invariant and intrinsic ways to join two boundary points in a simply connected domain . lawler , schrammm and werner proved in @xcite that such measures are fully characterized by one real parameter @xmath28 ( here and in the sequel , this means that there is an injection from the set of conformal restriction measures into @xmath29 ) that can be described as follows . for each chordal conformal restriction measure , there exists a positive @xmath28 such that for all @xmath30 such that @xmath15 is again a simply connected domain and @xmath31 , one has @xmath32 ( it is straightforward to see that the product @xmath33 does not depend on the choice of @xmath14 among the one - dimensional family of conformal maps from @xmath34 onto @xmath8 that leave @xmath3 and @xmath4 invariant ) . conversely , it is easy to see that for each given @xmath28 , there exists at most one law of @xmath6 satisfying this relation for all @xmath35 . the more challenging part is then to investigate for which values of @xmath28 such a random set @xmath6 does indeed exist . lawler , schramm and werner showed in the same paper @xcite that such a probability measure exists if and only if @xmath36 , and they provided a detailed description of these measures : when the smallest value @xmath37 , it is exactly the law of chordal sle@xmath0 from @xmath3 to @xmath4 in @xmath8 , so that @xmath6 is almost surely a simple curve from @xmath3 to @xmath4 in @xmath8 . when @xmath38 , they showed that @xmath6 is almost surely not a simple curve anymore ( the case @xmath39 is the aforementioned law of the filling of a brownian excursion in @xmath8 from @xmath3 to @xmath4 ) . in fact , they also described the law of the right boundary of @xmath6 for all @xmath40 in terms of a variant of sle@xmath0 ( the sle@xmath41 processes ) , which showed in particular that the boundary of all these random sets @xmath6 look locally like an sle@xmath0 or equivalently like the boundary of a two - dimensional brownian motion . intuitively , the larger @xmath28 is , the `` fatter '' the random set @xmath6 is . for instance , one can prove that @xmath6 will contain cut - points if and only if @xmath42 , see @xcite ( where the law of the left boundary given the right one is also described ) . these chordal restriction measures can in fact be viewed as special limiting cases of a larger class of restriction measures defined similarly , but with three marked boundary points instead of two ; this class will be the topic of the present paper : for a simply connected domain @xmath2 with three ( different ) marked boundary points @xmath13 and @xmath43 , we consider probability measures supported on simply connected and relatively closed @xmath5 such that @xmath44 . such a measure is said to satisfy the _ trichordal conformal restriction property _ if for @xmath45 such that @xmath9 is simply connected and @xmath46 , the law of @xmath6 conditioned to stay in @xmath9 is identical to the law of @xmath47 where @xmath12 is the unique conformal map from @xmath8 onto @xmath9 that leaves the points @xmath48 invariant , see figure [ fig : trichordal - restriction ] . one expects intuitively this family of measures to be larger ( ie . parametrized by more than one real parameter ) because condition ( i ) of the chordal case is no longer required , so that the measures are invariant under a smaller semi - group of transformations . is the conformal map from @xmath15 onto @xmath8 that leaves @xmath13 and @xmath43 invariant . the law of @xmath49 given @xmath17 is equal to the ( unconditioned ) law of @xmath6 . , scaledwidth=78.0% ] before going into the details of this trichordal case , let us say a few words about the radial case studied by wu in @xcite . given that the group of conformal automorphism of a domain is three - dimensional , this is the other natural variant to consider : for two simply connected domains , if we fix one interior point and one boundary point for each domain , then there is a unique conformal map from one domain onto the other that sends both of the prefixed interior point and boundary point of one domain to the corresponding points of the other . for a simply connected domain @xmath2 with an interior point @xmath3 and a boundary point @xmath4 , one looks at probability measures supported on simply connected and relatively closed sets @xmath5 such that @xmath50 and @xmath51 . such a measure is said to satisfy _ radial conformal restriction property _ if for @xmath45 such that @xmath9 is simply connected and @xmath52 , @xmath6 conditioned to stay in @xmath9 has the same law as @xmath47 where @xmath12 is the unique conformal map from @xmath8 onto @xmath9 that leaves the points @xmath13 invariant . wu showed that this family was characterized by two real parameter : for such measures , there exists @xmath28 and @xmath53 such that for all @xmath30 such that @xmath15 is again a simply connected domain that contains @xmath3 in its interior and @xmath4 on its boundary , one has @xmath54 she also showed that the range of admissible values of @xmath28 and @xmath53 is given by @xmath55 and @xmath56 where @xmath57 is the so - called disconnection exponent of @xmath28 . among the natural conformal restriction measures , the trichordal case was in some sense , the only one that was left to be studied . if ones adds more marked points , then there will typically be no conformal map @xmath14 that fix simultaneously all these points . even if it is possible to define a similar notion of @xmath58-point conformal restriction , we will not be able to speak of one measure that satisfies conformal restriction , but one has to consider instead a family of measures indexed by conformally equivalent configurations of the @xmath58 marked points . for @xmath59 , the family of all families of @xmath58-point chordal restriction measures will be much bigger than that of chordal , trichordal or radial cases , and it will in fact be infinite dimensional . intuitively speaking , one can associate to a four - point restriction sample @xmath6 , an intrinsic conformally invariant quantity , such as the modulus @xmath60 of the quadrilateral @xmath61 in @xmath6 ( where @xmath3 , @xmath4 , @xmath43 and @xmath62 are the four marked boundary points ) . one can then weight the law of @xmath6 by any function @xmath63 with mean @xmath64 , one thus still gets a four - point restriction measure . indeed , dubdat computed in @xcite formulae about @xmath58-point chordal restriction measures which involve such functions @xmath65 . this will be further explained in the preliminary section [ sec : dubedat ] . as in the chordal and radial cases , the goal in the trichordal case is to characterize all random sets satisfying the trichordal conformal restriction property . recall that one heuristic motivation is that one would like to describe all possible ways to connect three boundary points of a domain via random sets with `` intrinsic energy '' , and one major question is to see what the `` thinest '' sets @xmath6 look like . let us first make the following observation : if we consider @xmath66 three independent chordal restriction measures in @xmath8 that intersect @xmath7 respectively at pairs of points @xmath67 , then the filling @xmath6 of @xmath68 obviously satisfies trichordal restriction . moreover , if @xmath69 respectively have exponents @xmath70 then @xmath71 this suggests that the family of trichordal restriction measures might depend on three parameters . this indeed turns out to be the case . the following characterization is of the same type as the characterization of the chordal and radial cases : [ prop : charac][characterization ] for each trichordal restriction measure , one can find three real numbers @xmath72 so that for all @xmath30 such that @xmath15 is simply connected and @xmath73 , one has @xmath74 conversely , for each @xmath75 , there exists at most one probability measure so that this holds . we then denote the law of @xmath6 by @xmath76 . let us insist on the fact that this result does not tell us for which values of @xmath28 , @xmath53 and @xmath25 such a @xmath76 exists . the main contribution of the present paper will be to give the exact range of @xmath72 for which @xmath76 exist and to construct the corresponding restriction sets . the exponents @xmath72 of the trichordal case play symmetric roles and are interrelated , as opposed to the radial case . let us first make a few comments : * first note that the points @xmath48 cut @xmath7 into three arcs , namely @xmath77 and @xmath78 . if @xmath79 is a subset of the arc @xmath80 ( which is the case depicted in figure [ fig : trichordal - restriction ] ) , then it is easy to see that @xmath81 and @xmath82 . in order for the right - hand side of ( [ thm1 ] ) to be a probability , @xmath28 can therefore not be much bigger than both @xmath53 and @xmath25 . by symmetry , this indicates that each of the three exponents needs to be bounded from above by a certain function of the other two . on the other hand , it is easy to see that @xmath83 is always smaller than @xmath64 . hence , one can still say that in the symmetric family @xmath84 , the smaller @xmath28 is , the skinnier @xmath6 is ( because for each @xmath35 , the probability to intersect @xmath35 is an increasing function of @xmath28 ) . * another type of condition that one should expect is that @xmath28 , @xmath85 and @xmath25 should all be greater or equal to @xmath86 . intuitively , a random set @xmath6 with law @xmath76 should look like , in a infinitesimal neighborhood of one marked point ( say @xmath3 ) , a chordal restriction measure of the corresponding exponent ( which is @xmath28 in the case of @xmath3 ) . more precisely , if we let the point @xmath4 tend to the point @xmath43 , the limiting measure can be proved to be equal to the chordal restriction measure of exponent @xmath28 . since chordal restriction measures of exponent @xmath28 as characterized by ( [ two - point - formula ] ) exist only for @xmath36 , the same condition should hold here . a natural question is what is smallest @xmath28 for which the measure @xmath87 exists . for the chordal case , the measure of exponent @xmath37 corresponds to a simple curve , which is the thinest that one can obtain . if the measure @xmath88 exists , then the corresponding random set would a.s . be a simple curve near each of the boundary points @xmath48 . would the three legs of such an sle@xmath0 spider then merge at one single point in the middle or would there be a fat `` body '' set near the center ? the previously described method of taking the filled union of chordal restriction measures only constructs such measure with @xmath89 , which is unlikely to be the thinest choice . the answer to all these questions turns out to be somewhat surprising : a particular case of the following theorem is that that the smallest @xmath28 for which @xmath90 exists is actually @xmath91 . in this special case , the corresponding random set @xmath6 consists of three parts , that have only one common point which is the unique _ triple disconnecting point _ : when one removes this point , one disconnects @xmath6 into three disjoint connected components , that respectively contain @xmath3 , @xmath4 and @xmath43 . however , since @xmath92 , each of these three `` legs '' of this symmetric restriction spider are a bit `` fatter '' than simple curves ( even though they each of them will have quite a lot of cut - points ) . before stating this main result , let us first recall the formulas for the half - plane and whole - plane _ brownian intersection exponents _ that have been determined by lawler , schramm and werner in @xcite : @xmath93 we will use here only the formulas and not the interpretation in terms of non - intersection probabilities for brownian paths ( but the latter are of course related to restriction properties ) . [ thm : existence][existence ] the measure @xmath76 exists if and only if @xmath72 satisfy all the following conditions : * @xmath94 * @xmath95 * @xmath96 furthermore , if @xmath6 is a random set with law @xmath76 , then * @xmath6 has a triple disconnecting point if and only if @xmath97 . moreover in this case , each of the three legs away from this unique triple disconnecting point have almost surely infinitely many cut - points ( this can be viewed as a consequence of the that fact that necessarily , @xmath98 ) . see figure [ fg : tripple - cut - point ] . * the boundary point @xmath43 is a cut - point of @xmath6 if and only if @xmath99 . see figure [ fig : two - conditioned ] . + 0.4 + 0.4 note that if we define @xmath100 , @xmath101 , @xmath102 to be the respective image of @xmath28 , @xmath53 and @xmath25 under the monotone bijection from @xmath103 onto itself defined by @xmath104 , then one can easily express the conditions ( i ) , ( ii ) and ( iii ) without reference to the brownian intersection exponents : the condition ( i ) becomes @xmath105 , condition ( iii ) becomes @xmath106 ( while ( i ) implied only that this sum can not be smaller than 9 ) , and condition ( ii ) becomes three inequalities of the type @xmath107 . in other words , all these conditions can be summed up as @xmath108 we have already highlighted to special role of @xmath109 . another interesting case worth mentioning is the measure @xmath110 ( that also exhibits a triple disconnecting point ) . our construction will in fact implicitly describe this measure as being constructed by an sle@xmath0 from @xmath3 to @xmath4 , weighted according to its ( renormalized ) harmonic measure seen from @xmath43 ( this will make it more likely for the path to wander closer to @xmath43 ) , and to which one attaches a brownian excursion from @xmath43 to a point ( chosen according to this renormalized harmonic measure ) on this sle . in general , when @xmath111 , it is natural to guess that conditionally on the triple disconnecting point , @xmath6 consists of three radial restriction samples ( from the center point to the three points @xmath3 , @xmath4 and @xmath43 respectively ) conditioned not to intersect each other except at this center point . however , in practice , it would be a rather tedious and intricate venture to define this conditioning rigorously , and we will not follow this route . for the @xmath99 case , one can make a similar remark , and this time , it can be made rigorous more easily . it will indeed follow from our construction that conditioned on one branch of @xmath6 , the other branch is a chordal restriction sample in one of the connected components of the complement of the first branch . in this sense , one can view @xmath6 as the union of two chordal restriction samples conditioned not to intersect each other except at @xmath43 . an interesting example is of course @xmath112 , which corresponds to two chordal sle@xmath0 from @xmath3 to @xmath43 and from @xmath4 to @xmath43 , conditioned not to intersect . this ( and the three symmetric images when interchanging @xmath3 , @xmath4 and @xmath43 ) is the only trichordal restriction measure that consists of a simple path in @xmath113 . the family of measure @xmath114 exists exactly in the range @xmath115 $ ] , and the two cases @xmath116 and @xmath112 that we have just briefly described are the two extremal ones . the case @xmath117 corresponds to ( the filling of ) the union of two independent sle@xmath0 curves from @xmath3 to @xmath43 and from @xmath4 to @xmath43 . as explained above , when @xmath25 increases , as opposed to the symmetric case , one can not really argue anymore that the sets @xmath6 become larger ( and indeed , the @xmath118 case corresponds to a simple curve , while this is not the case for @xmath119 ) . instead , when @xmath25 grows , the sets are in some sense `` pushed towards @xmath43 '' . the proof of the characterization result will follow somewhat similar ideas than in the chordal and than in the radial cases . the proof of the existence part will be divided in two parts : first , we will construct trichordal restriction measures for all admissible values of the parameters @xmath28 , @xmath53 and @xmath25 , and then we will see that if a measure @xmath120 exists for the non - admissible part , one gets a contradiction . our construction of trichordal restriction measures will rely on a special family of sle processes with driving functions involving hypergeometric functions , that we call hypergeometric sles and denote by hsle . zhan first defined in @xcite intermediate sles to describe the inverse of sle@xmath121 processes . the intermediate sles are hypergeometric sles with special parameters . in our case , for @xmath122 , the hsle curves correspond to the boundaries of trichordal restriction samples . the construction goes in fact through several steps . first of all , we define the notion of one - sided restriction ( in this trichordal case ) which is reminiscent and analogous to the one - sided chordal restriction measures that were studied by lawler , schramm and werner . we consider measures supported on simply connected and relatively closed @xmath123 such that @xmath124 is the union of the arcs @xmath125 and @xmath80 . for all @xmath126 such that @xmath15 is again a simply connected domain and @xmath127 is a subset of the arc @xmath78 . such a measure is said to satisfy _ one - sided ( trichordal ) conformal restriction property _ if @xmath6 conditioned on @xmath17 has the same law as @xmath16 where @xmath12 is the unique conformal map from @xmath15 onto @xmath8 that preserves the points @xmath48 . see figure [ fig : one - sided ] . is the conformal map from @xmath15 onto @xmath8 that preserves the points @xmath48 . the law of @xmath16 conditioned on @xmath17 is equal to the ( unconditioned ) law of @xmath6.,scaledwidth=76.0% ] one - sided restriction measures are also characterized by ( [ thm1 ] ) with three parameters @xmath72 and we denote the measure by @xmath128 . the range of @xmath72 for which the measure @xmath128 exists is larger than the range for which the three - sided restriction measure @xmath76 exists . in particular , since we only consider @xmath35 that intersect @xmath7 at the arc @xmath129 , there is nothing that prevents @xmath28 or @xmath25 to be much bigger than the other two exponents . moreover , some negative values of @xmath53 will be allowed . we will show that the range is the following : a one - sided measure @xmath130 exists if and only if @xmath75 satisfy the following conditions : @xmath131 moreover , if @xmath6 has law @xmath130 where @xmath132 , then the point @xmath4 is on the right boundary of @xmath6 . these one - sided restriction measures @xmath128 will be constructed , in most of the cases , by a hsle@xmath0 curve . however for a certain range of parameters , this construction does not work , and we will use poisson point process of brownian excursions instead . next we will study two - sided restriction measures . their definition is similar to that of one - sided restriction , except that two - sided restriction measures are supported on @xmath6 such that @xmath133 is the union of @xmath134 and the arc @xmath80 , and the sets @xmath30 are such that @xmath127 is a subset of the union of the arcs @xmath78 and @xmath125 , see figure [ fig : two - sided ] . is the conformal map from @xmath15 onto @xmath8 that preserves the points @xmath48 . the law of @xmath16 conditioned on @xmath17 is equal to the ( unconditioned ) law of @xmath6.,scaledwidth=78.0% ] two sided restriction measures are also characterized by ( [ thm1 ] ) with three parameters @xmath72 and we denote the measure by @xmath135 . the range of @xmath72 for which the measure @xmath135 exists is given in the following theorem . the two - sided measure @xmath136 exists if and only if @xmath75 satisfy the following conditions : @xmath137 moreover , if @xmath6 has the law @xmath136 where @xmath138 , then there exist a point on the arc @xmath80 which is both on the left and the right boundary of @xmath6 . the two - sided restriction measures will be constructed , in most of the cases , as follows : construct first its boundary at one side ( say the right side ) which is a one - sided restriction measure , by a hsle , then conditionally on this side , sample an independent one - sided restriction measure in the connected component which is to the other side ( say the left side ) of the first boundary . however we will again use other methods to construct some limiting cases . in order to prove that the hsle define such trichordal restriction measures , we will use a martingale - type argument , in the spirit of the proof of the chordal restriction measure construction . however , the technical implementation of this strategy can appear somewhat daunting , but things are not as bad as they look : one derives that a certain process is a local martingale by longish but straightforward it formula calculations ( having the a priori information that the computation should work out nicely ) and in order to be able to apply the optional stopping theorem , we have to prove that the semi - martingale is anyway bounded ( this is not obvious from the expression of the process as product of terms that are not bounded , but we have again the a priori knowledge that in the end , this quantity will be a conditional probability , so that it should be bounded ) , which one can then show using some a priori knowledge on the hypergeometric functions that we use . having a full description of all possible one - sided and two - sided restriction measures , we will be able to construct the family of three - sided restriction measures by first constructing the boundary on one side ( say the right side ) as a one - sided measure and then conditionally on this side , sampling a two - sided restriction measure in the connected component which is to the other side ( say the left side ) of this first boundary . the determination of the exact range of admissible parameters in one - sided and two - sided cases , will be obtained by investigating some geometric properties of the corresponding random sets that we construct in the limiting cases of the parameter - range . in the three - sided case , we will need to do a kind of reverse procedure of the previous construction ( showing that a three - sided restriction measure can be decomposed as described above ) . this will be explained in [ sec : three - sided ] .

the sun is a variable star whose magnetic activity and total irradiance vary on a timescale of approximately 11 years . the current activity minimum has attracted considerable interest because of its unusual duration and depth . the surface activity can be linked to the conditions in the solar interior by the observation and analysis of the frequencies of the sun s natural seismic modes of oscillation - the @xmath0 modes . these seismic frequencies respond to changes in activity and are probes of conditions within the sun . we show that the bison data reveal significant variations of the @xmath0-mode frequencies during the current minimum . the level of the minimum is significantly deeper in the @xmath0-mode frequencies than in the surface observations . the stark differences in the behavior of the frequencies and the surface activity measures point to activity - related processes occurring in the solar interior , which are yet to reach the surface , where they may be attenuated .

i

0907.3417

the sun is a variable star whose magnetic activity and total irradiance vary on a timescale of approximately 11 years . the current activity minimum has attracted considerable interest because of its unusual duration and depth . this raises the question : what might be happening beneath the surface where the magnetic activity ultimately originates ? the surface activity can be linked to the conditions in the solar interior by the observation and analysis of the frequencies of the sun s natural seismic modes of oscillation - the @xmath0 modes . these seismic frequencies respond to changes in activity and are probes of conditions within the sun . the birmingham solar - oscillations network ( bison ) has made measurements of @xmath0-mode frequencies over the last three solar activity cycles , and so is in a unique position to explore the current unusual and extended solar minimum . we show that the bison data reveal significant variations of the @xmath0-mode frequencies during the current minimum . this is in marked contrast to the surface activity observations , which show little variation over the same period . the level of the minimum is significantly deeper in the @xmath0-mode frequencies than in the surface observations . we observe a quasi - biennial signal in the @xmath0-mode frequencies , which has not previously been observed at mid- and low - activity levels . the stark differences in the behavior of the frequencies and the surface activity measures point to activity - related processes occurring in the solar interior , which are yet to reach the surface , where they may be attenuated .

the level of the sun s magnetic activity is observed to vary on an 11-year time scale and we are currently in the minimum between cycles 23 and 24 . the current solar minimum is attracting a great deal of attention as it is proving to be quite unusual . observations of surface and atmospheric effects , such as the number of visible sunspots , the rate of occurrence of solar flares and the strength of the solar wind , highlight just how quiet the sun is . the sun s activity cycle influences everyday life on the earth . the rate of occurrence of solar flares is dependent on the number of spots on the sun s surface , and large solar flares can disrupt satellite communications and cause power outages . coronal mass ejections ( cmes ) , which are another source of radiation that can disrupt life on the earth , are still being observed regularly on the sun , even in this unusual solar minimum ( see the stereo cor1 cme catalog ) . cosmic rays , which are a significant space radiation hazard , are anticorrelated with the solar cycle . the level of solar activity is possibly correlated to the earth s climate ( see , for example , * ? ? ? * and references therein ) . space - weather groups use predictions of solar cycles to anticipate the amount of orbital drag experienced by satellites . the next solar cycle has already proven difficult to predict as the current solar minimum is lasting significantly longer than expected . @xcite reviews 50 predictions for the size and timing of cycle 24 and finds a wide range of results , especially in comparison to predictions made before the previous solar cycle @xcite . for example , predictions of when cycle 24 will reach its maximum range from 2009 december @xcite to 2014 december @xcite . in fact , the official noaa , nasa and ises solar cycle 24 prediction panel , which studied the predictions collated by @xcite , failed to reach a consensus on when the peak of cycle 24 will occur and how active the upcoming cycle will be . meanwhile , the number of predictions for cycle 24 is ever increasing . surface measures of the sun s activity , such as the number of sunspots , which are used to aid cycle predictions , indicate that we are still in an extended solar - cycle minimum . we ask the question : can we learn anything about this unusual solar minimum from the sun s interior ? to answer this question we investigate the variation with the solar cycle of the frequencies of the sun s natural resonant oscillations , which are known as @xmath0 modes . solar @xmath0 modes are trapped in cavities below the surface of the sun and their frequencies are sensitive to properties , such as temperature and mean molecular weight , of the solar material . it has been known since the mid 1980s @xcite that @xmath0-mode frequencies vary throughout the solar cycle with the frequencies being at their largest when the solar activity is at its maximum . by examining the changes in the observed @xmath0-mode frequencies throughout the solar cycle , we can learn about solar - cycle - related processes that occur beneath the sun s surface . the birmingham solar - oscillations network ( bison ; * ? ? ? * ) makes sun - as - a - star ( unresolved ) doppler velocity observations , which are sensitive to the @xmath0 modes with the largest horizontal scales ( or the lowest angular degrees , @xmath1 ) . consequently , the frequencies measured by bison are of the truly global modes of the sun . these modes travel to the sun s core but their dwell time at the surface is longer than at the solar core because the sound speed inside the sun increases with depth . consequently , the low-@xmath1 modes are most sensitive to variations in regions of the interior that are close to the surface and so are able to give a global picture of the influence of near - surface activity . bison is a network of autonomous ground - based observatories that are strategically positioned at various longitudes in order to provide as continuous coverage as possible of the sun . bison is in a unique position to study the changes in oscillation frequencies that accompany the solar cycle as it has now been collecting data for over 30 years . however , when the network was first established the quality of the data was relatively poor , in comparison to recent years , because of the sporadic coverage of the observations . here , we have been able to analyze the mode frequencies observed during the last two solar cycles in their entirety .

this raises the question : what might be happening beneath the surface where the magnetic activity ultimately originates ? the birmingham solar - oscillations network ( bison ) has made measurements of @xmath0-mode frequencies over the last three solar activity cycles , and so is in a unique position to explore the current unusual and extended solar minimum . we observe a quasi - biennial signal in the @xmath0-mode frequencies , which has not previously been observed at mid- and low - activity levels .

i

0907.3417

the sun is a variable star whose magnetic activity and total irradiance vary on a timescale of approximately 11 years . the current activity minimum has attracted considerable interest because of its unusual duration and depth . this raises the question : what might be happening beneath the surface where the magnetic activity ultimately originates ? the surface activity can be linked to the conditions in the solar interior by the observation and analysis of the frequencies of the sun s natural seismic modes of oscillation - the @xmath0 modes . these seismic frequencies respond to changes in activity and are probes of conditions within the sun . the birmingham solar - oscillations network ( bison ) has made measurements of @xmath0-mode frequencies over the last three solar activity cycles , and so is in a unique position to explore the current unusual and extended solar minimum . we show that the bison data reveal significant variations of the @xmath0-mode frequencies during the current minimum . this is in marked contrast to the surface activity observations , which show little variation over the same period . the level of the minimum is significantly deeper in the @xmath0-mode frequencies than in the surface observations . we observe a quasi - biennial signal in the @xmath0-mode frequencies , which has not previously been observed at mid- and low - activity levels . the stark differences in the behavior of the frequencies and the surface activity measures point to activity - related processes occurring in the solar interior , which are yet to reach the surface , where they may be attenuated .

the solar - cycle shifts that are observed in @xmath0-mode frequencies are usually well correlated with proxies of the sun s activity , such as the 10.7 cm radio flux . however , in the declining phase of cycle 23 and the current solar minimum we find unusually large differences between the frequencies observed in bison data and the activity levels . the current cycle minimum indicated by the helioseismic data is significantly deeper than the minima observed by the activity proxies and the structure that is clearly evident in the frequency shifts is not replicated in the proxy data . we also observe a quasi - biennial signal in the @xmath0-mode frequencies at _ all _ activity levels . interestingly , this signal is _ only _ visible at _ high_-activity levels in the proxy data . as the frequency shifts respond to conditions beneath the surface of the sun whereas the proxies respond to changes at or above the surface , we suggest that these differences may be caused by changes in the magnetic flux that have yet to manifest at the surface . it is also possible that the magnetic flux responsible for the discrepancies between the frequency shifts and the activity proxies will never reach the sun s surface . the analysis presented here was based on averages made over groups of modes ( @xmath12 , @xmath13 ) . further work on individual modes may allow one to isolate the location of the variability because each mode shows a different sensitivity to the latitudinal distribution of the surface activity . such an analysis is currently in progress . in the seismic data , the previous solar minimum exhibited a double minimum and it appears that the current solar minimum is showing a similar structure . furthermore , the most recent @xmath0-mode frequencies indicate that the current minimum is still declining . therefore , it may still be some time before we observe the rising phase of cycle 24 . there have been suggestions that this recent strange behavior of the sun is indicative that the current grand maximum is about to end @xcite . that would indeed be an occurrence of great significance . although our results can not predict whether this is true they do indicate that the next solar cycle should be observed with great interest . this letter utilizes data collected by the birmingham solar - oscillations network ( bison ) . we thank the members of the bison team , both past and present , for their technical and analytical support . we also thank p. whitelock and p. fourie at the south african astronomical observatory ( saao ) , the carnegie institution of washington , the australia telescope national facility ( australian commonwealth scientific and research organization , csiro ) , e.j . rhodes ( mt . wilson , californa ) and members ( past and present ) of the instituto de astrofisica de canarias ( iac ) , tenerife . bison is funded by the science and technology facilities council ( stfc ) . the authors also acknowledge the financial support of stfc . abreu , j.a . , beer , j. , steinhiber , f. , tobias , s.m . & weiss , n.o . , 2008 , , 35 , 20109 benevolonskaya , e. e. , 1998a , , 509l , 49 benevolonskaya , e. e. , 1998b , , 181 , 479 chaplin , w. j. , elsworth , y. , isaak , g. r. , miller , b. a. , & new , r. , 1999 , , 308 , 424 chaplin , w. j. , elsworth , y. , miller , b. a. , verner , g.a . & new , r. , 2007 , , 659 , 1749 chaplin , w. j. et al . , 1996 , , 168 , 1 christensen - dalsgaard et al . , 2008 , commun . in asteroseismol . , 157 , 266 elsworth , y. et al . , 1990 , , 345 , 536 howe , r. , 2008 , adv . space res . , 41 , 846 joselyn , j. a. et al . , 1997 , eos trans . , 78 , 205 lockwood , m. & frhlich , c. , 2007 , proc . r. s. , 463 , 2447 maris , g. & oncica , a. , 2006 , sun geosphere , 1 , 1 mccomas , d. j. et al . , 2008 , , 35 , 18103 pesnell , w. d. , 2008 , , 252 , 209 saar , s. h. , & brandenburg , a. , 2002 , astron . nachr . , 323 , 357 tsirulnik , l. b. , kuznetsova , t. v. & oraevsky , v. n. , 1997 , adv . s. res . , 20 , 2369 vecchio , a. & carbone , v. 2008 , , 683 , 536 viereck , r. et al . , 2001 , , 28 , 1343 woodard , m. f. & noyes , r. w. 1985 , , 318 , 449

this indicates that ulxs are similar to galactic bhbs . the brightest x - ray spectrum can be fitted with a relativistic disk model with either a highly super - eddington ( @xmath0 ) non - rotating black hole or a close to eddington ( @xmath1 ) rapidly rotating black hole . the thermal dominant states are all found during outbursts .

i

1003.0283

the thermal dominant state in black hole binaries ( bhbs ) is well understood but rarely seen in ultraluminous x - ray sources ( ulxs ) . using simultaneous observations of m82 with chandra and xmm - newton , we report the first likely identification of the thermal dominant state in a ulx based on the disappearance of x - ray oscillations , low timing noise , and a spectrum dominated by multicolor disk emission with luminosity varying to the 4th power of the disk temperature . this indicates that ulxs are similar to galactic bhbs . the brightest x - ray spectrum can be fitted with a relativistic disk model with either a highly super - eddington ( @xmath0 ) non - rotating black hole or a close to eddington ( @xmath1 ) rapidly rotating black hole . the latter interpretation is preferred , due to the absence of such highly super - eddington states in galactic black holes and active galactic nuclei , and suggests that the ulx in m82 contains a black hole of 200 - 800 solar masses with nearly maximal spin . on long timescales , the source normally stays at a relatively low flux level with a regular 62-day orbital modulation and occasionally exhibits irregular flaring activity . the thermal dominant states are all found during outbursts .

ultraluminous x - ray sources ( ulxs ) are non - nuclear x - ray sources with apparent luminosities above the eddington limit of stellar - mass black holes ( bhs ) . variable ulxs are black hole binaries ( bhbs ) and may harbor intermediate - mass bhs @xcite . the emission of bhbs has been classified into four states based on spectral and timing properties : the quiescent , hard , thermal dominant ( td ) , and steep power - law states @xcite . the td state is the best understood and is well described by the standard accretion disk model @xcite . the emergent x - ray spectrum is described by a multicolor disk ( mcd ) model with two parameters : the disk inner radius ( @xmath2 ) and the temperature ( @xmath3 ) at that radius . in the td state , @xmath2 is constant and the accretion disk is thought to extend all the way to the `` innermost stable circular orbit '' ( isco ) around the bh @xcite . the isco radius depends solely on the mass and spin of the bh . therefore , a td spectrum from an accreting bh can be used to shed light on its mass and spin . the td state has been found during outbursts of many bhbs and exhibits specific properties . the disk bolometric luminosity is @xmath4 . for constant @xmath2 , a 4th power relation between the luminosity and the disk inner temperature , @xmath5 , is observed @xcite . due to up scattering of disk photons in the corona , sometimes the observed exponent is lower than 4 , but can be recovered by applying hardening correction @xcite . moreover , sources in the td state have low levels of short term variability , with very weak or absent narrow band timing noise ( quasi - periodic oscillations ; qpos ) and weak broad band power continuum @xcite . spectral surveys of ulxs in nearby galaxies show they are rarely in the td state @xcite . the spectra of a few ulxs are super - soft and can be modeled by an mcd with an inner temperature close to 0.1 kev . however , repeated observations revealed an evolution pattern inconsistent with the @xmath5 relation ruling out interpretation as thermal dominant disk emission @xcite . some other ulxs show soft excesses in the spectra that could be fitted by cool disk emission @xcite . however , the cool disk is not the dominant component in their spectra , thus , the sources are not in the td state . finding a ulx in the td state would demonstrate that the ulx has emission states similar to galactic bhbs and allow inference of the bh mass and spin . the starburst galaxy m82 contains one of the most luminous ulxs , cxom82 j095550 + 694047 (= ; * ? ? ? * ; * ? ? ? * ) , in nearby galaxies . the ulx was first identified with chandra at a luminosity higher than the eddington limit of a @xmath6 bh @xcite . on the sky , it lies near a super star cluster , which was speculated to be the birth place of a massive bh @xcite . low frequency qpos and broadband timing noise , detected in the central region of m82 @xcite and later confirmed to originate from this ulx @xcite , suggest that the ulx harbors a massive bh . @xcite also suggests that the ulx contains a massive bh which is the nucleus of a satellite galaxy merging with m82 . positive identification of the emission states requires both timing and spectral information . here , we describe simultaneous observations exploiting the high angular resolution of chandra to isolate the ulx spectrum from diffuse emission and nearby sources and the large collecting area of xmm - newton to obtain timing information . we use the joint timing and spectral information to identify the ulx emission states and unveil the nature of the source .

the thermal dominant state in black hole binaries ( bhbs ) is well understood but rarely seen in ultraluminous x - ray sources ( ulxs ) . using simultaneous observations of m82 with chandra and xmm - newton , we report the first likely identification of the thermal dominant state in a ulx based on the disappearance of x - ray oscillations , low timing noise , and a spectrum dominated by multicolor disk emission with luminosity varying to the 4th power of the disk temperature .

r

1003.0283

the thermal dominant state in black hole binaries ( bhbs ) is well understood but rarely seen in ultraluminous x - ray sources ( ulxs ) . using simultaneous observations of m82 with chandra and xmm - newton , we report the first likely identification of the thermal dominant state in a ulx based on the disappearance of x - ray oscillations , low timing noise , and a spectrum dominated by multicolor disk emission with luminosity varying to the 4th power of the disk temperature . this indicates that ulxs are similar to galactic bhbs . the brightest x - ray spectrum can be fitted with a relativistic disk model with either a highly super - eddington ( @xmath0 ) non - rotating black hole or a close to eddington ( @xmath1 ) rapidly rotating black hole . the latter interpretation is preferred , due to the absence of such highly super - eddington states in galactic black holes and active galactic nuclei , and suggests that the ulx in m82 contains a black hole of 200 - 800 solar masses with nearly maximal spin . on long timescales , the source normally stays at a relatively low flux level with a regular 62-day orbital modulation and occasionally exhibits irregular flaring activity . the thermal dominant states are all found during outbursts .

three chandra ( obsids 10027 , 10025 , and 10026 ) and xmm - newton ( obsids 0560590101 , 0560590201 , and 0560590301 ) observations were performed on 2008 october 4 , 2009 april 17 and 29 , respectively . each chandra observation has an effective exposure of about 18 ks and overlapped with an xmm - newton observation that lasted 30 , 40 , and 50 ks , respectively . to reduce the effects of pileup , the chandra observations placed the ulx @xmath7 off the optical axis , so the source covers multiple pixels , and the ccd was operated in a 1/8th sub - array mode to reduce the readout frame time . using the pileup_map tool in ciao 4.1.2 , we measured that the ulx resulted in 0.25 counts per frame ( @xmath813% pileup fraction ) on the brightest 3-by-3 pixel island in the observation on 2008 oct 4 , and found that about 85% of the total events were recorded on pixel islands with counts per frame larger than 0.06 ( @xmath83% pileup fraction ) . therefore , pileup must be taken into account in the spectral fitting . we note that the other two observations have similar , mild pileup , which can be corrected by applying a pileup model in the spectral fitting . each chandra spectrum was extracted from a source region found by wavelet detection . instrument responses were calculated using the calibration files in caldb 4.1.3 . the spectrum channels were re - grouped by a factor of 8 in 0.3 - 1 kev , 4 in 1 - 4 kev , 8 in 4 - 6 kev and 16 in 6 - 8 kev , respectively and were fitted in xspec 12.5 to a power - law model or mcd model ( diskbb ) subject to interstellar absorption and ccd pileup with background subtracted from a nearby , source free region . to minimize contamination from diffuse emission and piled events , we fitted the data in the energy range from 0.7 to 7 kev . during the fits , the pileup grade migration parameter @xmath9 was free , and @xmath10 ( the fractional events in the spectrum being treated for pileup ) was frozen at 0.85 based on the estimate discussed above and is also the best - fit value found from the fits . lccc @xmath9 & @xmath11 & @xmath12 & @xmath13 + @xmath14 & @xmath15 & @xmath16 & @xmath17 + @xmath3 & @xmath18 & @xmath19 & @xmath20 + @xmath2 & @xmath21 & @xmath22 & @xmath23 + @xmath24 & @xmath25 & @xmath26 & @xmath27 + @xmath28 & @xmath29 & @xmath30 & @xmath31 + @xmath32 & 67.8/70 & 79.0/68 & 42.5/53 for parameters ) . ( b ) data to model ratio for the mcd model ( @xmath33 ) ( c ) data to model ratio for the power - law model ( @xmath34 ) with the pileup parameter @xmath9 fixed at its best value found from the mcd model . ( d ) data to model ratio for the power - law model ( @xmath35 ) with @xmath9 free during the fit , which , however , converged to an unphysical value ( @xmath36 ) indicative of a zero pileup fraction . therefore , the mcd model is favored and the power - law model is ruled out from the spectral fitting . [ fig : db_po],scaledwidth=40.0% ] we found that the mcd model provides an adequate fit to the data , while the power - law model does not . no reasonable pileup parameters can be found with the power - law model ; the @xmath9 parameter always goes to zero , indicating the pileup fraction in the spectrum is zero , which is contradicted by the pile - up estimates . for the 2008 oct 04 observation , the fit is not acceptable with @xmath37 for 70 degrees of freedom ( dof ) . if we fix @xmath9 at its best - fit value found from the disk model , the goodness of fit is even worse , with @xmath34 . in contrast , the mcd model provides a good fit @xmath33 and a reasonable value of @xmath9 . figure [ fig : db_po ] shows the spectrum from the chandra observation on 2008 oct 04 and the comparison between the mcd and power - law model . please note that the data / model ratios from the two power - law models are not evenly distributed . level . [ fig : lt],scaledwidth=40.0% ] the mcd model also provides better fits than power - law for the other two observations , see table [ tab : fit ] . for the observation on 2009 apr 17 , 26.3 of @xmath38 arise from instrumental response features on individual channels at 2.1 and 3.2 kev . ignoring these two channels does not change the spectral parameters at all . we excluded them because we are only interested in the broad continuum . for the observation on 2009 apr 29 , possible emission line features are seen at energies from 4.5 to 7 kev . for the same reason , we only use 0.7 - 4.5 kev for this observation . we note that for the other two observations the spectral parameters derived from the 0.7 - 4.5 kev range are completely consistent with from the 0.7 - 7 kev range . although adding a power - law component to the model does not improve the fits , we did that to place an upper limit on the power - law flux with the power - law photon index bounded in the range 2.1 - 4.8 as found in the td state . the upper limits on a power - law component in 2 - 20 kev are estimated to be 4% , 17% , and 20% , respectively . this is consistent with the definition of the td state . power spectra were calculated from xmm - newton data using combined pn and mos events in a circular region around the source with a radius of @xmath39 from the common good time intervals without timing gaps ( following * ? ? ? we searched for qpos from 1 to 1000 mhz in various energy ranges , but did not find significant signals . we repeated the search in the half of the circular source region where contamination from sources other than the ulx is minimized ( region a in fig . 2 of * ? ? ? * ) , but still found nothing . the power spectra are consistent with that from the white noise . the 3@xmath40 upper limits of the total noise power ( in units of rms / mean ) in 1 - 1000 mhz in the energy range of 0.3 - 10 kev are 6.3% , 6.6% , and 6.9% , respectively from the three observations . these xmm - newton observations are able to detect qpos at the strengths previously observed . the disappearance of qpos and the low noise level suggest that the source was not in the hard state . the chandra energy spectra show that they are incompatible with a power - law form , but can be adequately modeled with a dominated mcd model with a constant inner radius . figure [ fig : lt ] shows that the bolometric luminosity from the accretion disk varies with the 4th power of the temperature . the correlation coefficient between @xmath41 and @xmath42 is 0.9995 with a chance probability of 0.02 from the three points . all of the emission properties , low timing noise , spectrum dominated by an mcd with low power - law fraction , and luminosity proportional to disk temperature to the 4th power are consistent with the source being in the td state and are strong evidence in favor of the interpretation of the energy spectrum as emission from an optically thick accretion disk . , scaledwidth=50.0% ] the lightcurve from rxte for the whole m82 galaxy is shown in figure [ fig : lc ] from 2008 february 5 to 2009 august 2 . the chandra / xmm - newton described here all occurred when the flux from m82 was well above its nominal level . the ulx was , by far , the brightest source in the three chandra observations . therefore , these outbursts from m82 are dominated by the ulx , with a minor contribution from another source ( ) active only in the first joint observations . thus , the td states were all observed during bright outbursts of the ulx . only two other chandra observations have manageable pileup . an observation on 2005 february 4 revealed a relatively low x - ray flux and a hard power - law spectrum inconsistent with an mcd model @xcite suggesting the hard state . we previously analyzed an observation from 2007 july 2 , but fixed @xmath43 based on the assumption that pileup was important only in the 3-by-3 pixel cluster with the highest count rate @xcite . utilizing the new pileup_map tool , we realized that @xmath10 was underestimated . using the improved procedures described above , we find @xmath44 for a power - law model and @xmath45 for a mcd model with parameters similar to those from 2008 oct 04 . lack of timing information precludes firm conclusion , but the td state is suggested . the standard mcd model does not include relativistic effects . such effects are particularly important for rapidly spinning bhs . for accurate estimation of the bh properties , we fitted the spectrum from when the source was brightest , the 2008 observation , with a fully relativistic mcd model , kerrbb @xcite . we set zero torque @xcite at the inner edge of the disk , the distance to the source as 3.63 mpc @xcite , the hardening factor as 1.7 @xcite , and switched on self - irradiation and limb - darkening . the pileup parameters were fixed at their best values found from the mcd model . this left five free parameters in the model : the disk inclination , bh mass , spin , accretion rate , and the interstellar absorption column density . . for other parameters please refer to the discussion of this model in the text . the residues are for the observations on 2008 oct 4 , 2009 apr 17 , and 2009 apr 29 , respectively , from top to bottom and in units of @xmath40 . [ fig : kerrbb],scaledwidth=40.0% ] to test if the bh is maximally spinning , we fixed the spin parameter at two extreme values @xmath46 and 0.9986 , respectively , representing non - spinning and maximally spinning @xcite . for a non - rotating bh , the accretion rate exceeds the eddington limit by a factor of 160 . for galactic bhbs , the observed eddington ratio is as high as 7 in v4641 sgr despite the uncertainty on the distance @xcite . when the luminosity is high and the radiation pressure is dominant , the thin accretion disk is predicted to be able to exceed the eddington limit by a factor of a few @xcite . therefore , we adopt an upper limit of 10 for the eddington ratio as being physically reasonable . we note that active galactic nuclei do not appear to exceed the eddington limit by more than a factor of 10 in any accretion state @xcite . the eddington ratio for a non - rotating bh is too large and this scenario should be ruled out . in contrast , if the bh is maximally spinning , the derived eddington ratio is only 2 . freezing the spin at the maximum allowed value resulted in a best - fit bh mass of 660 solar masses and a 90% error range of 300 - 1250 solar masses , a disk inclination angle of at least @xmath47 , and @xmath48 . the other two observations produce similar results . we also applied the model to the three observations simultaneously , imposing the same mass , spin , and inclination , and allowing the mass accretion rate and absorption column density to vary individually . fixing the spin parameter @xmath49 led to a best - fit bh mass of 500 solar masses , a 90% error range of 300 - 810 solar masses , an inclination of 59 - 79 degrees , and @xmath50 ; see figure [ fig : kerrbb ] . the eddington accretion rate at the highest luminosity observed is 2.5 . the inferred eddington ratio exceeds 10 for @xmath51 , which we took as the lower limit of the spin . fixing @xmath52 , the best - fit bh mass is 430 solar masses with a 90% error range of 190 - 570 solar masses , and the inclination is larger than @xmath47 . thus , the spectral fitting suggests that the ulx contains a rapidly spinning ( @xmath53 ) intermediate mass bh of 200 - 800 solar masses .

the latter interpretation is preferred , due to the absence of such highly super - eddington states in galactic black holes and active galactic nuclei , and suggests that the ulx in m82 contains a black hole of 200 - 800 solar masses with nearly maximal spin . on long timescales , the source normally stays at a relatively low flux level with a regular 62-day orbital modulation and occasionally exhibits irregular flaring activity .

c

1003.0283

the thermal dominant state in black hole binaries ( bhbs ) is well understood but rarely seen in ultraluminous x - ray sources ( ulxs ) . using simultaneous observations of m82 with chandra and xmm - newton , we report the first likely identification of the thermal dominant state in a ulx based on the disappearance of x - ray oscillations , low timing noise , and a spectrum dominated by multicolor disk emission with luminosity varying to the 4th power of the disk temperature . this indicates that ulxs are similar to galactic bhbs . the brightest x - ray spectrum can be fitted with a relativistic disk model with either a highly super - eddington ( @xmath0 ) non - rotating black hole or a close to eddington ( @xmath1 ) rapidly rotating black hole . the latter interpretation is preferred , due to the absence of such highly super - eddington states in galactic black holes and active galactic nuclei , and suggests that the ulx in m82 contains a black hole of 200 - 800 solar masses with nearly maximal spin . on long timescales , the source normally stays at a relatively low flux level with a regular 62-day orbital modulation and occasionally exhibits irregular flaring activity . the thermal dominant states are all found during outbursts .

joint chandra and xmm - newton observations have enabled us to precisely measure the spectral and timing behavior of this ulx in m82 . disappearance of qpos and low timing noise , an x - ray spectrum best - fitted with an mcd model , and an @xmath5 pattern in the spectral evolution provide strong motivation to interpret this behavior in terms of the td state seen in stellar - mass bhbs . the mcd model indicates that the source spectrum shows spectral curvature at a few kev and thus could also be fitted by more complicated models like a cool optically thick corona which has been proposed recently as an indicator of a new ` ultraluminous state ' @xcite . however , a transition from the hard spectrum ( incompatible with the steep power - law state ) seen at lower luminosities to the ultraluminous state would be difficult to explain and we , therefore , do not discuss this proposed state in detail . simply scaling the @xmath5 pattern to those from galactic bhbs suggests that the source contains a more massive bh , because the compact object mass is proportional to the square root of the disk luminosity if two bhs have the same disk inner temperature and spin @xcite . fitting with a fully relativistic mcd model leads to a consistent result . a conservative estimate of the bh mass by allowing an eddington ratio of as high as 10 suggests a bh of at least 200 solar masses but less than 800 solar masses . this is coincident with the theoretical estimate of the mass of this bh if it is created in a nearby star cluster by runaway collisions @xcite . the fast spin of the source makes it efficient in extracting gravitational energy . the spectral fitting also indicates a relatively high inclination angle , 59 - 79 degrees , of the accretion disk . for a maximally spinning bh of a few hundred solar masses , the relativistic effect has largely eliminated the limb - darkening effect ; viewing the disk at a high inclination angle receives almost the same flux as at a low angle . therefore , the observed high flux is not a problem for a nearly edge - on disk . the x - ray flux from m82 is modulated at a period of 62 days , interpreted as due to orbital motion of this ulx binary , which must contain a giant or super - giant star inferred from the period assuming roche - lobe overflow @xcite . with knowledge of the bh mass ( assuming 200 - 800 solar masses ) and the 62-day binary orbital period , the binary separation of the ulx can be calculated with the assumption of roche lobe overflow as @xmath54 cm , which is insensitive to the mass of the companion star . this is larger than all separations of low - mass bhbs with a dynamical measurement of the mass , and larger than that of grs 1915 + 105 , which has the largest separation known so far , by a factor of a few . this ulx and grs 1915 + 105 share a similarity that they have both been active for many years without quenching to the quiescent state . the large separation and consequently a huge reservoir of accretion mass could be the factor that determines their long - term activity @xcite . we thank the referee for useful comments and the mission planning teams of chandra and xmm - newton for making these observations possible . hf acknowledges funding support from the national natural science foundation of china under grant no . 10903004 and 10978001 , the 973 program of china under grant 2009cb824800 , and the foundation for the author of national excellent doctoral dissertation of china under grant 200935 . pk acknowledges support from chandra grant go9 - 0034x .

however , the joint entropy of damped harmonic oscillator shows remarkable discontinuity with time for certain values of damping factor . according to the results , the envelop of the joint entropy curve increases with time monotonically . this results is the general properties of the envelop of the joint entropy curve for quantum systems .

r

0704.1370

the time dependent entropy ( or leipnik s entropy ) of harmonic and damped harmonic oscillators is extensively investigated by using time dependent wave function obtained by the feynman path integral method . our results for simple harmonic oscillator are in agrement with the literature . however , the joint entropy of damped harmonic oscillator shows remarkable discontinuity with time for certain values of damping factor . according to the results , the envelop of the joint entropy curve increases with time monotonically . this results is the general properties of the envelop of the joint entropy curve for quantum systems . keywords : path integral , joint entropy , simple harmonic oscillator , damped harmonic oscillator , negative joint entropy

to get the path integral solution for the sho , we must calculate its action function . the lagrangian of the system is given by @xmath18 following a straightforward calculation , it is given by : @xmath19\end{aligned}\ ] ] with @xmath20 and @xmath21 . substituting eq . ( 9 ) into eq . ( 7 ) , we obtain the feynman kernel @xcite : @xmath22\}.\end{aligned}\ ] ] by the use of the mehler - formula @xmath23\end{aligned}\ ] ] where @xmath24 is hermite polynomials , we can write the feynman kernel defining @xmath25 , @xmath26 and @xmath27 @xmath28 with energy - spectrum and wave - functions : @xmath29 @xmath30 time dependent wave function of the sho is defined as @xmath31 it can be written as @xmath32\end{aligned}\ ] ] where @xmath33 or @xmath34 is mean of the gaussian curve . the probability density has @xmath35\ ] ] where @xmath36 . thus it can be written as @xmath37\ ] ] this has been shown in fig.[eps1 ] . in momentum space , the probability density has the form @xmath38.\end{aligned}\ ] ] the joint entropy of harmonic oscillator becomes @xmath39 in fig.[eps2 ] , the joint entropy of this system was plotted by using mathematica in three dimension . as known from fundamental quantum mechanics and classical dynamics , displacement of simple harmonic oscillator from equilibrium depends on harmonic functions ( e.g sine or cosine function ) . therefore , other properties of the sho systems indicate the same harmonic behavior . if the frequency of the sho is sufficiently small , the system shows the same behavior as the free particle@xcite . as seen from fig.[eps3 ] and fig.[eps4 ] , envelop of the sinusoidal curve is also monotonically increase with omega and constant with time at constant omega , respectively . when the frequency increases , the joint entropy of this system indicates a fluctuation with increasing amplitude with time . if t goes to zero , it is important that eq.(20 ) is in agreement with following general inequality for the joint entropy : @xmath40 originally derived by leipnik for arbitrary one - dimensional one - particle wave functions . the dho is very important physical system in all physical systems defining an interaction with its environment . the lagrangian of the dho is given by @xmath41 damped free particle kernel is @xmath42 the dho kernel has the form @xcite @xmath43 or explicitly @xmath44.\end{aligned}\ ] ] where the coefficients a , b , c , d , f are @xcite @xmath45 @xmath46 @xmath47 @xmath48 @xmath49 @xmath50 the wave function @xmath51 and energy eigenvalues become @xmath52\end{aligned}\ ] ] and @xmath53 where @xmath54 is the hermite polynomial of order n and the coefficients are @xmath55 the time dependent wave function is obtained as @xcite @xmath56\big\}\exp[-(ax^2+\nonumber\\&+&2bx)]h_{n}[d(x - e)].\end{aligned}\ ] ] to simplify the evaluation , we set @xmath57 . such that kernel and wave function of the dho @xcite become @xmath58\big)\big]\end{aligned}\ ] ] where @xmath59 and @xmath60\big\}h_{n}[dx]\exp[-ax^2].\end{aligned}\ ] ] where d , a and n are @xmath61 @xmath62 @xmath63,\end{aligned}\ ] ] and @xmath64 the ground state wave function is given by @xmath65\big\}\exp[-a(t)x^2].\end{aligned}\ ] ] so the probability distribution in coordinate space becomes @xmath66 is defined by @xmath67.\end{aligned}\ ] ] the probability density in coordinate space is shown in fig.[eps5 ] and fig.[eps6 ] for the different values of @xmath68 . the probability density in momentum space can be written easily @xmath69.\end{aligned}\ ] ] the time dependent joint entropy can be obtained from eq . ( 2 ) as @xmath70-\ln2\pi.\end{aligned}\ ] ] the joint entropy depends on damping factor @xmath68 . when @xmath71 , all the above results are converged to simple harmonic oscillator . however , when the @xmath72 , the joint entropy has remarkably different features of the sho . as can be seen in fig.[eps7 ] and fig.[eps8 ] , the joint entropy of the dho has very interesting properties . one of the most important properties of the joint entropy is the probability of taking values for small @xmath68 values . as we know from literature the joint entropy must be positive and monotonically increase.however , this system has different properties from literature because of periodically discontinuity of the joint entropy . on the other hand , envelop of this curve is also monotonically increase with time for large @xmath68 . as can be shown these results , the envelop of the joint entropy curves has general properties as monotonically increase for quantum systems . thus , we have found that the joint entropy is depend on properties of investigated system .

the ultrahigh energy neutrino cross section is a crucial ingredient in the calculation of the event rate in high energy neutrino telescopes . currently there are several approaches which predict different behaviors for its magnitude for ultrahigh energies . in this contribution is presented a summary of current predictions based on the non - linear qcd evolution equations , the so - called perturbative saturation physics . in particular , predictions are shown based on the parton saturation approaches and the consequences of geometric scaling property at high energies are discussed . the scaling property allows an analytical computation of the neutrino scattering on nucleon / nucleus at high energies , providing a theoretical parameterization .

i

1112.0555

the ultrahigh energy neutrino cross section is a crucial ingredient in the calculation of the event rate in high energy neutrino telescopes . currently there are several approaches which predict different behaviors for its magnitude for ultrahigh energies . in this contribution is presented a summary of current predictions based on the non - linear qcd evolution equations , the so - called perturbative saturation physics . in particular , predictions are shown based on the parton saturation approaches and the consequences of geometric scaling property at high energies are discussed . the scaling property allows an analytical computation of the neutrino scattering on nucleon / nucleus at high energies , providing a theoretical parameterization .

the investigation of ultrahigh energy ( uhe ) cosmic neutrinos provides an opportunity for study particle physics beyond the reach of the lhc @xcite . as an example , nowadays the pierre auger observatory is sensitive to neutrinos of energy @xmath0 gev @xcite . a crucial ingredient in the calculation of attenuation of neutrinos traversing the earth and the event rate in high energy neutrino telescopes is the high energy neutrino - nucleon cross section , which provides a probe of quantum chromodynamics ( qcd ) in the kinematic region of very small values of bjorken-@xmath1 . the typical @xmath1 value probed is @xmath2 , which implies that for @xmath3 gev one have @xmath4 at @xmath5 gev@xmath6 . this kinematical range was not explored by the hera measurements of the structure functions @xcite . the description of qcd dynamics in such very high energy limit is a subject of intense debate @xcite . theoretically , at high energies ( small bjorken-@xmath1 ) one expects the transition of the regime described by the linear dynamics , where only the parton emissions are considered , to a new regime where the physical process of recombination of partons becomes important in the parton cascade and the evolution is given by a non - linear evolution equation . this regime is characterized by the limitation on the maximum phase - space parton density that can be reached in the hadron wavefunction ( parton saturation ) , with the transition being specified by a typical scale , which is energy dependent and is called saturation scale @xmath7 . moreover , the growth of the parton distribution is expected to saturate , forming a color glass condensate ( cgc ) , whose evolution with energy is described by an infinite hierarchy of coupled equations for the correlators of wilson lines @xcite . in the mean field approximation , the first equation of this hierarchy decouples and boils down to a single non - linear integro - differential equation : the balitsky - kovchegov ( bk ) equation @xcite . experimentally , possible signals of parton saturation have already been observed both in @xmath8 deep inelastic scattering at hera and in deuteron - gold collisions at rhic @xcite . currently , there are predictions of the neutrino nucleon cross sections with structure functions constrained by hera data are based on linear dynamics @xcite , using dglap or an unified dglap / bfkl evolution , or phenomenological models that resembles the expected behavior predicted by the non - linear qcd dynamics @xcite ( i.e. , the proton structure function saturating the froissart bound at asymptotic energies , @xmath9 ) . as a general feature , the nonlinear qcd dynamics predicts sizable suppression of uhe neutrino cross section in comparison with standard approaches . here , we summarize the main results of works presented in refs . @xcite . in ref . @xcite the contribution of non - linear effects was estimated considering distinct phenomenological models based on saturation physics . an update on those calculations have been done recently @xcite . in ref . @xcite , the geometric scaling property ( which is a natural consequence of the asymptotic solutions of the nonlinear qcd evolution equations ) is considered to obtain an analytical parameterization for the uhe neutrino cross sections . in what follows we introduce the theoretical and phenomenological tools and present the main results and predictions

the widespread use of nanodiamond as a biomedical platform for drug - delivery , imaging , and sub - cellular tracking applications stems from their non - toxicity and unique quantum mechanical properties . here , we extend this functionality to the domain of magnetic resonance , by demonstrating that the intrinsic electron spins on the nanodiamond surface can be used to hyperpolarize adsorbed liquid compounds at room temperature . by combining relaxation measurements with hyperpolarization , spins on the surface of the nanodiamond can be distinguished from those in the bulk liquid .

r

1606.06822

the widespread use of nanodiamond as a biomedical platform for drug - delivery , imaging , and sub - cellular tracking applications stems from their non - toxicity and unique quantum mechanical properties . here , we extend this functionality to the domain of magnetic resonance , by demonstrating that the intrinsic electron spins on the nanodiamond surface can be used to hyperpolarize adsorbed liquid compounds at room temperature . by combining relaxation measurements with hyperpolarization , spins on the surface of the nanodiamond can be distinguished from those in the bulk liquid . these results are likely of use in signaling the controlled release of pharmaceutical payloads .

the nanodiamonds used in these experiments are manufactured using the high pressure high temperature ( hpht ) technique and purchased from microdiamant . a micrograph showing nds with an average size of 125 nm is shown in fig . measurements were made on diamonds in a size range between 18 nm and 2 @xmath4 m . adsorption of the compounds onto the nd surface occurs passively when diamonds are mixed and sonicated with various liquids . hybridized carbon from the surface of the diamond and sp@xmath5 hybridized carbon from the core of the diamond . the sp@xmath6 raman cross section is @xmath7150 times larger than the sp@xmath5 raman cross section leading to a comparatively larger peak . the fluorescence of the diamond has been subtracted using a baseline correction , and spectra have been normalized to the sp@xmath5 hybridized peak . * c , d ) * comparison of the esr spectrum of 25 nm hpht nd and 25 nm ao nd . the data ( red ) is simulated ( blue ) using three components : a narrow spin-1/2 lorentzian component ( yellow ) , a broad spin-1/2 lorentzian component ( black ) and a p1 center component ( green ) . * e ) * the @xmath1h t@xmath8 relaxation time of water in water - nd mixtures as a function of nd size and concentration at @xmath2 = 330 mt . data points are fits to the @xmath1h t@xmath8 build up performed using an inversion recovery sequence . the solid lines are fits to the relaxivity equation [ see methods section ] . smaller nds ( 25 nm nd , blue dots , relaxivity : @xmath9=0.17mg@xmath10mls@xmath10 ) have a larger effect upon the t@xmath8 relaxation time of water than larger nds ( 2 @xmath4 m nd , purple dots , relaxivity : @xmath9 = 0.003 mg@xmath10 ml s@xmath10 ) . ] using raman spectroscopy , we observe that our nds comprise two phases of carbon , sp@xmath6 hybridized , attributed to carbon on the surface of the nd , at wavenumber @xmath11 = 1580 cm@xmath10 , and sp@xmath5 hybridized , attributed to carbon in the core of the nd , at @xmath11 = 1332 cm@xmath10 , as shown in fig . 1b . the sp@xmath6 carbon phase results in free electrons and provides a surface for liquid adsorption . we observe more sp@xmath6 hybridized carbon in smaller nds than larger nds , due to the much higher surface to volume ratio . air oxidation @xcite of the nds etches away some of the surface , removing sp@xmath6 hybridized carbon and surface electrons . much of the functionality of nd , including its fluorescence , magnetic field sensitivity , and use as an mri contrast agent stems from the presence of impurities and unbound electrons in the crystal lattice or nanoparticle surface . for dnp applications these intrinsic free - radicals provide a means of hyperpolarizing nuclear spins @xcite , but also open pathways for spin relaxation @xcite . for the smaller nds , the dominant electronic defects are carbon dangling bonds on the surface , contributing a broad spin-1/2 component in an electron spin resonance ( esr ) spectrum , ( see black trace in fig . air oxidation of the nds removes some of these surface electrons , resulting in a decrease in the broad spin-1/2 component in the spectrum , as shown in fig . other components of the esr spectrum include a narrow spin-1/2 component ( yellow ) , attributed to defects in the core of the nd and a p1 center component ( green ) which results from a substitutional nitrogen atom with the electron hyperfine coupled to the @xmath13n spin . increasing the diameter of the nds shrinks the surface to volume ratio and reduces the relative amplitude of the broad and narrow spin-1/2 components . at the same time , the larger nds have more p1 centers in the core . we first examine whether the presence of these free electron spins on the diamond surface can be identified by mixing the nanoparticles with various liquids containing @xmath1h spins at @xmath14 330 mt . in this configuration , the presence of free electrons on the nd surface enhances the spin relaxation ( with characteristic time @xmath15 ) of the surrounding @xmath1h from the liquid , as shown for the case of water in fig . 1e ( and supplementary figs . 1 - 2 ) . consistent with the esr measurements , we find that this relaxivity effect is more prominent for small nds , which have a larger surface to volume ratio , and a higher number of surface spins . we note that although the relaxivity effect is small when compared to commonly used contrast agents based on metal conjugates @xcite , it is significant enough to enable @xmath15-weighted imaging when using concentrations of order 1mg / ml . turning now to a key result of the paper , we make use of room temperature hyperpolarization as a means of further probing and identifying the spins at the liquid - nanodiamond interface . in contrast to high - field hyperpolarization modalities that aim to increase the mr signal for enhanced contrast , our focus here is the spectrum of the polarization with frequency , enabling different hyperpolarization methods to be distinguished . the overhauser effect , for instance , is commonly observed when polarizing liquid compounds comprising molecules that undergo rapid translational and rotational diffusion . this mechanism relies on scalar and dipolar relaxation pathways to build up a nuclear polarization when driving at the electron larmor frequency , @xmath16 , resulting in positive or negative enhancement depending on the electron - nuclear coupling . in contrast , if the nuclear and electron spins are bound such that the primary mode of nuclear spin relaxation is via the same electrons used for polarizing @xcite , then hyperpolarization occurs via the solid - effect , cross - effect , or thermal - mixing mechanism , see fig . 2a and 2b . involve a mutual electron and nuclear flip resulting in a positive nuclear polarization , shown in b. driven flip - flop transitions ( green ) result in a negative nuclear polarization . for overhauser effect hyperpolarization , saturating the esr transition can lead to positive or negative enhancement ( shown in b ) , through relaxation via the zero quantum ( green ) or double quantum ( red ) transitions respectively . * b ) * theoretical enhancement spectra for the solid effect ( black ) and overhauser effect ( grey ) hyperpolarization mechanisms . * c ) * @xmath1h signal enhancement as a function of driving microwave frequency at @xmath2=458mt ( black dots ) . the fit to the data ( grey line ) is based on the esr trace linewidths for the broad and narrow spin-1/2 impurities in the nd . the hyperpolarization spectrum is consistent with that given by the solid effect . enhancement is given by the hyperpolarized signal divided by the signal with microwaves off . ] using the naturally occurring electrons on the surface of nds , we are able to hyperpolarize the @xmath1h spins in a range of liquid - nanodiamond compounds including water , oil , acetic acid , and glycerol mixtures , despite their variation in chemical polarity . the data presented in fig . 2c is representative of the effect , showing in this case @xmath1h hyperpolarization from oil ( sigma o1514 ) mixed with 25 nm nd . the data clearly exhibit the signature of hyperpolarization via the solid - effect , with a positive signal enhancement when driving at @xmath17 and a negative signal enhancement at @xmath18 . no enhancement is seen at @xmath19 = @xmath20 , as would be expected if the overhauser effect was contributing to the hyperpolarization and there is no enhancement in liquid solutions without nds . the presence of the solid - effect provides a strong indication that the signal enhancement stems from hydrogen spins that are adsorbed at the nanodiamond surface . similar behavior is observed when hyperpolarizing other liquid - nanodiamond mixtures ( see supplementary fig 3 ) . we also note that the enhancement scales inversely with nanoparticle size ( see supplementary fig 4 . ) , a further indication that dnp is mediated via spins on the nd surface and consistent with the relaxivity measurements presented in fig . we further examine the hyperpolarization spectrum as a function of magnetic field over the range @xmath2=300mt-500mt , as shown in fig 3a . the position of the enhancement peaks follow @xmath17 and @xmath18 with a peak splitting of @xmath19 = 2@xmath21 ( black dashed lines ) at low magnetic fields , ( see fig . small deviations from the predicted splitting are evident , potentially due to a contribution from the cross effect or thermal mixing mechanism . a contribution from thermal mixing and the cross effect is expected given the esr spectrum contains a broad spin-1/2 component that is wider than the nuclear larmor frequency . surprisingly , we also observe that the @xmath1h signal enhancement increases with magnetic field , as shown in fig . this dependence with field is currently not understood , given that the solid- and cross - effect enhancements are expected to scale in proportion to @xmath22 and @xmath23 respectively @xcite . field - dependent spin relaxation of electrons , as well as a narrowing of the esr line with increasing field , may lead however , to more efficient hyperpolarization . . the positions of the peaks ( black dots ) follow the lines @xmath17 and @xmath18 ( black dashed lines ) . we see no hyperpolarization at @xmath16 ( blue dashed line ) . the microwave detuning is given by @xmath24 = @xmath19 - @xmath20 . the traces have been offset by the magnetic field scaling for clarity . * b)*the frequency splitting between the maximum and minimum @xmath1h signal from oil adsorbed on the nd surface for 18 nm nd ( red ) , 25 nm nd ( blue ) , 50 nm nd ( green ) , 210nmnd ( yellow ) , and 500 nm nd ( grey ) . the splitting follows the predicted value for the solid effect of @xmath25 ( dashed lines ) . error bars are 10 % of the lorentzian fit to the hyperpolarization data . traces have been offset for clarity . * c ) * the @xmath1h signal enhancement as a percentage of the non - polarized signal at magnetic fields between @xmath2 = 300mt-500mt for a 25 nm nd and oil mixture . positive enhancement at @xmath17 is shown in red and negative enhancement at @xmath18 is shown in blue . data points are the saturation value of an exponential fit to a polarization build up divided by the signal with far detuned microwaves . ] mixing nanodiamond with a significant amount of liquid leads to behavior indicative of a system with two independent spin baths . in our nd - water illustration shown in fig . 4a , the @xmath1h spins in the bulk of the liquid comprise one bath , with the other being those spins that are absorbed on the surface of the nanodiamond , in contact with free electrons . we isolate the independent contribution to the signal from each bath by comparing spin relaxation as a function of water concentration and in the presence of hyperpolarization using the pulse sequences shown in fig . 4b and 4c . consistent with the behavior expected for two spin baths , the relaxation decay exhibits a bi - exponential dependence with a short @xmath15 and long @xmath15 , as shown by the black curve in fig . we attribute the short @xmath15 ( green shading ) to spins adsorbed on the nd surface , where the presence of electrons can rapidly relax nuclear spins in close proximity . when the nd - water mixture is sufficiently diluted ( @xmath26 60 @xmath4l ) , a longer tail in the decay appears ( blue shading ) that likely stems from spins in the bulk liquid , decoupled from the nd surface . reducing the amount of water , fig . 4e shows that the long time component is suppressed since all spins can then be rapidly relaxed by the nd surface . relaxation in hyperpolarized liquids . * * a ) * schematic of a nd - water mixture . nd is shown in grey and water is shown in blue . surface electrons ( e ) on the nds are shown as a green circle representing the distance over which hyperpolarization occurs . * b , c ) * pulse sequences used to measure relaxation of a hyperpolarized liquid . * b ) * inversion recovery sequences probing both spins in the bulk and adsorbed water . * c ) * hyperpolarization followed by a @xmath27/2 pulse probes the relaxation of spins close to the nd surface . * d , e ) * relaxation of a water - nd mixture measured by the pulse sequences outlined in b , c. * d ) * we observe a double exponential behavior in the inversion recovery experiment ( black ) when sufficient water has been added ( 60 @xmath4l ) , indicating two distinct spin baths . the hp relaxation ( red ) falls off at a fast rate . * e ) * when only a small amount of water is added ( 40 @xmath4l ) , we only observe fast relaxation in both the hyperpolarization ( red ) and inversion recovery ( black ) experiments . solid lines are exponential and double exponential fits to the data . the short component of the relaxation is shaded green , and the long component is shaded blue . * f ) * summary of the @xmath1h t@xmath8 relaxation times in water - nd mixtures as a function of water concentration . we always observe a short component to the relaxation ( @xmath28ms ) and we begin to observe a long component ( @xmath29ms ) for inversion experiments once @xmath7 60 @xmath4l of water is added to the nd . data points are exponential and double exponential fits to five relaxation experiments : inversion recovery ( black ) , positive enhancement then relaxation ( red ) , negative enhancement then relaxation ( yellow ) , positive enhancement then inversion recovery ( blue ) , and negative enhancement then inversion recovery ( green ) . ] inserting a hyperpolarization ( hp ) pulse in place of the usual inversion recovery sequence leads to a small enhancement of the signal that rapidly decays , irrespective of the concentration of water in the system . this behavior , taken together with the relaxation measurements , suggests that hyperpolarization is again limited only to those nuclear spins absorbed on the nd surface , consistent with dnp occurring via the solid - effect . further , this data puts a bound on the extent to which diffusion can transport hyperpolarized spins from the nd surface to the bulk of the liquid . since no signal enhancement is ever observed in the long - time component of the relaxation , we conclude that the hyperpolarized spins that are bound to the surface are unable to diffuse into the bulk before relaxing . in further support of this picture , fig . 4f shows that relaxation ( without hyperpolarization ) , suddenly switches from a single exponential to bi - exponential decay when the amount of water exceeds 60 @xmath4l ( black dots ) . this behavior is symptomatic of any sequence that contains an inversion recovery pulse ( black , green , or blue dots ) , since the pulse acts on both the spins on the surface and those in the bulk ( see supplementary figs . 5 and 6 ) . hyperpolarization without inversion recovery however , acts only on nd - surface spins and always leads to fast , single - exponential decay independent of the amount of water . a complimentary picture emerges when nanodiamond is mixed with oil . we again conclude that the system comprises two distinct baths with different spin dynamics , in this instance by examining how the signal is enhanced by hyperpolarization beyond the thermal contribution , @xmath24s = s@xmath30 - s@xmath31 , shown in red in fig . 5a . in the limit of no oil , 5b shows that there is no enhancement in the signal since the electrons on the nd surface can not hyperpolarize @xmath1h spins elsewhere in the system . increasing the amount of oil has two effects . firstly , more oil leads to a steady increase in the number of spins in contact with electrons on the nd surface , thus increasing the hyperpolarized signal and @xmath24s . secondly , the additional oil in the mixture also increases the signal from spins in thermal equilibrium s@xmath31 , either at the surface or in the bulk of the liquid . to account for both the hyperpolarized and thermal contributions to the signal , fig . 5b also shows the enhancement @xmath32 = @xmath24s / s@xmath31 as a function of the amount of oil ( blue ) . similar to the case of the nd - water mixture , we observe a transition in behavior around 60 @xmath4l , where the contribution from hyperpolarization begins to saturate and adding further liquid simply leads to dilution . we speculate that the liquid concentration at which this transition occurs provides information about the packing density of nd , viscosity , and extent of diffusion present in the mixture . future efforts may exploit such identifiers to signal the adsorption and desorption of nd payloads such as chemotherapeutics . ) , the hyperpolarized nmr signal ( s@xmath33 ) , and the difference in these signal ( @xmath24s ) . * b ) * enhancement ( blue ) and the change in the @xmath1h nmr signal with hyperpolarization ( @xmath24s , red ) for a nd - oil mixture as a function of oil concentration . saturation of the nd surface occurs after 60 @xmath4l of oil is added . the data points are the saturation values of polarization build up curves ( at @xmath17 ) . the solid red line is a guide to the eye . * c ) * @xmath1h polarization build up at @xmath17 in an oil - nd mixture for 18 nm nd ( red ) , 25 nm nd ( yellow ) , 50 nm nd ( green ) , 75 nm nd ( blue ) , and 125 nm nd ( black ) . solid lines are either exponential fits ( 50 nm , 75 nm and 125 nm nd ) or double exponential fits ( 18 nm and 25 nm nd ) to the data . the data has been corrected for heating effects [ see methods section ] . the polarization build up times are : 18 nm nd : @xmath34=72ms , @xmath35=4.7s ; 25nmnd : @xmath34=72ms , @xmath35=4.4s ; 50 nm nd : @xmath36=46ms ; 75nmnd : @xmath36=45ms ; 125 nm nd : @xmath36=32ms . data has been normalized such that 0 corresponds to the signal with no microwaves , and 1 corresponds to saturation of the fast component of the polarization build - up . ] the combined data - sets for water and oil nanodiamond mixtures suggest that hydrogen spins become attached to the nd surface and remain there for times that are long compared with hyperpolarization and relaxation processes . to test this picture further , we examine lastly how the signal enhancement depends on the time over which microwaves are applied to produce hyperpolarization . the signal is observed to grow mostly between 10 and 100ms of hyperpolarization , saturating for longer times , as shown in fig . this saturation is consistent with the surface adsorbed @xmath1h spins undergoing little diffusion into the bulk liquid and thus blocking the surface from being further replenished with new , unpolarized spins . in this regime , the surface bound spins will reach a steady - state enhancement that is determined by the rates of hyperpolarization and relaxation . nanodiamonds below 50 nm in size exhibit this saturation in signal , but then undergo a slight further enhancement for hyperpolarization times longer than 1 second . this surprising behavior could be partially explained by diffusion in the oil - nd mixture that becomes enhanced for small diamonds . a further possibility is that the timescale over which @xmath1h spins remain adsorbed on the surface is reduced for nds below a certain size . the use of nanodiamond in a biological context is now widespread @xcite , given they are essentially non - toxic , exhibit a readily functionalized surface as well as attributes that enable new imaging and tracking modalities . here , we have focused on the spin interactions of the nd surface and liquid interface at room temperature , making strong use of nuclear hyperpolarization to uncover aspects of the dynamics that are otherwise challenging to observe . beyond a new means of characterization , the use of such hyperpolarization techniques offer a means of detecting the presence or absence of adsorbed compounds , of use in targeted delivery and release of chemotherapeutics . extending this approach into the spectroscopic domain , either correlating chemical shift or relaxation times , would enable the possibility of distinguishing local environments and compounds interacting with the nd surface . given the long relaxation times and significant @xmath0c hyperpolarization that is possible with nanodiamond @xcite , the surface spin interactions investigated here open the prospect of transferring polarization from the nd - core to the surface . in this mode , intrinsic surface electrons can act to mediate polarization transfer between @xmath0c storage and @xmath1h spins for detection . such an approach is amenable to techniques based on microfluidics @xcite . in conclusion , we have examined the use of nanodiamond and its surface in establishing polarized states of various liquids at room temperature . the presence of nd leads to enhanced relaxation of @xmath1h spins in solution , opening a means of generating nd - specific contrast for mri . the application of microwaves near the resonance frequency of the surface electrons leads to hyperpolarization of @xmath1h spins , consistent with dynamic nuclear polarization via the solid - effect and cross - effect . finally , the combined use of hyperpolarization and relaxation measurements allow for spins on the nd surface to be distinguished from those in the bulk liquid , opening a means to probe the local environment of nd in vivo . * nanodiamonds . * in these experiments hpht nds purchased from microdiamant were used . we refer to the diamonds by their median size . measurements were made on msy 0 - 0.030 , ( 0 - 30 nm , median 18 nm ) , msy 0 - 0.05 ( 0 - 50 nm , median 25 nm ) , msy 0 - 0.1 ( 0 - 100 nm , median 50 nm ) , msy 0 - 0.15 ( 0 - 150 nm , median 75 nm ) , msy 0 - 0.25 ( 0 - 250 nm , median 125 nm ) , msy 0 - 500 ( 0 - 500 nm , median 210 nm ) , msy 0.25 - 0.75 ( 250nm-500 nm , median 350 nm ) , msy 0.25 - 0.75 ( 250nm-750 nm , median 500 nm ) , msy 0.75 - 1.25 ( 750nm-1250 nm , median 1000 nm ) and msy 1.5 - 2.5 ( 1500nm-2500 nm , median 2000 nm ) . * adsorption . * initially nds were heated on a hot plate to remove any adsorbed water . the nds were mixed with various liquids and sonicated . adsorption occurred passively . the nd remained suspended in solution for the duration of the experiments . * experimental setup . * signals were acquired with a single spaced solenoid coil in a home built nmr probe in a magnetic field range of @xmath2 = 300mt - 500mt provided by either a permanent magnet ( @xmath2 = 460mt ) or an electromagnet . x - band microwave irradiation was amplified to a power of 10 w and coupled to the sample using a horn antenna and reflector . nmr signals were measured by initially polarizing the sample , then detecting the polarized signal using either a @xmath38 pulse or an echo ( @xmath39 ) sequence , and finally waiting for the polarization to return to thermal equilibrium . data was acquired using either a redstone nmr system ( tecmag ) or a spincore nmr system . * esr measurements . * esr measurements were made using a bruker emx - plus x - band esr spectrometer . the cavity q - factor ranged between @xmath42 = 5000 - 10000 for small and large nd particles respectively . esr power was @xmath41 = 0.25 @xmath4w , modulation amplitude was 1 gs , and the modulation frequency was 100 khz . simulations of the esr spectra were performed in easyspin @xcite . fit parameters were linewidth , signal amplitude and g - factor for each spin species . * relaxivity measurements . * the @xmath15 polarization build up curves were fitted with an exponential fit @xmath43 , where @xmath44 is the magnetization , @xmath45 is the equilibrium magnetization , @xmath15 is the spin lattice relaxation time and @xmath46 is the polarization build up time . relaxivity data was fitted with @xmath47 where @xmath48 is the concentration of nanodiamond , @xmath49 is the @xmath15 relaxation time of pure ( undoped ) water and @xmath9 is the relaxivity . the water had a t@xmath8 relaxation time of t@xmath50 = 2.6 s measured at @xmath2 = 300 mt . * hyperpolarization spectra of nd - liquid mixtures . * for the nd - oil mixtures , approximately 50 mg of nd was mixed with 60 @xmath4l of oil . the mixtures were polarized for 300ms , at @xmath2=458mt and for1s at other fields in the range @xmath2=300mt-500mt . solid lines are double lorentzian fits to @xmath51 . * enhancement as a function of oil concentration . * 75 mg of 125 nm nd was mixed incrementally with oil . polarization build up was measured out to 1 second and fitted with an exponential curve . all the curves reached saturation . * polarization build up . * 70 mg of nd was mixed with 40 @xmath4l of oil . with off - resonant microwaves , a signal decrease of 6% due to heating effects was seen after 1 second of polarization . data with on - resonant microwaves was corrected to account for this heating effect . the authors thank t. boele for useful discussions . for sem measurements the authors acknowledge the facilities and technical assistance of the australian centre for microscopy & microanalysis at the university of sydney . for raman measurements the authors acknowledge the staff and facilities at the vibrational spectroscopy core facility at the university of sydney . for esr measurements the authors acknowledge the staff and facilities at the nuclear magnetic resonance facility at the mark wainwright analytical centre at the university of new south wales . this work is supported by the australian research council centre of excellence scheme ( grant no . equs ce110001013 ) and arc dp1094439 . zhang , l. ; gu , f. ; chan , j. ; wang , a. ; langer , r. ; farokhzad , o. _ clinical pharmacology and therapeutics _ * 2008 * , _ 83 _ , 761769 mura , s. ; couvreur , p. _ advanced drug delivery reviews _ * 2012 * , _ 64 _ , 13941416 wang , m. ; thanou , m. _ pharmacological research _ * 2010 * , _ 62 _ , 9099 li , c. _ nature materials _ * 2014 * , _ 13 _ , 110115 hens , z. ; martins , j. c. _ chemistry of materials _ * 2013 * , _ 25 _ , 12111221 protesescu , l. et al . _ acs nano _ * 2014 * , _ 8 _ , 26392648 rossini , a. j. ; zagdoun , a. ; lelli , m. ; lesage , a. ; copret , c. ; emsley , l. _ accounts of chemical research _ * 2013 * , _ 46 _ , 19421951 grning , w. r. ; rossini , a. j. ; zagdoun , a. ; gajan , d. ; lesage , a. ; emsley , l. ; copret , c. _ physical chemistry chemical physics _ * 2013 * , _ 15 _ , 1327013274 rossini , a. j. ; zagdoun , a. ; lelli , m. ; gajan , d. ; rascn , f. ; rosay , m. ; maas , w. e. ; copret , c. ; lesage , a. ; emsley , l. _ chemical science _ * 2012 * , _ 3 _ , 108115 lelli , m. ; gajan , d. ; lesage , a. ; caporini , m. a. ; vitzthum , v. ; miville , p. ; hroguel , f. ; rascn , f. ; roussey , a. ; thieuleux , c. ; boualleg , m. ; veyre , l. ; bodenhausen , g. ; coperet , c. ; emsley , l. _ journal of the american chemical society _ * 2011 * , _ 133 _ , 21042107 lesage , a. ; lelli , m. ; gajan , d. ; caporini , m. a. ; vitzthum , v. ; miville , p. ; alauzun , j. ; roussey , a. ; thieuleux , c. ; mehdi , a. ; bodenhausen , g. ; coperet , c. ; emsley , l. _ journal of the american chemical society _ * 2010 * , _ 132 _ , 1545915461 piveteau , l. ; ong , t .- c . ; rossini , a. j. ; emsley , l. ; copret , c. ; kovalenko , m. v. _ journal of the american chemical society _ * 2015 * , _ 137 _ , 1396413971 gajan , d. et al . _ proceedings of the national academy of sciences _ * 2014 * , _ 111 _ , 1469314697 lingwood , m. d. ; siaw , t. a. ; sailasuta , n. ; abulseoud , o. a. ; chan , h. r. ; ross , b. d. ; bhattacharya , p. ; han , s. _ radiology _ * 2012 * , _ 265 _ , 418425 cassidy , m. ; ramanathan , c. ; cory , d. ; ager , j. ; marcus , c. m. _ physical review b _ * 2013 * , _ 87 _ , 161306 huang , h. ; pierstorff , e. ; osawa , e. ; ho , d. _ nano letters _ * 2007 * , _ 7 _ , 33053314 liu , k .- k . ; cheng , c .- l . ; chang , c .- c . ; chao , j .- _ nanotechnology _ * 2007 * , _ 18 _ , 325102 krger , a. ; liang , y. ; jarre , g. ; stegk , j. _ journal of materials chemistry _ * 2006 * , _ 16 _ , 23222328 zhang , x .- q . ; chen , m. ; lam , r. ; xu , x. ; osawa , e. ; ho , d. _ acs nano _ * 2009 * , _ 3 _ , 26092616 chow , e. k. ; zhang , x .- q . ; chen , m. ; lam , r. ; robinson , e. ; huang , h. ; schaffer , d. ; osawa , e. ; goga , a. ; ho , d. _ science translational medicine _ * 2011 * , _ 3 _ , 73ra21 chen , m. ; pierstorff , e. d. ; lam , r. ; li , s .- y . ; huang , h. ; osawa , e. ; ho , d. _ acs nano _ * 2009 * , _ 3 _ , 20162022 mochalin , v. n. ; pentecost , a. ; li , x .- m . ; neitzel , i. ; nelson , m. ; wei , c. ; he , t. ; guo , f. ; gogotsi , y. _ molecular pharmaceutics _ * 2013 * , _ 10 _ , 37283735 giammarco , j. ; mochalin , v. n. ; haeckel , j. ; gogotsi , y. _ journal of colloid and interface science _ * 2016 * , _ 468 _ , 253261 say , j. m. ; van vreden , c. ; reilly , d. j. ; brown , l. j. ; rabeau , j. r. ; king , n. j. _ biophysical reviews _ * 2011 * , _ 3 _ , 171184 mcguinness , l. ; yan , y. ; stacey , a. ; simpson , d. ; hall , l. ; maclaurin , d. ; prawer , s. ; mulvaney , p. ; wrachtrup , j. ; caruso , f. ; scholten , r. e. ; hollenberg , l. c. l. _ nature nanotechnology _ * 2011 * , _ 6 _ , 358363 maze , j. ; stanwix , p. ; hodges , j. ; hong , s. ; taylor , j. ; cappellaro , p. ; jiang , l. ; dutt , m. g. ; togan , e. ; zibrov , a. ; yacoby , a. ; walsworth , r. l. ; lukin , m. d. _ nature _ * 2008 * , _ 455 _ , 644647 balasubramanian , g. ; chan , i. ; kolesov , r. ; al - hmoud , m. ; tisler , j. ; shin , c. ; kim , c. ; wojcik , a. ; hemmer , p. r. ; krueger , a. ; hanke , t. ; leitenstorfer , a. ; bratschitsch , r. ; jelezko , f. ; wrachtrup , j. _ nature _ * 2008 * , _ 455 _ , 648651 rej , e. ; gaebel , t. ; boele , t. ; waddington , d. e. j. ; reilly , d. j. _ nature communications _ * 2015 * , _ 6 _ , 8459 casabianca , l. b. ; shames , a. i. ; panich , a. m. ; shenderova , o. ; frydman , l. _ the journal of physical chemistry c _ * 2011 * , _ 115 _ , 1904119048 dutta , p. ; martinez , g. v. ; gillies , r. j. _ the journal of physical chemistry letters _ * 2014 * , _ 5 _ , 597600 gaebel , t. ; bradac , c. ; chen , j. ; say , j. ; brown , l. ; hemmer , p. ; rabeau , j. _ diamond and related materials _ * 2012 * , _ 21 _ , 2832 furman , g. b. ; kunoff , e. m. ; goren , s. d. ; pasquier , v. ; tinet , d. _ phys . rev . b _ * 1995 * , _ 52 _ , 10182 manus , l. m. ; mastarone , d. j. ; waters , e. a. ; zhang , x .- q . ; schultz - sikma , e. a. ; macrenaris , k. w. ; ho , d. ; meade , t. j. _ nano letters _ * 2009 * , _ 10 _ , 484489 krebs , j. j. _ the journal of chemical physics _ * 1961 * , _ 34 _ , 326329 krebs , j. j. ; thompson , j. k. _ the journal of chemical physics _ * 1962 * , _ 36 _ , 25092514 uebersfeld , j. ; motchane , j. ; erb , e. _ j. phys . radium _ * 1958 * , _ 19 _ , 843844 maly , t. ; debelouchina , g. t. ; bajaj , v. s. ; hu , k .- n . ; joo , c .- g . ; mak jurkauskas , m. l. ; sirigiri , j. r. ; van der wel , p. c. a. ; herzfeld , j. ; temkin , r. j. ; griffin , r. g. _ the journal of chemical physics _ * 2008 * , _ 128 _ , 052211 abrams , d. ; trusheim , m. e. ; englund , d. r. ; shattuck , m. d. ; meriles , c. a. _ nano letters _ * 2014 * , _ 14 _ , 24712478 stoll , s. ; schweiger , a. _ journal of magnetic resonance _ * 2006 * , _ 178 _ , 4255

the x - ray imaging spectrometer ( xis ) on board the suzaku satellite is an x - ray ccd camera system that has superior performance such as a low background , high quantum efficiency , and good energy resolution in the 0.212 kev band . because of the radiation damage in orbit , however , the charge transfer inefficiency ( cti ) has increased , and hence the energy scale and resolution of the xis has been degraded since the launch of july 2005 . the ccd has a charge injection structure , and the cti of each column and the pulse - height dependence of the cti are precisely measured by a checker flag charge injection ( cfci ) technique . we have implemented the time - dependent energy scale and resolution to the suzaku calibration database .

i

0809.3665

the x - ray imaging spectrometer ( xis ) on board the suzaku satellite is an x - ray ccd camera system that has superior performance such as a low background , high quantum efficiency , and good energy resolution in the 0.212 kev band . because of the radiation damage in orbit , however , the charge transfer inefficiency ( cti ) has increased , and hence the energy scale and resolution of the xis has been degraded since the launch of july 2005 . the ccd has a charge injection structure , and the cti of each column and the pulse - height dependence of the cti are precisely measured by a checker flag charge injection ( cfci ) technique . our precise cti correction improved the energy resolution from 230 ev to 190 ev at 5.9 kev in december 2006 . this paper reports the cti measurements with the cfci experiments in orbit . using the cfci results , we have implemented the time - dependent energy scale and resolution to the suzaku calibration database .

after the first successful space flight use of the x - ray charge coupled device ( ccd ) of the sis ( @xcite ) on board asca , the ccd has been playing a major role in imaging spectroscopy in the field of x - ray astronomy . however , the charge transfer inefficiency ( cti ) of x - ray ccds increases in orbit due to the radiation damage ; the cti is defined as the fraction of electrons that are not successfully moved from one ccd pixel to the next during the readout . since the amount of charge loss depends on the number of the transfers , the energy scale of x - ray ccds depends on the location of an x - ray event . furthermore , there is a fluctuation in the amount of the lost charge . therefore , without any correction , the energy resolution of x - ray ccds in orbit gradually degrades . in the case of the x - ray imaging spectrometer ( xis ) @xcite on board the suzaku satellite @xcite launched on july 10 , 2005 , the energy resolution in full width at half maximum ( fwhm ) at 5.9 kev was @xmath0140 ev in august 2005 , but had degraded to @xmath0230 ev in december 2006 . the increase of the cti is due to an increase in the number of charge traps at defects in the lattice structure of silicon made by the radiation . since the trap distribution is not uniform , it would be best if we could measure the cti of each pixel as chandra acis @xcite . in the case of the xis , however , it is impossible to measure the cti values of all the pixels , mainly because the onboard calibration sources do not cover the entire field of view of the xis . therefore , we use the cti of each column to correct the positional dependence of the energy scale . the xis is equipped with a charge injection structure @xcite which can inject an arbitrary amount of charge in arbitrary positions . using this capability , we can precisely measure the cti of each column @xcite . by applying the column - to - column cti correction , the positional dependence of the cti corrected energy scale is greatly reduced , and the over - all energy resolution is also improved @xcite . in @xcite , the results of the cti correction was mainly based on the ground - based charge injection experiments . in - orbit measurements were limited within one year after the launch . this paper reports more comprehensive and extended in - orbit experiments up to two years after the launch . the results are based on the data with the normal full window mode @xcite without a spaced - row charge injection @xcite , and have been implemented to the suzaku calibration database and applied to all the data obtained with the same mode . all the errors are at the 1@xmath1 confidence level throughout this paper unless mentioned .

, we can construct a new zeta function of an element of the braid group . in this paper , we show that the alexander polynomial which is the most classical polynomial invariant of knots can be expressed in terms of this braid zeta function . we show that this function can be expressed by some braid zeta function for the case of special braids whose closures are isotopic to certain torus knots .

i

1611.08370

there is a well - known zeta function of the @xmath0-dynamical system generated by an element of the symmetric group . by considering this zeta function as a model , we can construct a new zeta function of an element of the braid group . in this paper , we show that the alexander polynomial which is the most classical polynomial invariant of knots can be expressed in terms of this braid zeta function . furthermore we define the function @xmath1 associated with some braids . we show that this function can be expressed by some braid zeta function for the case of special braids whose closures are isotopic to certain torus knots .

let @xmath2 be the symmetric group acting on the finite set @xmath3 . then , for any permutation @xmath4 , the zeta function of @xmath5 is defined as @xmath6 where @xmath7 . in ( * proposition.1 ) , the following interesting proposition is shown by kim , koyama and kurokawa . for any permutation @xmath4 , the zeta function @xmath8 has the following properties . + @xmath9 let @xmath10 be the set of primitive cycles of @xmath5 , and @xmath11 be the length of cycle @xmath12 . then , @xmath8 has the euler product : @xmath13 @xmath14 let @xmath15 be the permutation representation . then , @xmath8 has the following determinant expression : @xmath16 @xmath17 @xmath8 satisfies the following functional equation : @xmath18 where @xmath19 is the signature of the permutation . + @xmath20 @xmath21 satisfies an analogue of the riemann hypothesis : all poles of @xmath21 satisfy @xmath22 we call a permutation @xmath4 _ simple cycle _ if @xmath5 is a primitive cycle in itself . then , for a simple cycle @xmath4 , the zeta function @xmath8 has a simple pole at @xmath23 and we obtain @xmath24 remark that the residue of @xmath8 at @xmath23 gives us only the information of the length of @xmath5 . our first goal is to generalize such properties to the case of the braid group . consequently , we generalize @xmath8 to the zeta function of a braid by using the burau representation of the braid group . as an application the alexander polynomial @xmath25 which is the most classical invariant of knots can be expressed by the residue of this new zeta function . this is analogous to the fact that the residue of the dedekind zeta function at @xmath23 has invariants of an algebraic field such as the class number , discriminant and regulator . noting that the burau representation is @xmath26-deformation of the permutation representation , we obtain a fact that @xmath27 . we first recall the notations and settings on the braid group briefly . we refer to @xcite , @xcite and @xcite for more details . let us denote the braid group on @xmath28 strands by @xmath29 . it is known that @xmath29 has the following presentation : @xmath30 the generator @xmath31 can be identified with the crossing between the @xmath32-th and @xmath33-st strands as figure @xmath34 ( see ( * ? ? ? * theorem1.8 ) ) , c and the multiplication of generators implies that the braid obtained by attaching the generators from the top to the bottom . the @xmath35 of a braid is the link obtained from the braid by connecting upper ends and lower ends as figure @xmath36 . the closure of @xmath5 is denoted by @xmath37 . let @xmath38 be the @xmath39 , which is defined by @xmath40 here @xmath41 $ ] . we also define the braid zeta function of @xmath42 by the determinant expression : @xmath43 we now can state the main result of this paper . @xmath9 for @xmath42 , @xmath44 satisfies the functional equation : @xmath45 here @xmath46 . + @xmath14 if @xmath37 is a knot , the residue of @xmath44 at @xmath23 is given as follows : @xmath47_q}\delta_{\hat{\sigma}}(q)^{-1}.\end{aligned}\ ] ] here @xmath48 is the alexander polynomial of a knot @xmath37 , and @xmath49_q$ ] is the @xmath26-integer defined by @xmath50_q : = \frac{1-q^n}{1-q}.\end{aligned}\ ] ] @xmath17 assume that @xmath26 is a point of the unit circle on the complex plane , in other words , @xmath26 is expressed by @xmath51 , and that the argument of @xmath26 satisfies @xmath52 . then for any @xmath42 , the braid zeta function of @xmath5 satisfies an analogue of riemann hypothesis : all poles of @xmath53 satisfy @xmath22 remark that @xmath54 does not have the euler product expression , however , @xmath9 and @xmath17 are analogous to theorem @xmath55 . furthermore , @xmath14 is the characteristic property of the braid zeta function . we prove theorem @xmath56 in the next section . as corollaries of theorem @xmath56 , we obtain the generating function expression of @xmath57 for @xmath42 . moreover , in the last section , for two braids @xmath58 we introduce the function @xmath59 which is a @xmath26-analogue of @xmath60 for two permutations @xmath61 ( see @xcite ) . then we prove some formulae of the residue of the function @xmath1 at @xmath23 for the special braid whose closure is isotopic to the torus knot .

this article deals with input - to - state stability ( iss ) of continuous - time switched nonlinear systems . given a family of systems with exogenous inputs such that not all systems in the family are iss , we characterize a new and general class of switching signals under which the resulting switched system is iss .

i

1502.02440

this article deals with input - to - state stability ( iss ) of continuous - time switched nonlinear systems . given a family of systems with exogenous inputs such that not all systems in the family are iss , we characterize a new and general class of switching signals under which the resulting switched system is iss . our stabilizing switching signals allow the number of switches to grow faster than an affine function of the length of a time interval , unlike in the case of average dwell time switching . we also recast a subclass of average dwell time switching signals in our setting and establish analogs of two representative prior results .

a _ switched system _ comprises of two components a family of systems and a switching signal . the _ switching signal _ selects an active subsystem at every instant of time , i.e. , the system from the family that is currently being followed @xcite . stability of switched systems is broadly classified into two categories _ stability under arbitrary switching _ * chapter 2 ) and _ stability under constrained switching _ * chapter 3 ) . in the former category , conditions on the family of systems are identified such that the resulting switched system is stable under all admissible switching signals ; in the latter category , given a family of systems , conditions on the switching signals are identified such that the resulting switched system is stable . in this article our focus is on stability of switched systems with exogenous inputs under constrained switching . prior study in the direction of stability under constrained switching primarily utilizes the concept of _ slow switching _ vis - a - vis _ ( average ) dwell time switching_. exponential stability of a switched linear system under _ dwell time switching _ was studied in @xcite . in @xcite the authors showed that a switched nonlinear system is iss under dwell time switching if all subsystems are iss . a class of state - dependent switching signals obeying dwell time property under which a switched nonlinear system is integral input - to - state stable ( iiss ) was proposed in @xcite . the dwell time requirement for stability was relaxed to _ average dwell time switching _ to switched linear systems with inputs and switched nonlinear systems without inputs in @xcite . iss of switched nonlinear systems under average dwell time was studied in @xcite . it was shown that if the individual subsystems are iss and their iss - lyapunov functions satisfy suitable conditions , then the switched system has the iss , exponentially - weighted iss , and exponentially - weighted iiss properties under switching signals obeying sufficiently large average dwell time . given a family of systems such that not all systems in the family are iss , it was shown in the recent work @xcite that it is possible to construct a class of hybrid lyapunov functions to guarantee iss of the switched system provided that the switching signal neither switches too frequently nor activates the non - iss subsystems for too long . in @xcite input / output - to - state stability ( ioss ) of switched nonlinear systems with families in which not all subsystems are ioss , was studied . it was shown that the switched system is ioss under a class of switching signals obeying _ average dwell time _ property and constrained point - wise activation of unstable systems . given a family of systems , possibly containing non - iss dynamics , in this article we study iss of switched systems under switching signals that transcend beyond the average dwell time regime in the sense that the number of switches on every interval of time can grow faster than an affine function of the length of the interval . our characterization of stabilizing switching signals involve pointwise constraints on the duration of activation of the iss and non - iss systems , and the number of occurrences of the admissible switches , certain pointwise properties of the quantities defining the above constraints , and a summability condition . in particular , our contributions are : * we allow non - iss systems in the family and identify a class of switching signals under which the resulting switched system is iss . * our class of stabilizing switching signals encompasses the average dwell time regime in the sense that on every interval of time the number of switches is allowed to grow faster than an affine function of the length of the interval . earlier in @xcite we proposed a class of switching signals beyond the average dwell time regime for global asymptotic stability of continuous - time switched nonlinear systems . * although this is not the first instance when non - iss subsystems are considered ( see e.g. , @xcite ) , to the best of our knowledge , this is the first instance when non - iss subsystems are considered and the proposed class of stabilizing switching signals goes beyond the average dwell time condition . * we recast a subclass of average dwell time switching signals in our setting and establish analogs of an iss version of ( * ? ? ? * theorem 2 ) , and ( * ? ? ? * theorem 3.1 ) as two corollaries of our main result . the remainder of this article is organized as follows : in [ s : prelims ] we formulate the problem under consideration and catalog certain properties of the family of systems and the switching signal . our main results appear in [ s : mainres ] , and we provide a numerical example illustrating our main result in [ s : ex ] . in [ s : discussn ] we recast prior results in our setting . the proofs of our main results are presented in a consolidated manner in [ s : proofs ] . * notations * : let @xmath0 denote the set of real numbers , @xmath1 denote the euclidean norm , and for any interval @xmath2 we denote by @xmath3 the essential supremum norm of a map from @xmath4 into some euclidean space . for measurable sets @xmath5 we let @xmath6 denote the lebesgue measure of @xmath7 .

this article presents , in an illustrative fashion , a first step towards an extension of the spectral theory of constant length substitutions . our starting point is the general observation that the symbolic picture ( as defined by the substitution rule ) and its geometric counterpart with natural prototile sizes ( as defined by the induced inflation rule ) may differ considerably . on the geometric side , an aperiodic inflation system possesses a set of exact renormalisation relations for its pair correlation coefficients . here , we derive these relations for some paradigmatic examples and infer various spectral consequences . in particular , we consider the fibonacci chain , revisit the thue morse and the rudin shapiro sytem , and finally analyse a twisted extension of the silver mean chain with mixed singular spectrum .

i

1511.00885

this article presents , in an illustrative fashion , a first step towards an extension of the spectral theory of constant length substitutions . our starting point is the general observation that the symbolic picture ( as defined by the substitution rule ) and its geometric counterpart with natural prototile sizes ( as defined by the induced inflation rule ) may differ considerably . on the geometric side , an aperiodic inflation system possesses a set of exact renormalisation relations for its pair correlation coefficients . here , we derive these relations for some paradigmatic examples and infer various spectral consequences . in particular , we consider the fibonacci chain , revisit the thue morse and the rudin shapiro sytem , and finally analyse a twisted extension of the silver mean chain with mixed singular spectrum .

the spectral theory of primitive substitution rules and the symbolic dynamical systems defiend by them has a long history and is well studied , compare @xcite and references therein . nevertheless , as soon as one leaves the realm of constant length substitutions , many open questions challenge our present level of understanding . this is partly due to the fact that the substitution system picture and the inflation tiling picture , where one works with natural prototile lengths , may differ considerably ; compare @xcite . the majority of the dynamical systems literature on this subject deals with the symbolic case , where work by dekking @xcite and others , see @xcite and references therein , has led to a fairly complete understanding of the constant length case , which was recently extended in a systematic fashion in @xcite , including higher dimensions . in all these cases , the connection between the diffraction spectrum and the dynamical spectrum is rather well understood . the two notions are equivalent in the pure point case @xcite , and recent progress for symbolic systems also establishes a complete equivalence via the inclusion of certain factors @xcite . therefore , at least algorithmically , any constant length substitution can be analysed completely as far as its spectrum is concerned ; see @xcite for recent developments . the situation is less favourable outside this class . even if one stays within the realm of primitive inflation rules , the determination of the dynamical spectrum is generally difficult . here , the geometric counterpart studied in tiling theory has certain undeniable advantages . first , since such tilings are still of finite local complexity , the connection between the dynamical spectrum and the diffraction spectrum can still be used , if certain factors are included in the discussion @xcite . for this reason , we employ an approach via the diffraction spectrum of the tiling spaces . second , the geometric setting leads to the the existence of a set of _ exact _ renormalisation relations for the pair correlation coefficients of the system . we use the term ` exact ' to distinguish our approach from the widely used renormalisation schemes that are approximate or asymptotic in nature . this approach has not attracted much attention so far . in fact , we are not aware of _ any _ reference to this approach beyond the constant length case , though the principal idea has certainly been around for a while , and has been used , often in an approximate way , for several physical quantities such as electronic or transport properties ; see @xcite for an example and further references . in this paper , we we want to show the power of exact renormalisation relations for spectral properties , in the form of a first step via some illustrative examples . a more general approach will be presented in a forthcoming publication . it will be instrumental for our analysis that we formulate various aspects on the symbolic level , while the core of our analysis rests on the natural geometric realisation . to make the distinction as transparent as possible , we will speak of _ substitution rules _ on the symbolic side , but of _ inflation rule _ on its geometric counterpart , thus following the notation and terminology of the recent monograph @xcite . also , various results are briefly recalled from there . rather than repeating the proofs , we provide precise references instead . below , we work along a number of examples , all of them with pisot vijayaraghavan ( pv ) numbers as inflation multipliers . since we do _ not _ demand the characteristic polynomial to be irreducible over @xmath0 , there is still enough freedom to encounter systems with mixed spectrum . in fact , all point sets that we encounter along the way will be linearly repetitive meyer sets . an interesting linearly repetitive inflation point set with non - pv multiplier ( hence not a meyer set ) will be discussed in detail in @xcite . the paper is structured as follows . after recalling some facts about translation bounded measures on @xmath1 and their fourier transforms in section [ sec : prelim ] , we begin with a detailed analysis of the fibonacci substitution and inflation in section [ sec : fibo ] . this is both a paradigm of the theory and an instructive example along which we can develop our ideas as well as further notions , wherefore this is also the longest section . here , we introduce a set of exact renormalisation equations for the general pair correlation coefficients and compare the findings with what is known from the model set description . then , we use the new approach to derive an alternative proof of the pure point nature of the diffraction spectrum , and hence also of the dynamical spectrum via the known equivalence result for this case @xcite . after that , in section [ sec : tm - rs ] , we briefly revisit the classic thue morse and rudin shapiro sequences from the renormalisation point of view . the point of this exercise is to show that our approach , in the constant length setting where the symbolic and the geometric pictures coincide , is essentially equivalent to the traditional approach as described in @xcite and recently extended in @xcite . still , there are several aspects of a more algebraic nature that seem to deserve further attention . finally , by imposing an involutory _ symmetry , we construct an extension of the silver mean chain with mixed spectrum in section [ sec : sm - mixed ] . the main point here is that such extensions are not restricted to the constant length case ( where they are known from examples such as those of the previous section or many others as in @xcite ) . in fact , as our example indicates , there is an abundance of interesting and completely natural primitive inflation rules that produce repetitive meyer sets with mixed spectrum . in our opinion , this has hitherto been more or less neglected . for the explicit analysis , the exact renormalisation scheme is used to determine the spectral type by a somewhat subtle application of the riemann lebesgue lemma , which leads to a singular spectrum of mixed type . overall , we believe that the geometric picture with its exact renormalisation relations for the pair correlation coefficients provides a powerful tool also for the general case of primitive inflation rules . this will be further developed in a forthcoming publication .

this is the second of two papers describing the second data release ( dr2 ) of the australia telescope large area survey ( atlas ) at 1.4 ghz . in paper i we detailed our data reduction and analysis procedures , and presented catalogues of components ( discrete regions of radio emission ) and sources ( groups of physically associated radio components ) . in this paper we present our key observational results .

i

1403.5308

this is the second of two papers describing the second data release ( dr2 ) of the australia telescope large area survey ( atlas ) at 1.4 ghz . in paper i we detailed our data reduction and analysis procedures , and presented catalogues of components ( discrete regions of radio emission ) and sources ( groups of physically associated radio components ) . in this paper we present our key observational results . we find that the 1.4 ghz euclidean normalised differential number counts for atlas components exhibit monotonic declines in both total intensity and linear polarization from millijansky levels down to the survey limit of @xmath0 @xmath1jy . we discuss the parameter space in which component counts may suitably proxy source counts . we do not detect any components or sources with fractional polarization levels greater than 24% . the atlas data are consistent with a lognormal distribution of fractional polarization with median level 4% that is independent of flux density down to total intensity @xmath2 mjy and perhaps even 1 mjy . each of these findings are in contrast to previous studies ; we attribute these new results to improved data analysis procedures . we find that polarized emission from 1.4 ghz millijansky sources originates from the jets or lobes of extended sources that are powered by an active galactic nucleus , consistent with previous findings in the literature . we provide estimates for the sky density of linearly polarized components and sources in 1.4 ghz surveys with @xmath3 resolution . [ firstpage ] polarization radio continuum : galaxies surveys .

a number of studies have reported an anti - correlation between fractional linear polarization and total intensity flux density for extragalactic 1.4 ghz sources ; faint sources were found to be more highly polarized . as a result , the euclidean - normalised differential number - counts of polarized sources have been observed to flatten at linearly polarized flux densities @xmath4 @xmath5 1 mjy to levels greater than those expected from convolving the known total intensity source counts with plausible distributions for fractional polarization @xcite . the flattening suggests that faint polarized sources may exhibit more highly ordered magnetic fields than bright sources , or may instead suggest the emergence of an unexpected faint population . the anti - correlation trend for fractional linear polarization is not observed at higher frequencies ( @xmath6 ghz ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . to investigate possible explanations for the fractional polarization trend seen in previous studies , we have produced the second data release of the australia telescope large area survey ( atlas dr2 ) as described in paper i @xcite of this two paper series . atlas dr2 comprises reprocessed and new 1.4 ghz observations with the australia telescope compact array ( atca ) about the _ chandra _ deep field - south ( cdf - s ; galactic coordinates @xmath7 , @xmath8 ; * ? ? ? * ) and european large area _ infrared space observatory _ survey - south 1 ( elais - s1 ; @xmath9 , @xmath10 ; * ? ? ? * ) regions in total intensity , linear polarization , and circular polarization . the mosaicked multi - pointing survey areas for atlas dr2 are 3.626 deg@xmath11 and 2.766 deg@xmath11 for the cdf - s and elais - s1 regions , respectively , imaged at approximately @xmath12 resolution . typical source detection thresholds are 200 @xmath1jy in total intensity and polarization . in paper i we presented our data reduction and analysis prescriptions for atlas dr2 . we presented a catalogue of components ( discrete regions of radio emission ) comprising 2416 detections in total intensity and 172 independent detections in linear polarization . no components were detected in circular polarization . we presented a catalogue of 2221 sources ( groups of physically associated radio components ; grouping scheme based on total intensity properties alone , as described below ) , of which 130 were found to exhibit linearly polarized emission . we described procedures to account for instrumental and observational effects , including spatial variations in each of image sensitivity , bandwidth smearing with a non - circular beam , and instrumental polarization leakage , clean bias , the division between peak and integrated flux densities for unresolved and resolved components , and noise biases in both total intensity and linear polarization . analytic correction schemes were developed to account for incompleteness in differential component number counts due to resolution and eddington biases . we cross - identified and classified sources according to two schemes , summarized as follows . in the first scheme , described in 6.1 of paper i , we grouped total intensity radio components into sources , associated these with infrared sources from the _ spitzer _ wide - area infrared extragalactic survey ( swire ; * ? ? ? * ) and optical sources from @xcite , then classified them according to whether their energetics were likely to be driven by an active galactic nucleus ( agn ) , star formation ( sf ) within a star - forming galaxy ( sfg ) , or a radio star . due to the limited angular resolution of the atlas data , in paper i we adopted the term _ lobe _ to describe both jets and lobes in sources with radio double or triple morphologies . the term _ core _ was similarly defined in a generic manner to indicate the central component in a radio triple source . under this terminology , a core does not indicate a compact , flat - spectrum region of emission ; restarted agn jets or lobes may contribute or even dominate the emission observed in the regions we have designated as cores . agns were identified using four selection criteria : radio morphologies , 24 @xmath1 m to 1.4 ghz flux density ratios , mid - infrared colours , and optical spectral characteristics . sfgs and stars were identified solely by their optical spectra . of the 2221 atlas dr2 sources , 1169 were classified as agns , 126 as sfgs , and 4 as radio stars . we note that our classification system was biased in favour of agns . as a result , the atlas dr2 data are in general unsuited for statistical comparisons between star formation and agn activity . in the second scheme , described in 6.2 of paper i , we associated linearly polarized components , or polarization upper limits , with total intensity counterparts . in most cases it was possible to match a single linearly polarized component with a single total intensity component , forming a one - to - one match . in other cases this was not possible , due to ambiguities posed by the blending of adjacent components ; for example , a polarized component situated mid - way between two closely - separated total intensity components . in these cases , we formed group associations to avoid biasing measurements of fractional polarization . we classified the polarization total intensity associations according to the following scheme , which we designed to account for differing ( de-)polarized morphologies ( see paper i for graphical examples ) : * _ type 0 _ a one - to - one or group association identified as a lobe of a double or triple radio source . both lobes of the source are clearly polarized , having linearly polarized flux densities within a factor of 3 . ( the ratio between lobe total intensity flux densities was found to be within a factor of 3 for all double or triple atlas dr2 sources . ) * _ types 1/2 _ a one - to - one or group association identified as a lobe of a double or triple radio source that does not meet the criteria for type 0 . a lobe classified as type 1 indicates that the ratio of polarized flux densities between lobes is greater than 3 . a lobe classified as type 2 indicates that the opposing lobe is undetected in polarization and that the polarization ratio may be less than 3 , in which case it is possible that more sensitive observations may lead to re - classification as type 0 . sources with lobes classified as type 1 exhibit asymmetric depolarization in a manner qualitatively consistent with the laing - garrington effect @xcite , where one lobe appears more fractionally polarized than the opposite lobe . * _ type 3 _ a group association representing a source , involving a linearly polarized component situated midway between two total intensity components . it is not clear whether such associations represent two polarized lobes , a polarized lobe adjacent to a depolarized lobe , or a polarized core . * _ type 4 _ an unclassified one - to - one or group association representing a source . * _ type 5 _ a one - to - one association clearly identified as the core of a triple radio source ( where outer lobes are clearly distinct from the core ) . * _ type 6 _ a source comprising two type 0 associations , or a group association representing a non - depolarized double or triple radio source where blended total intensity and linear polarization components have prevented clear subdivision into two type 0 associations . * _ type 7 _ a source comprising one or two type 1 associations . * _ type 8 _ a source comprising one type 2 association . * _ type 9 _ an unpolarized component or source . in this work ( paper ii ) we present the key observational results from atlas dr2 , with particular focus on the nature of faint polarized sources . this paper is organised as follows . in [ ch5:secres ] we present the atlas dr2 source diagnostics resulting from infrared and optical cross - identifications and classifications , diagnostics resulting from polarization total intensity cross - identifications and classifications , differential component number - counts , and our model for the distribution of fractional polarization . in [ ch5:secdisc ] we compare the atlas dr2 differential counts in both total intensity and linear polarization to those from other 1.4 ghz surveys , and discuss asymmetric depolarization of classical double radio sources . we present our conclusions in [ ch5:secconc ] . this paper follows the notation introduced in paper i. we typically denote flux density by @xmath13 , but split into @xmath14 for total intensity and @xmath4 for linearly polarized flux density when needed for clarity .

we discuss the parameter space in which component counts may suitably proxy source counts . each of these findings are in contrast to previous studies ; we attribute these new results to improved data analysis procedures . [ firstpage ] polarization radio continuum : galaxies surveys .

r

1403.5308

this is the second of two papers describing the second data release ( dr2 ) of the australia telescope large area survey ( atlas ) at 1.4 ghz . in paper i we detailed our data reduction and analysis procedures , and presented catalogues of components ( discrete regions of radio emission ) and sources ( groups of physically associated radio components ) . in this paper we present our key observational results . we find that the 1.4 ghz euclidean normalised differential number counts for atlas components exhibit monotonic declines in both total intensity and linear polarization from millijansky levels down to the survey limit of @xmath0 @xmath1jy . we discuss the parameter space in which component counts may suitably proxy source counts . we do not detect any components or sources with fractional polarization levels greater than 24% . the atlas data are consistent with a lognormal distribution of fractional polarization with median level 4% that is independent of flux density down to total intensity @xmath2 mjy and perhaps even 1 mjy . each of these findings are in contrast to previous studies ; we attribute these new results to improved data analysis procedures . we find that polarized emission from 1.4 ghz millijansky sources originates from the jets or lobes of extended sources that are powered by an active galactic nucleus , consistent with previous findings in the literature . we provide estimates for the sky density of linearly polarized components and sources in 1.4 ghz surveys with @xmath3 resolution . [ firstpage ] polarization radio continuum : galaxies surveys .

in the following sections we present diagnostics of atlas dr2 sources resulting from the infrared and optical cross - identification and classification schemes described in 6.1 of paper i ( summarised in [ sec:1 ] of this work ) . we focus on three parameter spaces formed by comparing flux densities between different wavelength bands : radio to mid - infrared , mid - infrared colours , and radio to far - infrared . in fig . [ ch5:fig : rnir ] we compare the total intensity 1.4 ghz radio to 3.6 @xmath1 m mid - infrared flux densities for all 2221 atlas dr2 sources , taking into account infrared upper bounds for the 298 radio sources without detected infrared counterparts . the bottom - right panel of fig . [ ch5:fig : rnir ] indicates that the atlas sources classified as stars or sfgs typically exhibit radio flux densities @xmath5 1 mjy . the paucity of atlas sources with @xmath15 @xmath5 0.1 mjy and star or sfg classifications likely represents a selection bias , in which only those sources with relatively bright optical counterparts could be classified spectroscopically . the top - left panel highlights all 130 polarized atlas sources , 12 of which are represented by upper bounds . the paucity of polarized sources with @xmath16 @xmath5 1 mjy is due to the limited sensitivity of our linear polarization data ; fractional polarization trends will be presented in [ ch5:secresidentm ] . in fig . [ ch5:fig : nircc ] we present mid - infrared colour - colour diagrams in which the irac flux density ratios @xmath17 and @xmath18 have been compared for atlas dr2 sources . of the 2221 atlas sources , 988 were detected in all four irac bands , while 935 were detected in only 2 or 3 bands ; the remaining 298 sources were not detected in any band , and have not been shown in fig . [ ch5:fig : nircc ] . regarding the 130 polarized atlas sources , 55 were detected in all four irac bands , 63 were detected in only 2 or 3 bands , and 12 were not detected in any irac band ; thus 118 polarized sources are indicated in fig . [ ch5:fig : nircc ] . the dotted lines in each panel of fig . [ ch5:fig : nircc ] represent the divisions identified through simulations by @xcite . by considering the effects of redshift evolution on the observed mid - infrared colours of three general source classes with spectral characteristics dominated by old - population ( 10 gyr ) starlight , polycyclic aromatic hydrocarbon ( pah ) emission , or a power - law continuum , @xcite identified four regions that could be used to preferentially select different source classes at different redshifts within the @xmath19 range simulated . region 1 was found to preferentially select sources with spectra dominated by continuum emission , likely produced by dust tori associated with agns @xcite , over the full redshift range . region 2 was found to preferentially select pah - dominated sources , indicative of intense star formation , over the full redshift range . region 3 was found to preferentially select sources with spectra dominated by direct stellar light , but only for sources with @xmath20 @xmath5 0.4 . for increasing redshifts , region 3 was found to comprise a mixture of stellar- and pah - dominated sources as the latter migrated from region 2 . however , beyond @xmath20 @xmath21 1.6 , region 3 was found to be largely void of sources following the migrations of both stellar- and pah - dominated sources towards region 4 . region 4 was found to be largely void of sources for @xmath20 @xmath5 0.4 . for increasing redshifts , pah - dominated sources were found to migrate from region 2 into region 4 . for @xmath20 @xmath21 0.9 , stellar - dominated sources from region 3 were also found to migrate into region 4 . @xcite found that at all redshifts , sources dominated by pah emission were located slightly within the boundaries of region 1 . in order to classify as agns only those sources most likely to be such in fig . [ ch5:fig : nircc ] , we constructed the restricted locus indicated by the dashed lines ; we label this region 1r . in paper i we defined this locus ( following * ? ? ? * ) as the union of @xmath22>0 $ ] , @xmath23>0 $ ] , and @xmath22 < 11\log_{{\scriptscriptstyle}10}[s_{5.8\,\mu{\textrm}{\scriptsize m}}/s_{3.6\,\mu{\textrm}{\scriptsize m}}]/9 + 0.3 $ ] . continuum - dominated sources are expected to exhibit power - law spectra , given by the dot - dashed locus in each panel . as noted by @xcite , the spectra of continuum - dominated sources are only expected to exhibit blue irac colours for largely unobscured agns , in cases for which their rest - frame optical wavelengths are redshifted into the mid - infrared band for sources at @xmath24 . thus the atlas sources with blue irac colours in fig . [ ch5:fig : nircc ] are unlikely to be represented by continuum - dominated sources as defined by @xcite . however , this does not imply that a source observed with blue irac colours at @xmath25 can not be an agn , because sources with mid - infrared spectra dominated by old stellar light may yet exhibit stronger signs of agn activity at other wavelengths . the bottom - left panel of fig . [ ch5:fig : nircc ] indicates that atlas sources classified as agns are predominantly located in regions 1r and 3 . the sources classified as agns in region 2 perhaps suggest combinations of star formation and agn activity , or perhaps misclassifications due to the largely statistical nature of our classification system . the upper bounds classified as agns in the top - right panel are consistent with the observed distribution of agns presented in the bottom - left panel . these upper bounds suggest that additional agns are situated in region 4 , though likely in proportion with the additional agns remaining undetected in regions 1 and 3 . the bottom - right panel indicates that atlas sources classified as sfgs are predominantly located in region 2 , as well as between the boundaries of regions 1 and 1r , as expected . a small number of atlas sources classified as sfgs are located in regions 1r and 3 , consistent with the migratory paths of pah - dominated sources . the upper bounds classified as sfgs in the top - right panel are consistent with the majority of sfgs being located in region 2 . all 4 atlas sources classified as stars are located in region 3 . the polarized atlas sources detected in all four irac bands follow the distribution of agns , situated predominantly in regions 1 and 3 in almost equal proportions . the upper bounds for polarized sources presented in the top - right panel are consistent with this finding . the lack of polarized sources in region 2 suggests that the polarized atlas sources observed in region 3 are unlikely to be sfgs with rest - frame colours located in region 2 ( i.e. if sfgs are migrating from region 2 to region 3 with redshift , then a trail of sources would be expected ) . instead , we find two concentrations of polarized atlas sources , highly coincident with the regions of parameter space identified by @xcite in which starlight- and continuum - dominated sources were preferentially located . thus we find that the radio emission from polarized atlas sources is most likely powered by agns , where the active nuclei are embedded within host galaxies with mid - infrared spectra dominated by old - population stellar light ( blue irac colours ) or continuum likely produced by dusty tori ( red irac colours ) . this finding is in general agreement with the results from the elais - north 1 ( elais - n1 ) region presented by both @xcite and @xcite , but with the following two notable exceptions . first , both these works identified radio sources ( both polarized and unpolarized ) that were concentrated in region 3 about @xmath26 , @xmath27 , well beyond the parameter space typically occupied by the three generic source classes investigated by @xcite . @xcite reported that these sources were associated with elliptical galaxies dominated by old - population starlight . however , fig . 11 from @xcite indicates that these sources are located within a region of parameter space occupied by individual stars . it is not clear why the irac colours of so many of the radio sources presented by @xcite and @xcite were found to occupy this region of parameter space , though it is possible that their selection of isophotal flux densities for unresolved infrared sources may have biased their colour ratios ( aperture values are more appropriate for point sources ) . and second , unlike these previous works , we do not find any polarized atlas sources in which the radio emission is likely to be powered by star formation ( i.e. we do not see any polarized sources in region 2 ; cf . * ? ? ? * ) ; we can not conclude that any polarized sources have infrared colours suggestive of significant pah emission ( cf . * ? ? ? the fractional polarization properties of atlas agns and sfgs are described in [ ch5:secresidentm ] and modelled in [ ch5:secressubpi ] . in fig . [ ch5:fig : rfir ] we compare the total intensity 1.4 ghz radio to 24 @xmath1 m infrared flux densities for all atlas dr2 sources , taking into account infrared upper bounds for all radio sources without detected infrared counterparts . as noted in paper i , we use 24 @xmath1 m flux density as a proxy for far - infrared ( fir ) flux density . the bottom - left panel indicates that atlas sources classified as agns are prevalent both away from and on the fir - radio correlation ( frc ) . the presence of a substantial number of agns below the dashed line demonstrates the value of using multiple diagnostic criteria to classify sources ; only sources above the dashed line have been classified as agns using the radio to far - infrared diagnostic . the bottom - right panel indicates that , as expected , atlas sources classified as sfgs typically cluster along the frc and have radio flux densities @xmath5 1 mjy . however , a small number of sources classified as sfgs ( and stars ) are observed with upper bounds clearly located within the agn parameter space . the top - left panel highlights all 130 polarized atlas sources , indicating that each of these was classified as an agn . no polarized stars or sfgs were detected in our data . we now present diagnostics of components , groups , and sources in atlas dr2 , resulting from the linear polarization@xmath28total intensity cross - identification and classification procedures described in 6.2 of paper i ( summarised in [ sec:1 ] of this work ) . in this section we focus on a number of parameter spaces in which we detail relationships between the polarized flux densities , fractional polarizations , classifications , and angular sizes of sources and their constituents . in fig . [ ch5:fig : fracpolraw ] we plot the polarized flux densities and fractional polarizations for all atlas dr2 components , groups , and sources versus their total intensity flux densities , taking into account polarization upper limits . the fractional polarization uncertainties displayed in the lower - left panel were estimated following standard error propagation as @xmath29 fig . [ ch5:fig : fracpolraw ] shows that the polarization upper limits for components and sources are distributed almost identically , the reason being that the majority of unpolarized sources comprise a single component ( relevant statistics are detailed toward the end of this section ) . regarding polarization detections , we find that all components , groups , and sources exhibit @xmath30 . this finding is in contrast to the data from other 1.4 ghz polarization surveys . @xcite found that 1% ( 381/38454 ) of polarized sources in the nrao vla sky survey ( nvss ) exhibited @xmath31 . @xcite and @xcite found that 10% ( 8/83 ) and 7% ( 10/136 ) of polarized sources in the elais - n1 field exhibited @xmath31 , respectively . @xcite found that 10% ( 84/869 ) of polarized sources throughout the two australia telescope low - brightness survey ( atlbs ) fields exhibited @xmath31 . if a population of extragalactic sources with high 1.4 ghz fractional polarizations were to exist , then it would be unexpected for such sources to be detected in the surveys above [ with @xmath32 full - width at half - maximum ( fwhm ) beam sizes ] yet undetected in this work ( with @xmath3 fwhm beam size ) , because the former are more susceptible to both beam and bandwidth depolarization . instead , we attribute the lack of atlas sources with @xmath33 to our careful treatment of local ( rather than global ) root mean square ( rms ) noise estimates , in particular to our employment of blobcat s flood - fill technique for extracting polarized flux densities ( see @xcite for details regarding biases introduced through gaussian fitting ) , and to our statistical classifications of unresolved and resolved components . we found through testing that components with abnormally high levels of fractional polarization ( up to and even beyond 100% ) could be obtained if the features above were not taken into account . in fig . [ ch5:fig : fracpolclass ] we plot the polarized flux densities and fractional polarizations for all atlas dr2 sources only , indicating their infrared / optical classifications . panels in the left column highlight polarized sources with infrared counterparts detected in all four irac bands , or otherwise . we split those detected in all four bands into sources located within or just beyond region 3 in the lower - right panel of fig . [ ch5:fig : nircc ] [ i.e. polarized sources with @xmath34 and those located within or just beyond region 1r [ i.e. @xmath35 . we find no clear distinction between the fractional polarization properties of sources with blue ( region 3 ) or red ( region 1r ) mid - infrared colours . it is possible that the region 3 polarized sources exhibit a larger dispersion in fractional polarization than the region 1r polarized sources ( compare range of observed fractional polarizations in lower - left panel of fig . [ ch5:fig : fracpolclass ] ) , though given our sample size this marginal effect may be attributed to sampling variance . using data from @xcite , @xcite found that polarized sources in region 3 were more highly polarized than those in region 1r ; the atlas data do not support this result . the distributions of upper limits presented in the right - column panels of fig . [ ch5:fig : fracpolclass ] indicate that all sources with @xmath36 have been classified as agns . the fractional polarization upper limits for sources classified as sfgs are not particularly restrictive , as their total intensity flux densities are typically @xmath5 1 mjy . characteristic @xmath37 levels for the sub - millijansky sfg population are @xmath5 @xmath38 . focusing on the lower - left panel of fig . [ ch5:fig : fracpolclass ] , we note that a general observational consequence of the rising distribution of fractional polarization upper limits with decreasing total intensity flux density is that the mean or median fractional polarization of _ detected _ polarized sources will always _ appear _ to increase with decreasing flux density . this increase represents a selection bias ; it is not possible to detect low levels of fractional polarization for the faintest total intensity sources . any changes to the underlying distribution of fractional polarization with decreasing total intensity flux density will be masked , and thus dominated , by this selection bias . therefore , it is not possible to investigate the distribution of fractional polarization at faint flux densities without accounting for polarization non - detections . recently , 1.4 ghz polarimetric studies of the elais - n1 field @xcite and atlbs fields @xcite concluded that their observational data demonstrated an anti - correlation between fractional polarization and total intensity flux density . these studies found that sources with @xmath14 @xmath5 @xmath39 mjy were more highly polarized than stronger sources . however , @xcite did not account for polarization upper limits , leading to their misinterpretation of selection bias as an indication of true anti - correlation . @xcite accounted for selection bias using monte carlo analysis , effectively incorporating polarization upper limits . @xcite accounted for selection bias by comparing samples of sources in bins of polarized flux density rather than total flux density , at sufficient polarized flux densities to neglect upper limits . however , the findings of increased fractional polarization at faint total flux densities by @xcite and @xcite appear to be reliant on the increasing number of sources observed with @xmath33 at these faint levels . for example , both studies reported extreme sources with @xmath40 , but only at faint total intensities . both @xcite and @xcite found that @xmath41 of polarized sources with linearly polarized flux densities @xmath42 mjy ( i.e. a significant proportion of these sources ) exhibited @xmath33 , while no sources with such high levels of fractional polarization were found for @xmath43 mjy . as described earlier , the @xmath33 sources ( and perhaps many with lower @xmath37 ) are likely to reflect rms noise estimation and source extraction errors . the analytic form assumed by @xcite for the distribution of fractional polarization ( which will be described in [ ch5:secressubpi ] ) may have also contributed to their conclusion regarding increased fractional polarization ; spurious conclusions may be obtained if the observed fractional polarization data do not follow the assumed analytic form of the fit . the arguments above suggest that existing evidence for an anti - correlation between fractional polarization and total flux density may not be robust . similar to the studies above , earlier works by and @xcite concluded that nvss @xcite sources exhibited an anti - correlation between fractional linear polarization and total intensity flux density . these analyses in effect incorporated polarization upper bounds ( though not upper _ limits _ ; see * ? ? ? * ) because @xcite recorded a linearly polarized flux density for each nvss source , regardless of the statistical significance of the polarization measurement . to determine the significance of their findings and thus form a conclusion regarding evidence for anti - correlation , which we use to justify our own fractional polarization model presented in [ ch5:secressubpi ] , we need to examine their works in more detail . and @xcite presented fractional polarization distributions for steep- and flat / inverted - spectrum nvss sources in four flux density intervals : @xmath44 , @xmath45 , @xmath46 , and @xmath47 mjy . their distributions are remarkably consistent for @xmath48 , exhibiting a log - normal form with approximately equal dispersion and a peak at @xmath49 . a separate component with a peak at @xmath50 is also present in each distribution , representing sources with polarization dominated by instrumental leakage . we observe that the dispersions of their distributions broaden with increasing flux density , solely due to broadening at @xmath36 . found that the median fractional polarization was larger for the @xmath44 mjy data than for the @xmath47 mjy data , for both steep- and flat - spectrum sources . @xcite found the same result but for steep - spectrum sources only . these results were essentially based on the lack of sources with @xmath51 in the @xmath44 mjy data when compared with the increased presence of such sources at higher flux densities ; a proportional increase in the number of sources with @xmath48 for decreasing flux density was not observed . however , the presence of sources with @xmath51 ( i.e. less than the typical leakage level of @xmath50 ) , and more generally the slight changes in distribution shape observed for @xmath36 between different flux density intervals , may be more appropriately explained by the influence of noise on polarized flux densities rather than by variation in the underlying distribution of fractional polarization . to demonstrate , we first note that the expectation value of @xmath4 for an unpolarized nvss source is given by the mean of a rayleigh distribution ( i.e. a ricean distribution with no underlying polarized signal ) , which is @xmath52 mjy for @xmath53 mjy . this value is also characteristic of the expected observed polarized flux density for a source with true underlying polarized signal @xmath54 @xmath5 @xmath55 ( e.g. see the upper panel of fig . 1 from @xcite ) . thus , a tail of sources with true polarization @xmath54 @xmath5 0.29 mjy will appear in the fractional polarization distribution at @xmath37 @xmath21 0.18% for total intensity sources with @xmath56 mjy , and at @xmath37 @xmath5 0.05% for @xmath57 mjy . these estimates are consistent with the distributions presented by and @xcite ; a tail of sources with @xmath51 was observed for the @xmath47 mjy data but not for the @xmath44 mjy data . we therefore conclude that the results presented by and @xcite do not demonstrate a statistically significant anti - correlation between fractional linear polarization and total intensity flux density . furthermore , we note that the fractional polarization distributions presented in these works are likely to overestimate the population of sources with @xmath36 , even for the @xmath44 mjy data , for the following two reasons . first , all catalogued nvss measurements of polarized flux density were debiased using a modified version of the expectation value for a ricean distribution @xcite . this debiasing scheme is known to impart a significant overcorrection ( i.e. negative bias ) at low snr ( e.g. see ; the relevant scheme is labelled in reference to its application by @xcite ) . thus measurements of fractional polarization obtained using the nvss catalogue are likely to be negatively biased . and second , raw polarization measurements for nvss sources were obtained by interpolation at the total intensity centre position . therefore , polarized flux densities were underestimated for each source in which the spatial peak of polarized emission was located in an adjacent pixel to the total intensity peak . both of these effects could have been largely mitigated by obtaining polarization upper limits for sources , rather than upper bounds . returning to the lower - left panel of fig . [ ch5:fig : fracpolclass ] , we find that the maximum level of fractional polarization exhibited by atlas sources does not appear to be correlated with total intensity flux density . the maximum level appears to be limited to @xmath37 @xmath5 20% for @xmath14 @xmath21 1 mjy , which becomes a strict limit for @xmath58 mjy when accounting for the presence of all upper limits . furthermore , we find @xmath37 @xmath21 0.4% for sources with @xmath14 @xmath21 10 mjy , where sources exhibiting higher levels of fractional polarization significantly outnumber those potentially exhibiting @xmath59 as indicated by the upper limits . in paper i we found that 138 of the total 172 catalogued linearly polarized components exhibited a clear one - to - one match with individual total intensity components . the remaining 34 polarized components required grouping in order to be associated with total intensity counterparts . of the one - to - one associations , we classified 58 as type 0 , 4 as type 1 , 25 as type 2 , 48 as type 4 , and 3 as type 5 . all 3 sources containing type 5 core associations were found to exhibit unpolarized lobes . of the group associations comprising a total of 34 polarized components , 2 groups were classified as type 0 , 14 as type 3 , 1 as type 4 , and 8 as type 6 . there were 29 sources classified as type 6 , 2 as type 7 , and 25 as type 8 . these classifications are catalogued in appendix b of paper i. in fig . [ ch5:fig : fracpoltypes ] we indicate the polarization@xmath28total intensity classifications for all polarized atlas dr2 components , groups , and sources . in the lower - left panel we plot the levels of fractional polarization exhibited by classical double or triple radio sources ( types 68 ) and their individual lobes ( types 02 , respectively ) . we find that sources classified as type 6 , which comprise pairs of roughly equally polarized type 0 lobes , are located throughout most of the populated parameter space . we find that type 7 sources , which comprise pairs of type 1 lobes where one is clearly less polarized than the other , appear to occupy the same parameter space populated by type 6 sources . a selection bias against identifying type 0/1 lobes , and thus type 6/7 sources , is present within the diagonal region of parameter space populated by polarization upper limits ( for visual clarity these limits are not shown in fig . [ ch5:fig : fracpoltypes ] ; see fig . [ ch5:fig : fracpolraw ] ) . type 2 lobes and their parent type 8 sources , which represent ambiguous cases in which it is not possible to differentiate between types 0/1 or 6/7 , are largely confined to this diagonal region . given the observed prevalence of type 6 sources compared with type 7 , it seems likely that more sensitive observations would result in a majority of type 8 sources being reclassified as type 6 . from the lower - right panel of fig . [ ch5:fig : fracpoltypes ] we find that sources classified as type 3 , which exhibit a single polarized component situated midway between two total intensity components , appear to populate the same region of parameter space occupied by type 8 sources . similarly , associations classified as type 5 , which represent cores of triple radio sources , as well as the remaining unclassified sources denoted by type 4 , also appear to be concentrated within the diagonal region of parameter space populated by upper limits . we note that many of the type 4 associations are likely to represent individual type 0 or type 1 lobes of as - yet unassociated multi - component sources , having been erroneously assigned to single - component sources in our catalogue ( note 6.1 of paper i ; statistics regarding polarized multi - component sources are presented below ) . we find that type 5 associations occupy a parameter space consistent with type 6 and type 7 sources . as the latter represent average polarization properties for dual - lobed radio sources , it is possible that type 5 associations also represent dual - lobed structures but with small angular sizes , such as compact steep - spectrum ( css ) sources @xcite . curiously , we found that each of the 3 sources with type 5 cores was found to exhibit unpolarized outer radio lobes . it is possible that the type 5 cores represent restarted agn activity and that the outer lobes are unpolarized because any large - scale magnetic fields within them have dissipated over time since their production during an earlier distinct phase of agn activity . for example , we may be seeing sources similar to the double - double radio galaxy j1835@xmath60620 , though at an earlier stage of evolution where the inner lobes have not yet separated into two separate lobes ( note that fractional polarization levels for the inner lobes of j1835@xmath60620 are higher than for the outer lobes ) . in fig . [ ch5:fig : fracpoltheta ] we plot polarized flux density and fractional polarization versus largest angular size ( las ) for all polarized atlas dr2 sources , highlighted according to morphology and infrared colour . the las for a single - component source is given by its total intensity deconvolved angular size or size upper limit , while the las for a multi - component source is given by the maximum angular separation between its constituent total intensity components . for visual clarity we plot sources with polarization upper limits separately in fig . [ ch5:fig : fracpolthetauls ] , also highlighted according to morphology and infrared colour . note that the apparent anti - correlations between fractional polarization upper limits and angular size upper limits for single - component sources throughout fig . [ ch5:fig : fracpolthetauls ] are spurious ; the restrictiveness of both types of upper limits are intrinsically anti - correlated with total intensity flux density . in fig . [ ch5:fig : fracpoltheta2 ] we again plot polarized flux density and fractional polarization versus las for all polarized sources , but now highlighted according to the polarization@xmath28total intensity classification scheme from 6.2 of paper i. for reference , we note that 1 subtends a linear scale of 1.8 , 3.3 , 6.1 , 8.0 , and 8.5 kpc at redshifts 0.1 , 0.2 , 0.5 , 1.0 , and 2.0 , respectively @xcite , assuming a @xmath61cdm cosmology with parameters @xmath62 km s@xmath63 mpc@xmath63 , @xmath64 , and @xmath65 . following an evolutionary relationship for galaxy sizes given by @xmath66^{-\frac{1}{2 } } \;,\ ] ] and assuming that a typical galaxy has size @xmath67 kpc at @xmath68 ( e.g. * ? ? ? * ) , the corresponding sizes of typical galaxies at the redshifts above are approximately @xcite , may cause observed angular sizes of extended sources to be smaller than true sizes , due to faint source edges . ] 19 , 18 , 16 , 12 , and 7 kpc , respectively , or 10 , 56 , 26 , 15 , and 08 , respectively . we summarise our findings from figs . [ ch5:fig : fracpoltheta][ch5:fig : fracpoltheta2 ] as follows . of the 130 ( 2091 ) polarized ( unpolarized ) sources catalogued in atlas dr2 and presented in fig . [ ch5:fig : fracpoltheta ] ( fig . [ ch5:fig : fracpolthetauls ] ) , 81 ( 74 ) comprise multiple components in total intensity , 40 ( 140 ) comprise a single resolved component in total intensity , and 9 ( 1877 ) comprise a single unresolved component in total intensity . we note that while components observed in linear polarization in atlas dr2 are typically unresolved ( only 29/172 or 17% of polarized components are resolved ; see 5 of paper i ) , 121/130 or 93% of sources exhibiting polarized emission are resolved in total intensity . these statistics support the findings by @xcite that polarized 1.4 ghz sources tend to have structure at arcsecond scales and that , as a consequence , their polarized emission is unlikely to be beamed . combined with our earlier classification from fig . [ ch5:fig : rfir ] of all polarized atlas sources as agns , and our interpretation from fig . [ ch5:fig : fracpoltypes ] that most or all polarized components are associated with agn jets or lobes ( rather than cores ) , the statistics above demonstrate that ( sub-)millijansky polarized sources tend to be extended jet- or lobe - dominated active radio galaxies . this conclusion is supported by the finding from @xcite that polarized sources tend to have steep spectra , which are characteristic of lobes . in fig . [ ch5:fig : fracpolthetauls ] we find that atlas dr2 sources typically have las @xmath5 10 , suggesting that most sources are located at @xmath20 @xmath21 0.2 . this is consistent with the preliminary redshift distributions presented by @xcite and @xcite for atlas dr1 sources ( see also discussion of radio source redshift distribution by * ? ? ? focusing on the panels in the lower - left corners of fig . [ ch5:fig : fracpoltheta ] and fig . [ ch5:fig : fracpolthetauls ] , we find that single- and multi - component sources are distributed approximately equally in fractional polarization space ; their fractional polarization upper limits are not restrictive enough to identify any possible underlying trends . however , having found above that polarized sources are likely to represent lobed galaxies , it is perhaps surprising that we do not find a clear correlation between fractional polarization and las due to beam depolarization . given the @xmath3 resolution of atlas , in general a classical double radio source with dual polarized lobes should exhibit greater fractional polarization than a similar source with smaller las that is observed as a single - component source . a likely explanation may be that a significant number of the polarized single - component sources indicated in fig . [ ch5:fig : fracpoltheta ] are actually individual lobes of as - yet unassociated multi - component sources ( see 6.1 of paper i ) . note that all single - component sources in fig . [ ch5:fig : fracpoltheta ] are classified as type 4 in fig . [ ch5:fig : fracpoltheta2 ] . another potential explanation may be that for dual - lobed sources with small angular size observed as single - component sources , asymmetric depolarization between the lobes @xcite could result in overall source fractional polarization levels similar to those of type 7 sources ( see fig . [ ch5:fig : fracpoltheta2 ] ) , rather than resulting in significantly beam - depolarized ( and thus perhaps unpolarized ) sources overall . the upper limits presented in the left column of fig . [ ch5:fig : fracpolthetauls ] do not reveal any clear underlying trends within or between source classes . the multi - component sources classified as sfgs in fig . [ ch5:fig : fracpolthetauls ] , which are also shown located within the agn parameter space in the lower - right panel of fig . [ ch5:fig : rfir ] , require future study . these may represent composite sources exhibiting both agn and sfg characteristics , for example similar to the ultra - luminous infrared galaxy f001837111 investigated by @xcite or the more general classes of post - starburst quasars ( e.g. * ? ? ? focusing on the right column of fig . [ ch5:fig : fracpoltheta ] , we do not find any angular size distinctions between polarized sources based on their infrared colours . furthermore , we find no underlying trends within the associated upper limit data from the right column of fig . [ ch5:fig : fracpolthetauls ] . focusing on fig . [ ch5:fig : fracpoltheta2 ] , we find that type 6 sources typically extend to greater angular sizes than type 7 sources , though a larger sample size with proportionally fewer type 8 classifications is required to confirm this finding . we also find that each of the 3 polarized cores classified as type 5 are resolved , and that they populate the same region of parameter space as type 4 sources . we present euclidean - normalised differential number - counts derived from the atlas dr2 total intensity and linear polarization component catalogues in fig . [ ch5:fig : countsi ] and fig . [ ch5:fig : countsl ] , respectively , and in tabulated form in appendix a. counts for each bin have been plotted and tabulated at the expected average flux density , which we denote by @xmath69 , as given by equation ( 19 ) from . this value takes into account the number - count slope and becomes important when assigning flux densities for bins containing few counts or with large widths in flux density space ; @xmath69 only equals the bin geometric mean when @xmath70 , where @xmath71 is the slope of the differential number counts @xmath72 . bin widths for all total intensity counts were selected to be a factor of 0.07 dex for @xmath73 mjy , 0.13 dex for @xmath74 mjy , and 0.2 dex otherwise . in linear polarization , bin widths were selected to be a factor of 0.16 dex for @xmath75 mjy , and 0.3 dex otherwise . we removed all bins containing components with visibility area corrections @xmath76 , so as to prevent the number - counts from being dominated by the few components detected in the most sensitive and potentially least - representative regions of the atlas images . ( note that we did not remove individual offending components in order to retain the faintest bins , as this would have led to a bias in their resulting number - counts . ) in total intensity this resulted in the removal of the faintest few bins containing @xmath7730 components from each of the cdf - s component- and bin - corrected datasets , and @xmath7720 components from each of the elais - s1 component- and bin - corrected datasets . the maximum visibility area corrections for any components in the remaining valid cdf - s and elais - s1 bins were @xmath78 and @xmath79 , respectively . in linear polarization , the maximum visibility area corrections for any components in the cdf - s and elais - s1 datasets were @xmath80 and @xmath81 , respectively . as a result , we did not remove any bins in linear polarization . resolution and eddington bias corrections were calculated in 7 of paper i. the former was designed to correct for incompleteness to resolved components with low surface brightness , and for the redistibution of counts between bins resulting from systematic undervaluation of flux densities for components classified as unresolved . the latter was designed to correct for the redistribution of counts between bins due to random measurement errors in the presence of a non - uniformly distributed component population . these bias corrections were calculated in paper i by assuming that the true underlying differential number counts in total intensity were given by the sixth - order empirical fit to the phoenix and first surveys presented by @xcite . this fit , which we denote h03 , is given by @xmath82 = \sum_{j=0}^{6 } a_{j } \left [ \log\left ( \frac{i}{{\textrm}{mjy } } \right)\right]^{j}\,,\ ] ] with @xmath83 , @xmath84 , @xmath85 , @xmath86 , @xmath87 , @xmath88 , and @xmath89 . to illustrate the potential boosting effects of an exaggerated population of faint components , paper i also defined a modified h03 distribution , denoted h03 m , in which a euclidean slope was inserted between 30@xmath28300@xmath1jy , @xmath90 for bias corrections in linear polarization , we modelled the true underlying differential number counts @xmath91 by convolving the total intensity h03 distribution from equation ( [ ch4:eqn : h03 ] ) with a probability distribution for fractional linear polarization @xmath92 , which we denote @xmath93 . the @xmath94 distribution is presented in equation ( [ ch5:eqn : fracpol ] ) in [ ch5:secressubpi ] . the atlas dr2 component counts extend down to a flux density of approximately 140 @xmath1jy in both total intensity and linear polarization . the brightest flux density bins are sparsely sampled because the atlas survey areas are not large enough to include significant numbers of increasingly rare bright components . in both fig . [ ch5:fig : countsi ] and fig . [ ch5:fig : countsl ] we find that the number - counts from the two separate atlas fields are consistent within the errors over their full observed flux density ranges . the impacts of the combined resolution and eddington bias corrections on the number - counts appear to be relatively minor . in total intensity , the two corrections largely cancel each other out , while in linear polarization the resolution bias corrections dominate . in both total intensity and linear polarization , the combined corrections affect the underlying visibility area corrected counts by a factor of @xmath5 0.5 , and do not affect the counts for @xmath13 @xmath21 3 mjy . we find that differences between the two independent eddington bias correction schemes are largely negligible for both the total intensity and linear polarization number - counts , providing confidence in these approaches . in fig . [ ch5:fig : countsi ] we find that the total intensity counts closely follow the h03 model within a factor of @xmath95 , though the atlas counts may begin to systematically drop below the h03 model for @xmath13 @xmath5 @xmath96 mjy . it is likely that the drop is caused by residual incompleteness in our resolution bias corrections , in turn caused by uncertainties regarding our assumed true angular size distribution for @xmath97 as discussed in 7.1 of paper i. however , we note that if we assume that the model presented in fig . 19 of paper i is the best representation of the true angular size distribution ( without any flux density scaling ) , then the faintest bins at @xmath98 @xmath1jy only require an additional correction factor of at most approximately @xmath6030% . the faintest bins are therefore consistent with the h03 model . as we do not find any systematic divergence between the atlas total intensity counts and the h03 model at the faintest flux densities ( when accounting for the suspected residual resolution bias described above ) , we confirm that the h03 model is suitable for predicting 1.4 ghz component counts ( and source counts as described below ) down to at least @xmath0 @xmath1jy in surveys with resolution fwhm @xmath3 . should we have found a systematic divergence , it would have indicated that our predicted eddington bias corrections were unrealistic , and that in turn the h03 model underpinning these corrections formed an increasingly poor representation of the true number - counts for decreasing flux density . under this hypothetical situation , an iterative approach would have been required in order to correctly identify an input true number - count model so as to bring about convergence with the fully corrected observed counts . in 7.2 of paper i we predicted the levels of eddington bias that would be present within the observed atlas counts if the true counts were given by the h03 or h03 m models [ the latter model contains a larger population of components with @xmath99 mjy than the former ; see equation ( [ ch4:eqn : h03 m ] ) ] . we predicted that the h03 m model would induce significantly greater eddington bias at @xmath99 mjy than the h03 model ( see fig . 23 in paper i ) . therefore , if the h03 model was used to predict the observed eddington bias when in fact the h03 m model best represented the true counts , then the observed counts would exhibit significant positive residual eddington bias ; if vice versa , the residual bias would be negative . given that we do not observe a systematic rise ( or fall ) at faint flux densities in the fully corrected atlas counts ( again accounting for the suspected residual resolution bias described above ) , we conclude that the h03 m model is not supported by the atlas data . we note that the resolution bias corrections applied in this work are practically insensitive to changes between the h03 and h03 m models . this is because for any given flux density bin , the resolution bias corrections are unaffected by the assumed form of the number - count distribution at fainter flux densities . therefore , assuming that our resolution bias corrections are appropriate to begin with , we can focus on eddington bias alone in order to draw the conclusions described above . below a flux density of @xmath100 mjy , we expect the atlas total intensity component counts to be dominated by single - component sources , with negligible contributions from components within multi - component sources . while we are unable to explicitly quantify this expectation given present data , we note that conservatively @xmath101 of all 2416 atlas components reside within multi - component sources ( this fraction takes into account the number of components estimated to reside within as - yet unassociated multi - component sources ; see 6.1 of paper i ) . we expect that most of these multi - component sources represent frii sources , which are known to dominate the source counts at flux densities @xmath21 10 mjy and which diminish significantly below @xmath102 mjy ( e.g. * ? ? ? * ) . at sub - mjy levels , radio sources in general are expected to have angular sizes @xmath103 ; these are likely to be observed as single - component sources in atlas . therefore , we conclude that the atlas component counts may act as a suitable proxy for source counts at sub - mjy levels . we note that our characterisation of the faint component / source population using the h03 model in this work has relied on the similar resolutions of the atlas and phoenix surveys . should these resolutions have differed significantly , so too would have the properties of their observed components . @xcite obtained their model by using a sixth - order fit to the observed component counts from the phoenix survey , supplemented at @xmath104 mjy by source counts from the first survey @xcite . the h03 model was thus intended to characterise source counts at all flux densities , despite being derived from a component catalogue at faint flux densities . for @xmath104 mjy , the atlas total intensity component counts follow the h03 model and thus the first source counts . we explain this correspondence as follows by first presenting results that examine how source and component counts are expected to differ . given that frii sources dominate the source counts above @xmath2 mjy and that these sources are likely to comprise multiple components within a survey such as atlas , we expect the differential counts for sources to rise and extend to brighter flux densities than those for components . to roughly illustrate this behaviour and examine the difference between source and component counts in general , we considered an idealised scenario in which all sources were assumed to comprise two identical components , each with half the flux density of their parent . for illustrative purposes we assumed that the component count distribution was given by the h03 model . to derive the idealised differential source counts , we integrated the differential component counts to obtain integral component counts , divided these integral counts by two , doubled the flux density scale , and differentiated . for completeness , we also derived differential source counts in linear polarization by following a similar procedure , where the relevant differential component counts were assumed to follow the @xmath93 model . we present the resulting total intensity and linear polarization source counts in fig . [ ch5:fig : ratiosc ] . we find that the predicted source counts remain within @xmath105 of the component counts across the flux density ranges probed by the atlas data in total intensity ( @xmath14 @xmath5 1 jy ) and linear polarization ( @xmath4 @xmath5 100 mjy ) . ( separately , while not shown , we note that the integral counts for both components and sources within our rudimentary model are very similar , for both total intensity and linear polarization . ) as expected , at bright flux densities the component counts drop below the source counts , though these drops occur at brighter flux densities than relevant to the atlas data . note that in reality , the differential source and component counts are likely to overlap more closely than presented in fig . [ ch5:fig : ratiosc ] because of the presence of single - component sources . thus we conclude that for surveys with resolution fwhm @xmath3 similar to phoenix and atlas , the h03 model may be used to characterize both component and source counts in total intensity for @xmath13 @xmath5 1 jy . we conjecture that , as modelled above , the h03 model characterises component rather than source counts at all flux densities , including at @xmath106 jy . to justify this claim , we note that components in the first survey were only grouped into multi - component sources if they were located within 50@xcite . from fig . [ ch5:fig : fracpoltheta ] of this work we can see that a cutoff of 50 is likely to be too small to capture sources with the most widely - separated components , which are also likely to be the brightest sources . in addition , flux densities for extended first components are likely to be underestimated due to insensitivity to extended emission . therefore , the first source counts are likely to be deficient at the brightest flux densities . incidentally , the first source counts and thus the h03 model appear to form a suitable hybrid distribution for describing component counts at all flux densities in surveys with resolution fwhm @xmath3 such as atlas . we may therefore conclude that the @xmath93 model is suitable for characterising component counts in linear polarization at all flux densities , not just at @xmath4 @xmath5 100 mjy where differences between polarized component and source counts are likely to diminish as shown in fig . [ ch5:fig : ratiosc ] . if the h03 model were to better represent source counts rather than component counts at @xmath107 jy , then the polarized counts resulting from convolution with @xmath108 would reside ambiguously between a component and source count distribution for @xmath4 @xmath21 5 mjy . thus it would be inappropriate to estimate integral component or source counts from the @xmath93 ( or indeed h03 ) model ; this point is relevant to results presented shortly . in fig . [ ch5:fig : countsl ] we find that the atlas linear polarization component counts steadily decline with decreasing flux density , as generally predicted by all four models displayed in the background . the solid curve displays our assumed true component count model , namely @xmath93 , which we used to derive the corrections for resolution and eddington bias . the fully corrected atlas counts closely follow this model within statistical error , indicating consistency between the model , the corrections , and the observational data . each of the four background models in fig . [ ch5:fig : countsl ] were calculated by convolving the h03 model with a fractional polarization distribution . we note that these convolutions are only appropriate because , as described above , the h03 model appears to appropriately characterise the total intensity component counts at all flux densities relevant to atlas . in [ ch5:secressubpi ] we describe each of the fractional polarization distributions underlying the four background models , and compare their abilities to predict the atlas polarized counts and polarization data in general . the number of polarized components expected per square degree at or brighter than a given flux density , as constrained by the observed atlas component counts , can be estimated by integrating the @xmath93 polarized count distribution ( the solid curve in fig . [ ch5:fig : countsl ] ) . the resulting integral component counts are displayed in fig . [ ch5:fig:17 ] . we estimate that the sky density of polarized components for @xmath109 @xmath1jy is 30 deg@xmath110 , for @xmath111 @xmath1jy it is 50 deg@xmath110 , and for @xmath112 @xmath1jy it is 90 deg@xmath110 . if we make the rudimentary assumption described earlier regarding fig . [ ch5:fig : ratiosc ] that every polarized component belongs to a dual - component source with double the flux density , we can estimate the integral source count distribution ; this is displayed alongside the integral component count distribution in fig . [ ch5:fig:17 ] . we thus estimate that the sky density of polarized sources for @xmath109 @xmath1jy is @xmath113 deg@xmath110 , and for @xmath111 @xmath1jy it is @xmath114 deg@xmath110 . we expect that these integral source count estimates are accurate to within 10% , even if a more suitable model incorporating polarized single - component sources is utilised . in this section we present a model to describe the distribution of fractional polarization for agn sources and their components / groups observed at 1.4 ghz in surveys with resolution fwhm @xmath21 10 , as constrained by the atlas dr2 data . there appears to be a significant overlap between the fractional polarization properties of all classification types representing both components / groups and sources in fig . [ ch5:fig : fracpoltypes ] . taking into account the presence of upper limits ( see fig . [ ch5:fig : fracpolraw ] ) , we find that typical levels of fractional polarization are concentrated between 0.4% and 20% , regardless of whether the focus is on sources or on their constituent components / groups . given this apparent overlap , we assume for simplicity that the distribution of fractional polarization for both components / groups and sources can be modelled using the same pdf , which we denote by @xmath94 . before presenting our model for this distribution , we note three caveats . first , following our conclusions presented in [ ch5:secresidentm ] regarding potential correlation of the distribution of fractional polarization with total flux density , we assume that @xmath94 is independent of total intensity flux density . this assumption may not be suitable for @xmath14 @xmath5 @xmath39 mjy for which our atlas data become sparse . second , our model for @xmath94 may only be relevant for surveys with resolution fwhm @xmath21 10 . surveys with finer resolution may encounter less beam depolarization across components , and thus recover higher average levels of fractional polarization ( in 5 of paper i we found that @xmath115 of polarized atlas components were resolved ) . we note that surveys with coarser resolution will incur increased blending between components within multi - component sources , resulting in a greater number of low-@xmath37 sources than observed for atlas due to enhanced beam depolarization . and third , given that all polarized components in atlas dr2 are associated with agns , we restrict our model for @xmath94 to the characterisation of agns , rather than the characterisation of all radio sources including sfgs and individual stars . we do not attempt to differentiate between different types of agns or their components within our model , i.e. fri / frii / radio quiet / core / lobe . we discuss fractional polarization levels for sfgs in [ ch5:secdiscsfg ] . we modelled @xmath94 by qualitatively fitting two independent sets of atlas data : ( i ) the fractional polarizations of components , groups , and sources displayed in fig . [ ch5:fig : fracpolraw ] , importantly taking into account upper limits , and ( ii ) the differential number - counts for polarized components displayed in fig . [ ch5:fig : countsl ] . we obtained a concordance fit to these data by modelling @xmath94 using a log - normal distribution , @xmath116^{{\scriptscriptstyle}2 } } { 2 \sigma_{{\scriptscriptstyle}10}^{{\scriptscriptstyle}2}}\bigg\ } \,,\ ] ] where the parameters @xmath117 and @xmath118 are the median fractional polarization and scale parameter , respectively , given by best - fit values @xmath119 and @xmath120 . the fit given by equation ( [ ch5:eqn : fracpol ] ) is consistent with the result obtained by analysing the fractional polarization data alone , using the product - limit estimator @xcite as implemented within the survival package in the r environment . the mean level of fractional polarization for the distribution in equation ( [ ch5:eqn : fracpol ] ) is given by @xmath121 , which equates to @xmath122 . for values of @xmath117 or @xmath118 larger than the best - fit values above , we found that the @xmath93 model predicted differential counts in excess of the observed atlas counts . for smaller values , the predicted counts were deficient . we plot equation ( [ ch5:eqn : fracpol ] ) in fig . [ ch5:fig : pimodels ] . for comparison we also plot the 1.4 ghz fractional polarization distributions proposed by @xcite , @xcite , and @xcite . for clarity we explicitly document each of these distributions , as follows . @xcite investigated the distribution of fractional polarization for nvss sources with @xmath123 mjy , which they fit using the following quasi log - normal form , @xmath124^{{\scriptscriptstyle}2 } } { 2 \sigma_{{\textrm}{\tiny b04}}^{{\scriptscriptstyle}2}}\bigg\ } \,,\ ] ] where @xmath125 @xmath126 and where @xmath127 . the median and mean fractional polarization levels of the @xmath128 distribution are 2.1% and 3.3% , respectively . similarly , @xcite investigated the distribution of fractional polarization for nvss sources with @xmath129 mjy , which they fit using the following monotonic form , @xmath130^{{\scriptscriptstyle}-1 } + b_{{\textrm}{\tiny t04}}\right\}\ ] ] where @xmath131 , @xmath132 and where we have included a correction factor of 1.32 to ensure that the distribution is normalised . the median and mean fractional polarization levels of the @xmath133 distribution are 2.1% and 2.7% , respectively . @xcite fit the distribution of fractional polarization for sources with @xmath134 mjy in the elais - n1 field by modifying a gram - charlier series of type a ( e.g. * ? ? ? * ) , resulting in the following monotonic form , @xmath135\bigg\ } & \\ \hspace{4 cm } \textrm{if $ i<30$~mjy}\\ f_{{\textrm}{\tiny b04}}\left(\pi\right ) & \\ \hspace{4 cm } \textrm{if $ i\ge30$~mjy}\,,\\ \end{array } \right.\ ] ] where @xmath136 , @xmath137 , and where we have included a correction factor of 11.06 to ensure that the distribution is normalised . for @xmath138 mjy , @xcite found that the elais - n1 data were consistent with the @xmath128 distribution from equation ( [ ch5:eqn : fracpolb04 ] ) . the median and mean fractional polarization levels of the @xmath139 distribution for @xmath134 mjy are 4.8% and 6.0% , respectively . the four curves presented in fig . [ ch5:fig : pimodels ] are replicated in figs . [ ch5:fig : fracpolraw][ch5:fig : fracpoltheta ] and fig . [ ch5:fig : fracpoltheta2 ] . the four curves are also presented in fig.s [ ch5:fig : countsl ] and [ ch5:fig : countsl2 ] following convolution with the h03 differential count model . in fig . [ ch5:fig : countsl2 ] we find that the fractional polarization distributions proposed by @xcite , @xcite , and @xcite are in general agreement with the observed atlas polarized number counts . the models predict polarized counts that are within a factor of 5 of each other , and they all pass within a few standard errors of the atlas data points . however , we find that these three distributions are incompatible with the observed distribution of fractional polarization for atlas components , groups , sources , and in particular upper limits as presented in fig . [ ch5:fig : fracpolraw ] . the extended tails below @xmath36 for the distributions proposed by @xcite and @xcite are likely to reflect the various systematic biases we described earlier in [ ch5:secresidentm ] regarding the nvss data . polarized flux densities for nvss sources were recorded regardless of whether or not the measurements met statistical criteria for formal detection . if upper limits were calculated for the nvss data following a similar procedure to that described for the atlas data in 6.2 of paper i , then we suspect that far fewer detections strictly implying @xmath36 would have been made . we note that the @xmath108 model proposed in this work peaks at @xmath140 , which is consistent with the nvss data for @xmath48 from and @xcite . the extended tail below @xmath36 in the @xcite model reflects their assumption that the distribution peaks at @xmath141 and declines monotonically with increasing @xmath37 . the atlas dr2 data do not support this assumption . as noted earlier , a caveat of the @xmath108 model is that it may not be suitable for @xmath14 @xmath5 @xmath39 mjy , because the upper limits presented in fig . [ ch5:fig : fracpolraw ] do not constrain the behaviour of the true fractional polarization distribution for low values of @xmath37 . however , given that the maximum level of fractional polarization exhibited by atlas components and sources appears to be limited to @xmath37 @xmath5 @xmath142 , and given that this limit appears to be uncorrelated with flux density down to at least @xmath100 mjy ( see comments regarding fig . [ ch5:fig : fracpolclass ] in [ ch5:secresidentm ] ) , we may draw tentative conclusions regarding the true distribution of fractional polarization for @xmath143 @xmath5 @xmath14 @xmath5 @xmath39 mjy . the atlas dr2 data are consistent with 3 general alternatives . first , the @xmath108 distribution may remain unchanged for @xmath144 mjy . second , for decreasing @xmath14 , the mean of @xmath108 may decrease while its dispersion increases so as to maintain an approximately constant level of fractional polarization for outliers with large @xmath37 . and third , for decreasing @xmath14 , the mean of @xmath108 may increase while its dispersion decreases . more sensitive observations are required to distinguish between these alternatives .

we do not detect any components or sources with fractional polarization levels greater than 24% . the atlas data are consistent with a lognormal distribution of fractional polarization with median level 4% that is independent of flux density down to total intensity @xmath2 mjy and perhaps even 1 mjy . we find that polarized emission from 1.4 ghz millijansky sources originates from the jets or lobes of extended sources that are powered by an active galactic nucleus , consistent with previous findings in the literature . we provide estimates for the sky density of linearly polarized components and sources in 1.4 ghz surveys with @xmath3 resolution .

c

1403.5308

this is the second of two papers describing the second data release ( dr2 ) of the australia telescope large area survey ( atlas ) at 1.4 ghz . in paper i we detailed our data reduction and analysis procedures , and presented catalogues of components ( discrete regions of radio emission ) and sources ( groups of physically associated radio components ) . in this paper we present our key observational results . we find that the 1.4 ghz euclidean normalised differential number counts for atlas components exhibit monotonic declines in both total intensity and linear polarization from millijansky levels down to the survey limit of @xmath0 @xmath1jy . we discuss the parameter space in which component counts may suitably proxy source counts . we do not detect any components or sources with fractional polarization levels greater than 24% . the atlas data are consistent with a lognormal distribution of fractional polarization with median level 4% that is independent of flux density down to total intensity @xmath2 mjy and perhaps even 1 mjy . each of these findings are in contrast to previous studies ; we attribute these new results to improved data analysis procedures . we find that polarized emission from 1.4 ghz millijansky sources originates from the jets or lobes of extended sources that are powered by an active galactic nucleus , consistent with previous findings in the literature . we provide estimates for the sky density of linearly polarized components and sources in 1.4 ghz surveys with @xmath3 resolution . [ firstpage ] polarization radio continuum : galaxies surveys .

in this work we have presented results and discussion for atlas dr2 . our key results are summarised as follows . for convenience we use the term ` millijansky ' loosely below to indicate flux densities in the range @xmath179 mjy . a. radio emission from polarized millijansky sources is most likely powered by agns , where the active nuclei are embedded within host galaxies with mid - infrared spectra dominated by old - population ( 10 gyr ) starlight or continuum produced by dusty tori . we find no evidence for polarized sfgs or individual stars to the sensitivity limits of our data - all polarized atlas sources are classified as agns . b. the atlas data indicate that fractional polarization levels for sources with starlight - dominated mid - infrared hosts and those with continuum - dominated mid - infrared hosts are similar . c. the morphologies and angular sizes of polarized atlas components and sources are consistent with the interpretation that polarized emission in millijansky sources originates from the jets or lobes of extended agns , where coherent large - scale magnetic fields are likely to be present . we find that the majority of polarized atlas sources are resolved in total intensity , even though the majority of components in linear polarization are unresolved . this is consistent with the interpretation that large - scale magnetic fields that do not completely beam depolarize are present in these sources , despite the relatively poor resolutions of the atlas data . d. we do not find any components or sources with fractional polarization levels greater than 24% , in contrast with previous studies of faint polarized sources . we attribute this finding to our improved data analysis procedures . e. the atlas data are consistent with a distribution of fractional polarization at 1.4 ghz that is independent of flux density down to @xmath180 mjy , and perhaps even down to 1 mjy when considering the upper envelope of the distribution . this result is in contrast to the findings from previous deep 1.4 ghz polarization surveys ( with the very recent exception of * ? ? ? * ) , and is consistent with results at higher frequencies ( @xmath6 ghz ) . the anti - correlation observed in previous 1.4 ghz studies is due to two effects : a selection bias , and spurious high fractional polarization detections . both of these effects can become more prevalent at faint total flux densities . we find that components and sources can be characterised using the same distribution of fractional linear polarization , with a median level of 4% . we have presented a new lognormal model to describe the distribution of fractional polarization for 1.4 ghz components and sources , specific to agns , in surveys with resolution fwhms @xmath3 . f. no polarized sfgs were detected in atlas dr2 down to the linear polarization detection threshold of @xmath181 @xmath1jy . the atlas data constrain typical fractional polarization levels for the @xmath14 @xmath21 100 @xmath1jy sfg population to be @xmath161 . g. differences between differential number - counts of components and of sources in 1.4 ghz surveys with resolution fwhm @xmath3 are not likely to be significant ( @xmath5 20% ) at millijansky levels . h. the atlas total intensity differential source counts do not exhibit any unexpected flattening down to the survey limit @xmath182jy . i. the atlas linearly polarized differential component counts do not exhibit any flattening below @xmath100 mjy , unlike previous findings which have led to suggestions of increasing levels of fractional polarization with decreasing flux density or the emergence of a new source population . the polarized counts down to @xmath0 @xmath1jy are consistent with being drawn from the total intensity counts at flux densities where luminous fr - type radio galaxies and quasars dominate . j. constrained by the atlas data , we estimate that the surface density of linearly polarized components in a 1.4 ghz survey with resolution fwhm @xmath3 is 50 deg@xmath110 for @xmath183 @xmath1jy , and 90 deg@xmath110 for @xmath184 @xmath1jy . we estimate that the surface density for polarized sources is @xmath185 deg@xmath110 for @xmath186 @xmath1jy , assuming that most polarized components belong to dual - component sources ( e.g. fr - type ) at these flux densities . k. we find that the statistics of atlas sources exhibiting asymmetric depolarization are consistent with the interpretation that the laing - garrington effect is due predominantly to source orientation within a surrounding magnetoionic medium . to our knowledge , this work represents the first attempt to investigate asymmetric depolarization in a blind survey .

this paper focuses on stochastic partial differential equations ( spdes ) under two - time - scale formulation . the inclusion of the markov chain is for the needs of treating random environment , whereas the addition of the fast jump process enables the consideration of discontinuity in the sample paths of the fast processes . assuming either a fast changing markov switching or an additional fast - varying jump process , this work aims to obtain the averaging principles for such systems . there are several distinct difficulties . first , the noise is not square integrable . second , in our setup , for the underlying spde , there is only a unique mild solution and as a result , there is only mild it s formula that can be used . moreover , another new aspect is the addition of the fast regime switching and the addition of the fast varying jump processes in the formulation , which enlarges the applicability of the underlying systems . to overcome these difficulties , a semigroup approach is taken . under suitable conditions , it is proved that the @xmath2th moment convergence takes place with @xmath3 , which is stronger than the usual weak convergence approaches .

i

1609.09287

this paper focuses on stochastic partial differential equations ( spdes ) under two - time - scale formulation . distinct from the work in the existing literature , the systems are driven by @xmath0-stable processes with @xmath1 . in addition , the spdes are either modulated by a continuous - time markov chain with a finite state space or have an addition fast jump component . the inclusion of the markov chain is for the needs of treating random environment , whereas the addition of the fast jump process enables the consideration of discontinuity in the sample paths of the fast processes . assuming either a fast changing markov switching or an additional fast - varying jump process , this work aims to obtain the averaging principles for such systems . there are several distinct difficulties . first , the noise is not square integrable . second , in our setup , for the underlying spde , there is only a unique mild solution and as a result , there is only mild it s formula that can be used . moreover , another new aspect is the addition of the fast regime switching and the addition of the fast varying jump processes in the formulation , which enlarges the applicability of the underlying systems . to overcome these difficulties , a semigroup approach is taken . under suitable conditions , it is proved that the @xmath2th moment convergence takes place with @xmath3 , which is stronger than the usual weak convergence approaches . ./style / arxiv - general.cfg ,

averaging principles for stochastic differential equations ( sdes ) have been studied extensively , for example , in liu and vanden - eijnden @xcite , freidlin and wentzell @xcite , khasminskii @xcite , yin and zhang @xcite . recently , averaging principles for stochastic partial differential equations ( spdes ) have also drawn much attention ; see , for example , kuksin and piatnitski @xcite and maslowski _ et al . in particular , blmker _ @xcite derived averaging results with explicit error bounds for spdes with quadratic nonlinearities , where the limiting system is an sde ; cerrai and freidlin @xcite investigated the weak convergence for two - time - scale stochastic reaction diffusion equations with additive noise by using an approach based on kolmogorov equations and martingale solutions of stochastic equations ; cerrai @xcite generalized cerrai and freidlin @xcite to the case of slow fast reaction diffusion equations driven by multiplicative noise , where the reaction terms appear in both equations ; brhier @xcite gave the strong and weak orders in averaging for stochastic evolution equation of parabolic type with slow and fast time scales . for the finite - dimensional jump diffusion case , we refer to givon @xcite . in view of the development on the aforementioned singularly perturbed spdes , the noise processes considered to date are mainly square integrable processes . however , such requirement rules out the interesting @xmath0-stable processes . it is well known that both wiener processes and poisson - jump processes have finite moments of any order , whereas an @xmath0-stable process only has finite @xmath2th moment for @xmath4 . stochastic equations driven by @xmath0-stable processes have proven to have numerous applications in physics because such processes can be used to model systems with heavy tails . as a result , such processes have received increasing attentions recently . for example , priola and zabczyk @xcite gave a proper starting point on the investigation of structural properties of spdes driven by an additive cylindrical stable noise ; dong _ et al . @xcite studied ergodicity of stochastic burgers equations driven by @xmath5-subordinated cylindrical brownian motions with @xmath1 . for finite - dimensional sdes driven by @xmath0-stable noises , wang @xcite derived gradient estimate for linear sdes , zhang @xcite established the bismut elworthy li derivative formula for nonlinear sdes , and ouyang @xcite established harnack inequalities for ornstein uhlenbeck processes by the sharp estimates of density function for rotationally invariant symmetric @xmath0-stable lvy processes . nevertheless , two - time - scale formulation for stochastic processes driven by @xmath0-stable processes have not yet been considered to date to the best of our knowledge . motivated by the previous works , in this paper we develop averaging principles for two - time - scale spdes driven by @xmath0-stable noises that admit unique mild solutions . the time - scale separation is given by introducing a small parameter @xmath6 . for the case of mean - square integrable noise , the it formula plays an important role in the error analysis between the slow component and the averaging systems ; see , for example , givon @xcite , fu and duan @xcite and fu and liu @xcite . it has been noted that when the diffusion operators in fu and duan @xcite and fu and liu @xcite are hilbert schmidt , the mild solution is indeed a strong solution . nevertheless , in our case , only _ mild it s formula _ ( see , e.g. , da prato _ et al . _ @xcite , theorem 1 ) is available since the stochastic systems considered only admit mild solutions , not strong solutions . moreover , the technique adopted in brhier @xcite , lemma 3.1 , which is a key ingredient in discussing averaging principle , does not work for the case of spdes driven by @xmath0-stable noises either , although the mild solution is treated there . in our study , in addition to the spdes , we assume that the systems are modulated by a continuous - time markov chain . this markov chain has a finite state space resulting in a system of stochastic differential equations switching back and forth according to the state of the markov chain . the markov chain can be used to model discrete events that are not representable otherwise . it is by now widely recognized that such regime - switching formulation is an effective way of modeling many practical situations in which random environment and other random factors have to be taken into consideration . perhaps , one of the first efforts in modeling random environment using a finite - state markov chain can be traced back to griego and hersh @xcite ( see also the extended survey in hersh @xcite , where multiple time scale was also used ) . much of the recent modeling and analysis effort stems from the work of hamilton and susmel @xcite , who revealed the feature of the so - called regime - switching systems under which the dynamics of the systems can be quite different under different regimes . their idea stimulated much of the subsequent study . for example , in the simplest setting , the successfully used regime - switching models in financial market portraits the random environment with two states bull and bear markets , whose volatilities are drastically different . our study is divided into two parts . in the first part , we assume that the switching process is subject to fast variation , either within a weakly irreducible class or within a number of nearly decomposable weakly irreducible classes ( see yin and zhang @xcite , chapter 4 ) . the idea is that the original system subject to fast switching is more complex , but the limit system is much simpler . for many applications , it will be desirable to find the structure of the limit system leading substantial reduction of computational complexity for such tasks as control and optimization etc . we show that under suitable conditions , a limit process that is a solution of either an spde or an spde with switching is obtained . the key is that in the limit , the coefficients are averaged out with respect to the stationary measure of the switching processes . in the second part , we assume that there is an additional fast - varying random process . although the process is fast varying , it does not blow up , but rather has an invariant measure . the ergodicity of the fast process helps us to get a limit process that is a solution of the spdes with the coefficients being averaged out with respect to the stationary distribution of the fast - varying process . to summarize , there are several distinct difficulties in our problems . first , the noise is not square integrable . second , the underlying spde admits only a unique mild solution and as a result , there is only mild it s formula that can be used . moreover , another new aspect is the addition of the fast regime switching and the addition of the fast varying jump processes in the formulation , which enlarges the applicability of the underlying systems . to overcome these difficulties , using the mild solutions , a semigroup approach is taken . under suitable conditions , it is proved that the @xmath2th moment convergence takes place with @xmath3 , which is stronger than the usual weak convergence approaches . we thus term such a convergence as strong convergence . the rest of the paper is organized as follows . in section [ sec:2-sw ] , we obtain not only averaging principles for spdes with two - time - scale markov switching with a single weakly recurrent class but also for the case of two - time - scale markov switching with multiple weakly irreducible classes . in section [ fast - jump ] , we demonstrate the strong convergence for spdes with an additional fast - varying random process driven by cylindrical stable processes .

this paper is the first part of a work which consists in proving the stabilization to zero of a fluid - solid system , in dimension 2 and 3 . the considered system couples a deformable solid and a viscous incompressible fluid which satisfies the incompressible navier - stokes equations . by deforming itself , the solid can interact with the environing fluid and then move itself . the control function represents nothing else than the deformation of the solid in its own frame of reference . we there prove that the velocities of the linearized system are stabilizable to zero with an arbitrary exponential decay rate , by a boundary deformation velocity which can be chosen in the form of a feedback operator . we then show that this boundary feedback operator can be obtained from an internal deformation of the solid which satisfies the linearized physical constraints that a _ self - propelled _ solid has to satisfy . sbastien court ( communicated by the associate editor name )

i

1303.6832

this paper is the first part of a work which consists in proving the stabilization to zero of a fluid - solid system , in dimension 2 and 3 . the considered system couples a deformable solid and a viscous incompressible fluid which satisfies the incompressible navier - stokes equations . by deforming itself , the solid can interact with the environing fluid and then move itself . the control function represents nothing else than the deformation of the solid in its own frame of reference . we there prove that the velocities of the linearized system are stabilizable to zero with an arbitrary exponential decay rate , by a boundary deformation velocity which can be chosen in the form of a feedback operator . we then show that this boundary feedback operator can be obtained from an internal deformation of the solid which satisfies the linearized physical constraints that a _ self - propelled _ solid has to satisfy . sbastien court ( communicated by the associate editor name )

in this two - part work we are interested in the way a solid immersed in a viscous incompressible fluid ( in dimension 2 or 3 ) can deform itself and then interact with the environing fluid in order to stabilize exponentially to zero the velocity of the fluid and also its own velocities . the domain occupied by the solid at time @xmath0 is denoted by @xmath1 . we assume that @xmath2 , where @xmath3 is a bounded smooth domain . the fluid surrounding the solid occupies the domain @xmath4 . ( 0,0)(-100,-90 ) ( 0,0)(0,0)[lb ] ( 80,-30)(0,0)[lb ] ( -20,25)(0,0)[lb ] the movement of the solid in the inertial frame of reference is described through the time by a lagrangian mapping denoted by @xmath5 , so we have @xmath6 the mapping @xmath7 can be decomposed as follows @xmath8 where the vector @xmath9 describes the position of the center of mass and @xmath10 is the rotation associated with the angular velocity of the solid . in dimension 3 the angular velocity is a vector field whereas it is only a scalar function in dimension 2 . however , @xmath11 can be immersed in @xmath12 and this scalar function can be read on the third component of a 3d - vector . more generally in this work , since all the calculations made in dimension 3 make sense in dimension 2 , we will consider only vector fields of @xmath12 and matrix fields of @xmath13 . for instance , @xmath14 and @xmath15 are related to each other through the following cauchy problem @xmath16 will represent the identity matrix of @xmath13.]where in dimension 2 we have @xmath17 and @xmath18 . + the couple @xmath19 describes the position of the solid and is unknown , whereas the mapping @xmath20 can be imposed . this latter represents the deformation of the solid in its own frame of reference and is considered as the control function on which we can act physically . when this lagrangian mapping @xmath20 is invertible , we can link to it an eulerian velocity @xmath21 through the following cauchy problem @xmath22 without loss of generality , we assume that @xmath23 , for a sake of simplicity . if @xmath24 denotes the inverse of @xmath20 , we have @xmath25 the fluid flow is described by its velocity @xmath26 and its pressure @xmath27 which are assumed to satisfy the incompressible navier - stokes equations . for @xmath28 satisfying a set of hypotheses given further , the system which governs the dynamics between the fluid and the solid is the following @xmath29 @xmath30 @xmath31 @xmath32 where @xmath33 and where the velocity @xmath34 is defined by the following change of frame @xmath35 the symbol @xmath36 denotes the cross product in @xmath12 . the linear map @xmath37 can be represented by the matrix @xmath38 . in equations and , the mass of the solid @xmath39 is constant , whereas the inertia moment depends _ a priori _ on time . in dimension 2 the inertia moment is a scalar function which can be read on the inertia matrix given by @xmath40 in dimension 3 it is a tensor written as @xmath41 the quantity @xmath42 denotes the density of the solid , and obeys the principle of mass conservation @xmath43 where @xmath44 denotes the jacobian matrix of the mapping @xmath5 . for a sake of simplicity we assume that the solid is homogeneous at time @xmath45 : @xmath46 in system , @xmath47 is the kinematic viscosity of the fluid and the normalized vector @xmath48 is the normal at @xmath49 exterior to @xmath50 . it is a coupled system between the incompressible navier - stokes equations and the differential equations - given by the newton s laws . the coupling is in particular made in the fluid - structure interface , through the equality of velocities and through the cauchy stress tensor given by @xmath51 indeed , the dirichlet condition partially imposed by the deformation of the solid ( through the velocity @xmath34 ) influences the behavior of the fluid whose the response is the quantity @xmath52 in the fluid - solid interface . it represents the force that the fluid applies on the solid , and then it determines the global dynamics of the solid ( through equations et ) and thus its position . + the problem is the following : what is the deformation @xmath28 of the solid we have to impose in order to stabilize the environing fluid and thus induce a behavior of the fluid which stabilizes the velocities of the solid ? we shall assume a set of hypotheses on the control function @xmath28 , that we state as follows : h1 : : for all @xmath53 , @xmath20 is a @xmath54-diffeomorphism from @xmath55 onto @xmath56 . + h2 : : in order to respect the incompressibility condition given by , the volume of the whole solid has to be preserved through the time . that is equivalent to assume that @xmath57 h3 : : , which leads us to assume that @xmath58 h4 : : , which leads us to assume that @xmath59 imposing constraints and enables us to get the two following constraints on the undulatory velocity @xmath34 @xmath60 as equations and are written , the constraints and are implicitly satisfied in system . hypotheses * h3 * and * h4 * are made to guarantee the _ self - propelled _ nature of the motion of the solid , that means no other help than its own deformation enables it to interact and to move in the surrounding fluid . + the existence of global - in - time strong solutions for system has been studied in @xcite in dimension 2 and more recently in @xcite in dimension 3 . in particular , this existence in dimension 3 is conditioned by the smallness of the data , namely the initial condition @xmath61 and the displacement of the solid @xmath62 will represent the identity mapping of @xmath63 . ] ( in some sobolev spaces ) . for the full nonlinear system , the equations are written in the eulerian configuration , and thus we are lead to think that the eulerian velocity @xmath21 is the more suitable quantity to be chosen as a control function ( instead of @xmath28 ) . but such a mapping is defined on the domain @xmath64 , which is itself defined by @xmath20 . moreover , the study of such a nonlinear system is based on the preliminary study of the corresponding linearized system which is @xmath65 @xmath66 @xmath67 @xmath68 and where the more suitable control to be chosen is the function @xmath69 , related to the lagrangian velocity @xmath70 by @xmath71 notice that the constraints and are nonlinear with respect to the mapping @xmath28 . we linearize them when we consider the linear system . for this linear system , the constraint induced by hypothesis * h1 * can be relaxed , since we only consider mappings @xmath72 continuous in time and such that @xmath73 . thus the notion of _ admissible control _ for this linearized problem is made precise in definition [ deflincontrol ] . the main result of this first part is theorem [ thstablinx ] , which is equivalent to the following one : assume that @xmath74 . for all @xmath61 satisfying @xmath75 and the following compatibility conditions @xmath76 system is stabilizable with an arbitrary exponential decay rate @xmath77 , that is to say that for all @xmath78 there exists a boundary control @xmath79 and a positive constant c , @xmath80 or @xmath81 will denote some generic positive constants which do not depend on time or on the unknowns . ] depending only on @xmath61 such that for all @xmath82 the solution @xmath83 of system satisfies @xmath84 for proving this theorem we study the system that has to satisfy the functions @xmath85 and the goal is then to prove that there exists a control @xmath69 such that this system admits a solution @xmath86 bounded in some infinite time horizon space . the strategy we follow is globally the same as the one used in @xcite , at least for the linearized problem . it first consists in rewriting the full nonlinear system in space domains which do not depend on time anymore , by using a change of variables and a change of unknowns . then we can make appear all the nonlinearities ( specially those which are due to the variations of the geometry through the time ) and we can set properly the linearized system . the second step of the proof consists in formulating the linearized system in terms of operators where the pressure is actually eliminated and encodes a _ mass - added effect_. this writing enables us to define an analytic semigroup of contraction generated by an operator which presents interesting spectral properties : indeed the unstable modes that we have to stabilize are actually countable and in finite number . besides , we prove by a unique continuation argument the approximate controllability of this linearized system . thus , in order to define the boundary control that stabilizes the full linearized system , it is sufficient to consider a finite - dimension linear system for which the approximate controllability is equivalent to the feedback stabilizability . the aforementioned control can be defined on a finite - dimension space in a feedback operator form , what will be useful for proving the stabilization of the full nonlinear system . + with regards to the methods , a novelty is the means provided in a last section which enables us to define from a boundary control an internal deformation satisfying the linearized constraints . this result too will be useful for the definition of a deformation of the solid - which has to satisfy the nonlinear constraints - that stabilizes the nonlinear system : considering a deformation which satisfies in a first time the linearized constraints is not necessarily from a mathematical point of view , but the method with which we obtain it will be important for defining a deformation satisfying the nonlinear constraints ( see section 5 of part ii ) ; besides , from a physical point of view , considering for the linearized system a deformation which satisfies the linear constraints is relevant since it ensures the conservation of the momenta for the whole fluid - solid linear system . + the idea of considering first the linearized problem relies on the fact that for small perturbations ( that is to say for small initial conditions @xmath87 , @xmath88 and @xmath89 ) the behavior of the nonlinear system is close to the one of the linearized system . + + thus the same statement will be proven in the second part of this work for the unknowns of the full nonlinear system . the result is nonintuitive : it says somewhat that all the fluid in which the solid swims can be stabilized just by the help of this swimmer , at an intermediate reynolds number . this kind of problem has been investigated in @xcite for instance , where it is considered other types of fluid - swimmer systems . the same kind of purpose has been also investigated at a low reynolds number in @xcite and more recently in @xcite , for the stokes system , and in @xcite in the case of a perfect fluid . the control of the motion of a boat at a high reynolds number has been recently studied in @xcite . besides , the same kind of techniques that we use in this work have been used for other coupled systems involving the incompressible navier - stokes equations ; let us cite @xcite and @xcite for instance , where the stabilization of other fluid - structure problems is proven . definitions and notation are given in section [ secdef ] . the linearized system is studied in section [ linearsec ] where it is rewritten through an operator formulation for which we prove useful properties . the approximate controllability of this linearized system is proven in section [ secapproxcont ] . it leads to the main result of this paper , namely the feedback stabilization of the linearized system in section [ secfeedback ] . finally in section [ secahah ] we provide a means to recover an internal deformation of the solid from a feedback boundary control which lives only in the fluid - solid interface . this final section is the transition to the second part of this work where the considered control is an internal deformation of the solid .

, the low - lying excitation spectrum is found at the yang - lee edge singularity . based on transfer matrix techniques , the single structure constant the results of both types of measurements are found to be fully consistent with the predictions for the @xmath1 minimal conformal field theory , which was previously identified with this critical point .

i

0912.3654

this paper studies the yang - lee edge singularity of 2-dimensional @xmath0 ising model based on a quantum spin chain and transfer matrix measurements on the cylinder . based on finite - size scaling , the low - lying excitation spectrum is found at the yang - lee edge singularity . based on transfer matrix techniques , the single structure constant is evaluated at the yang - lee edge singularity . the results of both types of measurements are found to be fully consistent with the predictions for the @xmath1 minimal conformal field theory , which was previously identified with this critical point .

in 1978 , fisher @xcite proposed that yang - lee edge singularities @xcite are critical points . later , cardy @xcite argued that the yang - lee edge singularity of the 2d ising model should be identified with the @xmath1 minimal conformal field theory ( cft ) @xcite of the ade classification @xcite . cardy s identification provides cft predictions for this yang - lee edge singularity . this article tests different predictions coming from cardy s identification . in section 2 , we provide measurements of the low - lying excitation spectrum at yang - lee edge singularity of the 2d ising model . the measured low - lying excitation spectrum is also compared with predictions from cardy s identification of the @xmath1 minimal cft with this yang - lee edge singularity of the 2d ising model @xcite . cardy s identification also determines the forms of 2-point and 3-point correlations . in particular , these correlations define universal amplitudes , which are known as structure constants @xcite . such predictions are an important advance that cft brought to the understanding of critical points of 2d statistical models . no tests of such predictions have been performed for critical points associated with non - unitary cfts . in section 3 , we provide a measurement of the universal amplitude associated with the yang - lee edge singularity of the 2d ising model . the measured amplitude is also compared with the prediction from cardy s identification of the @xmath1 minimal cft with this yang - lee edge singularity .

though it is generally assumed that massive molecular clouds are the progenitors of globular clusters , their detailed formation mechanism is still unclear . standard scenarios based on the collapse of a smooth matter distribution suffer from strong requirements with respect to cluster formation time scale , binding energy and star formation efficiency . an alternative model assuming cluster formation due to the recollapse of a supernova - induced , fragmented shell can relax these difficulties . in this paper the final collapse stages of the different scenarios are compared by n - body simulations for shells and spheres .

i

astro-ph0007144

though it is generally assumed that massive molecular clouds are the progenitors of globular clusters , their detailed formation mechanism is still unclear . standard scenarios based on the collapse of a smooth matter distribution suffer from strong requirements with respect to cluster formation time scale , binding energy and star formation efficiency . an alternative model assuming cluster formation due to the recollapse of a supernova - induced , fragmented shell can relax these difficulties . in this paper the final collapse stages of the different scenarios are compared by n - body simulations for shells and spheres . it is shown that fragmentation is much more pronounced for shells . taking a galactic tidal field into account shells preferably form twin ( or multiple ) systems , whereas spheres end up as single clusters . the twins are characterized by identical metallicities , and stellar mass functions ; some of them show counter - rotating cores . their orbital evolution can result in both , a final merger or well separated twins sharing a common galactic orbit .

most formation scenarios of globular clusters commence with giant molecular clouds ( gmcs ) undergoing a phase of rapid star formation . this star formation can be triggered by several processes , e.g. a thermal instability ( fall & rees 1985 ; murray & lin 1990 ) , a radiative shock ( kang et al . 1990 ; shapiro 1993 ) or other perturbations like collisions of clouds ( fujimoto & kumai 1997 ; lee , schramm , & mathews 1995 ) or galaxy interactions ( ashman & zepf 1992 ) . a common characteristic of all these scenarios is , that globulars are formed from smooth gaseous distributions ( if we neglect the clumpy structure of the gmcs for the moment ) which are transformed into stars . this assumption leads to several difficulties : first , the gravitational binding energy of a homogeneous gmc with @xmath0 and a radius of 30 pc is about @xmath1 ergs , whereas it decreases for a @xmath2 cloud of 10 pc to less than @xmath3 ergs . thus , already a single supernova injects sufficient energy to destroy a small cloud completely , and a few ob stars can even disrupt a @xmath0 cloud . therefore , the formation of the globular must have been finished within a few myrs , before the first ob stars explode . a second problem is related to the star formation efficiency ( sfe ) . assuming that the gmc is in virial equilibrium prior to the cluster formation and that the newly born stars keep the velocity of their parent gas packages , the total energy @xmath4 of the stellar system can be estimated by @xmath5 ( with the gmc mass @xmath6 , its radius @xmath7 and the gravitational constant @xmath8 ) . thus , the system is only gravitationally bound ( i.e. @xmath4 becomes negative ) , if the sfe @xmath9 , which is the mass fraction of the gmc transformed into stars , is larger than 50% . though mass redistribution in a violent relaxation stage and a detailed treatment of the energy injection can reduce the critical level down to 20% ( goodwin 1997 ) , the required sfe still exceeds the typical observed values for gmcs by at least one order of magnitude ( blitz 1993 ) . with respect to these problems , an alternative suggestion by brown , burkert , & truran ( 1991 ) is very interesting : they suggest that cluster formation starts with an ob - association undergoing typeii supernova events near the center of a molecular cloud . the expanding supernova remnant sweeps up the cloud material , decelerates and might almost be stopped by the external pressure of the ambient hot gas . meanwhile the shell breaks into fragments and forms stars . if the total energy of this stellar shell is negative , the stars will recollapse and form a bound system . for a simplified spherical configuration burkert , brown , & truran ( 1993 ) demonstrated that the binding energy of an isolated shell always becomes negative _ independent _ of the sfe , provided the star formation process does not start too early . thus , the sfe efficiency problem is less severe for this scenario . in case of an homogeneous ambient medium ( e.g. in the core of a gmc ) ehlerov et al . ( 1997 ) demonstrated that fragmentation in an expanding shell takes sufficient time to prevent too rapid star formation . this result holds also for non - homogeneous power - law density profiles , if the density distribution in the gmc is not steeper than isothermal ( theis et al . 1998 ) . according to the shell - scenario the dynamics of its last stage , i.e. the collapse of a thin stellar shell , is studied and compared with the collapse of homogeneous spheres representing the standard scenarios . n - body simulations are performed for isolated configurations as well as for collapses within a galactic tidal field . the main question addressed here is , whether we can discern between different formation scenarios by means of their collapse dynamics .

the overall spectral energy distribution ( sed ) in @xmath1 peaks at a rest wavelength @xmath2 and is reddened by 1.6 visual magnitudes . correction for reddening brings 1556 + 3517 within 1.3 sigma from the @xmath3 dividing line between radio - loud and radio - quiet sources . the mid - ir luminosity integrated over the 1.86 @xmath0 rest wavelength range is @xmath4 ( @xmath5 ) , which requires at least @xmath6 of dust and @xmath7 of associated gas . it is unlikely that such a large mass stems from the bal wind itself .

c

astro-ph9711314

to date , the quasar 1556 + 3517 is the only radio loud broad absorption line qso ( balqso ; becker et al . 1997 ) . this prompted narrow band filter imaging observations in the range 415 @xmath0 with the iso satellite . the source is clearly detected in all filters and appears point - like and isolated at the resolution of iso . the overall spectral energy distribution ( sed ) in @xmath1 peaks at a rest wavelength @xmath2 and is reddened by 1.6 visual magnitudes . correction for reddening brings 1556 + 3517 within 1.3 sigma from the @xmath3 dividing line between radio - loud and radio - quiet sources . the mid - ir luminosity integrated over the 1.86 @xmath0 rest wavelength range is @xmath4 ( @xmath5 ) , which requires at least @xmath6 of dust and @xmath7 of associated gas . it is unlikely that such a large mass stems from the bal wind itself .

the overall rest frame spectral energy distribution ( sed ) of 1556 + 3517 , from 1.5 ghz to the b band , is plotted in fig.[sed ] , where the optical and radio data are taken from becker et al . all observed fluxes have been converted to rest frame luminosities @xmath37 ( in ergs@xmath38 ) assuming @xmath39 , @xmath40 and using the standard equations ( e.g. weedman 1986 ) : where l@xmath43 is the monochromatic luminosity per unit frequency in the rest frame of the qso , f@xmath44 is the monochromatic flux per unit frequency in the observer s frame , d is the distance to the qso and the other symbols have their usual meanings . the sed of the quasar iras 14026 + 4341 is also shown in fig.[sed ] for comparison , the data being taken from low et al . the comparison is illustrative since iras 14026 + 4341 is an iras discovered balqso with a large ir - to - optical luminosity ratio ( low et al . it is immediately apparent that , despite similar ultraviolet luminosities , 1556 + 3517 is almost an order of magnitude more luminous in the near to mid - ir than 14026 + 4341 . this presumably indicates the presence of a large amount of warm dust in 1556 + 3517 which causes a depression of the optical - uv continuum by reddening and an enhancement of the near and mid - ir flux because of grain thermal emission . the 1556 + 3517 spectral index ( @xmath45 ) from the b band ( @xmath46 ) to the lw1 filter ( @xmath47 ) is @xmath48 . using the r band ( @xmath49 ) flux instead yields @xmath50 . both indices are significantly steeper than those of `` normal '' non - bal quasars . note that only the hottest dust grains at @xmath51 k yield a significant contribution to the 1.81 @xmath0 flux . since such a temperature is higher or equal to the grain sublimation temperature , relatively little dust thermal emission is expected at this wavelength . hence , to a first approximation , the steep uv - to - near - ir spectral index of 1556 + 3517 is mostly a consequence of dust extinction . 1 . the 1774.2 band lies in a region relatively free of any strong emission or absorption lines . this is not the case of the 2823 band which is contaminated by the @xmath53 emission and absorption . 2 . more importantly , the 2823 band is definitely enhanced by balmer continuum ( bac ) emission and blended low - contrast feii emission lines which create a pseudo - continuum in quasar spectra often referred to as the `` small bump '' . 1 . the `` intrinsic '' , i.e. un - reddened , optical - uv spectral index of 1556 + 3517 is -0.5 . within the uncertainty , this is equal to the mean uv spectral index @xmath54 of the sample of 33 high redshift ( z@xmath551 ) qsos of obrien , gondhalekar and wilson ( 1988 ) as well as to the mean optical spectral index @xmath56 of the large 227 qso sample of cheney and rowan - robinson ( 1981 ) or that obtained by neugebauer et al . ( 1987 ) from their sample of 104 quasars ( @xmath57 ) . the reddening law is as parametrized by seaton ( 1979 ) in the optical - ultraviolet range and as tabulated by rieke and lebofsky ( 1985 ) from 1 to 13@xmath0 . where @xmath60 $ ] is the ( rest ) wavelength range over which the spectral index is measured ( 0.1771.810 @xmath0 in the present case ) and the function @xmath61 is the reddening law at wavelength @xmath10 . this yields a visual extinction @xmath62 magnitudes which implies that the continuum is reddened by 4.01 magnitudes at a rest wavelength of 1774 but only 0.256 magnitudes at 1.81 @xmath0 . note that the foreground galactic extinction in the direction of 1556 + 3517 ( @xmath63 ) is only 0.05 v magnitudes and can be neglected . after correction for extinction , the radio to optical flux ratio becomes @xmath64 if the b band data are used to derive the flux at @xmath65 ( k correction ) and @xmath66 if one uses the r flux instead . the two estimates differ at the 1.1 sigma level only . i therefore adopt the mean of the two @xmath67 . such a ratio is less than 1.3 sigma away from the @xmath3 dividing line between radio - loud and radio - quiet quasars . one therefore concludes that the case for 1556 + 3517 being radio - loud is marginal , at best . it is also worth pointing - out that de - reddening brings 1556 + 3517 close to the @xmath3 line where data suggests that there is an apparent excess of balqsos over non - balqsos ( francis , hooper and impey 1993 ) . the near to mid - ir luminosity @xmath68 of 1556 + 3517 was computed by integrating all the de - reddened rest - frame emission over the range @xmath69 to @xmath70 after subtraction of an -0.5 index power - law matching the de - reddened b band and lw1 band luminosities : @xmath71 . one can use @xmath68 to estimate the mass of dust responsible for near to mid - ir emission in 1556 + 3517 . the mean rest wavelength of the mir emission corresponds to a black - body temperature of @xmath8740 k. under the assumptions that the dust grains have a mean size of 0.1 @xmath0 and radiate like black - bodies and following rudy and puetter ( 1982 ) , i obtain a dust mass @xmath72 . this should in fact be seen as a lower limit since actual grains are likely to emit less efficiently than black - body thereby requiring an even larger mass to produce the observed mir luminosity . for a normal galactic dust to gas mass ratio of 200 , this implies a total mass of gas of about @xmath7 . the color temperature of the dust is higher than that of typical hii regions which suggests that it is closely associated to the active nucleus . it is therefore legitimate to ask whether the dusty gas responsible for the mir emission could be the bal wind itself . in the disk wind model of murray et al . ( 1995 ) , the bal region covering factor is about 10 % , its column density @xmath73 and its inner radius is of the order of @xmath74 cm . this yields a bal mass @xmath75 , more than 4 orders of magnitude smaller than the above estimate . of course , there is more mass available as the wind will accumulate material over the years . for an axially symmetrical wind , the mass flow rate is given by : @xmath76 where , @xmath77 is the solid angle sustained by the wind as seen from the central source , @xmath78 its column density in units of @xmath79 , @xmath80 its radius in units of @xmath81 , and @xmath82 its velocity in units of @xmath83 . assuming parameters value as in murray et al s model yields @xmath84 . this implies that the bal phenomenon should have lasted at least @xmath8 250,000 years to accumulate the mir emitting gas . while such a value in itself is not unreasonable , there are problems with this scenario : * on the one hand , the dust must somehow `` see '' the central uv source in order to retain a temperature of @xmath8 700 k for such a long time . however , given the mass involved and the geometry of the wind , the opacity will be extremely high and the bulk of the dust and gas will be ( self-)shielded from the central source . * this gas would presumably be at least partially ionized . since the total column would far exceed @xmath85 , the gas would be opaque to free - free absorption and the continuum totally suppressed , contrary to what is observed . it therefore seems unlikely that the observed mir emission originates from the wind itself . a more plausible origin would be e.g. , the molecular torus , the narrow line region , or a recent burst of star formation . it is a pleasure to thank the time allocation committee for awarding discretionary iso observing time to this project . i am also grateful to the referee , dr . ray weymann , for valuable comments which improved the manuscript .

transport and torque magnetometry measurements are performed at high magnetic fields and low temperatures in a series of p - type ( ca - doped ) bi@xmath0se@xmath1 crystals . the angular dependence of the shubnikov - de haas and de haas - van alphen quantum oscillations enables us to determine the fermi surface of the bulk valence band states as a function of the carrier density . at low density , the angular dependence exhibits a downturn in the oscillations frequency between @xmath2 and @xmath3 , reflecting a bag - shaped hole fermi surface .

i

1603.02603

transport and torque magnetometry measurements are performed at high magnetic fields and low temperatures in a series of p - type ( ca - doped ) bi@xmath0se@xmath1 crystals . the angular dependence of the shubnikov - de haas and de haas - van alphen quantum oscillations enables us to determine the fermi surface of the bulk valence band states as a function of the carrier density . at low density , the angular dependence exhibits a downturn in the oscillations frequency between @xmath2 and @xmath3 , reflecting a bag - shaped hole fermi surface . the detection of a single frequency for all tilt angles rules out the existence of a fermi surface with different extremal cross - sections down to @xmath4 mev . there is therefore no signature of a camel - back in the valence band of our bulk samples , in accordance with the direct band gap predicted by @xmath5 calculations .

bi@xmath0se@xmath1 is a narrow gap layered semiconductor which together with bi@xmath0te@xmath1 have been studied for decades for their thermo - electric properties.@xcite the interest in this class of materials has recently surged because of the prediction @xcite and observation @xcite of a unique type of charge carriers existing at their surface , the so - called `` helical dirac fermions '' , which behave as massless relativistic particles with a spin locked to their translational momentum . bi@xmath0se@xmath1 therefore now belongs to the 3d topological insulators family characterized by a bulk gap coexisting with 2d conducting surface states . as a matter of fact , the existence of gapless states at the boundary of the material is related to a well defined change in the _ bulk _ band structure . in bi@xmath0se@xmath1 , this originates from a parity inversion of the valence and conduction bands at the @xmath6 point of the brillouin zone in the presence of a large spin orbit coupling . @xcite the linear - in - momentum dispersion relation which characterizes the 2d surface states thus emerges from the general hamiltonian of massive dirac fermions , @xcite theoretically expected to describe the bulk states in bi@xmath0se@xmath1 . pioneering experimental studies of the bulk conduction band at low energy @xcite have reported an ellipsoidal electron fermi surface , which was described within a simple model of massive carriers with a parabolic ( non - parabolic ) dispersion in the k@xmath7 ( k@xmath8 ) direction , where k@xmath7 ( k@xmath8 ) is the momentum in the direction perpendicular ( parallel ) to the @xmath9-axis of the crystal . this is accompanied by an increasing anisotropy of the fermi surface observed as the fermi level increases in the conduction band . more recent transport , @xcite nmr , @xcite and magneto - optics @xcite measurements have confirmed the original parameters phenomenologically describing the bulk conduction band , and in some cases @xcite connected them to the 3d dirac hamiltonian for massive fermions applied to topological insulators . however , experimental studies of the _ valence band _ bulk fermi surface are to our knowledge scarce . the principal reason is that as - grown bi@xmath0se@xmath1 is electron - doped due to the presence of se vacancies . the discovery of 2d surface states has nevertheless triggered large efforts to reach the topological insulator regime , where the fermi level lies in the band gap of the bulk band structure . for instance , substituting trace amounts of ca@xmath10 for bi@xmath11 in as - grown bi@xmath0se@xmath1 can lower the fermi energy of the native n - type crystals . above a certain value of ca - doping @xmath12 , the electrical conduction in bi@xmath13ca@xmath14se@xmath1 is supported by hole carriers rather than electrons . @xcite further doping brings the fermi level deep in the previously inaccessible valence band . very recently , shubnikov - de haas ( sdh ) measurements have been reported @xcite in p - type bi@xmath0se@xmath1 samples with hole concentrations estimated between @xmath15 @xmath16 and @xmath17 @xmath16 . a bag - like closed fermi surface was observed at low concentration , with the suggestion of open tubes appearing in the fermi surface at high carrier density . in spite of these first experimental advances , and several theoretical works , @xcite the low - energy details of the valence band are still not unambiguously determined . in particular , a local minimum was suggested to form at the @xmath6 point as a consequence of the spin - orbit coupling . while a camel - back structure is observed in the valence band near the surface , @xcite it is absent in some bulk measurements . @xcite more recent @xmath5 calculations @xcite show that the electron - electron interactions reduce the band gap at the @xmath6 point and wash out the camel - back structure . this issue brings further motivation to experimentally investigate the bulk valence band , in particular close to the @xmath6 point . in this article , we present a doping dependent study of the bulk valence band fermi surface in bi@xmath0se@xmath1 in a previously unexplored low energy range . high quality calcium - doped bi@xmath0se@xmath1 crystals are studied by magneto - transport and torque magnetometry at low temperatures and under magnetic fields up to 30 t. a high resolution angular dependence of the quantum oscillations ( both shubnikov - de haas ( sdh ) and de haas - van alphen ( dhva ) ) enables us to map out the fermi surface of the bulk valence band states , in the energy range @xmath18 20 - 60 mev . at low fermi energies , a downturn is observed in the angular dependence of the oscillations frequency between @xmath2 and @xmath3 , demonstrating a bag - shaped closed fermi surface . importantly , a single frequency dominates the fft spectra regardless of the magnetic field orientation , showing that no camel - back structure is observed for energies down to @xmath19 24 mev . the existence of a camel - back structure for lower energies is hardly probable in respect to the experimental @xmath20 dependence , which points to a direct band gap . the fermi surface anisotropy increases rapidly as the fermi level goes higher in the valence band , and pipe - like structures previously reported at high energy are confirmed and attributed to trigonal warping . the apparent hole effective mass , defined in the parabolic band approximation , is obtained by temperature - dependent studies for @xmath21-axis , and lies in the @xmath22 range for @xmath23 mev . high magnetic fields measurement in the lowest density samples enable us to approach the quantum limit for holes which is finally discussed .

a rather moderate non - violent evolution of the density in the first `` topology - preserved '' scenario is contrasted with a highly - non - equilibrium dynamics characterizing an explosive changes of the density profiles in the second scenario . the universality of the discovered scenarios is explicitly confirmed in 1d , 2d and 3d many - body computations in ( a)symmetric traps and repulsive finite / long range inter - particle interaction potentials of different shapes . the respective many - body hamiltonian is @xmath4 \!+\!\sum_{j < k}^n \lambda_0 w(\r_j\!-\!\r_k ) , \nonumber$ ] @xmath5 , @xmath6 . all the results reported in this letter have been obtained for @xmath7 bosons interacting via inter - particle interaction function @xmath8 of half - width @xmath9 with @xmath10 in 1d , 2d and 3d . is called permanent @xmath18 : @xmath19 . here @xcite for a few applications . s1(b ) of the supplemental material . at @xmath44 we suddenly displace the trap with respect to its origin @xmath45 . [ fig1](a ) . [ fig1](b ) . s1(a ) of the supplementary material . [ fig1](c ) . the wave - packet reveals highly - non - equilibrium explosive dynamics which is accompanied by the formation of complicated oscillating patterns in the density . the character of this dynamics differs drastically from the evolutions studied above , compare panels ( a - b ) with panel ( c ) of fig . [ fig1 ] . a main claim of this letter is that these reactions are generic features of disturbed strongly interacting repulsive systems . to confirm this generality fig . trapping potentials and computed density are shown on the lower panels . fig2](a ) ; from @xmath62 , at @xmath63 in the fig . [ fig2](b ) ; from @xmath64 , at @xmath65 in the fig . [ fig2](c ) . [ fig2](a ) , we have scaled them by a factor of 40 . let us digest the physics of the above observed dynamical regimes . in the non - violent evolutions , see e.g. fig . [ fig2](b ) for 2d , the strong repulsion prevents an exchange of the particles between the sub - clouds , so they do not come to a proximity for a contact . the available energy is redistributed between the excited states which have multi - node structures and can be delocalized over the entire trap . as a result computation time on the bwgrid , hlrs and k100 clusters are greatly acknowledged . a partial financial support by the dfg is acknowledged . 64 m. girardeau , j. math . phys . * 1 * , 516 ( 1960 ) . rev . lett . * 95 * , 190406 ( 2005 ) . m. a. baranov , phys . rep . * 464 * , 71 ( 2008 ) . t. lahaye _ et al . _ , rep . . phys . * 72 * , 126401 ( 2009 ) . soc . am . b _ * 6 * , a208 ( 2010 ) . phys . rev . a * 82 * , 033412 ( 2010 ) . phys . rev . lett . * 104 * , 195302 ( 2010 ) . m. viteau , m. g. bason , j. radogostowicz , n. malossi , d. ciampini , o. morsch , and e. arimondo , phys . rev . lett . * 107 * , 060402 ( 2011 ) . see supplemental material at ` http://link.aps.org/supplemental/ ` for discussion on possible experimental control and realization of the predicted phenomena in `` rydberg - dressed '' ultra - cold systems @xcite , and for movies of the reported 2d and 3d mctdhb dynamics . a. i. streltsov , phys . rev . a * 88 * , 041602(r ) ( 2013 ) . rev . lett . * 99 , * 030402 ( 2007 ) . rev . a * 77 , * 033613 ( 2008 ) . rev . lett . * 100 * , 130401 ( 2008 ) . rev . lett . * 103 * , 220601 ( 2009 ) . rev . lett . * 106 * , 240401 ( 2011 ) . rev . a * 86 * , 063606 ( 2012 ) . natl . acad . sci . usa * 109 * , 13521 ( 2012 ) . m. greiner _ rev . a * 78 * , 023615 ( 2008 ) . # 1@xmath75 *o *

r

1312.6174

two generically different but universal dynamical quantum many - body behaviors are discovered by probing the stability of trapped fragmented bosonic systems with strong repulsive finite / long range inter - particle interactions . we use different time - dependent processes to destabilize the systems a sudden displacement of the trap is accompanied by a sudden quench of the strength of the inter - particle repulsion . a rather moderate non - violent evolution of the density in the first `` topology - preserved '' scenario is contrasted with a highly - non - equilibrium dynamics characterizing an explosive changes of the density profiles in the second scenario . the many - body physics behind is identified and interpreted in terms of self - induced time - dependent barriers governing the respective under- and over - a - barrier dynamical evolutions . the universality of the discovered scenarios is explicitly confirmed in 1d , 2d and 3d many - body computations in ( a)symmetric traps and repulsive finite / long range inter - particle interaction potentials of different shapes . implications are briefly discussed . one of the most bright universal features shared by many - body systems with strong repulsive interaction is the formation of multi - hump structures in the ground states densities . driven by the strong repulsive interaction they can be formed in the systems with short- and finite / long - range inter - particle interactions in one- ( 1d ) , two- ( 2d ) and three - dimensional ( 3d ) setups . the famous examples in the context of ultra - cold systems are strong contact interaction and tonks - girardeu gases in 1d @xcite and in more general physical contents the formation of super - solids and crystals in 2d systems with long - range interactions @xcite . while ground state properties of these systems have been accessed at different levels of the quantum theory , the many - body studies on excited states , needed to digest dynamical behavior and stability of these systems are rather scarce . because of the intrinsic complexity and correlations of these systems , the understanding of their dynamical stability as a time - dependent process at a proper many - body level is a challenging theoretical and cumbersome computational task and is still missed . in this letter we investigate the stability of such strongly repulsive many - boson systems with muti - hump many - body states as a time - dependent process by solving the time - dependent many - boson schrdinger equation @xmath0 in 1d , 2d and 3d setups for several dynamical scenarios involving manipulations with external trap @xmath1 and with the strength @xmath2 of inter - boson interaction potential @xmath3 . the respective many - body hamiltonian is @xmath4 \!+\!\sum_{j < k}^n \lambda_0 w(\r_j\!-\!\r_k ) , \nonumber$ ] @xmath5 , @xmath6 . all the results reported in this letter have been obtained for @xmath7 bosons interacting via inter - particle interaction function @xmath8 of half - width @xmath9 with @xmath10 in 1d , 2d and 3d . the inter - particle interactions of similar shapes naturally appear in the so - called `` rydberg - dressed '' ultra - cold systems @xcite which are of current experimental interest @xcite . the repulsive inter - particle interaction functions of other shapes with similar range and strength would result in qualitatively the same physics as reported here , see also the supplemental material @xcite for discussion . recently , we have verified at an accurate many - body level @xcite that in bosonic systems with strong repulsion confined in simple , barrier - less traps particular patterns of the ground state density , i.e. , number of the humps and correlations , are governed by the geometrical interplay between the width / range of the inter - boson interaction potential and the available volume ( length of the trap ) . examples of such two - hump states in 1d and 3d setups are depicted in fig . [ fig1 ] and fig . [ fig3 ] at t=0 . intuitively , one can associate each hump of a multi - hump state with a localized subsystem and to describe , therefore , the overall wave - function @xmath11 as a superposition of all constituting fragments . a configuration where @xmath12 bosons are residing in the first fragment @xmath13 , @xmath14 in @xmath15 , etc . , and @xmath16 in @xmath17 is called permanent @xmath18 : @xmath19 . here we have already admitted that the shapes of the constituting sub - clouds can evolve in time . for a realistic description this idealized picture of a single configuration with a fixed number of particle residing in each fragment should be augmented by other processes describing , e.g. , the exchange and hopping of particles between the fragments . the many - body theory naturally taking into account this time - dependency of the fragments as well as all possible hopping processes within has recently been developed and called multi - configurational time - dependent hartree method for bosons ( mctdhb ) @xcite , also see refs . @xcite for a few applications . the mctdhb many - body wavefunction is a linear combination of all above described _ time - dependent _ permanents @xmath20 the evolutions of the coefficients @xmath21 describing all possible hopping processes in the system and the dynamical changes of the shapes of every fragment @xmath22 are determined by solving the mctdhb equations : @xmath23.\nonumber\end{aligned}\ ] ] here @xmath24 is the single particle hamiltonian , @xmath25 and @xmath26 are the matrix elements of the reduced one- and two - body densities of @xmath27 . the local time - dependent potentials @xmath28 originate from the two - body interaction and play a crucial role in the physics studied here . to investigate the dynamical stability of a desired state as a time - dependent process we , first , specify this state by providing corresponding initial conditions @xmath29 and @xmath30 , and then monitor how these quantities change in time in a response to the applied modification of the trap @xmath31 and/or to a quench of the interaction strength @xmath2 of @xmath32 . our goal is to investigate the dynamical stability of the multi - hump multi - fold fragmented states . in ref . @xcite we have shown that in simple , barrier - less traps the number of humps and fragmentation ratio of the bosonic system with finite- and long - range repulsive interactions in the ground state can be equivalently controlled by varying either the strength of the inter - particle repulsion @xmath2 , the tightness / strength of harmonic confinement @xmath33 , or by changing the number @xmath34 of trapped particles . in the supplemental material @xcite , a detail control of the humps structures of the ground state in parabolic trap and inter - particle interaction @xmath35 of half - width @xmath36 with @xmath37 , studied throughout this work , is presented . so , from now on we assume that a ground state with a desired humps structures and fragmentation ratio is available . and a simultaneous quench of the inter - particle repulsion . the initial state is the ground state of @xmath38 bosons confined in @xmath39 with @xmath40 . minkovski - like space - time evolutions of the density are plotted for the scenarios activated by the displacement of the trap ( a ) without quench of the repulsion ; ( b ) with small increase of the repulsion @xmath41 ; ( c ) with substantial decrease of the repulsion @xmath42 . panels ( a , b ) reveal a first generic regime non - violent , under - a - barrier dynamics . panel ( c ) represents a second , over - a - barrier regime with a highly - non - equilibrium , explosive changes of the density . all quantities shown are dimensionless.,title="fig:",width=94 ] and a simultaneous quench of the inter - particle repulsion . the initial state is the ground state of @xmath38 bosons confined in @xmath39 with @xmath40 . minkovski - like space - time evolutions of the density are plotted for the scenarios activated by the displacement of the trap ( a ) without quench of the repulsion ; ( b ) with small increase of the repulsion @xmath41 ; ( c ) with substantial decrease of the repulsion @xmath42 . panels ( a , b ) reveal a first generic regime non - violent , under - a - barrier dynamics . panel ( c ) represents a second , over - a - barrier regime with a highly - non - equilibrium , explosive changes of the density . all quantities shown are dimensionless.,title="fig:",width=94 ] and a simultaneous quench of the inter - particle repulsion . the initial state is the ground state of @xmath38 bosons confined in @xmath39 with @xmath40 . minkovski - like space - time evolutions of the density are plotted for the scenarios activated by the displacement of the trap ( a ) without quench of the repulsion ; ( b ) with small increase of the repulsion @xmath41 ; ( c ) with substantial decrease of the repulsion @xmath42 . panels ( a , b ) reveal a first generic regime non - violent , under - a - barrier dynamics . panel ( c ) represents a second , over - a - barrier regime with a highly - non - equilibrium , explosive changes of the density . all quantities shown are dimensionless.,title="fig:",width=94 ] let us first take a two - hump two - fold fragmented system in 1d , obtained as the ground state of @xmath38 bosons confined in @xmath43 with @xmath40 , see fig . s1(b ) of the supplemental material . at @xmath44 we suddenly displace the trap with respect to its origin @xmath45 . the computed density of the evolving many - body wave - packet in a minkovskii - like space - time representation is depicted in fig . [ fig1](a ) . the main observation is that this manipulation of the trap induces only a non - violent many - body dynamics the two - hump topology and the two - fold fragmentation of the system persist for all the presented times . now we enrich the dynamical scenario studied above by imposing onto the same initial system together with the sudden displacement of the trap at @xmath44 also a sudden small quench of the inter - particle repulsion form @xmath41 . the computed wave - packet evolution is depicted in a minkovski - like manner in fig . [ fig1](b ) . the wave - packet dynamics reveals along with a relative simple motion induced by the trap displacement also new additional features . the sub - clouds forming the wave - packet change their widths during the evolution back and fourth , i.e. , they `` breath '' . these breathings slightly disturb and modulate the perfect harmonic - like oscillations of both sub - clouds . next , in a third scenario we take the same initial state as before , suddenly displace the trap at @xmath44 but now significantly decrease the strength of the inter - particle repulsion form @xmath42 . at this value of the inter - particle interaction the ground state of the final system has a one - hump topology and is fully condensed , see fig . s1(a ) of the supplementary material . so , this scenario can be considered as an attempt to make a super - fluid from an initially fragmented system . the corresponding minkovski - like evolution of the density is shown in fig . [ fig1](c ) . the wave - packet reveals highly - non - equilibrium explosive dynamics which is accompanied by the formation of complicated oscillating patterns in the density . the character of this dynamics differs drastically from the evolutions studied above , compare panels ( a - b ) with panel ( c ) of fig . [ fig1 ] . the studied 1d many - body systems demonstrate two , generically different reactions to the applied manipulations with the external trapping and inter - particle interaction potentials a non - violent and a highly - non - equilibrium , explosive ones . a main claim of this letter is that these reactions are generic features of disturbed strongly interacting repulsive systems . to confirm this generality we have extended the above reported manipulations with trap displacements and quenches of the inter - particle interactions to 2d and 3d setups , see figs . [ fig2],[fig3 ] and the supplementary material for details . a this point it is worthwhile to stress that all the multi - hump systems studied here are initially fragmented and remain fragmented during the non - violent and explosive time - evolutions . in fragmented systems , there are no definite phase relations ( correlation ) between the sub - fragments , pretty much as in mott - like states @xcite . in fully condensed systems , in contrast , the phase between different humps is fixed . fig . s2 of the supplemental material shows how one - body correlation functions @xcite can be used to distinguish fragmented and condensed systems . to understand the physics behind the non - violent and explosive regimes of the time - dependent many - body dynamics of the trapped multi - hump multi - fold fragmented systems with strong finite - range inter - particle interactions , we extend the concept of self - induced effective potentials introduced in ref . @xcite to explain static properties of the multi - hump ground states . as in the static case , we associate each hump with a well - isolated , now time - evolving sub - system @xmath46 . during the propagation , as one can see from the mctdhb equations of motion , eqs . ( [ mctdhb_eq ] ) , each of these fragments `` feels '' the external trap potential and , also , effective time - dependent potential barriers @xmath47 induced by the other ( counterpart ) sub - clouds as a result of the inter - particle interaction . the intensity , i.e. , the height of the induced , time - dependent barriers , is proportional to the strength of the repulsion @xmath2 and to the ratio @xmath48 of the involved elements of reduced two- and one - body density matrices , see mctdhb equations , eqs . ( [ mctdhb_eq ] ) . in the case of an ideal fragmented state with well - localized fragments , this ratio is proportional to the number of particles residing in each fragment . for instance , in the case of a perfect two - fold fragmented system it approaches @xmath49 , where @xmath34 is the total number of particles . with a simultaneous quench of the inter - particle repulsion : ( a ) strong decrease @xmath42 , snap - shot at @xmath50 ; ( b ) moderate increase @xmath51 , snap - shot at @xmath52 ; ( c ) stronger increase @xmath53 , snap - shot at @xmath54 . upper panels show the densities @xmath55 of the @xmath56 fragments [ working mctdhb orbitals , eqs . ( [ mctdhb_eq ] ) ] and the time - dependent barriers @xmath57 induced by the complimentary @xmath58 sub - clouds . trapping potentials and computed density are shown on the lower panels . the over - a - barrier dynamics ( a , c ) happens when the energy per particle of the out - of - equilibrium state is larger than the heights of the induced barriers , otherwise the dynamics is under - a - barrier ( b ) . the induced barriers depicted in ( a ) have been multiplied by a factor of 40 , for better visualization . all quantities shown are dimensionless.,title="fig:",width=217 ] with a simultaneous quench of the inter - particle repulsion : ( a ) strong decrease @xmath42 , snap - shot at @xmath50 ; ( b ) moderate increase @xmath51 , snap - shot at @xmath52 ; ( c ) stronger increase @xmath53 , snap - shot at @xmath54 . upper panels show the densities @xmath55 of the @xmath56 fragments [ working mctdhb orbitals , eqs . ( [ mctdhb_eq ] ) ] and the time - dependent barriers @xmath57 induced by the complimentary @xmath58 sub - clouds . trapping potentials and computed density are shown on the lower panels . the over - a - barrier dynamics ( a , c ) happens when the energy per particle of the out - of - equilibrium state is larger than the heights of the induced barriers , otherwise the dynamics is under - a - barrier ( b ) . the induced barriers depicted in ( a ) have been multiplied by a factor of 40 , for better visualization . all quantities shown are dimensionless.,title="fig:",width=217 ] with a simultaneous quench of the inter - particle repulsion : ( a ) strong decrease @xmath42 , snap - shot at @xmath50 ; ( b ) moderate increase @xmath51 , snap - shot at @xmath52 ; ( c ) stronger increase @xmath53 , snap - shot at @xmath54 . upper panels show the densities @xmath55 of the @xmath56 fragments [ working mctdhb orbitals , eqs . ( [ mctdhb_eq ] ) ] and the time - dependent barriers @xmath57 induced by the complimentary @xmath58 sub - clouds . trapping potentials and computed density are shown on the lower panels . the over - a - barrier dynamics ( a , c ) happens when the energy per particle of the out - of - equilibrium state is larger than the heights of the induced barriers , otherwise the dynamics is under - a - barrier ( b ) . the induced barriers depicted in ( a ) have been multiplied by a factor of 40 , for better visualization . all quantities shown are dimensionless.,title="fig:",width=217 ] for illustrative purposes we examine and validate the applicability of this analysis in 2d setups where the dynamics is induced by a sudden displacement of the trap potential @xmath59 with simultaneous quenches of the repulsion . the initial state is the two - hump two - fold fragmented ground state , trapped in @xmath60 with @xmath40 . in the lower panels of fig . [ fig2 ] we depict snapshots of the evolving densities and respective trapping potential at several different time - slices for the above described scenarios of the trap displacement and quenches of the repulsion : from @xmath42 , at @xmath61 in the fig . [ fig2](a ) ; from @xmath62 , at @xmath63 in the fig . [ fig2](b ) ; from @xmath64 , at @xmath65 in the fig . [ fig2](c ) . the initial two - hump state studied here has a dominant ( @xmath66 ) contribution from the @xmath67 configuration , indicating on an essentially perfect two - fold fragmentation of the system . during the propagation the fragmentation ratios change , of course , but the systems still remain two - fold fragmented . in the upper panels of fig . [ fig2 ] we plot snap - shots of the densities @xmath68 of the @xmath56 left / right sub - clouds and the effective time - dependent barriers @xmath69 induced by the counterpart @xmath58 ( right / left ) fragments at the same time - slices . to make the induced barriers visible in the case of a strong decrease of the interaction from @xmath42 depicted in the fig . [ fig2](a ) , we have scaled them by a factor of 40 . the full movies of the respective many - body dynamics are available in the supplemental material @xcite . in fig . [ fig2 ] one can clearly distinguish two qualitatively different regimes of evolutions . a non - violent one , plotted in the middle ( b ) sub - figure , can be contrasted with highly - non - equilibrium ones , depicted in the left ( a ) and right ( c ) sub - figures . to explore and confirm the existence of these two generic regimes observed in one- and two- dimensional setups also in 3d , we plot in fig . [ fig3 ] an example of a highly non - equilibrium violent dynamics induced by a sudden displacement of the trap @xmath70 and strong decrease of the finite - range repulsion from @xmath42 . here , to visualize the 3d functions we plot several isosurfaces of the density and an equipotential cut of the trap . the snap - shots of the densities are taken at @xmath71 . full movies of this and two other 3d scenarios are provided in the supplemental material @xcite . let us digest the physics of the above observed dynamical regimes . in the non - violent evolutions , see e.g. fig . [ fig1](a , b ) for 1d and fig . [ fig2](b ) for 2d , the strong repulsion prevents an exchange of the particles between the sub - clouds , so they do not come to a proximity for a contact . the superposition of the induced time - dependent barriers and external trap results in effective potentials which are high enough to confine the sub - clouds even in the case when they are moving . hence , the non - violent dynamics of the trapped multi - hump , multi - fold fragmented repulsive systems appears when the manipulations exerted on the system are not strong enough to destroy or overcome the induced time - dependent barriers . so , the physics behind is an under - a - barrier dynamics . complimentary , the violent dynamics appears when the induced barriers are not high enough to keep the sub - clouds apart from each other . indeed , in the above studied sudden decreases of the inter - particle repulsion from @xmath42 , depicted in the fig . [ fig1](c ) for 1d , fig . [ fig2](a ) for 2d , and fig . [ fig3 ] for 3d , reduce the heights of the induced barriers , which are proportional to @xmath2 . the sub - clouds start to leak out and eventually become delocalized over the entire trap . the @xmath53 quench in 2d , depicted in the fig . [ fig2](c ) , formally leads to an increase of the heights of the induced barriers , but , simultaneously , it pumps too much internal energy into the system . at this new value of the inter - particle interaction strength the ground state is three - fold fragmented and , hence , the shapes of the initial two - hump sub - clouds are no more optimal . it also implies that the energy per - particle of each sub - cloud is larger than the heights of the induced time - dependent barriers . during the violent evolutions the available energy is redistributed between the excited states which have multi - node structures and can be delocalized over the entire trap . as a result , the density reveals the observed highly violent explosive behavior . so , the physics behind is a complex over - a - barrier dynamics . and strong , sudden decrease of the repulsion from @xmath42 . to visualize the 3d functions we plot several isosurfaces of the density and an equipotential cut of the trap . the snap - shots of the density are taken to show initial ( @xmath44 ) , coalescing ( @xmath72 ) , penetrating ( @xmath73 ) and highly - excited ( @xmath74 ) momentary instances of the violent over - a - barrier dynamics . all quantities shown are dimensionless.,title="fig:",width=132 ] and strong , sudden decrease of the repulsion from @xmath42 . to visualize the 3d functions we plot several isosurfaces of the density and an equipotential cut of the trap . the snap - shots of the density are taken to show initial ( @xmath44 ) , coalescing ( @xmath72 ) , penetrating ( @xmath73 ) and highly - excited ( @xmath74 ) momentary instances of the violent over - a - barrier dynamics . all quantities shown are dimensionless.,title="fig:",width=132 ] and strong , sudden decrease of the repulsion from @xmath42 . to visualize the 3d functions we plot several isosurfaces of the density and an equipotential cut of the trap . the snap - shots of the density are taken to show initial ( @xmath44 ) , coalescing ( @xmath72 ) , penetrating ( @xmath73 ) and highly - excited ( @xmath74 ) momentary instances of the violent over - a - barrier dynamics . all quantities shown are dimensionless.,title="fig:",width=132 ] and strong , sudden decrease of the repulsion from @xmath42 . to visualize the 3d functions we plot several isosurfaces of the density and an equipotential cut of the trap . the snap - shots of the density are taken to show initial ( @xmath44 ) , coalescing ( @xmath72 ) , penetrating ( @xmath73 ) and highly - excited ( @xmath74 ) momentary instances of the violent over - a - barrier dynamics . all quantities shown are dimensionless.,title="fig:",width=132 ] now , we are able to deduce a set of practical recommendations on possible experimental preparations and manipulations of the multi - hump , multi - fold fragmented states . ( i ) once prepared , these states remain very stable and robust with respect to possible imperfectness of experimental setups . ( ii ) a protocol where the non - interacting system is first prepared and then the interaction is diabatically quenched seems to be ineffective because , it would lead to explosive dynamics . ( iii ) finally , a formation of the systems with a desired number of humps ( fragments ) can be provoked and controlled by pre - imposing a weak optical lattice of the required periodicity from the beginning of the quench process . by switching it off afterwords , one could , in principle , induce only a non - destructive non - violent under - a - barrier dynamics . concluding , we have shown that the physics behind the two hitherto found generic regimes of the many - body non - equilibrium dynamics of trapped ultracold bose systems with strong repulsive finite / long range interactions is driven by the mechanism of interaction - induced time - dependent barriers . the non - violent dynamics of the first , under - a - barrier regime is contrasted to a highly - non - equilibrium explosive quantum many - body dynamics of the second , over - a - barrier regime . the generality of the discovered time - dependent physics is verified in one- , two- , and three - spatial dimensions . computation time on the bwgrid , hlrs and k100 clusters are greatly acknowledged . a partial financial support by the dfg is acknowledged . 64 m. girardeau , j. math . phys . * 1 * , 516 ( 1960 ) . t. kinoshita , t. wenger , and d. s. weiss , phys . rev . lett . * 95 * , 190406 ( 2005 ) . m. a. baranov , phys . rep . * 464 * , 71 ( 2008 ) . t. lahaye _ et al . _ , rep . . phys . * 72 * , 126401 ( 2009 ) . d. comparat , and p. pillet , _ j. opt . soc . am . b _ * 6 * , a208 ( 2010 ) . phys . rev . a * 82 * , 033412 ( 2010 ) . phys . rev . lett . * 104 * , 195302 ( 2010 ) . m. viteau , m. g. bason , j. radogostowicz , n. malossi , d. ciampini , o. morsch , and e. arimondo , phys . rev . lett . * 107 * , 060402 ( 2011 ) . see supplemental material at ` http://link.aps.org/supplemental/ ` for discussion on possible experimental control and realization of the predicted phenomena in `` rydberg - dressed '' ultra - cold systems @xcite , and for movies of the reported 2d and 3d mctdhb dynamics . a. i. streltsov , phys . rev . a * 88 * , 041602(r ) ( 2013 ) . a. i. streltsov , o. e. alon , and l. s. cederbaum , phys . rev . lett . * 99 , * 030402 ( 2007 ) . o. e. alon , a. i. streltsov , and l. s. cederbaum , phys . rev . a * 77 , * 033613 ( 2008 ) . a. i. streltsov , o. e. alon , and l. s. cederbaum , phys . rev . lett . * 100 * , 130401 ( 2008 ) . k. sakmann , a. i. streltsov , o. e. alon , and l. s. cederbaum , phys . rev . lett . * 103 * , 220601 ( 2009 ) . a. i. streltsov , o. e. alon , and l. s. cederbaum , phys . rev . lett . * 106 * , 240401 ( 2011 ) . a. u. j. lode , k. sakmann , o. e. alon , l. s. cederbaum , and a. i. streltsov , phys . rev . a * 86 * , 063606 ( 2012 ) . a. u. j. lode , a. i. streltsov , k. sakmann , o. e. alon , and l. s. cederbaum , proc . natl . acad . sci . usa * 109 * , 13521 ( 2012 ) . m. greiner _ et al . _ , nature ( london ) * 415 * , 39 - 44 ( 2002 ) . k. sakmann , a. i. streltsov , o. e. alon , and l. s. cederbaum , phys . rev . a * 78 * , 023615 ( 2008 ) . # 1@xmath75 *o *

let us start from the issue of possible experimental realizations of the predicted physics . to observe the predicted effects the first necessary condition is that the length / range of the inter - particle interaction should be comparable with the length of trapping potentials . the second necessary condition is that the interaction should be strong enough . we expect to observe the formation of few - hump fragmented ground states in trapped ultra - cold systems made of `` rydberg - dressed '' atoms [ 5 - 7 ] . let us discuss how to realize the predicted multi - hump muti - fold fragmented physics in rydberg - dressed " systems . the off - resonant optical coupling of ground state atoms to highly excited rydberg states [ 6 , 7 ] allows one to modify and control the shape and strength of effective two - body interactions . the advantage of this technique is that a small component of the rydberg state is admixed to the ground state of atoms , providing thereby an additional degree of manipulation of the interaction strength . the shape of the potential energy of the two many - electron atoms excited to a rydberg state depends very much on details of the electronic structure . the most common long - range behavior , however , is of a standard van der waals ( @xmath76 ) type with possible admixture of terms of other degrees , e.g. , a pure dipole interaction ( @xmath77 ) . these additional contributions are responsible for the tails of the interaction potentials . the dressing " of two rydberg atoms with van der waals type of interaction results , see refs . [ 6 , 7 ] , in the two - body effective inter - particle potential : @xmath78 let us make a change of variables @xmath79 , where @xmath33 is the frequency of the external trap . in the units of the external confining potential s length , @xmath80 , the inter - particle interaction reads @xmath81 where @xmath82 is the rescaled interaction strength and @xmath83 . in the present study , we have used one- , two- and three - dimensional versions of inter - particle interactions of a similar shape @xmath84 of half - width @xmath36 with @xmath37 . this degree of the inter - particle repulsion function corresponds to an `` intermidiate '' situation between the pure dipole - dipole and van der waals interactions . we have used it to demonstrate the generality of the observed physics , which holds for @xmath85 and @xmath86 as well . the strength @xmath2 of the inter - particle interaction depends on experimentally tunable parameters : @xmath87 a two - photon rabi frequency between the involved atomic levels , @xmath88 detunings of lasers with respect to the atomic transitions , and the external confinement @xmath33 . the screening " constant @xmath89 defines the critical distance , below which the interaction is constant , i.e. , originates to the blockade phenomenon [ 5 ] . this range depends on the detuning @xmath88 and on the pure spectroscopic @xmath90 coefficient governed by the electronic structure of the excited state , i.e. , it can be manipulated by a proper choice of an atomic rydberg level . what are the presently available / reachable experimental conditions for rydberg excitations ? in recent experiment , see ref . [ 8 ] , with @xmath91rb bose - einstein condensates , a few tens of rydberg atoms in a quasi-1d trap have been successfully detected . the reported blockade radii were between 5- while the radial dipole trap frequencies used were around , resulting in a radial length of order of 1- , i.e. , a ratio @xmath92 , where @xmath93 is the screening " constant of the rb atoms . it means that the range of the interaction was larger than the the size of the trap in the transverse direction . the strength of the interaction of the dressed rydberg atoms is defined by the @xmath94 ratio and can be tuned between 0.1- , implying that in a trap the corresponding dimensionless interaction strength @xmath82 can be @xmath95 1 - 100 . so , formally , the lengths / ranges and interaction strength needed to observe the predicted multi - hump muti - fold fragmented states and their dynamics are already reachable with ultra - cold dressed " rydberg atoms .

we find that for collisions between heavy nuclei such as au+au , both plasma screening and gluon scattering are important . as a result , the effect due to absorption by hadrons becomes relatively minor . the final @xmath0 survival probability thus remains appreciable after comparable absorption effects due to gluons and hadrons .

r

nucl-th0007003

using a multiphase transport model , we study the relative importance of @xmath0 suppression mechanisms due to plasma screening , gluon scattering , and hadron absorption in heavy ion collisions at the relativistic heavy ion collider . we find that for collisions between heavy nuclei such as au+au , both plasma screening and gluon scattering are important . as a result , the effect due to absorption by hadrons becomes relatively minor . the final @xmath0 survival probability in these collisions is only a few percent . in the case of collisions between light nuclei such as s+s , the effect of plasma screening is , however , negligible in spite of the initial high parton density . the final @xmath0 survival probability thus remains appreciable after comparable absorption effects due to gluons and hadrons .

in fig . [ fig : auauden5 ] , we show the time evolution of the particle number and energy densities of partons and hadrons in central au+au collisions at @xmath21 gev . they are the densities in the central cell , which has a transverse radius of 1 fm for partons and 2 fm for hadrons . the longitudinal dimension of the central cell is taken to be @xmath22 of the time @xmath23 , which is equivalent to taking the central space - time rapidity cell . the results are not significantly changed if @xmath24 of the time is used for the longitudinal dimension . we see that the initial parton density is about @xmath25 @xmath17 and is much higher than the @xmath0 dissociation critical density ( about @xmath26 @xmath17 ) given above . the time evolution of these densities is seen to deviate from that based on the ideal bjorken boost invariant scenario @xcite , which would lead to a linear curve on the log - log plot . this difference is mainly due to the more realistic treatment of initial collisions by using the the gyulassy - wang model for the formation time and the presence of radial flow as well as a gradual freeze - out @xcite at the later hadronic stage . from the ratio of the parton energy density to its number density , one sees that the average energy of a parton is more than @xmath19 gev . the parton stage lasts about @xmath27 fm/@xmath6 , while the hadron stage starts gradually at around @xmath28 fm/@xmath6 and lasts until about @xmath29 fm/@xmath6 . the average energy of a hadron is less than @xmath19 gev , since the central rapidity is dominated by mesons instead of baryons in ultrarelativistic nuclear collisions . in fig . [ fig : ssden9 ] , we show the results for central collisions of s+s at @xmath21 agev . due to the smaller size of the system comparing to that of au+au collisions , the plasma lifetime is shorter , i.e. , about @xmath30 fm/@xmath6 , and the hadron stage sets in at about @xmath27 fm/@xmath6 . we note that even in the smaller parton system produced in s+s collisions , the initial density is much higher than the critical density for @xmath0 dissociation . in fig . [ fig : auaurho4c ] and fig . [ fig : ssrho4a6 ] , we show , respectively , the parton density in central au+au and s+s collisions at different times . as minijet gluons are produced from initial hard collisions , their densities at different radii reflect the number of initial binary nucleon - nucleon collisions . as seen from the figure , they are different from the initial nuclear density distribution given by a woods - saxon form . as expected , both the size and lifetime of the partonic matter produced in s+s collisions are smaller than those in au+au collisions . from the time evolution of the parton density , one can determine the time evolution of the critical radius for @xmath0 dissociation , and this is shown in fig . [ fig : auaurhoc3 ] by full dots for au+au collisions and open dots for s+s collisions . the solid lines are polynomial fits to the above results using the form , @xmath31 for @xmath32 , with @xmath33 for @xmath34 and @xmath35 for @xmath36 . for the partonic matter produced in au+au collisions , we have @xmath37 fm/@xmath6 , @xmath38 fm/@xmath6 , @xmath39 , @xmath40 , @xmath41 , and @xmath42 . for s+s collisions , they are @xmath43 fm/@xmath6 , @xmath44 fm/@xmath6 , @xmath45 , @xmath46 , @xmath47 , and @xmath48 . in au+au collisions , the critical radius for @xmath0 dissociation extracted from our model is about 6 fm at beginning of the parton cascade and vanishes after about 1.2 fm/@xmath6 . the critical radius is reduced to about 2 fm initially and vanishes after only about 0.5 fm in s+s collisions . since the duration of the partonic matter that is above the critical density for @xmath0 dissociation is shorter than the @xmath0 formation time , @xmath0 suppression due to plasma screening is therefore unimportant in central s+s collisions . including the above three mechanisms for @xmath0 suppression in the ampt model , we have evaluated the @xmath0 survival probability in ultrarelativistic heavy ion collisions at rhic energies . in fig . [ fig : prob2a ] , we show for central au+au collisions the time evolution of the @xmath0 formation probability @xmath49 , the @xmath0 absorption probability @xmath50 by gluon scattering , the @xmath0 dissociation probability @xmath51 by plasma screening , the @xmath0 absorption probability @xmath52 by hadrons , and the @xmath0 survival probability @xmath53 . the results are taken for the @xmath0 produced in the central rapidity interval @xmath54 . it is seen that the @xmath0 formation probability increases quickly with time and about @xmath55 of the @xmath0 are formed by @xmath56 fm/@xmath6 . absorption by gluons starts very early in the process and ends at about @xmath19 fm/@xmath6 after dissociation due to plasma screening begins . the latter also ends at about @xmath19 fm/@xmath6 . both dissociation due to plasma screening and absorption by gluon collisions give comparable contributions , accounting for the suppression of about 90% of the @xmath0 , while absorption by hadrons contributes only about a few percent . the final @xmath0 survivability is about 6% . the results for the case without plasma screening is shown in fig . [ fig : prob2b ] . comparing to fig . [ fig : prob2a ] , we see that the @xmath0 absorption probability by gluons is similar for time up to @xmath56 fm/@xmath6 , but it lasts longer until @xmath27 fm/@xmath6 . this indicates that there is a competition between @xmath0 suppression due to gluon scattering and plasma screening , i.e. , some @xmath0 s that are destroyed by collisions with gluons would have been dissociated by plasma screening if they are not allowed to scatter with gluons . [ fig : prob2c ] shows the results without @xmath0 absorption by gluon scattering . in this case , the plasma dissociation probability saturates quickly . compared to that shown in fig . [ fig : prob2b ] , the @xmath0 suppression probability is seen to start late but saturate early . this difference in the survival probability may be seen by studying the azimuthal distribution of final survival @xmath0 in mid - central collisions . it is interesting to note that @xmath0 suppression during the parton stage is similar whether when both plasma screening and gluon scattering are present or when only one of them is present . the effect of reducing the @xmath0 scattering cross section by gluon is shown in fig . [ fig : prob2d ] . compared with fig . [ fig : prob2a ] , we see that the decrease in the contribution from gluon scattering is partly compensated by the plasma screening . in table [ table : auauprob ] , we summarize the final absorption probabilities due to gluons ( @xmath57 ) , hadrons ( @xmath58 ) , plasma dissociation ( @xmath59 ) , and the survival probability ( @xmath60 ) in central au+au collisions . it is seen that the @xmath0 survival probability after the parton stage , @xmath61 , is about 9% and 17% for @xmath62 3 mb and 1 mb , respectively . the parton stage thus has a large effect on @xmath0 suppression in heavy ion collisions at rhic . in both cases , the @xmath0 suppression factor in the hadron stage is @xmath63 . depending on the different assumptions on the mechanisms for @xmath0 suppression , the final survival probability can range from about @xmath64 to about @xmath65 . this indicates that finite size effects may be important in @xmath0 suppression at rhic energies . we have also studied @xmath0 suppression in s+s collisions at rhic energies , and the results are summarized in table [ table : ssprob ] . as expected from the discussion of fig . [ fig : auaurhoc3 ] , there is no contribution from plasma screening in collisions of such light system , although the initial density is above the critical density . as a result , the @xmath0 has an appreciable survival probability ( about 50% ) after absorption by gluons and hadrons . since @xmath0 absorption by gluon scattering still contributes appreciably to the final @xmath0 suppression , it may provide an opportunity for studying this mechanism . we note that the @xmath0 suppression factor in the hadron stage is about @xmath66 , which is smaller than in au+au collisions . .final @xmath0 absorption probability @xmath57 by gluon scattering , @xmath0 dissociation probability @xmath59 by plasma screening , @xmath0 absorption probability @xmath58 by hadrons , and @xmath0 survival probability @xmath60 for au+au ( @xmath67 , @xmath21 agev ) . @xmath68 indicates @xmath69 mb while @xmath70 indicates @xmath71 mb . [ cols="<,^,^,^,^ " , ]

using a new approach , we have obtained a formula for calculating the rotation period and radius of planets . in the ordinary gravitomagnetism the gravitational spin ( @xmath0 ) orbit ( @xmath1 ) coupling , @xmath2 , while our model predicts that @xmath3 , where @xmath4 and @xmath5 are the central and orbiting masses , respectively .

i

1301.4720

using a new approach , we have obtained a formula for calculating the rotation period and radius of planets . in the ordinary gravitomagnetism the gravitational spin ( @xmath0 ) orbit ( @xmath1 ) coupling , @xmath2 , while our model predicts that @xmath3 , where @xmath4 and @xmath5 are the central and orbiting masses , respectively . hence , planets during their evolution exchange @xmath1 and @xmath0 until they reach a final stability at which @xmath6 , or @xmath7 , where @xmath8 is the orbital velocity of the planet . rotational properties of our planetary system and exoplanets are in agreement with our predictions . the radius ( @xmath9 ) and rotational period ( @xmath10 ) of tidally locked planet at a distance @xmath11 from its star , are related by , @xmath12 and that @xmath13 . = 18.5 cm = -1.5 cm

kepler s laws best describe the dynamics of our planetary system as regards to the orbital motion . however , newton s law of gravitation provided the theoretical framework of these laws . in central potential the orbital angular momentum is conserved . in polar coordinates , the gravitational force consists of the ordinary attraction gravitational force and a repulsive centripetal force . the newton s law of gravitation has been successful in many respect . however , this law fails to account for very minute gravitational effect like deflection of light by an intervening star , precession of the perihelion of the planetary orbit and the gravitational red - shift of light passing a differential gravitational potential . einstein s general theory of gravitation generalizes newton s theory of gravitational to give a full account for all these observed gravitational phenomena . einstein treats these phenomena as arising from the curvature of space . hence , einstein s theory has become now the only accepted theory of gravitation . the inclusion of energy and momentum of matter ( mass ) in question leads to the curvature of space , while the inclusion of spin leads to torsion in space . einstein s theory deals with matter of the former case , while einstein - cartan deals with the latter case . thus , einstein space if torsion free . in classical electrodynamics the spin of a particle is a quantum effect with no classical analogue . however , the spin of a gravitating object ( e.g. , planets ) is defined as a rotation of an object relative to its center of mass . this is expressed as @xmath14 , where @xmath15 and @xmath16 are the moment of inertia and angular velocity of the rotating object , respectively . the spin is generally a conserved quantity in physics . besides the spin , an object ( @xmath5 ) revolving at a distant @xmath17 around a central mass ( @xmath4 ) with speed @xmath8 is described by its orbital angular momentum . this is defined as @xmath18 . this quantity is also conserved , except when an external torque is acting on the object . in quantum mechanics , the spin and angular momentum of a fundamental particle are quantized . no such quantization is deemed to exist in gravitation . to incorporate quantum mechanics in gravitation we invoke a planck - like constant characterizing every gravitational system [ 1 , 2 ] . this would facilitate a bridging to quantum gravity that has not yet been uniquely formulated so far . the spin and orbital angular momentum may couple to each other as the case in the earth - moon system . therefore , neither the spin nor the orbital angular momentum are separately conserved . their sum is always conserved . a similar coupling occurs in atomic system . for instance , because of the spin of the electron such effect is found to be present in hydrogen - like atoms . owing to the existing similarities between gravitation and electromagnetism , some analogies were drawn which led to gravitomagnetism paradigm . it is believed that an effect occurring in electromagnetism will have its counter analogue in gravitomagnetism . in this paper we formulate the proper spin - orbit coupling in a gravitational system , and then deduce a formula for the spin of a gravitating object . this is done by equating the spin - orbit coupling energy to the gravitomagnetic energy . the resulting equation relates the spin of a gravitating object to its orbital angular momentum . while in standard gravitomagnetism , the gravitational spin - orbit coupling , @xmath2 , in our model of gravitomagnetism one has @xmath3 . this relation suggests a balance equation , @xmath19 . for this reason any orbiting object must spin in order to be dynamically stable . so planets during their course of evolution exchange @xmath1 and @xmath0 , but eventually come to a state of stability . the bigger the planet the larger its spin . hence , jupiter spins faster than other planets in the solar system . equivalently , the spin @xmath20 , where @xmath21 is the gravitational constant , and @xmath8 is the orbital velocity . this formula is found to be consistent when applied to our planetary system and exoplanetary system . astronomers have discovered so far more than 800 new giants planets , but could nt identify all of their radii and spin periods . the present formulation helps identify these latter properties . we consider here all possibilities to account for the observationally derived data pertaining to the exoplanetary system and their consistency .

using arcminute microkelvin imager ( ami ) sz observations towards ten clash clusters we investigate the influence of cluster mergers on observational galaxy cluster studies . varying pressure profile shape parameters , illustrating an influence of mergers on scaling relations , induces small deviations from the canonical self - similar predictions in agreement with simulations of @xcite who found that merger activity causes only small scatter perpendicular to the relations . we demonstrate this effect observationally using the different dependencies of sz and x - ray signals to @xmath0 that cause different sensitivities to the shocking and/or fractionation produced by mergers . lcclcluster & relaxed & unrelaxed & notes + + a611 & & & widely agreed relaxed , see e.g. @xcite , @xcite + & & & relaxed : e.g. classified ` non - distorted ' by @xcite and ` regular ' by @xcite + & & & unrelaxed : due to centroid shift , cuspiness and cooling time @xcite + & & & widely considered relaxed , see e.g. @xcite , @xcite + & & & unrelaxed due to extra structure to the south - west , @xcite + & & & classified relaxed e.g. @xcite , @xcite + & & & merger given x - ray morphology , @xcite , and temperature map , @xcite + maj0647 + 7015 & & & strong - lens selected , highly unrelaxed : @xcite + maj0717 + 3745 & & & strong - lens selected , highly unrelaxed and complex merger : @xcite + & & & in samples of large relaxed clusters @xcite , @xcite , and @xcite + & & & substructure identified , e.g. @xcite , @xcite . disturbed , @xcite + maj1149 + 2223 & & & strong - lens selected , highly complex merger , see @xcite + maj1423 + 2404 & & & highly relaxed state , pronounced cool - core , e.g. @xcite and @xcite + & & & presence of a cool - core e.g. @xcite , @xcite classifies it as relaxed + & & & cold front possibly from low - level merger turbulence @xcite +

i

1604.06120

using arcminute microkelvin imager ( ami ) sz observations towards ten clash clusters we investigate the influence of cluster mergers on observational galaxy cluster studies . although selected to be largely relaxed , there is disagreement in the literature on the dynamical states of clash sample members . we analyse our ami data in a fully bayesian way to produce estimated cluster parameters and consider the intrinsic correlations in our nfw / gnfw - based model . varying pressure profile shape parameters , illustrating an influence of mergers on scaling relations , induces small deviations from the canonical self - similar predictions in agreement with simulations of @xcite who found that merger activity causes only small scatter perpendicular to the relations . we demonstrate this effect observationally using the different dependencies of sz and x - ray signals to @xmath0 that cause different sensitivities to the shocking and/or fractionation produced by mergers . plotting @xmath1@xmath2 relations ( where @xmath3 ) derived from ami sz and from @xmath4 x - ray gives ratios of ami and @xmath4 @xmath1 and @xmath2 estimates that indicate movement of clusters _ along _ the scaling relation , as predicted by @xcite . clusters that have moved most along the relation have the most discrepant @xmath5 and @xmath6 estimates : all the other clusters ( apart from one ) have sz and x - ray estimates of @xmath2 , @xmath7 and @xmath1 that agree within @xmath8 . we use sz vs x - ray discrepancies in conjunction with @xmath4 maps and @xmath6 profiles , making comparisons with simulated cluster merger maps in @xcite , to identify disturbed members of our sample and estimate merger stages . = 1 [ firstpage ] galaxies : clusters : general methods : observational techniques : interferometric large - scale structure of the universe . lcclcluster & relaxed & unrelaxed & notes + + a611 & & & widely agreed relaxed , see e.g. @xcite , @xcite + & & & relaxed : e.g. classified ` non - distorted ' by @xcite and ` regular ' by @xcite + & & & unrelaxed : due to centroid shift , cuspiness and cooling time @xcite + & & & widely considered relaxed , see e.g. @xcite , @xcite + & & & unrelaxed due to extra structure to the south - west , @xcite + & & & classified relaxed e.g. @xcite , @xcite + & & & merger given x - ray morphology , @xcite , and temperature map , @xcite + maj0647 + 7015 & & & strong - lens selected , highly unrelaxed : @xcite + maj0717 + 3745 & & & strong - lens selected , highly unrelaxed and complex merger : @xcite + & & & in samples of large relaxed clusters @xcite , @xcite , and @xcite + & & & substructure identified , e.g. @xcite , @xcite . disturbed , @xcite + maj1149 + 2223 & & & strong - lens selected , highly complex merger , see @xcite + maj1423 + 2404 & & & highly relaxed state , pronounced cool - core , e.g. @xcite and @xcite + & & & presence of a cool - core e.g. @xcite , @xcite classifies it as relaxed + & & & cold front possibly from low - level merger turbulence @xcite +

physical parameters of glaxy clusters , such as total mass and gas mass , are commonly studied through scaling relations . these relations assume that both growing and mature clusters are relaxed , self - similar systems such that relations between e.g. @xmath9 , @xmath10 , @xmath11 , @xmath2 , @xmath7 , etc . are simple power laws ( see e.g. @xcite and @xcite for a recent review ) . deviations from hydrostatic equilibrium ( hse ) ( or from virialisation ) and self - similarity during cluster mergers will cause scatter around the scaling relations . studies in the literature aim to use these relations to make accurate determinations of e.g. total cluster mass , and therefore often focus on minimising the scatter either by careful sample selection of low - redshift , relaxed clusters ( e.g. , , @xcite , @xcite ) , or by finding a particularly low - scatter mass proxy ( e.g. @xcite , , , @xcite ) . these approaches often produce low - scatter relations that agree with the self - similar predictions . however , @xcite , using simulations of two - body cluster mergers to track the evolution of a merger ( from a relaxed system before the start of the merger through to relaxation of the merged system ) in the plane of a scaling relation , find large changes in cluster observables _ along _ the relation with little perpendicular displacement . assessment of these cluster parameter values through calculation from sunyaev zeldovich ( sz , @xcite ) and x - ray observation provides a critical probe of the dynamical state of the cluster gas due to the difference in dependencies of the sz and x - ray flux densities on the electron number density , @xmath0 . the sz effect is the inverse compton scattering of cmb photons by hot cluster gas , and is @xmath12 , where @xmath7 is the plasma temperature and @xmath13 the line element along the line of sight through the cluster . the x - ray bremsstrahlung signal is @xmath14 , where @xmath15 is the cooling function ( @xmath15@xmath16 @xmath17 for the clusters in this paper ) . parameter values estimated from measurement of sz and x - ray signals will , therefore , also depend differently on @xmath0 and @xmath7 . as cluster mergers are known to produce regions of higher density gas , through processes such as shocking , x - ray parameter estimation is likely more sensitive to dynamical state , and will produce larger displacements along scaling relations during a merger than sz parameter values . this implies that merger activity can be identified by looking at discrepancies between sz and x - ray measurements . to test this observationally , we use the clash sample of well - studied clusters selected by @xcite to form a sample of massive clusters , most of which are classified in the literature as relaxed , plus a small number of clusters with pronounced strong gravitational lensing ( see section [ sec : sample ] ) . here we discuss measurements of a sub - sample of clash clusters via the sz effect using the arcminute microkelvin imager ( ami , @xcite ) . the sz signal measures the comptonization parameter , @xmath18 , the line - of - sight integral of the number of collisions multiplied by the mean fractional energy change of the cmb photons per collision : @xmath19 where @xmath20 is the thomson scattering cross - section , @xmath21 the electron mass , @xmath22 the speed of light . equation [ eq : ypar ] shows that the sz surface brightness is proportional to the electron pressure , @xmath23 , assuming an ideal gas law , integrated along the line of sight . integrating @xmath18 over the solid angle @xmath24 subtended by the cluster gives @xmath25 , which quantifies the internal energy of the cluster gas , providing a proxy for total mass , given redshift information . in x - ray studies @xmath1 , found from @xmath26 , is used as an analogue of @xmath25 which is proportional to the product of the gas mass and the mean temperature measured from sz within a sphere ( or a cylinder ) . @xcite find , using simulated data , that @xmath1 provides an equally good proxy for total mass as @xmath25 . the mean cluster temperature has also been widely used as a proxy for total cluster mass . cluster @xmath7 has traditionally been measured through x - ray spectroscopy ; with good enough sensitivity and angular resolution , annular averaging gives temperature profiles out to , for some clusters , radii of @xmath271mpc ( see e.g. accept database , @xcite , @xcite , ) . @xcite and @xcite show that a gas temperature profile can also be obtained via sz observation , given assumed geometry and dynamical state , and given a prior on the gas fraction @xmath28 at @xmath29 . in this study , cluster parameters are derived from our ami sz measurements in a fully bayesian way using the model described in @xcite and ( 2013 ) . this model uses a navarro , frenk and white ( nfw ) profile to describe the dark matter density , which is believed , from cosmological n - body simulations , to accurately model all dark matter halos @xcite . a generalised navarro , frenk and white ( gnfw ) profile is used to describe the gas pressure , shown to follow self - similarity more closely than the density or temperature at high radius @xcite . further conditions of spherical symmetry , hse , and a small @xmath30 compared to unity , produces cluster properties as functions of radius . throughout , we assume @xmath31 = 70 km @xmath32 and a concordance @xmath15cdm cosmology with @xmath33 = 0.3 , @xmath34 = 0.7 , @xmath35 = 0 , @xmath36 = 0.041 , @xmath37 = @xmath381 , @xmath39 = 0 and @xmath40 = 0.8 . all cluster parameter values are at the redshift of the cluster . we emphasise that we denote @xmath41 as @xmath1 for either sz or x - ray .

although selected to be largely relaxed , there is disagreement in the literature on the dynamical states of clash sample members . plotting @xmath1@xmath2 relations ( where @xmath3 ) derived from ami sz and from @xmath4 x - ray gives ratios of ami and @xmath4 @xmath1 and @xmath2 estimates that indicate movement of clusters _ along _ the scaling relation , as predicted by @xcite . clusters that have moved most along the relation have the most discrepant @xmath5 and @xmath6 estimates : all the other clusters ( apart from one ) have sz and x - ray estimates of @xmath2 , @xmath7 and @xmath1 that agree within @xmath8 . = 1 [ firstpage ] galaxies : clusters : general methods : observational techniques : interferometric large - scale structure of the universe .

c

1604.06120

using arcminute microkelvin imager ( ami ) sz observations towards ten clash clusters we investigate the influence of cluster mergers on observational galaxy cluster studies . although selected to be largely relaxed , there is disagreement in the literature on the dynamical states of clash sample members . we analyse our ami data in a fully bayesian way to produce estimated cluster parameters and consider the intrinsic correlations in our nfw / gnfw - based model . varying pressure profile shape parameters , illustrating an influence of mergers on scaling relations , induces small deviations from the canonical self - similar predictions in agreement with simulations of @xcite who found that merger activity causes only small scatter perpendicular to the relations . we demonstrate this effect observationally using the different dependencies of sz and x - ray signals to @xmath0 that cause different sensitivities to the shocking and/or fractionation produced by mergers . plotting @xmath1@xmath2 relations ( where @xmath3 ) derived from ami sz and from @xmath4 x - ray gives ratios of ami and @xmath4 @xmath1 and @xmath2 estimates that indicate movement of clusters _ along _ the scaling relation , as predicted by @xcite . clusters that have moved most along the relation have the most discrepant @xmath5 and @xmath6 estimates : all the other clusters ( apart from one ) have sz and x - ray estimates of @xmath2 , @xmath7 and @xmath1 that agree within @xmath8 . we use sz vs x - ray discrepancies in conjunction with @xmath4 maps and @xmath6 profiles , making comparisons with simulated cluster merger maps in @xcite , to identify disturbed members of our sample and estimate merger stages . = 1 [ firstpage ] galaxies : clusters : general methods : observational techniques : interferometric large - scale structure of the universe . lcclcluster & relaxed & unrelaxed & notes + + a611 & & & widely agreed relaxed , see e.g. @xcite , @xcite + & & & relaxed : e.g. classified ` non - distorted ' by @xcite and ` regular ' by @xcite + & & & unrelaxed : due to centroid shift , cuspiness and cooling time @xcite + & & & widely considered relaxed , see e.g. @xcite , @xcite + & & & unrelaxed due to extra structure to the south - west , @xcite + & & & classified relaxed e.g. @xcite , @xcite + & & & merger given x - ray morphology , @xcite , and temperature map , @xcite + maj0647 + 7015 & & & strong - lens selected , highly unrelaxed : @xcite + maj0717 + 3745 & & & strong - lens selected , highly unrelaxed and complex merger : @xcite + & & & in samples of large relaxed clusters @xcite , @xcite , and @xcite + & & & substructure identified , e.g. @xcite , @xcite . disturbed , @xcite + maj1149 + 2223 & & & strong - lens selected , highly complex merger , see @xcite + maj1423 + 2404 & & & highly relaxed state , pronounced cool - core , e.g. @xcite and @xcite + & & & presence of a cool - core e.g. @xcite , @xcite classifies it as relaxed + & & & cold front possibly from low - level merger turbulence @xcite +

we have observed the eleven clusters in the clash sample that are accessible to ami , and discard one due to a very bright source on the edge of the field of view . the remaining ten clusters have been analysed in a fully bayesian way to give estimated parameter values from sz measurement . 1 . although 20 out of the 25 clash sample members were selected to be relaxed , we find disagreement in the literature on the dynamical states of many of our ami - clash sub - sample , illustrating the difficulty in determining cluster dynamical state and identifying mergers . we investigate the correlations in our model and use it to calculate @xmath87@xmath88 curves , varying @xmath30 and redshift . we discuss the effect these parameters have on the power - laws fitted to the curves : @xmath87@xmath88 is dependent on the cluster redshift and on the value of @xmath30 . x - ray studies have found sensitivity of the scatter about scaling relations to the dynamical states of the clusters included . here , we investigate the sensitivity of our model correlations to dynamical state by introducing variations in cluster pressure profile shape parameters : a consequence of merger activity that can be induced in the analysis . in our analysis these are fixed to the universal " values . varying @xmath70 , the shape parameter best constrained by ami sz data , over a large range induces only small changes in scaling relation power - laws . this is consistent with @xcite who track cluster observables of merging systems in the plane of scaling relations , finding very little perpendicular scatter but large variations along the scaling relation , over the course of a merger . 4 . due to the difference in dependence of sz and x - ray measurement on @xmath0 , x - ray observables are much more sensitive to changes in mass , pressure , temperature and density during a merger . discrepancies between parameter estimates derived from sz and x - ray measurement can help identify clusters undergoing mergers . denoting @xmath41 by @xmath1 ( for x - ray and sz ) , we compare two @xmath1@xmath2 scaling relations of the sub - sample members : one plotted using ami sz parameter values and the second using @xmath4 x - ray parameters from @xcite . in addition to a difference in scatter we see an apparent movement " of sample members along the line of the relation , between sz and x - ray . these discrepancies are visualised by plotting the ratios of ami and @xmath4 @xmath1 and @xmath2 values showing a population of our sub - sample for which the sz and x - ray parameters agree well . other clusters are discrepant by up to @xmath602 , all towards higher x - ray @xmath1 and @xmath2 values _ along _ the line of the relation . we also plot temperature estimates made from sz and x - ray observation and find a similar split of clusters into two populations that are in agreement with those found from the ratios of ami and @xmath4 @xmath1 and @xmath2 values . this result comes from the comparison of ami sz parameter estimates with those from three independent x - ray analyses , addressing possible inconsistencies between methods . dynamical state classifications in the literature of the ten clusters report : a611 , maj1423 + 2404 and rxj1532 + 3021 are relaxed ; maj0647 + 7015 , maj0717 + 3745 and maj1149 + 2223 are mergers ; and a1423 , a2261 , clj1226 + 3332 , and maj0744 + 3927 have mixed reports . using discrepancies in sz and x - ray parameter estimates and comparisons of @xcite merger simulations with x - ray morphology we determine the dynamical states of the ten clusters in the sub - sample . we class a611 , a1423 , a2261 and maj1423 + 2404 as relaxed . maj0647 + 7015 and maj0717 + 3745 , selected for their lensing strength , we find to be mergers . as expected from the mixed classifications in the literature , maj0744 + 3927 and clj1226 + 3332 , although selected as relaxed , are also mergers . maj1149 + 2223 , although reported in the literature as highly disturbed , shows no significant discrepancies between sz and x - ray parameters . we conclude that low mass infalling cluster groups with high impact - parameters will cause less gas shocking and/or fractionation than lower mass - ratio mergers . we find evidence supporting the presence of an old , low level merger in rxj1532 + 3021 , postulated by @xcite .

using density - functional perturbation theory and the grneisen formalism , we directly calculate the linear thermal expansion coefficients ( tecs ) of a hexagonal bulk system mos@xmath0 in the crystallographic @xmath1 and @xmath2 directions . our theoretical tec results are compared with experiment . the symmetry - preserving approach adopted here

i

1608.08315

using density - functional perturbation theory and the grneisen formalism , we directly calculate the linear thermal expansion coefficients ( tecs ) of a hexagonal bulk system mos@xmath0 in the crystallographic @xmath1 and @xmath2 directions . the tec calculation depends critically on the evaluation of a temperature ( @xmath3 ) dependent quantity @xmath4 , which is the integral of the product of heat capacity and @xmath5 , of frequency @xmath6 and strain type @xmath7 , where @xmath5 is the phonon density of states weighted by the grneisen parameters . we show that to determine the linear tecs we may use minimally two uniaxial strains in the @xmath8 , and either @xmath9 or @xmath10 direction . however , a uniaxial strain in either @xmath9 and @xmath10 direction drastically reduces the symmetry of the crystal from a hexagonal one to a base - centered orthorhombic one . we propose to use an efficient and accurate symmetry - preserving biaxial strain in the @xmath11 plane to derive the same result for @xmath12 . we highlight that the grneisen parameter associated with a biaxial strain may not be the same as the average of grneisen parameters associated with two separate uniaxial strains in the @xmath9 and @xmath10 directions due to possible preservation of degeneracies of the phonon modes under a biaxial deformation . large anisotropy of tecs is observed where the linear tec in the @xmath2 direction is about @xmath13 times larger than that in the @xmath1 or @xmath14 direction at high temperatures . our theoretical tec results are compared with experiment . the symmetry - preserving approach adopted here may be applied to a broad class of two lattice - parameter systems such as hexagonal , trigonal , and tetragonal systems , which allows many complicated systems to be treated on a first - principles level .

transition metal dichalcogenides ( tmds ) @xmath15 , where @xmath3 is a transition metal such as w and mo , and @xmath16 is a chalcogen such as s , se , and te , receive considerable attention due to their important mechanical and electronic properties@xcite . molybdenum disulfide mos@xmath0 , a prototypical example of tmds , is a layered system where mo atoms form hexagonal layers@xcite . each of the mo hexagonal layer is sandwiched between two similar lattices of s atoms , forming a trilayer@xcite . the atoms within each trilayer are held together by strong covalent bonds , while the trilayers of mos@xmath0 interact primarily through weak van der waals interactions . it is this sandwiched structure that endows mos@xmath0 with the important mechanical properties for solid lubricants@xcite . the electronic , optical , and lattice dynamical properties have been under intense investigations@xcite . the research on multilayers of mos@xmath0 , among many other multilayers of tmds , have been fueled by their novel properties intrinsic to 2d materials . for example , successes of mos@xmath0 multilayers have been demonstrated for the purposes of energy - efficient field - effect transistor@xcite , advanced electrocatalysts@xcite , thermoelectric devices@xcite with a large and tunable seebeck coefficient , phototransistors@xcite , superconductivity@xcite , etc . mos@xmath0 is joining the rank of other low - dimensional companions , demanding both efficient and accurate treatment of a first - principles approach@xcite . even though the mechanical , electronic , and lattice dynamical properties of the equilibrium structure of mos@xmath0 have been studied extensively@xcite , there are relatively few first - principles studies of the anharmonic effects@xcite that contribute to the thermal properties such as thermal conductivity and thermal expansion coefficients ( tecs ) . the linear tecs of 2h - mos@xmath0 have been measured @xcite where it was found that the tec along the @xmath2 direction is larger than that along the @xmath1 direction . on the theoretical side , tecs may be calculated by solving the vibrational self - consistent - field equations@xcite or the nonequilibrium green s function method@xcite . tecs may also be determined from a quasiharmonic approximation ( qha ) calculation where a set of calculations is to be carried out over a grid or mesh of lattice - parameter points , where the dimensionality of the grid depends on the number of independent lattice parameters@xcite . recently ding _ et al._@xcite chose six volumes to perform phonon calculations to first obtain the volumetric tec . another relation involving the linear tecs for @xmath1 and @xmath2 ( eq . 15 of ref . [ ] ) was set up and the values of tecs were solved . in this work , we develop a direct approach based on the grneisen formalism to calculate the tecs in the @xmath1 and @xmath2 directions . our tec results are then compared with experiment . the outline of this paper is as follows : section [ sec : method ] discusses the methodology used to efficiently calculate the thermal expansion coefficients of a general hexagonal system . section [ sec : results ] reports the results and discussions on the application of the method to mos@xmath0 . section [ sec : conclusions ] contains the conclusions .

the tec calculation depends critically on the evaluation of a temperature ( @xmath3 ) dependent quantity @xmath4 , which is the integral of the product of heat capacity and @xmath5 , of frequency @xmath6 and strain type @xmath7 , where @xmath5 is the phonon density of states weighted by the grneisen parameters . we show that to determine the linear tecs we may use minimally two uniaxial strains in the @xmath8 , and either @xmath9 or @xmath10 direction . however , a uniaxial strain in either @xmath9 and @xmath10 direction drastically reduces the symmetry of the crystal from a hexagonal one to a base - centered orthorhombic one . we propose to use an efficient and accurate symmetry - preserving biaxial strain in the @xmath11 plane to derive the same result for @xmath12 .

m

1608.08315

using density - functional perturbation theory and the grneisen formalism , we directly calculate the linear thermal expansion coefficients ( tecs ) of a hexagonal bulk system mos@xmath0 in the crystallographic @xmath1 and @xmath2 directions . the tec calculation depends critically on the evaluation of a temperature ( @xmath3 ) dependent quantity @xmath4 , which is the integral of the product of heat capacity and @xmath5 , of frequency @xmath6 and strain type @xmath7 , where @xmath5 is the phonon density of states weighted by the grneisen parameters . we show that to determine the linear tecs we may use minimally two uniaxial strains in the @xmath8 , and either @xmath9 or @xmath10 direction . however , a uniaxial strain in either @xmath9 and @xmath10 direction drastically reduces the symmetry of the crystal from a hexagonal one to a base - centered orthorhombic one . we propose to use an efficient and accurate symmetry - preserving biaxial strain in the @xmath11 plane to derive the same result for @xmath12 . we highlight that the grneisen parameter associated with a biaxial strain may not be the same as the average of grneisen parameters associated with two separate uniaxial strains in the @xmath9 and @xmath10 directions due to possible preservation of degeneracies of the phonon modes under a biaxial deformation . large anisotropy of tecs is observed where the linear tec in the @xmath2 direction is about @xmath13 times larger than that in the @xmath1 or @xmath14 direction at high temperatures . our theoretical tec results are compared with experiment . the symmetry - preserving approach adopted here may be applied to a broad class of two lattice - parameter systems such as hexagonal , trigonal , and tetragonal systems , which allows many complicated systems to be treated on a first - principles level .

we shall first present the expressions for tecs for a general hexagonal system obtained from the grneisen formalism.@xcite results specific to the hexagonal mos@xmath0 will be presented later . the linear tecs of the crystal along the @xmath9 , @xmath10 and @xmath8 directions , denoted by @xmath17 , @xmath18 , and @xmath19 , at temperature @xmath3 can be described by a matrix equation @xmath20 where @xmath21 is the equilibrium volume of the primitive cell , @xmath22 is the elastic compliance matrix@xcite . the values @xmath23 are the matrix elements of the elastic constant matrix @xmath24 that corresponds to a hexagonal system@xcite where @xmath25 the integrated quantities in eq . [ eq : alpha ] are given by @xmath26 where the integral is over the first brillouin zone ( bz ) . the frequency @xmath27 of a phonon mode depends on the mode index @xmath28 and wavevector @xmath29 . the heat capacity contributed by a phonon mode with frequency @xmath6 at temperature @xmath3 is @xmath30 with @xmath31 , @xmath32 and @xmath33 are the planck and boltzmann constants , respectively . the grneisen parameter @xmath34 measures the relative change of a phonon frequency @xmath35 as a result of an @xmath7 type deformation with strain size @xmath36 applied to the crystal . for example , if a uniaxial strain is applied in the @xmath9 direction then the strain parameters are @xmath37 ( in the voigt notation@xcite ) , i.e. , @xmath38 , and @xmath39 , for @xmath40 . we apply uniaxial strains in the @xmath9 , @xmath10 , and @xmath8 directions to give @xmath41 , @xmath42 , and @xmath43 , respectively . grneisen parameters are evaluated using a central - difference scheme , where a change in the dynamical matrices before and after deformation is used in the perturbation theory to deduce the changes in eigenfrequencies@xcite . by a proper sampling in the @xmath44-space , we may calculate the phonon density of states as @xmath45 next we introduce a related quantity , @xmath46 , the phonon density of states weighted by the grneisen parameters as @xmath47 the usefulness of @xmath5 is that we may obtain @xmath4 in eq . [ eq : integ ] from another relation @xmath48 to calculate the linear tecs , it appears that a set of three uniaxial deformations in the @xmath9 , @xmath10 , and @xmath8 directions are needed . however , due to the symmetry of the hexagonal system , we should have @xmath49 on physical ground and hence @xmath50 , so that the tec eq . [ eq : alpha ] reduces to @xmath51 & c_{13 } \\ 2c_{13 } & c_{33 } \\ \end{pmatrix}^{-1 } \begin{pmatrix } i_{1}\\ i_{3 } \end{pmatrix } \label{eq:2d1}\ ] ] or @xmath52 \\ \end{pmatrix } \begin{pmatrix } i_{1}\\ i_{3 } \end{pmatrix}\ ] ] where @xmath53 . therefore , for a hexagonal system two uniaxial strains , the first one either in the @xmath9 or @xmath10 direction , and a second one in the @xmath8 direction are sufficient to determine the linear tecs . for mos@xmath0 , the symmetry of the hexagonal system is not altered ( the space group remains as @xmath54 @xmath55 ) when a uniaxial strain is applied in the @xmath8 direction . however , the symmetry is significantly lowered from hexagonal with a space group of @xmath54 @xmath55 to base - centered orthorhombic with a space group of @xmath56 @xmath57 after a uniaxial strain is applied in the @xmath9 or @xmath10 direction . this will result in an increase of the computational cost compared to that which preserves the hexagonal symmetry where a phonon calculation is to be performed . for example , after applying a uniaxial strain in the @xmath9 direction , a @xmath58 @xmath59-mesh required in a phonon calculation will result in @xmath60 irreducible @xmath59-points and @xmath61 irreducible representations or @xmath61 self - consistent - field calculations . this is to be compared with the symmetry - preserving deformations ( e.g. , a uniaxial strain in the @xmath8 direction ) where the number of irreducible @xmath59-points is @xmath62 and the number of irreducible representations is @xmath63 , which clearly shows a substantial computational saving . more savings are expected when complicated crystal structures are treated . we propose to use a computationally efficient , symmetry - preserving biaxial strain in the @xmath11 plane ( hereafter it shall be called an @xmath11 biaxial strain ) where @xmath64 to evaluate the grneisen parameters @xmath65 and use eq . [ eq : integ ] or eq . [ eq : integ2 ] to obtain @xmath66 . due to the underlying symmetry , @xmath67 . however it should be noted that grneisen parameters due to an @xmath11 biaxial strain may not the same as the average of the grneisen parameters due to @xmath9 and @xmath10 uniaxial strains . these points will be elaborated later . the phonon spectra of mos@xmath0 are calculated with density functional perturbation theory ( dfpt)@xcite . for the unstrained structure , a @xmath59-mesh of @xmath68 is used for the phonon calculations , which is equivalent to evaluating the force constants@xcite using a @xmath68 supercell . the phonon calculations proceed by evaluating dynamical matrices at a number of irreducible @xmath59 points . from the the dynamical matrices the inter - atomic force constants in the real space are obtained by an inverse fourier transform , and these force constants are used to construct dynamical matrices at any @xmath69 to calculate the phonon eigenfrequencies @xmath27 . for the strained structures , a @xmath59-mesh of @xmath58 is also used . for the unstrained structure , a larger @xmath59-mesh of @xmath70 is used to confirm that a @xmath59-mesh of @xmath68 is sufficient for the purpose of tec calculations .

we highlight that the grneisen parameter associated with a biaxial strain may not be the same as the average of grneisen parameters associated with two separate uniaxial strains in the @xmath9 and @xmath10 directions due to possible preservation of degeneracies of the phonon modes under a biaxial deformation . large anisotropy of tecs is observed where the linear tec in the @xmath2 direction is about @xmath13 times larger than that in the @xmath1 or @xmath14 direction at high temperatures . may be applied to a broad class of two lattice - parameter systems such as hexagonal , trigonal , and tetragonal systems , which allows many complicated systems to be treated on a first - principles level .

c

1608.08315

using density - functional perturbation theory and the grneisen formalism , we directly calculate the linear thermal expansion coefficients ( tecs ) of a hexagonal bulk system mos@xmath0 in the crystallographic @xmath1 and @xmath2 directions . the tec calculation depends critically on the evaluation of a temperature ( @xmath3 ) dependent quantity @xmath4 , which is the integral of the product of heat capacity and @xmath5 , of frequency @xmath6 and strain type @xmath7 , where @xmath5 is the phonon density of states weighted by the grneisen parameters . we show that to determine the linear tecs we may use minimally two uniaxial strains in the @xmath8 , and either @xmath9 or @xmath10 direction . however , a uniaxial strain in either @xmath9 and @xmath10 direction drastically reduces the symmetry of the crystal from a hexagonal one to a base - centered orthorhombic one . we propose to use an efficient and accurate symmetry - preserving biaxial strain in the @xmath11 plane to derive the same result for @xmath12 . we highlight that the grneisen parameter associated with a biaxial strain may not be the same as the average of grneisen parameters associated with two separate uniaxial strains in the @xmath9 and @xmath10 directions due to possible preservation of degeneracies of the phonon modes under a biaxial deformation . large anisotropy of tecs is observed where the linear tec in the @xmath2 direction is about @xmath13 times larger than that in the @xmath1 or @xmath14 direction at high temperatures . our theoretical tec results are compared with experiment . the symmetry - preserving approach adopted here may be applied to a broad class of two lattice - parameter systems such as hexagonal , trigonal , and tetragonal systems , which allows many complicated systems to be treated on a first - principles level .

in summary , we have proposed a direct way to calculate the linear thermal expansion coefficients ( tecs ) of a hexagonal system based on the grneisen formalism . we have also proposed a way to replace the inefficient symmetry - lowering uniaxial strains by the efficient symmetry - preserving biaxial strains . we successfully implemented the computational schemes and applied them to a technologically important material mos@xmath0 . we found that mos@xmath0 has a large tec anisotropy where the thermal expansion coefficient in the @xmath2 direction is @xmath13 times larger than that in the @xmath1 direction at high temperatures . we highlighted that even though the integrated quantities @xmath4 required by the tec calculations can be obtained via a symmetry - preserving biaxial strain , the grneisen parameters from a biaxial strain may not be a simple average of the grneisen parameters from uniaxial @xmath9 and @xmath10 strains . we demonstrated that we only need a minimum of two symmetry - preserving deformations to directly calculate the tecs of a general hexagonal system . in contrast , the quasiharmonic approximation , when dealing with a two - parameter system , may require an expensive search in the two - dimensional search space . therefore , we expect the strategies adopted in this paper to treat a general two lattice - parameter hexagonal system can be similarly applied to treat other two lattice - parameter systems such as trigonal or tetragonal systems , thus opening the door for a truly predictive tec calculations for many important materials . we also expect the tec calculations based on the gruneisen formalism via symmetry - preserving deformations may be readily incorporated in any phonon related codes such as phonopy@xcite .

using floquet theory , we illustrate that floquet weyl fermions can be created in circularly - polarised - light - irradiated three - dimensional stacked graphene systems . one or two semi - dirac points can be formed due to overlapping of floquet sub - bands . each pair of weyl points have a two - component semi - dirac point parent , instead of a four - component dirac point parent . decreasing the light frequency will make the weyl points move in the momentum space , and the weyl points can approach to the dirac points when the frequency becomes very small . the frequency - amplitude phase diagram is worked out . it is shown that there exist fermi arcs in the surface brillouin zones in circularly - polarised - light - irradiated semi - infinitely - stacked and finitely - multilayered graphene systems . the floquet weyl points emerging due to the overlap of floquet sub - bands provide a new platform to study weyl fermions .

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using floquet theory , we illustrate that floquet weyl fermions can be created in circularly - polarised - light - irradiated three - dimensional stacked graphene systems . one or two semi - dirac points can be formed due to overlapping of floquet sub - bands . each pair of weyl points have a two - component semi - dirac point parent , instead of a four - component dirac point parent . decreasing the light frequency will make the weyl points move in the momentum space , and the weyl points can approach to the dirac points when the frequency becomes very small . the frequency - amplitude phase diagram is worked out . it is shown that there exist fermi arcs in the surface brillouin zones in circularly - polarised - light - irradiated semi - infinitely - stacked and finitely - multilayered graphene systems . the floquet weyl points emerging due to the overlap of floquet sub - bands provide a new platform to study weyl fermions .

for experimentally realizing floquet weyl fermions in such graphene - based models , one has to prepare the circularly - polarized light of suitable frequency and amplitude . because the nn hopping constants ( @xmath1122.8ev , @xmath113 ) are very large , we usually need a high frequency ( order of magnitude of @xmath114hz ) and a strong amplitude ( order of magnitude of @xmath115v / m ) . as shown in the phase diagram , however , the floquet weyl fermions can also be realized when the frequency is low or the amplitude is weak . it should be pointed out that in the regime of low frequency , other floquet sub - bands , such as those with @xmath116 , will play roles in creating floquet weyl points at @xmath117 , and therefore some complex situations may appear . fortunately , in the regime of weak field amplitude , one can realize one or two pairs of floquet weyl fermions at experimentally achievable frequency levels . in addition , some self - assembled graphene - like lattices of cdse nanostructures @xcite can be used to realize such floquet weyl fermions . because their hopping parameters are approximately two order of magnitude smaller compared to graphene and their lattice constant is one order of magnitude larger , much lower frequency and weaker amplitude are needed to realize floquet weyl fermions in good multilayer structures of such cdse nanostructures@xcite . in conclusion , we have proposed an interesting method to create floquet weyl fermions with a two - component semi - dirac parent in a circularly - polarised - light - irradiated 3d stacked graphene system instead of a four - component dirac parent . one or two semi - dirac points can appear at @xmath118 or / and @xmath119 in momentum space when the frequency @xmath77 of light is on the order of magnitude of hopping parameters @xmath14 and @xmath15 . upon decreasing the light frequency , each semi - dirac point will split into two symmetrical weyl points with opposite chirality . further decreasing the frequency will make the weyl points move in the momentum space , and the weyl points can approach to the dirac points when the frequency becomes very small . the frequency - amplitude phase diagram has been worked out , indicating that the floquet weyl femions always appear in pair . furthermore , it has been shown that there exist fermi arcs in the surface brillouin zones in circularly - polarised - light - irradiated semi - infinitely - stacked and finitely - multilayered graphene systems . these theoretical results can lead to a new platform to create weyl fermions in graphene - based and similar systems . this work is supported by nature science foundation of china ( grant nos . 11174359 and 11574366 ) , by chinese department of science and technology ( grant no . 2012cb932302 ) , and by the strategic priority research program of the chinese academy of sciences ( grant no . xdb07000000 ) . z. k. liu , b. zhou , y. zhang , z. j. wang , h. m. weng , d. prabhakaran , s .- k . mo , z. x. shen , z. fang , x. dai , z. hussain , and y. l. chen , discovery of a three - dimensional topological dirac semimetal na@xmath122bi , science * 343 * , 864 ( 2014 ) . z. k. liu , j. jiang , b. zhou , z. j. wang , y. zhang , h. m. weng , d. prabhakaran , s. k. mo , h. peng , p. dudin , t. kim , m. hoesch , z. fang , x. dai , z. x. shen , d. l. feng , z. hussain , and y. l. chen , a stable three - dimensional topological dirac semimetal cd@xmath122as@xmath120 , nat . mater . * 13 * , 677 ( 2014 ) . m. neupane , s .- y . xu , r. sankar , n. alidoust , g. bian , c. liu , i. belopolski , t .- chang , h .- jeng , h. lin , a. bansil , f. chou , and m. z. hasan , observation of a three - dimensional topological dirac semimetal phase in high - mobility cd@xmath122as@xmath120 , nat . commun . * 5 * , 3786 ( 2014 ) . xu , c. liu , s. k. kushwaha , r. sankar , j. w. krizan , i. belopolski , m. neupane , g. bian , n. alidoust , t .- r . chang , h .- jeng , c .- y . huang , w .- f . tsai , h. lin , p. p. shibayev , f .- chou , r. j. cava , and m. z. hasan , observation of fermi arc surface states in a topological metal , science * 347 * , 294 ( 2015 ) . huang , s .- y . xu , i. belopolski , c .- c . lee , g. chang , b. wang , n. alidoust , g. bian , m. neupane , c. zhang , s. jia , a. bansil , h. lin , and m. z. hasan , a weyl fermion semimetal with surface fermi arcs in the transition metal monopnictide taas class , nat . commun . * 6 * , 7373 ( 2015 ) . s .- y . xu , i. belopolski , n. alidoust , m. neupane , g. bian , c .- zhang , r. sankar , g .- q chang , z. yuan , c .- c . huang , h. zheng , j. ma , d. s. sanchez , b. wang , a. bansil , f. chou , p. p. shibayev , h. lin , s. jia , and m. z. hasan , discovery of a weyl fermion semimetal and topological fermi arcs , science * 349 * , 613 ( 2015 ) . b. q. lv , h. m. weng , b. b. fu , x. p. wang , h. miao , j. ma , p. richard , x. c. huang , l. x. zhao , g. f. chen , z. fang , x. dai , t. qian , and h. ding , experimental discovery of weyl semimetal taas , phys . x * 5 * , 031013 ( 2015 ) . m. a. sentef , m. claassen , a. f. kemper , b. moritz , t. oka , j. k. freericks , and t. p. devereaux , theory of floquet band formation and local pseudospin textures in pump - probe photoemission of graphene , nat . commun . * 6 * , 7047 ( 2015 ) . e. kalesaki , c. delerue , c. m. smith , w. beugeling , g. allan , and d. vanmaekelbergh , dirac cones , topological edge states , and nontrivial flat bands in two - dimensional semiconductors with a honeycomb nanogeometry , phys . x * 4 * , 011010 ( 2014 ) . m. p. boneschanscher , w. h. evers , j. j. geuchies , t. altantzis , b. goris , f. t. rabouw , s. van rossum , h. s. j. van der zant , l. d. a. siebbeles , g. van tendeloo , i. swart , j. hilhorst , a. v. petukhov , s. bals , and d. vanmaekelbergh , long - range orientation and atomic attachment of nanocrystals in 2d honeycomb superlattices , science * 344 * , 1377 ( 2014 ) .

uv radiation from massive stars is thought to be the dominant heating mechanism of the nuclear ism in the late stages of evolution of starburst galaxies , creating large photodissociation regions ( pdrs ) and driving a very specific chemistry . we report the first detection of pdr molecular tracers , namely hoc@xmath0 , and co@xmath0 , and confirm the detection of the also pdr tracer hco towards the starburst galaxy ngc253 , claimed to be mainly dominated by shock heating and in an earlier stage of evolution than m82 , the prototypical extragalactic pdr . this strongly supports the idea that these molecules are tracing the pdr component associated with the starburst in the nuclear region of ngc253 .

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uv radiation from massive stars is thought to be the dominant heating mechanism of the nuclear ism in the late stages of evolution of starburst galaxies , creating large photodissociation regions ( pdrs ) and driving a very specific chemistry . we report the first detection of pdr molecular tracers , namely hoc@xmath0 , and co@xmath0 , and confirm the detection of the also pdr tracer hco towards the starburst galaxy ngc253 , claimed to be mainly dominated by shock heating and in an earlier stage of evolution than m82 , the prototypical extragalactic pdr . our co@xmath0 detection suffers from significant blending to a group of transitions of @xmath1ch@xmath2oh , tentatively detected for the first time in the extragalactic interstellar medium . these species are efficiently formed in the highly uv irradiated outer layers of molecular clouds , as observed in the late stage nuclear starburst in m82 . the molecular abundance ratios we derive for these molecules are very similar to those found in m82 . this strongly supports the idea that these molecules are tracing the pdr component associated with the starburst in the nuclear region of ngc253 . the presence of large abundances of pdr molecules in the ism of ngc253 , which is dominated by shock chemistry , clearly illustrates the potential of chemical complexity studies to establish the evolutionary state of starbursts in galaxies . a comparison with the predictions of chemical models for pdrs shows that the observed molecular ratios are tracing the outer layers of uv illuminated clouds up to two magnitudes of visual extinction . we combine the column densities of pdr tracers reported in this paper with those of easily photodissociated species , such as hnco , to derive the fraction of material in the well shielded core relative to the uv pervaded envelopes . chemical models , which include grain formation and photodissociation of hnco , support the scenario of a photo - dominated chemistry as an explanation to the abundances of the observed species . from this comparison we conclude that the molecular clouds in ngc253 are more massive and with larger column densities than those in m82 , as expected from the evolutionary stage of the starbursts in both galaxies .

intense uv radiation from massive stars is one of the main mechanisms responsible for the heating of the interestelar medium in the nuclear region of starburst galaxies . this mechanism is particularly important in the latest stages of starburst ( sb ) galaxies where the newly formed massive star clusters are responsible for creating large photodissociation regions ( pdrs ) . this is the case for the prototypical sb galaxy m82 , where the large observed abundances of molecular species such as hco , hoc@xmath0 , co@xmath0 , and h@xmath2o@xmath0 are claimed to be probes of the high ionization rates in large pdrs formed as a consequence of its extended evolved nuclear starburst @xcite . observational evidences point to a significant enhancement in the abundance of hoc@xmath0 in regions with large ionization fractions . the abundance ratio [ hco@xmath0]/[hoc@xmath0]@xmath4 is found in the prototypical galactic pdrs of the orion bar @xcite . similar or even lower abundance ratios are observed in the pdrs ngc7023 ( 50 - 120 , * ? ? ? * ) , sgrb2(oh ) and ngc2024 ( 360 - 900 , * ? ? ? * ; * ? ? ? * ) , and the horsehead ( 75 - 200 * ? ? ? * ) , as well as in diffuse clouds ( 70 - 120 , * ? ? ? this is in contrast with the much larger ratios of @xmath5 found in dense molecular clouds well shielded from the uv radiation . however , these low hco@xmath0/hoc@xmath0 ratios are not found in other galactic pdrs . large values of this ratio of @xmath6 are found in the pdrs m17-sw , s140 , and ngc2023 @xcite . the hco molecule has also been observed to be a particularly good tracer of the pdr interfaces . low ratios of [ hco@xmath0]/[hco]@xmath7 are found in prototypical galactic pdrs @xcite . the large hco abundance ( @xmath8 ) altogether with the low ratio [ hco@xmath0]/[hco]@xmath9 in the horsehead pdr is claimed to be a diagnostic for an ongoing fuv - dominated photochemistry @xcite . co@xmath0 is also claimed to be particularly prominent in the chemical modeling of pdrs and high abundances of this molecule appear to be correlated to similar enhancements of hoc@xmath0 @xcite . [ co@xmath0]/[hoc@xmath0 ] ratios in the range of 1 - 10 are observed in a number of pdrs @xcite , but only of @xmath10 towards the horsehead pdr @xcite . as mentioned above , this set of pdr probes has been extensively studied towards m82 . however , no such complete studies have been carried out towards other prototypical galaxies , but for the detection of hco and hoc@xmath0 towards ngc1068 @xcite and h@xmath2o@xmath0 in arp220 @xcite . m82 and ngc253 are the brightest prototypes of nearby sb galaxies , at a similar distance and showing very similar ir luminosities and star formation rates of about @xmath11 @xcite.however , both galaxies show very different chemical composition . the chemistry and to a large extend the heating in the central region of ngc253 is believed to be dominated by large scale low velocity shocks @xcite . the similar chemical composition found in the nuclear region of ngc253 to that in galactic star forming molecular complexes points to an earlier evolutionary stage of the starburst in this galaxy than that in m82 @xcite . furthermore , our recent observations of the pdr component as traced by the easily photodissociated hnco molecule towards a sample of galaxies @xcite showed the non - detection of hnco in m82 , at a very low abundance limit . this low hnco abundance supports the scenario that the pdr chemistry dominates the molecular composition of the ism in this galaxy . however , from the hnco measured abundance in ngc253 , it would be placed in an intermediate stage of evolution where photodissociation should be starting to play a significant role in driving a uv - dominated chemistry which has not been yet identified towards this galaxy . the presence of a significant pdr component in ngc253 claimed from the hnco abundance is also inferred from the similar intensity of the atomic fine structure line intensities from pdr tracers like cii and oi @xcite observed in both m82 and ngc253 . in this paper we present the first detection of pdr molecular tracers hoc@xmath0 and co@xmath0 , and confirm the detection hco ( tentatively detected by * ? ? ? * ) in the central region of ngc253 which allows the evaluation of the influence of the photodissociation radiation in the nuclear ism of this sb galaxy . the results presented here support the scenario of the presence of a significant pdr component and clearly show the potential of molecular complexity in estimating the contribution of the different heating mechanisms of the ism in the nuclei of galaxies .

we analyse the spatial distribution within host galaxies and chemical properties of the progenitors of long gamma ray bursts as a function of redshift . by using hydrodynamical cosmological simulations which include star formation , supernova feedback and chemical enrichment and based on the hypothesis of the collapsar model with low metallicity , we investigate the progenitors in the range @xmath0 . we find that scenarios with low metallicity cut - offs best fit current observations . [ firstpage ] gamma - rays : bursts galaxies : abundances , evolution

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we analyse the spatial distribution within host galaxies and chemical properties of the progenitors of long gamma ray bursts as a function of redshift . by using hydrodynamical cosmological simulations which include star formation , supernova feedback and chemical enrichment and based on the hypothesis of the collapsar model with low metallicity , we investigate the progenitors in the range @xmath0 . our results suggest that the sites of these phenomena tend to be located in the central regions of the hosts at high redshifts but move outwards for lower ones . we find that scenarios with low metallicity cut - offs best fit current observations . for these scenarios long gamma ray bursts tend to be [ fe / h ] poor and show a strong @xmath1-enhancement evolution towards lower values as redshift decreases . the variation of typical burst sites with redshift would imply that they might be tracing different part of galaxies at different redshifts . [ firstpage ] gamma - rays : bursts galaxies : abundances , evolution

long gamma - ray bursts ( lgrbs , see the reviews by * ? ? ? * ; * ? ? ? * ) are energetic radiation events , lasting between 2 and @xmath21000 seconds , and with photon energies in the range of kev mev . our current understanding of these sources indicates that the emission is produced during the collapse of massive stars , when the recently formed black hole accretes the debris of the stellar core . during the accretion , highly collimated ultrarelativistic jets consisting mainly of an expanding plasma of leptons and photons ( fireball ) are launched , which drill the stellar envelope . internal shocks in the fireball accelerate leptons and produce the @xmath3-ray radiation through synchrotron and inverse compton processes . external shocks from the interaction of the jets with the interstellar medium produce later emission at lower energies , from x - rays to radio ( afterglow ) . optical afterglow spectra allowed the measurement of lgrb redshifts @xcite , locating these sources at cosmological distances ( @xmath4 ) , and revealing that their energetics is similar to that of supernovae ( sne ) . some lgrbs have indeed been observed to be associated to hydrogen - deficient , type ib / c supernovae ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? afterglows allowed also the identification of lgrb host galaxies ( hgs ) , which turned out to be mostly low - mass , blue and subluminous galaxies with active star formation @xcite . although the general picture is clear enough , its details are still a matter of discussion . among other unanswered questions , the exact nature of the lgrb stellar progenitors is still being debated . stellar evolution models provide a rough picture of the production of a lgrb in a massive star . according to the _ collapsar _ model @xcite , lgrbs are produced during the collapse of single wolf - rayet ( wr ) stars . wr stars have massive cores that may collapse into black holes , and are fast rotators , a condition needed to support an accretion disc and launch the collimated jets . wrs have also large mass - loss rates , needed to lose their hydrogen envelope before collapsing , that would otherwise brake the lgrb jet . this model agrees with the observed association between lgrbs and hydrogen deficient sne . however , wrs large mass - loss rates imply large angular momentum losses that would brake their cores , which would inhibit the production of the lgrb . to overcome this problem , @xcite proposed low - metallicity wrs ( wos ) as progenitors . wos have lower mass - loss rates , diminishing the braking effect , but also preventing the loss of the envelope . another possibility was proposed by @xcite . according to these authors , low - metallicity , rapidly rotating massive stars evolve in a chemically homogeneous way , hence burning the hydrogen envelope , instead of losing it . low - metallicity progenitor models are consistent with different pieces of evidence . first , the works of @xcite and @xcite show that the collapse of high - metallicity stars produces mainly neutron stars , while those of low - metallicity stars form black holes . second , lgrb hgs have been found to be low - metallicity systems @xcite . finally , the analysis of the statistical properties of the population of lgrbs suggests that their cosmic production rate should increase with respect to the cosmic star formation rate at high redshift , which could be explained as an effect of the low metallicity of the progenitors , combined with the cosmic metallicity evolution @xcite . another possibility for wr to lose the envelope without losing too much angular momentum is to be part of binary systems as proposed by @xcite . understanding the nature of lgrb progenitors is beyond the interest of only stellar evolution , black hole formation , and high energy astrophysics . the visibility of lgrbs up to very high redshifts ( @xmath5 ) , allows their use as tools to explore star formation and galaxy evolution in the early universe . on the other hand , observations of the environment and hgs of lgrbs could reveal important clues about the progenitors of these phenomena . given that star formation shifts outward within a galaxy due to the depletion of gas in the central regions as the galaxy evolves , that the interstellar medium of galaxies is not chemically homogeneous , and that the chemical enrichment is affected by variations of the star formation rate and the production of different types of sne , it is expected that both the lgrb positions within a galaxy and the chemical properties of the environment in which lgrbs occur depend on redshift and on the metallicity of the lgrb progenitors . using high - precision astrometry , @xcite and @xcite have measured the positions of @xmath235 lgrbs with respect to the centres of their hosts , supporting the collapsar model against the ( now disproved ) neutron star merger model . the question of the metallicity dependence of lgrb progenitors could also be investigated comparing these data with model predictions . the chemical abundances of lgrb circumburst and hg environments were investigated by several authors @xcite . however , only in a few cases of low - redshift bursts a direct measure of the metallicity of the star - forming region that produced the lgrb is available . at intermediate redshift observers usually measure the mean hg metallicity , while at high redshift they must resort to grb - dla techniques , which give the metallicity of galactic clouds intercepting the line of sight to the lgrb , but not necessarily associated with the burst itself @xcite . in this paper , we use cosmological hydrodynamical simulations which include star formation and sn feedback to investigate the predictions of different progenitor scenarios regarding the positions of lgrbs and the chemical abundances of their environment . since galaxy formation is a highly non - linear process , cosmological numerical simulations @xcite are the best tools to investigate these lgrb properties . in the past , this method has been used by several authors to investigate different aspects of the lgrb environment and hgs . @xcite have shown that requiring hgs to have high star formation efficiency , the observed hg luminosity function can be reproduced . @xcite developed a monte carlo simulation to synthesize lgrb and hg populations in hydrodynamical simulations of galaxy formation , in the framework of the collapsar model . they have found that a bias to low - metallicity progenitors ( @xmath6 ) is needed to explain the observed properties of hgs . @xcite and @xcite used semi - analytical models of galaxy formation to study the properties of hg populations . particularly @xcite developed a new approach to model the detectability of the lgrbs . both teams explored models with mass and metallicity cut - offs for lgrb progenitors , finding that models with a metallicity cut - off could explain the hg properties , and hence supporting previous claims that lgrbs are biased tracers of star formation . however in these semi - analytical models , the spatial distribution of individual stellar populations within hgs can not be investigated . the chemical abundances of lgrb - dlas were investigated using numerical simulations by @xcite , finding that the clouds producing the absorption lie at galactocentric distances of the order of 1 kpc . in this work , we use cosmological numerical simulations of galaxy formation to construct synthetic lgrb populations , which allow us to investigate the properties of individual stellar populations within hgs . our simulations are similar to those of @xcite , but with a higher resolution , and include the effects of the energy feedback of sne into the interstellar medium . the metallicities of each stellar populations can be estimated , and used to construct different metallicity - dependent scenarios for lgrb production within the collapsar model . as stated by @xcite , the detectability of lgrbs and their hgs is an important aspect that should not be disregarded for a proper comparison with the observed samples , hence we included it in our population synthesis in the same way as these authors . this work is organized as follows . in sections [ sim ] and [ mod ] we describe the cosmological simulations of galaxy formation used , and our lgrb population synthesis models , respectively . we present our results and compare the to available observational data in section [ res ] . finally , in section [ con ] we present our conclusions .

for these scenarios long gamma ray bursts tend to be [ fe / h ] poor and show a strong @xmath1-enhancement evolution towards lower values as redshift decreases . the variation of typical burst sites with redshift would imply that they might be tracing different part of galaxies at different redshifts .

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1104.5201

we analyse the spatial distribution within host galaxies and chemical properties of the progenitors of long gamma ray bursts as a function of redshift . by using hydrodynamical cosmological simulations which include star formation , supernova feedback and chemical enrichment and based on the hypothesis of the collapsar model with low metallicity , we investigate the progenitors in the range @xmath0 . our results suggest that the sites of these phenomena tend to be located in the central regions of the hosts at high redshifts but move outwards for lower ones . we find that scenarios with low metallicity cut - offs best fit current observations . for these scenarios long gamma ray bursts tend to be [ fe / h ] poor and show a strong @xmath1-enhancement evolution towards lower values as redshift decreases . the variation of typical burst sites with redshift would imply that they might be tracing different part of galaxies at different redshifts . [ firstpage ] gamma - rays : bursts galaxies : abundances , evolution

aiming at understanding the relation between lgrbs and star formation , we analysed the spatial distribution and chemical abundances of stellar populations producing these phenomena . we investigated four different scenarios for the progenitors of lgrbs based on the collapsar model with different metallicity cut - offs . we compared the spatial distribution of lgrbs within their hgs in our scenarios and with the available observations . we found that in all our scenarios lgrb progenitors reside on average in the outer regions of their galaxies at low redshifts , shifting toward the centre as redshift increases . scenarios favouring low metallicity progenitors tend to produce lgrbs further out from the central regions than those allowing high metallicity progenitors . the confrontation of our models with available observations supports scenarios with low metallicity cut - offs , in agreement with previous results @xcite . particulary we best reproduce current available observations for a model where lgrb progenitors are massive stars with @xmath72 . further precise lgrb position measurements would help to confirm these trends . regarding [ fe / h ] abundances of the stellar populations producing lgrbs , we found that in all our scenarios [ fe / h ] increases as redshift decreases . this effect is less conspicuous in the scenarios with low metallicity progenitors , as in these cases the metallicity cut - off restricts the chemical abundances of the stellar populations producing lgrbs . the @xmath1-enhancement decreases with redshift in all our scenarios , as a result of the different contributions of snii and snia . contrary to the detected trend in [ fe / h ] , the @xmath1-enhancement shows a stronger evolution with redshift as @xmath44 decreases . as previously discussed , these chemical trends can be understood within the context of chemical evolution in hierarchical clustering scenarios . considering that the results on the spatial distribution of lgrb progenitors favours low - metallicity progenitor models , one would expect that the iron abundance of the stellar populations producing lgrbs remains low at all redshifts with little variations ( @xmath73}\sim-1 $ ] ) . on the other hand , one would expect that the @xmath1-enhancement strongly decreases with redshift ( by 0.2 dex between @xmath71 and @xmath74 ) . this means that , if lgrbs are produced by low metallicity massive stars , their location will be shifted on average from the central regions to the outskirts of galaxies . if lgrbs can trace the chemical properties of the interestelar medium , they may map different regions of galaxies at different redshifts . a test of these prediction could be set up as further dust - corrected measurements of the chemical abundances of the stellar populations producing lgrbs become available .

we analyze the callan - gross ratio @xmath0 in heavy - quark leptoproduction as a probe of the charm content of the proton . to estimate the charm - initiated contributions , we use the acot(@xmath1 ) variable - flavor - number scheme . our analysis shows that charm densities of the recent cteq sets of parton distributions have sizeable impact on the callan - gross ratio in a wide region of @xmath2 and @xmath3 . in particular , the acot(@xmath1 ) predictions for the quantity @xmath4 are about half as large as the corresponding expectations of the photon - gluon fusion mechanism for @xmath5 and @xmath6 . this is because the structure functions @xmath7 and @xmath8 have different dependences on the mass logarithms of the type @xmath9 . on the other hand , our recent studies indicate that , contrary to the production cross sections , the callan - gross ratio is sufficiently stable under radiative corrections to the photon - gluon fusion component for @xmath10 . we conclude that the quantity @xmath4 in heavy - quark leptoproduction is perturbatively stable but sensitive to resummation of the mass logarithms . for this reason , in contrast to the structure functions , the ratio @xmath11 could be good probe of the charm density in the proton .

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0812.0722

we analyze the callan - gross ratio @xmath0 in heavy - quark leptoproduction as a probe of the charm content of the proton . to estimate the charm - initiated contributions , we use the acot(@xmath1 ) variable - flavor - number scheme . our analysis shows that charm densities of the recent cteq sets of parton distributions have sizeable impact on the callan - gross ratio in a wide region of @xmath2 and @xmath3 . in particular , the acot(@xmath1 ) predictions for the quantity @xmath4 are about half as large as the corresponding expectations of the photon - gluon fusion mechanism for @xmath5 and @xmath6 . this is because the structure functions @xmath7 and @xmath8 have different dependences on the mass logarithms of the type @xmath9 . on the other hand , our recent studies indicate that , contrary to the production cross sections , the callan - gross ratio is sufficiently stable under radiative corrections to the photon - gluon fusion component for @xmath10 . we conclude that the quantity @xmath4 in heavy - quark leptoproduction is perturbatively stable but sensitive to resummation of the mass logarithms . for this reason , in contrast to the structure functions , the ratio @xmath11 could be good probe of the charm density in the proton .

the notion of the intrinsic charm ( ic ) content of the proton has been introduced over 25 years ago in ref . it was shown that , in the light - cone fock space picture @xcite , it is natural to expect a five - quark state contribution , @xmath12 , to the proton wave function . this component can be generated by @xmath13 fluctuations inside the proton where the gluons are coupled to different valence quarks . the original concept of the charm density in the proton @xcite has nonperturbative nature since a five - quark contribution @xmath14 scales as @xmath15 where @xmath16 is the @xmath17-quark mass @xcite . in the middle of nineties , another point of view on the charm content of the proton has been proposed in the framework of the variable - flavor - number scheme ( vfns ) @xcite . the vfns is an approach alternative to the traditional fixed - flavor - number scheme ( ffns ) where only light degrees of freedom ( @xmath18 and @xmath19 ) are considered as active . within the vfns , the mass logarithms of the type @xmath9 are resummed through the all orders into a heavy quark density which evolves with @xmath3 according to the standard dglap @xcite evolution equation . hence this approach introduces the parton distribution functions ( pdfs ) for the heavy quarks and changes the number of active flavors by one unit when a heavy quark threshold is crossed . note also that the charm density arises within the vfns perturbatively via the @xmath20 evolution . some recent developments concerning the vfns are presented in refs . @xcite . presently , both nonperturbative ic and perturbative charm density are widely used for a phenomenological description of available data . ( a recent review of the theory and experimental constraints on the charm quark distribution may be found in ref . in particular , practically all the recent versions of the cteq @xcite and mrst @xcite sets of pdfs are based on the vfn schemes and contain a charm density . at the same time , the key question remains open : how to measure the charm content of the proton ? the basic theoretical problem is that radiative corrections to the heavy - flavor production cross sections are large : they increase the leading order ( lo ) results by approximately a factor of two . moreover , soft - gluon resummation of the threshold sudakov logarithms indicates that higher - order contributions can also be substantial . ( for reviews , see refs . @xcite . ) on the other hand , perturbative instability leads to a high sensitivity of the theoretical calculations to standard uncertainties in the input qcd parameters : the heavy - quark mass , @xmath16 , the factorization and renormalization scales , @xmath21 and @xmath22 , the asymptotic scale parameter @xmath23 and the pdfs . for this reason , one can only estimate the order of magnitude of the pqcd predictions for charm production cross sections in the entire energy range from the fixed - target experiments @xcite to the rhic collider @xcite . since production cross sections are not perturbatively stable , they can not be a good probe of the charm density in the proton . as the radiative corrections to the dominant photon - gluon fusion mechanism . ] for this reason , it is of special interest to study those observables that are well - defined in pqcd . nontrivial examples of such observables were proposed in refs . @xcite , where the azimuthal @xmath24 asymmetry and callan - gross ratio @xmath0 in heavy quark leptoproduction were analyzed.@xmath25 in particular , the born - level results were considered @xcite and the nlo soft - gluon corrections to the basic mechanism , photon - gluon fusion ( gf ) , were calculated @xcite . it was shown that , contrary to the production cross sections , the azimuthal asymmetry in heavy flavor photo- and leptoproduction is quantitatively well defined in pqcd : the contribution of the dominant gf mechanism to the asymmetry is stable , both parametrically and perturbatively . therefore , measurements of this asymmetry should provide a clean test of pqcd . as was shown in ref . @xcite , the azimuthal asymmetry in open charm photoproduction could be measured with an accuracy of about ten percent in the approved e160/e161 experiments at slac @xcite using the inclusive spectra of secondary ( decay ) leptons . in ref . @xcite , the photon-(heavy ) quark scattering ( qs ) contribution to @xmath26-dependent lepton - hadron deep - inelastic scattering ( dis ) was investigated . it turned out that , contrary to the basic photon - gluon fusion component , the qs mechanism is practically @xmath24-independent . this is due to the fact that the quark - scattering contribution to the @xmath24 asymmetry is , for kinematic reasons , absent at lo and is negligibly small at nlo , of the order of @xmath27 . this indicates that the azimuthal distributions in charm leptoproduction could be good probe of the charm pdf in the proton . the perturbative and parametric stability of the gf predictions for the callan - gross ratio @xmath0 in heavy - quark leptoproduction was considered in ref . it was shown that large radiative corrections to the structure functions @xmath28 and @xmath29 cancel each other in their ratio @xmath30 with good accuracy . as a result , the next - to - leading order ( nlo ) contributions of the dominant gf mechanism to the callan - gross ratio are less than @xmath31 in a wide region of the variables @xmath2 and @xmath32 . in the present paper , we continue the studies of the heavy - quark - initiated contributions to heavy - flavor production in dis : @xmath33(p_{x } ) . \label{1}\ ] ] in the case of unpolarized initial states and neglecting the contribution of @xmath34-boson exchange , the cross section of reaction ( [ 1 ] ) can be written as @xmath35 f_{t } ( x , q^{2 } ) + 2\left(1-y\right ) f_{l}(x , q^{2})\right\ } \nonumber \\ & = & \frac{2\pi \alpha^{2}_{\mathrm{em}}}{xq^{4}}\left\ { \left [ 1+(1-y)^{2}\right ] f_{2 } ( x , q^{2 } ) -2xy^{2 } f_{l}(x , q^{2})\right\ } , \label{2}\end{aligned}\ ] ] where @xmath36 is sommerfeld s fine - structure constant , @xmath37 and the kinematic variables are defined by @xmath38 in this paper , we investigate the qs contribution to the callan - gross ratio in heavy - quark leptoproduction defined as @xmath39 to estimate the charm - initiated contributions to the ratio @xmath4 , we use the acot(@xmath1 ) vfns proposed in ref . @xcite . our analysis shows that charm densities of the recent cteq @xcite sets of pdfs lead to a sizeable reduction of the gf predictions for the callan - gross ratio at @xmath40 . for instance , the acot(@xmath1 ) vfns predictions for the ratio @xmath4 are about half of the corresponding ffns ones for @xmath41@xmath42 and @xmath6 . this is due to the fact that resummation of the mass logarithms has different effects on the structure functions @xmath7 and @xmath8 because they have different dependences on the quantities @xmath43 . in particular , contrary to the transverse structure function , @xmath7 , the longitudinal one , @xmath8 , does not contain potentially large mass logarithms at both lo and nlo @xcite . on the other hand , our recent studies indicate that radiative corrections to the callan - gross ratio do not exceed @xmath31 for @xmath10 practically at all values of @xmath32 @xcite . we conclude that the quantity @xmath4 in heavy - quark leptoproduction is perturbatively stable but sensitive to resummation of the mass logarithms of the type @xmath44 . for this reason , in contrast to the structure functions , the ratio @xmath11 in dis could be good probe of the charm density in the proton . concerning the experimental aspects , the ratio @xmath4 in charm leptoproduction can , in principle , be measured in future studies at the proposed erhic @xcite and lhec @xcite colliders at bnl and cern , correspondingly . this paper is organized as follows . in section [ parton ] , we briefly discuss the gf and qs predictions for the parton - level cross sections . resummation of the mass logarithms for the transverse and longitudinal structure functions within the acot(@xmath1 ) vfns is considered in section [ resum ] . hadron - level predictions of both ffns and vfns for the structure function @xmath45 and callan - gross ratio @xmath0 in charm leptoproduction are discussed in section [ hadron ] .

we analyze the efficiency of quantum simulations of fermionic and bosonic models in trapped ions . in particular , we study the optimal time of entangling gates and the required number of total elementary gates . furthermore , we exemplify these estimations in the light of quantum simulations of quantum field theories , condensed - matter physics , and quantum chemistry . finally , we show that trapped - ion technologies are a suitable platform for implementing quantum simulations involving interacting fermionic and bosonic modes , paving the way for overcoming classical computers in the near future .

i

1312.2849

we analyze the efficiency of quantum simulations of fermionic and bosonic models in trapped ions . in particular , we study the optimal time of entangling gates and the required number of total elementary gates . furthermore , we exemplify these estimations in the light of quantum simulations of quantum field theories , condensed - matter physics , and quantum chemistry . finally , we show that trapped - ion technologies are a suitable platform for implementing quantum simulations involving interacting fermionic and bosonic modes , paving the way for overcoming classical computers in the near future . 03.67.ac , 03.67.lx , 37.10.ty

quantum simulation is one of the most promising fields in quantum information science . feynman already pointed out in 1982 @xcite that a controllable quantum platform could simulate the dynamics or static properties of another quantum system exponentially faster than classical computers . since then , this hypothesis has been demonstrated @xcite , and important theoretical and experimental work followed @xcite . furthermore , quantum simulators establish analogies between previously unconnected fields , and have as a main aim to overcome classical computers . many proposals and experimental realizations of quantum simulations in a broad variety of platforms have been put forward , as for example spin systems @xcite , the bose - hubbard model implemented with cold atoms @xcite , quantum chemistry @xcite and quantum statistics @xcite simulated with photonic systems , condensed matter models with rydberg atoms @xcite , relativistic quantum mechanics @xcite , quantum field theories @xcite , and the lattice schwinger model @xcite . on the other hand , quantum simulations of fermionic and bosonic systems in trapped ions have been recently proposed @xcite . therefore , it is timely to study the experimental requirements needed , to assess the feasibility of the proposal and to compare it with other implementations . in this article , we analyze the necessary resources to implement a quantum simulation of fermions and bosons with trapped ions @xcite . we show that the methods developed for simulating fermionic and bosonic systems with ions can save a large amount of resources in terms of gates with respect to other platforms . this demonstrates that trapped ions are a promising quantum technology for a wide variety of quantum simulations , including high energy physics , condensed matter , or quantum chemistry . trapped - ion systems are one of the most advanced technologies for implementing quantum information protocols . ions are charged particles that can be confined either in penning traps @xcite or radio - frequency ( rf ) paul traps @xcite . the former uses electrostatic and magnetic fields , whereas the latter requires time - dependent fields to confine the ions in an effective harmonic potential . here , we will focus on rf paul traps , see fig [ innsbrucktrap]@xmath0 . two different kinds of qubits are currently employed , optical qubits and radio - frecuency qubits ( rf qubits ) . in the first ones , see fig . [ innsbrucktrap]@xmath1 , two internal metastable electronic levels corresponding to an optical transition are used to encode the qubit . in the second ones , see fig . [ innsbrucktrap]@xmath2 , a third level is used to mediate a two - photon transition between the hyperfine or zeeman electronic levels of the qubit . via sideband cooling , the ionic motional modes are able to reach their ground state , which is commonly used as a quantum bus to perform two - qubit gates between any pair of ions in a string . finally , using resonance fluorescence by means of a cyclic transition , quantum nondemolition measurements of the qubit can be realized . fidelities of state preparation , single- and two - qubit gates , and qubit measurement , are currently above 99% @xcite . the basic hamiltonian describing the coupling of a two - level cold ion with a laser beam is ( @xmath3 ) @xmath4 + \exp [ -i(kz-\omega_l t + \phi ) ] \big ) , \end{aligned}\ ] ] where @xmath5 and @xmath6 are pauli matrices associated with the ionic internal levels , @xmath0 ( @xmath7 ) is the annihilation ( creation ) operator of the corresponding motional mode , @xmath8 is the frequency of the internal ionic transition , @xmath9 is the frequency of the trap , @xmath10 is the frequency of the laser field drive , @xmath11 is the laser phase , @xmath12 is the laser wave vector , and @xmath13 is the rabi frequency associated with the ion - laser coupling . transforming into an interaction picture with respect to the internal and motional free - energy term @xmath14 , and after application of the optical rotating - wave approximation , one obtains @xmath15 + { \rm h.c . } , \label{basichionslaser}\end{aligned}\ ] ] where @xmath16 is the laser detuning with respect to the internal ionic transition , @xmath17 is the so called lamb - dicke parameter , where @xmath18 is the ground state width of the motional harmonic oscillator mode . in the lamb - dicke regime , namely , @xmath19 , eq . ( [ basichionslaser ] ) can be expressed as @xmath20 .\end{aligned}\ ] ] by choosing different internal vibrational transitions appropriately changing the laser detuning , @xmath16 , one can obtain the three basic interactions in trapped - ion technology . namely , the carrier interaction ( @xmath21 ) , @xmath22 the red - sideband interaction ( @xmath23 ) , @xmath24 and the blue - sideband interaction ( @xmath25 ) , @xmath26 one can also take into account several laser drivings acting upon different ions in a string . in this situation , one can express the basic interactions as @xmath27 where @xmath28 and @xmath29 are the raising and lowering operators of the @xmath30-th ion and the creation(annihilation ) bosonic operators of the @xmath12-th vibrational mode , respectively . by appropriately combining the interactions appearing in eq . ( [ carriers ] ) one may obtain the basic single and two - qubit gates necessary for universal quantum computing . prototypical cases of two - qubit gates that can be realized in trapped ions are : the cirac - zoller gate @xcite , corresponding basically to a controlled - not ( cnot ) gate , and the mlmer - srensen ( ms ) gate @xcite , that is the basic building block for our quantum simulations of fermions and bosons in trapped ions . the structure of the article is as follows . in section [ fermionsbosons ] , we summarize the method for simulating fermionic systems in trapped ions introduced in ref . @xcite , and we propose a novel approach with an ultrafast gate that may speed up the implementation of the method . in section [ feasibility ] we assess the efficiency of the method in terms of the number of elementary gates and realization time , and show that it can be highly advantageous as compared to other platforms . finally , we give our conclusions in section [ conclusions ] .

this is in qualitative agreement with computer models which predict that variations in radioactive nickel yield have less impact on the rise than on the spread of the decline rates . the sdss - ii supernova set and the local sne ia with well - observed early light curves show no significant differences in their average rise - time properties . this distribution is in contrast to the bimodality in this parameter that was first suggested by @xcite from an analysis of a small set of local sne ia .

i

1001.3428

we analyze the rise and fall times of type ia supernova ( sn ia ) light curves discovered by the sloan digital sky survey - ii ( sdss - ii ) supernova survey . from a set of 391 light curves @xmath0-corrected to the rest - frame @xmath1 and @xmath2 bands , we find a smaller dispersion in the rising portion of the light curve compared to the decline . this is in qualitative agreement with computer models which predict that variations in radioactive nickel yield have less impact on the rise than on the spread of the decline rates . the differences we find in the rise and fall properties suggest that a single ` stretch ' correction to the light curve phase does not properly model the range of sn ia light curve shapes . we select a subset of 105 light curves well observed in both rise and fall portions of the light curves and develop a ` 2-stretch ' fit algorithm which estimates the rise and fall times independently . we find the average time from explosion to @xmath1-band peak brightness is @xmath3 days , but with a spread of rise times which range from 13 days to 23 days . our average rise time is shorter than the @xmath4 days found in previous studies ; this reflects both the different light curve template used and the application of the 2-stretch algorithm . the sdss - ii supernova set and the local sne ia with well - observed early light curves show no significant differences in their average rise - time properties . we find that slow - declining events tend to have fast rise times , but that the distribution of rise minus fall time is broad and single peaked . this distribution is in contrast to the bimodality in this parameter that was first suggested by @xcite from an analysis of a small set of local sne ia . we divide the sdss - ii sample in half based on the rise minus fall value , @xmath5 days and @xmath6 days , to search for differences in their host galaxy properties and hubble residuals ; we find no difference in host galaxy properties or hubble residuals in our sample .

type ia supernovae ( sne ia ) are bright stellar explosions important for their role as distance indicators . sn ia distances have been used to constrain the value of the hubble constant @xcite , and they also showed that our universe has a lower than critical matter density @xcite . @xcite and @xcite used distant ia sne to show that the universe currently has an accelerating rate of expansion implying a ` dark ' energy component . as more sn ia observations have confirmed this result @xcite , the focus has shifted to constraining the properties of dark energy @xcite . systematic uncertainties in measuring dark energy parameters with supernovae now dominate over statistical errors @xcite and a better understanding of supernova physics may help to constrain dark energy properties using sne ia . it is widely accepted that sne ia are the result of thermonuclear explosions of carbon - oxygen white dwarfs ( wds ) , but the nature of the progenitor remains uncertain . in most models , the explosion occurs when the wd nears the chandrasekhar limit by gaining mass from a binary companion . this mass gain is achieved either by single - degenerate ( sd ) mass transfer or wd coalescence in a double - degenerate ( dd ) scenario . for a comprehensive review of these models , see @xcite . observers have attempted to distinguish between the two models , with conflicting results . @xcite found that the extremely luminous supernova snls-03d3bb ( sn 2003fg ) had low ejecta velocity that could have resulted from a super - chandrasekhar progenitor . the high total mass and large nickel yield suggested that snls-03d3bb was the product of a dd merger . @xcite found that sn 2006gz had attributes consistent with the dd model . its spectrum showed significant amounts of unburned carbon , and a low silicon velocity at early phases . the very broad light curve implies a large yield of radioactive nickel as expected in the dd model @xcite , although late - time observations show only weak iron emission lines @xcite . even though the sd model is generally accepted as the most plausible @xcite , there is evidence that it might not be the complete story @xcite . some mixture of progenitors may be producing events with subtle differences in character . the explosion rates for these progenitor systems will depend on the age and the star formation history of the parent population , and the ratio of the different progenitors may not be constant through the history of the universe @xcite . understanding the origin of the phillips relation ( the correlation between light curve shape and peak luminosity ; @xcite ) and its dispersion is critical to improving sne ia as reliable distance indicators . @xcite argued that radioactive nickel yield should be determined by progenitor metallicity , but age of the host galaxy stellar population appears to control the mass of @xmath7ni @xcite . progenitor metallicity may play a secondary role @xcite or have no significant effect on radioactive yield @xcite . recent models by @xcite show that variations in kinetic energy ( ke ) , metallicity , and mixing between burning layers provide light curves beyond the range of the observed phillips relation , implying that not all combinations of variables are found in real sne ia . sn ia luminosity and light curve shape may be influenced by the physics of the explosions . there is a consensus that normal sne ia result from a detonation ( supersonic burning ) of much of the progenitor wd , but it likely begins as a deflagration ( subsonic fusion front ) to allow expansion and some burning at low densities . this model was first introduced by @xcite ; @xcite showed that the model matched the observed light curves and spectra very well . in the delayed detonation " scenario , the timing of the transition from deflagration to detonation provides a natural means of varying the radioactive nickel yield and generating the observed range of luminosities and decline rates @xcite . deflagrations tend to be very asymmetric , and if the asymmetries survive the detonation then viewing angle can result in perceived variations even for similar explosions @xcite . study of the early - time light curve may be important in diagnosing the progenitor problem and explosion physics @xcite . the work by @xcite to constrain the early light curves of local supernovae established the decline - rate - corrected average rise time of 19.5 @xmath8 0.2 days . here , rise time " is defined as the time elapsed from explosion to peak _ b_-band flux . @xcite and @xcite demonstrated the consistency between high- and low - redshift rise times , and similar results were found by @xcite with a large set of snls @xcite supernovae . @xcite studied the rise times of sne ia discovered behind the large magellanic cloud during the supermacho survey lens project and measured a 17.6@xmath9-day rise time in the equivalent of the @xmath2 bandpass . recently , @xcite analyzed eight low - redshift sne ia with well - observed early light curves from a new perspective . a single stretch " parameter has commonly been used to describe the full range of @xmath1 and @xmath2 light curves by compressing or expanding the time axis around the epoch of peak brightness @xcite . @xcite decoupled the rise and decline portions of the eight nearby light curves and found that sne ia can have a range of rise times for a given decline rate . his rise - time minus fall - time distribution ( @xmath10 ; hereafter defined as rmf ) roughly divided his small supernova sample into two groups , possibly suggesting two progenitors or explosion mechanisms . a larger set of sne is required to rigorously test this possibility . here , we analyze light curves from the sloan digital sky survey - ii ( sdss - ii ) supernova survey @xcite which spectroscopically identified approximately 500 sne ia over its three - year lifetime . the sdss - ii supernova survey scanned 300 deg@xmath11 of sky with a cadence as rapid as 2 days between visits ( weather and lunar phase often increased the time between observations of the same field ) , making the survey well suited to an early rise - time study . we also introduce a new fitting method that independently estimates the rise and the fall times of sne ia light curves .

our average rise time is shorter than the @xmath4 days found in previous studies ; this reflects both the different light curve template used and the application of the 2-stretch algorithm . we find that slow - declining events tend to have fast rise times , but that the distribution of rise minus fall time is broad and single peaked . we divide the sdss - ii sample in half based on the rise minus fall value , @xmath5 days and @xmath6 days , to search for differences in their host galaxy properties and hubble residuals ; we find no difference in host galaxy properties or hubble residuals in our sample .

c

1001.3428

we analyze the rise and fall times of type ia supernova ( sn ia ) light curves discovered by the sloan digital sky survey - ii ( sdss - ii ) supernova survey . from a set of 391 light curves @xmath0-corrected to the rest - frame @xmath1 and @xmath2 bands , we find a smaller dispersion in the rising portion of the light curve compared to the decline . this is in qualitative agreement with computer models which predict that variations in radioactive nickel yield have less impact on the rise than on the spread of the decline rates . the differences we find in the rise and fall properties suggest that a single ` stretch ' correction to the light curve phase does not properly model the range of sn ia light curve shapes . we select a subset of 105 light curves well observed in both rise and fall portions of the light curves and develop a ` 2-stretch ' fit algorithm which estimates the rise and fall times independently . we find the average time from explosion to @xmath1-band peak brightness is @xmath3 days , but with a spread of rise times which range from 13 days to 23 days . our average rise time is shorter than the @xmath4 days found in previous studies ; this reflects both the different light curve template used and the application of the 2-stretch algorithm . the sdss - ii supernova set and the local sne ia with well - observed early light curves show no significant differences in their average rise - time properties . we find that slow - declining events tend to have fast rise times , but that the distribution of rise minus fall time is broad and single peaked . this distribution is in contrast to the bimodality in this parameter that was first suggested by @xcite from an analysis of a small set of local sne ia . we divide the sdss - ii sample in half based on the rise minus fall value , @xmath5 days and @xmath6 days , to search for differences in their host galaxy properties and hubble residuals ; we find no difference in host galaxy properties or hubble residuals in our sample .

we obtain an average rise time for the sdss - ii sne ia of @xmath24 days ( standard error of the mean ) ; this is significantly different from the result obtained in @xcite . for the entire nearby sample , we obtain an average rise time of @xmath25 days ( standard error ) . the standard deviation in the rise time is @xmath26 days . this is in general agreement with the value reported for the sdss - ii data . the reason that our results differ from the 19.5 days found by @xcite is the difference in shape of the fiducial curves used in the two studies , and the application of the single - stretch fitter in previous methods . @xcite prove that even slight variations in the declining portion of the template can change the measured rise time by 2 or more days using a single - stretch method . figure [ fiducial ] shows that the leibundgut " template @xcite used by @xcite differs greatly from the mlcs2k2 curves in the pre - maximum phase . the leibundgut template is 0.66 mag fainter than maximum light at @xmath27 days while the mlcs2k2 fiducial curve reaches 0.66 mag at @xmath28 days . such a broad template combined with a single - stretch fit tends to force the rise to be very slow and to push the estimated time of maximum later than the true peak brightness ( see figure 7 in @xcite ) . the narrower mlcs2k2 fiducial combined with the 2-stretch fitter shows that the rise is faster than that found by several previous studies and that there is a wide range of observed rise times for a given fall time . we created extrapolations to the leibundgut template in the exact same manner as for the mlcs2k2 template , ranging in rise time from 14 to 20 days in half - day intervals . using the template determination method described in section 4.3 , we found the best extrapolated leibundgut template had a rise time of 19.5 days ( note that this utilizes the 2-stretch fitter ) . however , after our error cutting , we obtain an average rise time of @xmath29 days using this template . even though the extrapolated leibundgut template has a longer rise time than the mlcs2k2 template , the stretches obtained are smaller so that the average is consistent . indeed this should be expected with the 2 stretch fitter ; the template with the best relationship between early rise and later rise is selected , but the overall rise time remains constant despite the difference in the fiducial relationship between rise and fall . to further demonstrate this point , we also performed a rise - time extrapolation using the same method as @xcite , as well as using the leibundgut template . we fit all 391 sdss - ii sne ia with a single - stretch fit using only data from -10 days to 25 days , and we cut sne with stretch errors greater than 2.0 days . after stretch correcting the full light curve , we used the data less than -10 days ( which was not used in the fitting process ) to fit a parabolic extrapolation to explosion . using this method , we obtain an extrapolation of 19.64 days for the sdss - ii sne ia . this agrees quite well with both the results of @xcite and our own template selection using leibundgut template extrapolations and the 2 stretch fitter . we have shown in this section that the difference between our rise time and that of previous studies revolves around the flexibility of the 2 stretch fitter regarding the template used . a single - stretch fitter that is used to determine the best extrapolation to explosion is much too reliant on the relationship between rise and fall in the template . the 2 stretch fitter is more flexible in the sense that the input template can have any relationship between rise and fall and the average rise time will be consistent with other templates . performing a single - stretch fit and extrapolating to explosion gives the same result as our template determination method from section 4.3 . however , in order to find the average rise time , the addition of another parameter to independently estimate the rise stretch is required , because the rise and fall are not strictly correlated . as with previous studies , we have assumed that the optical flux rises as @xmath30 soon after explosion . @xcite showed that adiabatic losses should nearly balance heating by radioactive decay and keep the effective temperature relatively constant . so the luminosity goes as the radius squared and therefore the time squared for a constant expansion rate . @xcite directly tested this model by fitting light curves with the temporal power - law index as a free parameter . they found the temporal index @xmath31 that best matched the low- and high - redshift supernovae was 1.8@xmath32 , consistent with the arnett calculation . to estimate the shape of the early rise , we fit the 105 sdss - ii light curves with good rise and fall data with the 2-stretch fitter using only epochs later than @xmath27 days . we then corrected all the light curves to the fiducial curve using the rise and fall stretches which provides 103 @xmath1-band observations between @xmath33 and @xmath27 days before maximum . we then calculate the @xmath18 parameter over this interval by comparing the data to the function @xmath34 , where the time of explosion ( @xmath35 ) and power - law index ( @xmath31 ) are allowed to float . the value of the parameter @xmath36 is set by the condition that the function must meet the mlcs2k2 fiducial curve at @xmath27 days . we found the best - fit power - law index for the sdss - ii data was @xmath37 . the index is strongly correlated with the time of explosion which we found to be @xmath38 days . the result is consistent with the arnett prediction and the @xcite estimate for the early light curve shape . we can also test whether or not the early color of the sdss - ii supernovae follows arnett s prediction of slow and modest temperature changes . for each sdss - ii observation where there is a good rest - frame @xmath1 and @xmath2 measurement , we construct a color based on the @xmath39 normalized flux difference . this essentially compares the supernova color to the color at @xmath1-band maximum and avoids the problem of dealing with magnitudes at low flux levels . as a consistency check , for each supernova we take the flux color averaged between @xmath40 and @xmath27 days to see how it varies with redshift . we find that the color is essentially constant as a function of redshift which gives us confidence that the snana @xmath0-corrections at early times are self - consistent . we also see that the colors for @xmath41 are very noisy and we restrict our color analysis to the 332 events at redshifts less than 0.3 . figure [ color ] shows the flux color as a function of supernova phase . the colors have been binned by rest - frame day and the median calculated for each bin . as expected , the supernovae get significantly red after maximum as the @xmath2-band light curve fades more slowly than the @xmath1 . near the time of explosion , the color is slightly red and shifts to the blue just before maximum . this observed color change is exactly what is expected given the 2-stretch fit of the individual @xmath1- and @xmath2-band light curves ( and this is shown by the solid line in the figure ) . using the median @xmath1-band flux , we convert the flux color into magnitudes and find the color index at @xmath40 days is @xmath42 which shifts to @xmath43 at @xmath44 days . the data earlier than @xmath40 days is too noisy to attempt estimating a reliable magnitude color index . we convert the color index to an effective temperature using the empirical relation from @xcite and find that @xmath45 rises linearly from 6000 k at @xmath40 days to 9500 k at @xmath44 days and then stays nearly constant until maximum . flux color relative to b@xmath46 as a function of sn phase . the data have been binned in 1-day ( rest - frame ) intervals and the median of each bin calculated . the diamonds represent the sdss - ii sne with redshift less than 0.3 . the solid line represents the color of the template . the dotted line is the 1@xmath47 spread of the data . calculating a color index for times later than -15 days , we find that the effective temperature increases linearly from -15 to -9 days then remains nearly constant until maximum . this is not expected from @xcite , which predicts that the effective temperature should remain constant . this implies that the power - law index should be nearer to @xmath48 , rather than the @xmath49 calculated from the observations . [ color ] ] this linear rise in temperature over the first week after explosion is not expected from @xcite , and is puzzling . if the color variation represents a temperature change and the optical bands are following the bolometric flux , then we expect a temporal power - law index of at least @xmath50 instead of the observed @xmath51 . in conclusion , we find that the power - law index for the sdss sne ia agrees with the arnett prediction ; however , we find that the early light curves do not follow the prediction of slow and modest temperature changes . our sdss - ii supernovae show a range of rise times for a fixed fall time , suggesting that the physics of the rise and fall epochs differ . @xcite and @xcite show that the light curves of sne ia can be simply described by the deposition of energy from synthesized radioactive elements combined with the diffusion rate of energy out of the expanding nebula . before maximum brightness the energy input rate from radioactivity exceeds the energy lost to luminosity . at maximum , the luminosity matches the instantaneous energy deposition rate and the decline from maximum correlates with the total radioactive yield . using more detailed models , @xcite show that the shape of the light curve depends on more than the radioactive yield . for example , increasing the production of intermediate mass elements ( e.g. , silicon and calcium ) at a fixed nickel mass ( @xmath7ni ) narrows the light curve while increasing the peak luminosity . this occurs because the total burned mass correlates with the ke of explosion , and the faster the supernova expands , the earlier the radioactive energy diffuses out . in contrast , a low ke means a slow rise and faint maximum . note that the variation in ke trends in the opposite direction to the phillip s relation . observationally , the radioactive yield and ke influence the rise and fall times in different ways and variation in these two parameters could help explain the range of rise times seen in the sdss - ii supernovae . other explosion parameters , such as non - radioactive iron yield or degree of mixing , could also impact the rise versus fall times @xcite . for illustration , we consider only ke variation here . @xcite have calculated model light curves for sne ia with fixed ke and varying radioactive nickel masses to show that they can match the phillip s relation fairly well . we can apply the 2-stretch method to these model curves almost as easily as to real data . from this we can see if the rise and fall times of the models can refine the physics of the observed light curve shapes . unfortunately , the mlcs2k2 fiducial does not match the model light curves sufficiently well to estimate accurate rise and fall times . instead , we chose the @xmath52 m@xmath53 model curve as a fiducial and applied the 2-stretch fitter to the remaining models . the resulting rise times for fixed ke models with varying nickel yield are shown as a dashed line in figure [ kasen ] and compared with observed low - redshift rise / fall times . the model rise time varies only modestly with 15 ( slope of @xmath54 days/15 ) compared to the fall time ( slope of @xmath55 days/15 at 15=1.1 ) . this is in stark contrast to the single - stretch parameterization where the rise time parallels the fall time in this diagram . ni yield would change the position of a specific sn ia from the kasen models . [ kasen ] ] we compare the predicted effect on rise / fall times from varying @xmath7ni yield with the sdss - ii data in figure [ rise - fall ] . the observed trend of @xmath10 increasing with larger 15 is well matched by the model , although there are still many supernovae in the sample that lie far from the model . clearly , the single - stretch parameterization of light curve shape is not justified by the observed rise / fall - time variations or predictions of the @xmath7ni model . the small scatter in the rise portion of the sn ia light curves seen in the full sdss - ii sample ( figure [ alldata ] ) should not be a surprise if it is a direct consequence of @xmath7ni yield being the dominant source of diversity in sne ia @xcite . this is a popular interpretation for variations in peak brightness in sne ia . @xcite models that vary ke at fixed nickel yield were also fit with the 2-stretch method . arrows in figure [ kasen ] illustrate the amplitude and direction in the rise / fall time versus 15 plane of a supernova that increases its nickel yield by 25% at fixed ke and then increases its ke by 25% at fixed radioactive yield . the change in ke produces a steeper variation in rise time than does nickel and in the opposite sense , i.e. , increasing ke results in a faster light curve decay as well as a shorter rise time . unlike nickel variations , changes in ke affect the rise time ( slope of @xmath56 days/15 ) as strongly as the fall time , meaning pure variations in ke result in almost no change in @xmath10 ( and would be well fit by a single - stretch parameterization ) . while this analysis focuses on the effects of ke and @xmath7ni yield , there are other parameters that may be important to the light curve shape as well . in particular , mixing the @xmath7ni to a larger radius may result in faster rise times @xcite . this effect plays a secondary role @xcite in light curve shape , however , and is not included in this analysis . the @xcite models used in this analysis contain no effects from variations in @xmath7ni distribution . we have only employed model light curves with fixed iron mass yields , which is the parameter that controls the @xmath7ni distribution in the one - dimensional @xcite models . in principle , varying both @xmath7ni yield and ke will allow a supernova to reach any point on the @xmath10 versus 15 diagram ( figure [ rise - fall ] ) . changes in radioactive yield will move supernovae diagonally , while ke variations shift supernovae horizontally . given these motions , it is difficult to explain the handful of events with very slow rise times and normal decline rates ( @xmath57 and 15@xmath58 ) . sn 1990n may be a member of this group in the low - redshift set . the kasen models also predict that peak luminosity should be related to nickel yield and ke variations , with an increase in @xmath7ni and ke resulting in brighter events . @xcite found , however , that the effect of these parameters on light curve width works in the opposite sense . an increase in ke narrows the light curve while increasing peak luminosity and a larger nickel mass widens the light curve while making a brighter peak . examining the absolute magnitude estimates of the sdss - ii events may help sort out the origin of the rise / fall variations . @xcite and @xcite have shown that rates of sne ia are strongly connected with host galaxy star formation rate . they model the rates as coming from two sources , one from a passive population of stars and the other a prompt population of supernovae correlated with high star formation rates . it is natural to speculate that the range of rmf corresponds to the sources of supernovae in the two stellar populations . to test this idea , we construct the @xmath59 color of the host galaxies of our sample of 105 sdss - ii supernovae . the @xmath59 color index correlates well with specific star formation rate measured from the sdss spectroscopic sample . the host magnitudes are taken from the sdss - dr5 catalog and are color corrected to the rest frame by interpolating from tables in @xcite . the host galaxy color versus supernova @xmath10 is shown in figure [ galaxy ] for supernovae with 15@xmath60 mag . very fast declining supernovae are known to be associated with early - type galaxies ( e.g. , @xcite ) and might confuse the result . days are plotted as diamonds while hosts with high rmf sne are circles . the size of the plotting symbol correlates with the total brightness of the galaxy . the rmf cut at 2 days was selected arbitrarily . the host color distributions do not appear different between these two groups . [ galaxy ] ] there is no significant correlation between host @xmath59 color and the rise - time properties of the supernovae . supernovae with rmf @xmath61 days tend to have slower decline rates than the other supernovae and can be expected to result from the prompt , high star - formation rate population . we do not observe this relation in our sample . the phillip s relation shows that the sn ia light curve decline rate is related to the optical peak luminosity . the sdss - ii light curves suggest that there are a range of basic light curve shapes and this leads to several questions : * which parameter is the best indicator of peak luminosity : fall time , rise time , total width , or rise minus fall time ? * is there a difference in the average peak luminosity between fast and slow risers for a fixed decline rate ? * do the color or dust properties vary with rise time ? to investigate these questions , we estimated the apparent peak @xmath2-band magnitude , and peak color by fitting the 105 light curves with good rise / fall - time measurements with mlcs2k2 . we relaxed all priors to the fits ( flatnegav ) and assumed a fixed extinction law of @xmath62 . despite the good rise - time information in the light curve data , we restricted the fit to include only those points later than @xmath27 days before maximum ; this was done because we found rather poor fits to the light curves when using the mlcs2k2 template extrapolations that put the explosion date at @xmath33 days before @xmath1 maximum . for this analysis , we cut nine supernovae with 15@xmath63 because their colors are strongly dependent on decline rate @xcite . we also fit the light curves using the salt - ii software @xcite and compared the color parameter , @xmath64 , and peak apparent magnitudes to those from mlcs2k2 . the average color difference was @xmath65 with an rms dispersion of 0.045 mag and the average apparent magnitude difference was @xmath66(mlcs)@xmath67(salt)@xmath68 with an rms dispersion of 0.038 mag . we conclude that for these well - sampled light curves the differences in fit parameters between mlcs2k2 and salt - ii are insignificant . given the estimated apparent peak magnitude , redshift , @xmath69 color , and our measured rise / fall stretches , we minimized the residuals on the hubble diagram calculated from @xmath70 , where @xmath71 , @xmath72 , @xmath73 , @xmath74 , and @xmath75 are coefficients allowed to vary in the minimization . the luminosity distance ( @xmath76 in mpc ) is calculated from the known redshift and assuming the cosmological parameters of @xmath77 km s@xmath78 mpc@xmath78 , @xmath79 , and @xmath80 . choosing a different set of cosmological parameters changes the relative absolute magnitudes by only a few percent at these redshifts . an ` amoeba ' algorithm was employed for the minimization of the @xmath18 parameter , @xmath81 , where @xmath82 is the distance modulus uncertainty from the mlcs2k2 fit . we calculate @xmath18 for several combinations of the free parameters and the results of these fits are shown in table [ tbl-2 ] . lccccccc @xmath83 ( @xmath71 ) & @xmath84 & @xmath85 & @xmath86 & @xmath87 & @xmath88 & @xmath89 & @xmath90 + @xmath69 ( @xmath72 ) & ... & @xmath91 & @xmath92 & @xmath93 & @xmath94 & @xmath95 & @xmath96 + @xmath97 ( @xmath73 ) & ... & ... & 0.614 & 0.583 & ... & ... & ... + @xmath98 ( @xmath74 ) & ... & ... & ... & 0.792 & ... & ... & ... + @xmath99 ( @xmath75 ) & ... & ... & ... & ... & 0.691 & 0.600 & 0.765 + @xmath47 & 0.206 & 0.175 & 0.163 & 0.145 & 0.145 & 0.143 & 0.145 + @xmath18/dof & 214/95 & 147/94 & 131/93 & 100/92 & 101/93 & 59/49 & 42/41 + the scatter about the hubble line for a one parameter fit ( zero point ) applied to the remaining 96 events provides an rms scatter of 0.21 mag . this small scatter is not surprising given that the quality of the data is excellent and we have eliminated intrinsically red supernovae with the 15@xmath63 cut . adding a color term reduces the scatter to 0.18 mag . the size of the color term , @xmath100 , should correspond to @xmath101 , the ratio between @xmath2-band extinction and reddening in @xmath102 , if dust were the source of the color variation . as noted for both local and high - redshift supernovae ( e.g. , @xcite ) , the best - fit color term tends to be much smaller than the standard milky way extinction value of @xmath103 . this may indicate non - standard dust in other galaxies or that the supernova colors are not well understood . minimizing the scatter by adding the fall stretch , @xmath104 , as a third parameter has some effect on the hubble residuals , reducing the scatter to 0.16 mag . a fourth parameter that includes the rise stretch , @xmath105 , or the rise minus fall time , @xmath10 , provides the smallest scatter of 0.145 mag . surprisingly , the hubble residuals are minimized when both the rise and fall stretches have large , positive coefficients . the kasen models that vary both nickel yield and ke predict that increasing rise time ( lowering ke ) should reduce the supernova peak brightness , so the rise - time parameter would have the opposite sign from the fall - time parameter . our hypothesis that ke has a strong influence on light curve shape and brightness does not match the observations well , but other variables should be explored . varying the mass of stable iron elements appears to affect the rise time and brightness in the same directions as the ke variation so are also disfavored by this analysis . applying a three - parameter minimization with the light curve characterized by @xmath106 results in the same scatter as a four - parameter fit with @xmath107 and @xmath108 as separate light curve shape indicators . this result suggests that it is the total width of the light curve that correlates with peak luminosity and not the rise or fall separately . indeed , a three - parameter fit with @xmath10 does no better in reducing the scatter than a two - parameter minimization with just zero point and color . when we divide the sample into a ` low rmf ' group with @xmath109 days and a ` high rmf ' subset with @xmath110 days there appears to be no substantial differences in the hubble residuals . applying a three - parameter minimization ( zero point , color , and total stretch ) , we find the color term for the low and high rmf is only marginally different ( see figure [ hubble1 ] ) . we note , however , that the low rmf group has more blue supernovae than the high rmf group , with 9 of the 10 bluest events having @xmath109 days . the relation between luminosity and full width of the light curve also shows a little difference between the two rise - time divisions . -band magnitude vs. peak color for fast - rising ( @xmath109 days ; filled diamonds ) and slow - rising ( @xmath110 days ; open diamonds ) sdss - ii supernovae after correction for light curve shape . no difference in peak luminosity or color slope is apparent . note , however , that the fast - rising events tend to be more blue at peak with 9 of the bluest 10 supernovae having @xmath109 . [ hubble1 ] ] the average absolute magnitudes of the two groups after color and light curve shape correction differ by less than 0.05 mag , implying that the presence of a range in rise times has very little direct impact on cosmological measurements . arnett s rule @xcite states that the bolometric luminosity of a sn ia at maximum light is very close to the instantaneous energy being deposited by the synthesized radioactive elements . this equality has been used by several studies ( e.g. , @xcite ; @xcite ; @xcite ) to estimate the mass of @xmath7ni created in the supernova . however , the time between explosion and maximum light is a key parameter in this calculation and it has often been assumed to be a constant 19.5 days . in this paper , we have found that the average rise time is shorter than that estimated in previous studies and it is not strictly linked to the decline speed . this will change the distribution of @xmath111ni yields when compared with earlier assumptions about rise - time properties . we estimate @xmath7ni yields using the prescription of @xcite but with a simplified technique for measuring the bolometric luminosity . we used the time from explosion to peak flux as our measured rise - time values . we have already calculated the extinction - corrected absolute @xmath2-band magnitudes for the well - observed objects in the sdss - ii sample and we use these to scale an average type ia spectrum which we integrate over a wide wavelength range to get quasi - bolometric @xmath112 luminosity . for a supernova with absolute magnitude @xmath83=0.00 ( vega system ) and the @xcite spectral template at @xmath1-band maximum , we find a bolometric flux of 2.04@xmath113 erg @xmath114 s@xmath78 between 300 and 1000 nm . this approximation is best for normal type ia and is not as accurate for sub - luminous events which tend to be more red than normal at maximum . however , @xcite found that the @xmath2 band is an excellent indicator of bolometric energy even at late phases when the spectrum has become red . under these assumptions , the @xmath7ni yield is simply @xmath115 , where @xmath107 is the rise time in days and @xmath71 is a constant describing the accuracy of arnett s rule ( we assume @xmath116 ) . ni mass for the sdss - ii supernovae vs. the full width ( rise plus fall times ) of the @xmath1-band light curve . the @xmath7ni mass is estimated from arnett s rule so it is a function of both the peak bolometric luminosity and the rise time . the solid line is a least - squares fit to the points . supernovae with slow rise times ( @xmath117 days ) are plotted as stars while those with slow declines ( @xmath118 days ) are shown as diamonds . only one light curve had both a slow rise and decline and it is plotted as a triangle with a full width of 38 days . the supernovae with the largest @xmath7ni yields ( @xmath119 ) have slowly rising light curves while slowly fading events produce more typical amounts ranging between 0.4 and 0.6 m@xmath120 of @xmath7ni . clearly , knowledge of the rise time is critical in understanding the physics of type ia events . [ nimass ] ] the estimated @xmath7ni yields for the sdss - ii events range from 0.2 to 0.8 @xmath121 , which are typical for this method @xcite . figure [ nimass ] shows the @xmath7ni yield as a function of the total light curve width ( @xmath106 ) and there is a strong correlation between these two quantities . most of the supernovae producing the largest amount of @xmath7ni are events with @xmath117 days ( slowest rising 20% ) . in contrast , the slowest declining supernovae ( @xmath118 days ) produce average yields of @xmath7ni . this demonstrates the importance of independently measuring the rise time of sn ia to understand the physics of the thermonuclear explosion mechanisms .

we analyze the rise and fall times of type ia supernova ( sn ia ) light curves discovered by the sloan digital sky survey - ii ( sdss - ii ) supernova survey . from a set of 391 light curves @xmath0-corrected to the rest - frame @xmath1 and @xmath2 bands , we find a smaller dispersion in the rising portion of the light curve compared to the decline . the differences we find in the rise and fall properties suggest that a single ` stretch ' correction to the light curve phase does not properly model the range of sn ia light curve shapes . we select a subset of 105 light curves well observed in both rise and fall portions of the light curves and develop a ` 2-stretch ' fit algorithm which estimates the rise and fall times independently . we find the average time from explosion to @xmath1-band peak brightness is @xmath3 days , but with a spread of rise times which range from 13 days to 23 days .

c

1001.3428

we analyze the rise and fall times of type ia supernova ( sn ia ) light curves discovered by the sloan digital sky survey - ii ( sdss - ii ) supernova survey . from a set of 391 light curves @xmath0-corrected to the rest - frame @xmath1 and @xmath2 bands , we find a smaller dispersion in the rising portion of the light curve compared to the decline . this is in qualitative agreement with computer models which predict that variations in radioactive nickel yield have less impact on the rise than on the spread of the decline rates . the differences we find in the rise and fall properties suggest that a single ` stretch ' correction to the light curve phase does not properly model the range of sn ia light curve shapes . we select a subset of 105 light curves well observed in both rise and fall portions of the light curves and develop a ` 2-stretch ' fit algorithm which estimates the rise and fall times independently . we find the average time from explosion to @xmath1-band peak brightness is @xmath3 days , but with a spread of rise times which range from 13 days to 23 days . our average rise time is shorter than the @xmath4 days found in previous studies ; this reflects both the different light curve template used and the application of the 2-stretch algorithm . the sdss - ii supernova set and the local sne ia with well - observed early light curves show no significant differences in their average rise - time properties . we find that slow - declining events tend to have fast rise times , but that the distribution of rise minus fall time is broad and single peaked . this distribution is in contrast to the bimodality in this parameter that was first suggested by @xcite from an analysis of a small set of local sne ia . we divide the sdss - ii sample in half based on the rise minus fall value , @xmath5 days and @xmath6 days , to search for differences in their host galaxy properties and hubble residuals ; we find no difference in host galaxy properties or hubble residuals in our sample .

the sdss - ii supernova sample provides tight constraints on the rise time and shape of sn ia light curves . the @xmath0-corrected , median light curves of 391 events shows a @xmath1-band rise time of 16.8 days and a significantly smaller dispersion on the rise portion of the curve than on the fading side . this implies that the rise time is less impacted by variations in radioactive nickel yield than the fall , as predicted by the @xcite model light curves . it is clear that the single - stretch parameter commonly used to characterize sn ia light curves is not capable of capturing the full range of light curve shapes , especially when pre - maximum observations are available . we selected 105 sne ia from the larger sample that had sufficient photometric precision and cadence to yield rise- and fall - time errors of less than 2.0 days . from this set , we find the rise time in the @xmath1 band is @xmath122 days ( standard error of the mean ) . this is significantly different from the rise time of 19.5 days measured from local supernovae @xcite and high - redshift events @xcite . we find the cause of this discrepancy to be the difference in the fiducial curves used in the analyses and our application of a 2-stretch fitting method that permits the rise and fall to be fit independently . we find rise times ranging from 13 days to 23 days for events with normal " decline times of around 15 days , demonstrating that the rise and fall are not strictly correlated . we applied our 2-stretch light curve fitting method to data from sdss - ii to test the conjecture by @xcite of a bimodal distribution in sn ia light curve shape . from our 105 high - quality light curves , we are not able to reproduce this bimodal distribution in the difference between rise and fall times . we do find a significant spread in rmf times for the sample , which implies again that the rise and fall are not strictly correlated . this large range in rmf is expected from explosion models that simply vary the radioactive nickel yield . contrary to the premise of the single - stretch method , many of the slowest declining sne are among the fastest risers . this effect is better modeled through mlcs2k2 , as shown by our simulations , and this may be a result of mlcs2k2 being trained on a large number of real nearby sne ia . while mlcs2k2 is better than single stretch at representing the observed light curves , the simulations with mlcs2k2 do not capture the full spread in rise times evident for normal - declining sne ia . specifically our simulations using mlcs2k2 do not contain normal - declining events that are slow rising . we investigated the relation between peak luminosity , light curve shape , and color by minimizing the scatter on the hubble diagram for the 96 sne ia with good rise / fall data and 15@xmath60 . the hubble residuals have the smallest scatter when using both rise and fall time as fit parameters . the correlation of rise and fall time with luminosity have the same sign , meaning that the full width of the light curve is the best indicator of luminosity . twelve models suggested that a second parameter , such as ke , competing with radioactive nickel yield , could be revealed in the rise and fall times and their correlation with luminosity . however , rise and fall times are found to act in concert in the sdss - ii sne , implying that ke ( or other physical parameters that broaden the light curve and lower peak luminosity ) is not a major contributor to light curve shape . @xcite recently suggested that sne ia with high si ii velocity gradients ( hvg ) may have fast- rising light curves . we are analyzing the spectra of the sdss sample to see if there is a rise - time , spectral velocity gradient correlation . it is interesting to note that sn 1990n , a low - redshift supernova with a very slow rise , has a low si ii velocity gradient , but a more complete sample needs to be constructed . the application of the 2-stretch fitting method we have developed provides a better fit to sn ia light curves than simply stretching the entire time axis . by independently fitting the rise and fall portions of each light curve , we found that the rise and fall times are not strictly correlated . when correcting sn ia luminosity for light curve shape , adding the rise - time parameter to the fall time reduces the scatter in the hubble diagram when compared to using the fall time alone . however , we find that the full width of the light curve ( rise plus fall time ) minimizes the scatter about the hubble line as well as using both rise and fall times as independent parameters . this does suggest some danger doing cosmology by combining a low - redshift supernova set dominated by poor pre - maximum sampling with a well - sampled high - redshift set . our results show that measurement of rise time as a separate parameter characterizing sn ia light curve shape may be a useful diagnostic in understanding the progenitors and explosion mechanisms of thermonuclear events . based on @xmath7ni yield calculations in @xcite and @xcite , our average rise time would result in a 15%-20% reduction in @xmath7ni yield as compared to models that use a 19.5-day rise time . however , there are also some sne ia that have rise times longer than 19.5 days , resulting in a higher @xmath7ni yield . it is clear that accurate nickel yield estimates require a good measurement of the rise time for individual events . future supernova searches that provide well - sampled , high - quality data well before maximum light will reveal more about the nature of sn ia . funding for the creation and distribution of the sdss and sdss - ii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , the u.s . department of energy , the national aeronautics and space administration , the japanese monbukagakusho , the max planck society , and the higher education funding council for england . the sdss web site the sdss is managed by the astrophysical research consortium for the participating institutions . the participating institutions are the american museum of natural history , astrophysical institute potsdam , university of basel , cambridge university , case western reserve university , university of chicago , drexel university , fermilab , the institute for advanced study , the japan participation group , johns hopkins university , the joint institute for nuclear astrophysics , the kavli institute for particle astrophysics and cosmology , the korean scientist group , the chinese academy of sciences ( lamost ) , los alamos national laboratory , the max - planck - institute for astronomy ( mpa ) , the max - planck - institute for astrophysics ( mpia ) , new mexico state university , ohio state university , university of pittsburgh , university of portsmouth , princeton university , the united states naval observatory , and the university of washington . this work is based in part on observations made at the following telescopes . the hobby - eberly telescope ( het ) is a joint project of the university of texas at austin , the pennsylvania state university , stanford university , ludwig - maximillians - universitt mnchen , and georg - august - universitt gttingen . the het is named in honor of its principal benefactors , william p. hobby and robert e. eberly . the marcario low - resolution spectrograph is named for mike marcario of high lonesome optics , who fabricated several optical elements for the instrument but died before its completion ; it is a joint project of the hobby - eberly telescope partnership and the instituto de astronoma de la universidad nacional autnoma de mxico . the apache point observatory 3.5 m telescope is owned and operated by the astrophysical research consortium . we thank the observatory director , suzanne hawley , and site manager , bruce gillespie , for their support of this project . the subaru telescope is operated by the national astronomical observatory of japan . the william herschel telescope is operated by the isaac newton group , and the nordic optical telescope is operated jointly by denmark , finland , iceland , norway , and sweden , both on the island of la palma in the spanish observatorio del roque de los muchachos of the instituto de astrofisica de canarias . observations at the eso new technology telescope at la silla observatory were made under program ids 77.a-0437 , 78.a-0325 , and 79.a-0715 . kitt peak national observatory , national optical astronomy observatory , is operated by the association of universities for research in astronomy , inc . ( aura ) under cooperative agreement with the national science foundation . the wiyn observatory is a joint facility of the university of wisconsin - madison , indiana university , yale university , and the national optical astronomy observatories . the w. m. keck observatory is operated as a scientific partnership among the california institute of technology , the university of california , and the national aeronautics and space administration . the observatory was made possible by the generous financial support of the w. m. keck foundation . the south african large telescope of the south african astronomical observatory is operated by a partnership between the national research foundation of south africa , nicolaus copernicus astronomical center of the polish academy of sciences , the hobby - eberly telescope board , rutgers university , georg - august - universitt gttingen , university of wisconsin - madison , university of canterbury , university of north carolina - chapel hill , dartmouth college , carnegie mellon university , and the united kingdom salt consortium . the italian telescopio nazionale galileo is operated on the island of la palma by the fundacion galileo galilei of the instituto nazionale di astrofisica at the spanish observatorio del roque de los muchachos of the instituto de astrofisica de canarias . dark is funded by the danish national research foundation . the oskar klein centre is funded by the swedish research council . jesper sollerman is a royal academy of sciences research fellow supported by a grant from the knut and alice wallenberg foundation . this research is supported at rutgers university by the us department of energy grant de - fg02 - 08er41562 ( pi : jha ) . this work is partially supported by u.s . national science foundation through grant ast-0507475 ( essence ) . abazajian , k. n. , et al . 2009 , , 182 , 543 aldering , g. , knop , r. , & nugent , p. 2000 , , 119 , 2110 arnett , w. d. 1982 , , 253 , 785 arnett , w. d. , branch , d. , & wheeler , j. c. 1985 , , 314 , 337 arnett , d. , & livne , e. 1994 , , 427 , 330 astier , p. , et al . 2006 , , 447 , 31 barris , b. j. , et al . 2006 , , 602 , 571 benetti , s. , et al . 2004 , , 348 , 261 branch , d. , baron , e. , thomas , r. c. , kasen , d. , li , w. , & filippenko , a. v. 2004 , , 116 , 903 conley , a. , et al . 2006 , , 132 , 1707 contardo , g. , leibundgut , b. , & vacca , w.d . 2000 , , 359 , 876 eisenstein , d.j . , et al . 2007 , , 664 , 675 freedman , w. l. , et al . 2001 , apj , 553 , 47 frieman , j.a . , et al . 2008 , , 135 , 338 fukugita , m. , ichikawa , t. , gunn , j. e. , doi , m. , shimasaka , k. , schneider , d. p. 1996 , aj , 111 , 1748 gallagher , j.s . , et al . 2005 , , 634 , 210 gallagher , j. s. , garnavich , p. m. , caldwell , n. , kirshner , r. p. , jha , s. w. , li , w. , ganeshalingam , m. , & filippenko , a. v. 2008 , , 685 , 752 garg , a. , et al . 2007 , , 133 , 403 garnavich , p.m. , et al . 1998 , , 493 , l53 garnavich , p.m. , et al . 1998 , , 509 , 74 garnavich , p. m. , et al . 2004 , , 613 , 1120 goldhaber , g. , et al . 2001 , , 558 , 359 gunn , j. e. , et al . 1998 , aj , 116 3040 gunn , j. e. , et al . 2006 , , 131 , 2332 guy , j. , et al . 2007 , , 466 , 11 hamuy , m. , phillips , m. m. , suntzeff , n. b. , schommer , r. a. , maza , j. , & aviles , r. 1996 , , 112 , 2391 hamuy , m. , et al . 1996 , , 112 , 2398 hamuy , m. , et al . 2003 , , 424 , 651 hayden , b. , garnavich , p. m. , jha , s. w. , & survey , s .- s. 2010 , bulletin of the american astronomical society , 41 , 362 hicken , m. , et al . 2007 , , 669 , l17 hicken , m. , et al . 2009 , , 700 , 331 hoeflich , p. , & khokhlov , a. 1996 , , 457 , 500 hflich , p. , et al . 2010 , , 710 , 444 hogg , d. w. , finkbeiner , d. p. , schlegel , d. j. , & gunn , j. e. 2001 , , 122 , 2129 holtzman , j. a. , et al . 2008 , , 136 , 2306 howell , d.a . , 2006 , nature , 443 , 308 howell , d. a. , et al . 2009 , , 691 , 661 hsiao , e. y. , conley , a. , howell , d. a. , sullivan , m. , pritchet , c. j. , carlberg , r. g. , nugent , p. e. , & phillips , m. m. 2007 , , 663 , 1187 ivezi , . , et al . 2004 , astronomische nachrichten , 325 , 583 jha , s. , et al . 1999 , apjs , 125 , 73 jha , s. , branch , d. , chornock , r. , foley , r. j. , li , w. , swift , b. j. , casebeer , d. , & filippenko , a. v. 2006 , , 132 , 189 jha , s. , riess , a.g . , & kirshner , r.p . 2007 , , 659 , 122 kasen , d. & woosley , s. e. 2007 , , 656 , 661 kasen , d. , & plewa , t. 2007 , , 662 , 459 kasen , d. 2010 , , 708 , 1025 kessler , r. , et al . 2009 , , 185 , 32 kessler , r. , et al . 2009 , , 121 , 1028 khokhlov , a. m. 1991 , , 245 , 114 knop , r.a . , 2003 , , 598 , 102 krisciunas , k. , et al . 2003 , , 125 , 166 lampeitl , h. , et al . 2010 , , 401 , 2331 leibundgut , b. 1989 , ph.d . thesis , univ . basel lira , p. , et al . 1998 , 115 , 234 livio , m. 2000 , type ia supernovae : theory and cosmology , ( cambridge : cambridge univ . press ) , 33 , astro - ph/990326v1 maeda , k. , kawabata , k. , li , w. , tanaka , m. , mazzali , p. a. , hattori , t. , nomoto , k. , & filippenko , a. v. 2009 , , 690 , 1745 mannucci , f. , della valle , m. , & panagia , n. 2006 , , 370 , 773 mcclelland , c. , et al . 2010 , in prep miknaitis , g. , et al . 2007 , , 666 , 674 pastorello , a. , et al . 2007a , , 376 , 1301 pastorello , a. , et al . 2007b , , 377 , 1531 patat , f. , et al . 1996 , , 278 , 111 perlmutter , s. , et al . 1997 , , 483 , 565 perlmutter , s. , et al . 1998 , , 391 , 51 perlmutter , s. , et al . 1999 , , 517 , 565 phillips , m.m . 1993 , , 413 , l105 phillips , m. m. , et al . 2007 , , 119 , 360 pier , j. r. , munn , j. a. , hindsley , r. b. , hennessy , g. s. , kent , s. m. , lupton , r. h. , & ivezi , . 2003 , , 125 , 1559 pignata , g. , et al . 2008 , mnras , 388 , 971 pinto , p. a. , & eastman , r. g. 2000a , , 530 , 744 pinto , p. a. , & eastman , r. g. 2000b , arxiv : astro - ph/0006171 prieto , j. l. , rest , a. , & suntzeff , n. b. 2006 , , 647 , 501 prieto , j. l. , et al . 2007 , arxiv:0706.4088 pritchet , c.j . & the snls collaboration 2005 , asp conference series , 339 , 60p pritchet , c.j . , howell , d.a . , & sullivan , m. 2008 , , 638 , l25 riess , a.g . , et al . 1998 , , 116 , 1009 riess , a.g . , et al . 1999 , , 118 , 2675 riess , a.g . , 2004 , , 607 , 665 riess , a.g . , 2005 , baas , 37 , 1460 riess , a.g . , et al . 2007 , , 659 , 98 sako , m. , et al . 2008 , , 135 , 348 scannapieco , e. , & bildsten , l. 2005 , , 629 , l85 sekiguchi , m. , & fukugita , m. 2000 , , 120 , 1072 smith , j. a. , et al . 2002 , , 123 , 2121 sollerman , j. , et al . 2009 , , 703 , 1374 stanishev , v. , et al . 2007 , , 469 , 645 strovink , m. , 2007 , , 671 , 1084 stritzinger , m. , & leibundgut , b. 2005 , , 431 , 423 stritzinger , m. , mazzali , p. a. , sollerman , j. , & benetti , s. 2006 , , 460 , 793 stoughton , c. , et al . 2002 , , 123 , 485 sullivan , m. , et al . 2006 , 648 , 868 timmes , f. x. , brown , e. f. , & truran , j. w. 2004 , cosmic explosions in three dimensions , 179 tonry , j. l. , et al . 2003 , , 594,1 tucker , d. l. , et al . 2006 , astronomische nachrichten , 327 , 821 wood - vasey , w. m. , et al . 2007 , , 666 , 694 woosley , s. e. , kasen , d. , blinnikov , s. , & sorokina , e. 2007 , , 662 , 487 woosley , s. e. , kerstein , a. r. , sankaran , v. , aspden , a. j. , rpke , f. k. 2009 , , 704 , 255 york , d. g. , et al . 2000 , , 120 , 1579 zheng , c. , et al . 2008 , , 135 , 1766

we analyzed high resolution spectra of interstellar c i absorption toward @xmath0 ori , 1 sco , and @xmath1 sco that were obtained with the goddard high resolution spectrograph on the @xmath2 . we extracted accurate column densities and doppler parameters from lines with precise laboratory - based @xmath3-values . these column densities and @xmath4-values were used to obtain a self - consistent set of @xmath3-values for all the observed c i lines . for many of the lines with wavelength below 1200 ,

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astro-ph0103220

we analyzed high resolution spectra of interstellar c i absorption toward @xmath0 ori , 1 sco , and @xmath1 sco that were obtained with the goddard high resolution spectrograph on the @xmath2 . several multiplets were detected within the wavelength interval 1150 to 1200 , where most c i lines have ill - defined oscillator strength ; multiplets at longer wavelengths with well - defined atomic parameters were also seen . we extracted accurate column densities and doppler parameters from lines with precise laboratory - based @xmath3-values . these column densities and @xmath4-values were used to obtain a self - consistent set of @xmath3-values for all the observed c i lines . for many of the lines with wavelength below 1200 , the derived @xmath3-values differ appreciably from the values quoted in the compilation by morton ( 1991 ) . the present set of @xmath3-values extends and in some cases supersedes those given in zsarg et al . ( 1997 ) , which were based on lower resolution data . = 8.75 in

accurate oscillator strengths ( @xmath3-values ) are needed for spectroscopic studies in astronomy . for instance , they are required when extracting reliable abundances from interstellar absorption lines , when modeling opacities in stellar atmospheres , or when utilizing temperature and density diagnostics . while analyzing such spectra from space - borne , high - resolution uv spectrographs , one can encounter the problem that uncertainties associated with observational sources are less than those from atomic physics . this is especially true when the astronomical data have signal - to - noise ratios greater than 100 to 200 . one can take advantage of the situation by refining @xmath3-values for lines giving discordant results . the basic premise involves obtaining column densities and doppler parameters from lines where there is consensus on @xmath3-values and then using this information in refining other @xmath3-values . several recent studies based on interstellar spectra acquired with the goddard high resolution spectrograph ( ghrs ) on the _ hubble space telescope _ ( @xmath5 ) have adopted this methodology . federman & cardelli ( 1995 ) provided new @xmath3-values for lines of s i ; many of their determinations were confirmed by subsequent theoretical ( tayal 1998 ) and experimental work ( e.g. , biemont et al . cardelli & savage ( 1995 ) analyzed fe ii lines , and zsarg , federman , & cardelli ( 1997 ) refined @xmath3-values for c i lines with central wavelength below 1200 as well as for some forbidden lines above this limit . relative @xmath3-values were derived for singly - ionized nickel ( zsarg & federman 1998 ) and singly - ionized cobalt ( mullman et al . the latter analysis was performed in parallel with laboratory measurements that placed astronomical oscillator strengths on an absolute scale . laboratory measurements on ni ii by fedchak , wiese , & lawler ( 2000 ) validated the relative @xmath3-values in our earlier work on singly - ionized nickel . in the present paper , following the method outlined in zsarg et al . ( 1997 ) , we improved upon their @xmath3-values for c i lines with wavelength below 1200 and expand the number of lines in their list . in section [ section : obs ] we briefly describe the astronomical measurements available for our analysis , and in section [ section : model ] we discuss how we obtained column densities and doppler parameters for each absorbing component ( [ subsection : profilesynthesis ] ) and how we adjusted @xmath3-values ( [ subsection : revision ] ) . finally , we discuss our results in section [ section : disc ] .

we are able to detect clear signatures of dephasing a distinct trait of many - body localisation ( mbl ) via the dynamics of two - sites entanglement , quantified through the concurrence . using the protocol implemented in [ science * 349 * , 842 ( 2015 ) ] we show that in the mbl phase the average two - site entanglement decays in time as a power law , while in the anderson localised phase it tends to a plateau . this behaviour is also qualitatively different in the ergodic phase where the two - site entanglement decays exponentially . two - site entanglement has been already measured in cold atoms : our analysis paves the way for the first direct experimental test of many - body dephasing in the mbl phase .

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we are able to detect clear signatures of dephasing a distinct trait of many - body localisation ( mbl ) via the dynamics of two - sites entanglement , quantified through the concurrence . using the protocol implemented in [ science * 349 * , 842 ( 2015 ) ] we show that in the mbl phase the average two - site entanglement decays in time as a power law , while in the anderson localised phase it tends to a plateau . the exponent of the power law is not universal and shows a clear dependence on the strength of the interaction . this behaviour is also qualitatively different in the ergodic phase where the two - site entanglement decays exponentially . all the results are obtained by means of time - dependent density matrix renormalisation group simulations ; they are corroborated by analytical calculations on an effective model . two - site entanglement has been already measured in cold atoms : our analysis paves the way for the first direct experimental test of many - body dephasing in the mbl phase .

the phenomenon of many - body localisation @xcite ( mbl ) refers to the breakdown of ergodicity in generic , disordered many - body systems due to quantum effects . this is a striking counterexample to the fundamental assumptions of statistical mechanics about the thermalization of an isolated system . for any non - integrable , classical many - body hamiltonian system , the dynamics is ergodic in phase space leading eventually to thermalization . in classical mechanics this occurs even for systems close to integrability via arnold diffusion , a phenomenon strictly related to the celebrated kam theorem @xcite . in quantum systems there is a striking exception : destructive interference between matter waves forbids a system in the mbl phase to thermalize . quantum effects make the system non - ergodic : no part of it acts as reservoir for the rest of the system . the existence of mbl is astonishing at first sight : due to presence of interactions one expects the quantum system to be non - integrable and to show ergodicity and thermalization @xcite . this behaviour is however strange only apparently : it has been shown that a system in the mbl phase can be mapped to an integrable system with an extensive number of local integrals of motion @xcite . traditionally , integrable systems are isolated points in the space of hamiltonians , both from a classical @xcite and a quantum @xcite perspective ; in mbl , on the opposite , integrability and non - ergodicity properties do not require any fine tuning . remarkably , mbl has been recently conjectured even in systems without disorder @xcite : the contrast with the behaviour of classical systems is even more striking . in some sense , the mbl phase is the continuation of the anderson localised ( al ) phase @xcite of non - interacting particles when interaction is turned on : the two phases share several properties , mainly the absence of transport of any physical quantity . at the same time mbl has distinct features that make it qualitatively different from anderson localisation . from one side , while transport is frozen , correlations can still propagate in the mbl phase . this gives rise to a non - trivial dynamics of entanglement which is absent in the al phase and which we will better discuss later . from the other , the transition to the mbl phase does not emerge in thermodynamic quantities , but rather in transport and time - correlation functions . it is a _ dynamical _ transition and therefore we need appropriate observables to identify it . these very special properties have been recognised thanks to a constantly growing theoretical activity whose aims are elucidating the distinguishing features of mbl and finding the ways to detect them in experiments . several works have characterised the mbl phase by absence of transport of charge , spin or mass @xcite or energy@xcite ; emergent , robust integrability @xcite ; logarithmically slow but unbounded growth of entanglement @xcite ; a peculiarly sparse structure of eigenfunctions @xcite ; the behaviour of observables after a quantum quench @xcite ; the persistence of area law for entanglement to arbitrary temperatures and for eigenstates of arbitrary energy in the spectrum @xcite , and the ability to protect discrete symmetries @xcite even at infinite temperature . a comprehensive description of this activity can be found in the reviews @xcite . at the same time several different proposals were put forward in order to experimentally detect mbl . the interferometric probe based on coherent spin manipulations @xcite , the search for revivals of the magnetization @xcite or the temporal fluctuations around stationary values of local observables @xcite are some of the examples . the intense theoretical efforts of the last decade stimulated an exciting race towards its experimental verification . last year the first beautiful experiments providing evidence of mbl appeared in cold atomic systems @xcite and trapped ions @xcite . however , it is still debatable if unique features of mbl which are not present in al systems have been observed : experiments have focused on propagation of particles which are frozen in both phases . it would be highly desirable to have a direct experimental test discriminating between these two cases and to have a direct probe of the dephasing mechanism of the mbl phase . from a theoretical perspective , several different observables / protocols have been proposed to this aim ( see above ) , but , in many cases , they are difficult to implement experimentally . purpose of this paper is to overcome these difficulties : we analyse in detail a probe of mbl which is able to discriminate it from the al phase and is experimentally accessible , within the existing technology . in the rest of the paper we are going to show that this probe is the two - site entanglement . the dynamics of two - site entanglement was recently measured in optical lattices and in trapped ions respectively in @xcite and @xcite . in the experiment of fukuhara _ et al . _ @xcite , a system of atoms governed by a bose - hubbard hamiltonian was considered . the spins of the atoms are initially in a ferromagnetic phase : after flipping a spin at a given site ( local quench protocol ) , the entanglement between neighbouring spins is measured as a function of time . as we are going to discuss in detail , we consider a slight modification of this quench protocol , the one implemented in @xcite . using this protocol , and measuring both imbalance and two - site entanglement , we will be able to extract the key properties of mbl phase . in particular , we will be able to find clear differences of the mbl phase and the the al phase in the measure of the two - site entanglement . entanglement plays an important role in mbl . while transport ( of energy , spin , mass or other macroscopically conserved quantities ) is frozen both in the mbl and al cases , quantum correlations can still propagate in the mbl phase , giving rise to entanglement between distant sites of the system . in this context , the mapping of any mbl system to an integrable system with an extensive number of local integrals of motion is crucial . thanks to this mapping , even in absence of transport , when the _ populations _ in every site are stationary , it can be shown that the _ coherences _ of distant sites evolve in a non - trivial way ( more details are in section [ lbit - model ] ) . this phenomenon is defined as many - body dephasing : it is the ultimate responsible for an unbounded ( but slow ) growth of the entanglement entropy . the situation in the al phase is very different . in this case , the propagation of correlations and the entanglement growth stop after a while : entanglement properties give indeed a clear signature of mbl . several studies ( see e.g. @xcite ) show the evolution of the entanglement entropy of large blocks in disordered spin chains . the logarithmic growth of the entropy @xcite , intimately related to the existence of an extensive number of local integrals of motions , has been identified as a unique trait of mbl . however , despite recent very interesting progresses @xcite , block entanglement entropy is very hard to be measured in a many - body context ( virtually impossible on increasing the size of the block ) . on the opposite , the two - site entanglement we are considering is directly accessible in a cold - atoms experiment . the paper is organised as follows . in the next section we will introduce the model and the quench protocol we are going to simulate . both are chosen to be essentially identical to those implemented in the experiment @xcite . the two - site entanglement will be quantified through the concurrence defined in section [ concu ] . section [ results ] contains the results of our density matrix renormalisation group simulations . they show that the mbl phase is characterised by a typical power - law decay of the concurrence . this behaviour strongly contrasts with al where the concurrence reaches a non - vanishing stationary value ; it is also very different from the ergodic phase , where the concurrence abruptly vanishes after a short transient . we are able to study how the al phase is reached as a vanishing - interaction limit of the mbl : the power - law decay of the concurrence starts after a stationary , metastable , plateau whose extension in time diverges as a power law when the interaction vanishes . in section [ lbit - model ] , we will show that the power - law decay of the concurrence is reproduced by a phenomenological integrable model of interacting qubits ( the so - called `` @xmath0-bit model '' ) : this is in agreement with the fact that our mbl system can be mapped over an integrable system . in section [ bound ] , we will discuss a number of additional effects ( the role of number fluctuations , finite temperature , control of laser pulses ) that may arise when extracting the entanglement from experimental data . in the same section we will show that a ( more easily measurable ) bound to the concurrence exists : it gives very accurate results and faithfully reproduces the essential phenomenology . finally , section [ conclusions ] is devoted to our conclusions and perspectives of future work .

we are dealing with two - dimensional gravitational anomalies , specifically with the einstein anomaly and the weyl anomaly , and we show that they are fully determined by dispersion relations independent of any renormalization procedure ( or ultraviolet regularization ) . we find an equivalence between the dispersive approach and the dimensional regularization procedure . the schwinger terms appearing in the equal time commutators of the energy momentum tensors can be calculated by the same dispersive method .

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we are dealing with two - dimensional gravitational anomalies , specifically with the einstein anomaly and the weyl anomaly , and we show that they are fully determined by dispersion relations independent of any renormalization procedure ( or ultraviolet regularization ) . the origin of the anomalies is the existence of a superconvergence sum rule for the imaginary part of the relevant formfactor . in the zero mass limit the imaginary part of the formfactor approaches a @xmath0-function singularity at zero momentum squared , exhibiting in this way the infrared feature of the gravitational anomalies . we find an equivalence between the dispersive approach and the dimensional regularization procedure . the schwinger terms appearing in the equal time commutators of the energy momentum tensors can be calculated by the same dispersive method . although all computations are performed in two dimensions the method is expected to work in higher dimensions too .

an anomaly in field theory occurs if a symmetry of the action or the corresponding conservation law , valid in the classical theory , is violated in the quantized version . this surprising feature of quantum theory discovered by adler @xcite , bell and jackiw @xcite , and by bardeen @xcite in 1969 plays a fundamental role in physics ( for details see refs.@xcite @xcite ) . physically there is a difference between external and internal symmetries . the breakdown of an external symmetry is not dangerous for the consistency of the theory , on the contrary , it provides for instance the physical explanation for the @xmath1-decay @xcite , @xcite or the solution to the @xmath2 problem in qcd @xcite . on the other hand , the breakdown of an internal symmetry ( i.e. gauge symmetry ) leads to an inconsistency of the quantum theory , the anomalous ward identities destroy the renormalizability of the theory @xcite , and also the unitarity of the @xmath3-matrix may be lost @xcite . to avoid such anomalies imposes severe restrictions to the physical content of a theory . for instance , in the famous @xmath4 standard theory for electroweak interactions one had to demand the existence of the top quark long before it was discovered . gravitation regarded as a gauge theory also suffers from anomalies . the gauges are the general coordinate transformations ( diffeomorphisms ) or the rotations in the tangent frame ( lorentz transformations ) or the conformal transformations ( weyl transformations ) . then in the quantum case the classical conservation law of the energy - momentum tensor can be broken an einstein anomaly occurs or an antisymmetric part of the energy - momentum tensor can exist a lorentz anomaly occurs or the trace of the tensor is nonvanishing a weyl anomaly arises ( for details see e.g. refs.@xcite,@xcite , @xcite ) . whereas the anomaly in the tensor trace has been found already in the seventies @xcite @xcite the study of the gravitational anomalies started with the pioneering work of alvarez - gaum and witten @xcite in the eighties . the anomalies have been first found within perturbation theory , they are local polynomials in the connection and curvature . the authors @xcite @xcite have calculated ( ultraviolet divergent ) feynman diagrams where the external gravitational field couples to a fermion loop via the energy - momentum tensor . of course , the anomaly reflecting the deep laws of quantum physics must show up within other approaches too . so they have been calculated by the heat kernel method @xcite , @xcite , by fujikawa s path integral approach @xcite , @xcite , and by modern mathematical techniques such as differential geometry and cohomology @xcite @xcite and topology ( index theorems ) @xcite , @xcite , @xcite , ( for an overview see ref.@xcite ) . deeply related to anomalies are the socalled schwinger terms @xcite @xcite ( for an introduction see e.g. refs . @xcite , @xcite ) . in a yang - mills gauge theory schwinger terms ( st ) show up as additional terms ( extensions ) in the canonical algebra of the equal time commutators ( etc ) of the gauss law operators ( see e.g. @xcite cohomologically they are described by the faddeev - mickelsson cocycle @xcite , @xcite , and geometrically they can be related to a berry phase in the vacuum functional @xcite @xcite . st are frequently calculated within perturbation theory where the bjorken - johnson - low limit @xcite , @xcite works very well . however , the definition of a point - splitting method turns out to be more subtle and might not lead to the correct result @xcite , @xcite . in gravitation schwinger terms occur in the etc of the energy - momentum tensors , c - number terms that are proportional to derivatives of the @xmath0-function . they can be related to the gravitational anomalies @xcite , and they have been calculated explictly via the invariant spectral function and via cohomological techniques @xcite . furthermore there exists an interesting relation of the st to the curvature of the determinant line bundle @xcite , @xcite . our work deals with the calculation of the gravitational anomalies , specifically the einstein anomaly and the weyl anomaly . the lorentz anomaly is not independent of the einstein anomaly , both types of anomalies can be shifted into each other by a suitable counterterm @xcite . for convenience we choose the case where the lorentz anomaly is vanishing . we also calculate the gravitational schwinger terms . the purpose of our work is to show that all these anomalous features are easily obtained by the method of dispersion relations , a less familiar but very useful approach . some of our results we have briefly presented in refs . @xcite , @xcite . already since their first introduction into quantum field theory @xcite dispersion relations ( dr ) proved to be a very valuable tool . in connection with anomalies dr have been fomulated by dolgov and zakharov @xcite and also by kummer @xcite . in the following several authors @xcite @xcite used successfully dr to determine the anomalies in the chiral current . recently hoej ' i and schnabl @xcite have applied the method to the well - known trace anomaly @xcite , @xcite which is related to the broken dilatation ( or scale ) invariance . we extend in our work the method of dr to the case of pure gravitation . so we consider chiral fermion loops coupled to gravitation for their evaluation it is enough to use gravitation as an external or nonquantized field and we show that the gravitational anomalies and the schwinger terms are , in fact , completely determined by dispersion relations . all calculations are performed in two dimensions . conceptuelly the dr approach is an independent and complementary view of the anomaly phenomenon as compared to the ultraviolet regularization procedures . within dr the anomaly manifests itself as a very peculiar infrared feature of the imaginary part of the amplitude . but as we shall show there is a link between the two approaches , the dr method and the n - dimensional regularization precedure . our paper is organized as follows . in section 2 we present the general structure of the considered ( pseudo- ) tensor amplitude and we discuss the ward identities which we have to study . in section 3 we introduce the dispersion relations for the relevant formfactors of the amplitude and calculate their imaginary parts via the cutkosky rule . in order to reproduce the dr results in a definite ultraviolet regularization scheme we have worked out in detail the t hooft - veltman regularization procedure in section 4 and we have compared the several amplitudes with the results of tomiya @xcite and alvarez - gaum and witten @xcite . the equivalence between the dispersive approach and the dimensional regularization procedure is given in section 5 . in section 6 we derive the anomalous ward identities and explain the source of the anomaly in the dr approach . from the ward identities we deduce the linearized gravitational anomalies the einstein- and the weyl anomaly and we also determine their covariant versions , a comparison with the exact results is given . the gravitational schwinger terms occuring in the etc of the energy - momentum tensors we calculate in section 7 , where we adapt the dispersive approach to a method proposed by klln @xcite . finally we summarize our main results in section 8 .

the origin of the anomalies is the existence of a superconvergence sum rule for the imaginary part of the relevant formfactor . in the zero mass limit the imaginary part of the formfactor approaches a @xmath0-function singularity at zero momentum squared , exhibiting in this way the infrared feature of the gravitational anomalies .

c

hep-th0011067

we are dealing with two - dimensional gravitational anomalies , specifically with the einstein anomaly and the weyl anomaly , and we show that they are fully determined by dispersion relations independent of any renormalization procedure ( or ultraviolet regularization ) . the origin of the anomalies is the existence of a superconvergence sum rule for the imaginary part of the relevant formfactor . in the zero mass limit the imaginary part of the formfactor approaches a @xmath0-function singularity at zero momentum squared , exhibiting in this way the infrared feature of the gravitational anomalies . we find an equivalence between the dispersive approach and the dimensional regularization procedure . the schwinger terms appearing in the equal time commutators of the energy momentum tensors can be calculated by the same dispersive method . although all computations are performed in two dimensions the method is expected to work in higher dimensions too .

we have investigated the gravitational anomalies , specifically the pure einstein anomaly and the weyl anomaly . so we demanded the quantized energy - momentum tensor to be symmetric no lorentz anomaly occurs which is a possible choice . the relevant amplitude , the two - point function of the energy - momentum tensors @xmath57 , we have separated into its pure tensor part @xmath29 and into its pseudo - tensor part @xmath30 , eqs.([amplitude expressed by t - product ] ) ( [ formfactors3 ] ) , and we have decomposed the amplitudes into a general structure of tensors containing 8 formfactors @xmath31 . these formfactors we have expressed by dispersion relations where we had to calculate only the imaginary parts via the cutkosky rules . our subtraction procedure for the formfactors no subtraction for @xmath83 , one subtraction for @xmath203 and two subtractions for @xmath204 is _ the _ natural choice dictated by the @xmath122behaviour of the imaginary parts @xmath123 . it implies that the pure tensor wi ( [ vwi1 ] ) ( [ vwi3 ] ) for the renormalized formfactors is satisfied ( in the limit @xmath95 ) , so that the total anomaly is automatically shifted into the pseudotensor part of the wi ( [ pta ] ) . it turns out that the anomalous ward identity and the anomalous trace identity depend only on the finite formfactor @xmath121 , with its explicit result ( [ t1 for wi ] ) , demonstrating such the independence of a special renormalization procedure . from the anomalous ward identity and the anomalous trace identity we could deduce the linearized gravitational anomalies the linearized einstein- and weyl anomaly and determine their covariant versions . the origin of the anomaly is the existence of a superconvergence sum rule for the imaginary part of the formfactor @xmath63 . in the zero mass limit the imaginary part of the formfactor approaches a @xmath0-function singularity at zero momentum squared , exhibiting in this way the infrared feature of the gravitational anomalies this is an independent and complementary view of the anomalies as compared to the ultraviolet regularization procedures . if we compare , however , the dr approach with the n - dimensional regularization procedure of t hooft veltman we find an equivalence . the two approaches are linked by the substitutions ( [ substitution dis rel - dim reg ] ) . we have also calculated the gravitational schwinger terms which occur in the etc of the energy - momentum tensors . we have adapted our dispersive approach to the method of klln . as a result all gravitational schwinger terms are determined by the formfactor @xmath205 which in the zero mass limit approaches a @xmath0-function singularity at zero momentum squared as in the case of anomalies . so also the schwinger terms show this peculiar infrared feature of the anomalies . we have performed all calculations in two dimensions , where already all essential features of the dr approach show up , analogously to the chiral current case . from a practical point of view the method appears quite appealing . all one has to calculate is the imaginary part of an amplitude ( formfactor ) , which is an easy task . however , this computational simplicity is a special ( and convenient ) feature of the two space - time dimensions . in higher dimensions the amplitude will contain more formfactors and we have to calculate dispersion relations for higher loop diagrams , which is a much more delicate task , but nevertheless we expect the method to work here too . r. jackiw , _ field theoretic investigations in current algebra , topological investigations of quantized gauge theories _ , in : _ current algebra and anomalies _ , treiman , r. jackiw , b. zumino and e. witten ( eds . ) , p.81 , and p.211 , world scientific , singapore ( 1985 ) . p. van nieuwenhuizen , _ anomalies in quantum field theory : cancellation of anomalies in @xmath206 supergravity . leuven notes in mathematical and theoretical physics _ , vol . 3 , leuven university press ( 1988 ) .

we clarify relations between the higher dimensional quantum hall effect and a - class topological insulator . in particular , we elucidate physical implications of the higher dimensional non - commutative geometry in the context of a - class topological insulator . this presentation is based on @xcite .

i

1408.0564

we clarify relations between the higher dimensional quantum hall effect and a - class topological insulator . in particular , we elucidate physical implications of the higher dimensional non - commutative geometry in the context of a - class topological insulator . this presentation is based on @xcite .

the non - commutative geometry ( ncg ) is the underlying geometry of the quantum hall effect ( qhe ) . in the lowest landau level ( lll ) , the electron coordinates are identified with the center of mass coordinates that satisfy the nc algebra : @xmath0=i{\ell}^2.\ ] ] almost a decade ago , the time - reversal symmetric counterpart of qhe , dubbed as quantum spin hall effect , was theoretically proposed @xcite and experimentally confirmed @xcite . subsequently , the 3d version of the quantum spin hall effect , topological insulator ( ti ) , was also discovered @xcite . now we understand there exist a variety of topological classes of qhe with different symmetries as summarized in the topological periodic table @xcite . one may wonder what kind of geometry will describe such tis . recently two groups , @xcite and @xcite , independently proposed the quantum nambu bracket @xcite for higher dimensional topological insulators . in ref.@xcite , the authors considered the quantum nambu 3-bracket for chiral tis ( aiii - class ) . meanwhile the authors in ref.@xcite adopted the the even dimensional quantum nambu - bracket for a - class tis , and 3-bracket for 3d ti . inspired by the recent developments , we discuss a - class tis with emphasis on their relation to higher d. qhe and ncg . the a - class tis live in arbitrary even dimensional spaces and do not respect any symmetries such as time - reversal , particle - hole , and chiral symmetries like qhe . indeed qhe is a 2d entity of a - class tis , and the a - class tis can be regarded as higher d counterparts of the qhe , @xmath1 higher d. qhe . the higher d. qhe was first constructed by zhang and hu in 4d @xcite as a natural generalization of 2d qhe on haldane s sphere @xcite . their 4d model was soon generalized in even higher dimensions@xcite , such as complex projective spaces and even dimensional spheres . in the modern point of view , the higher d. qhe can be considered as a realization of the a - class ti with landau levels . ncg naturally fits in even dimensional space since each commutator needs a pair of nc coordinates , and so all of the even dimensional coordinates of a - class tis are neatly fitted in the commutators and ncg is realized in the whole space . thus , a - class tis are a good starting point to see what physical implications the higher d. ncg brings . we will discuss the spherical higher d. a - class tis @xcite on the basis of the former works @xcite .

we combine techniques from quantum and from classical density functional theory ( dft ) to describe electron - ion mixtures . for homogeneous systems , we also sketch out how to apply the dft formulation to inhomogeneous electron - ion mixtures , and use this to study the electron distribution at the liquid - solid interface of al .

c

cond-mat0110386

we combine techniques from quantum and from classical density functional theory ( dft ) to describe electron - ion mixtures . for homogeneous systems , we show how to calculate ion - ion and ion - electron correlation functions within chihara s quantum hypernetted chain approximation , which we derive within a dft formulation . we also sketch out how to apply the dft formulation to inhomogeneous electron - ion mixtures , and use this to study the electron distribution at the liquid - solid interface of al . pacs numbers:71.22.+i,61.10.-i,61.20.gy,61.12.bt

in conclusion , we have shown how dft provides a unified formalism from which to derive the qoz equations , and the related qhnc approach , first pioneered by chihara . the qhnc reduces the many - centre electronic problem to an effective one - centre one . this dramatically reduces the computational time needed to calculate ion - electron and ion - ion correlation functions . it also has the advantage that no explicit use of effective pair potentials or pseudo - potentials is needed . the most important approximation in the qhnc approach is to treat the electron - electron correlations as those of jellium . it is not yet clear under which conditions this approximation begins to break down . with this caveat in mind , the other approximations entering the qhnc are reasonably well understood . we used the qhnc to calculate the ion - electron radial distribution functions for a number of simple metals , finding very good agreement with ab - initio molecular dynamics calculations where these are available . we have also discussed an exploratory application of the simple ry dft approach to liquid metals as two - component electron - ion mixtures . we found that describing the freezing transition suffers from a similar problem to that found for classical simple fluids : the solid phase does not develop a stable minimum if the full direct correlation functions are used as input . this is rather disappointing . slightly more ( partial ) success was found when we attempted to use the dft to describe the inhomogeneous electron density at a liquid - solid al interface . although this result was only a partial application of the dft , since the ionic density profile came from the simulations , it does suggest that developing a full fledged dft could be very fruitful . finally , it is clear that our rudimentary dft approach is not yet accurate enough , and could be improved in a number of ways . we are attempting to generalize more sophisticated dft schemes like the mdwa@xcite or gela@xcite to the two - component ion - electron problem . we are also studying the effect of using different local field factors and different kinetic energy functionals . aal acknowledges support from the isaac newton trust , cambridge , and the hospitality of lydric bocquet at the ecole normale superieure in lyon , where some of this work was completed . he thanks n.w . ashcroft , p. madden , and m. sprik for illuminating discussions . 99 w. kohn , rev . mod . phys . * 71 * , 1253 ( 1999 ) . p. hohenberg and w. kohn , phys . rev . * 136 * , b864 ( 1964 ) . w. kohn and l. j. sham , phys . 140 * , a1133 ( 1965 ) . n. d. mermin phys . rev . * 137 * , a1441 ( 1965 ) . see e.g. _ density functional theory _ , edited by e. k. u. gross and r. m. dreizler ( plenum press , new york 1995 ) . ) r. car and m. parrinello , lett . * 55 * , 2471 ( 1985 ) . m. pearson , e. smargiassi , and p. a. madden , j. phys . : condens . matter , * 5 * , 3221 ( 1993 ) . m. baus , j. phys . condensed matter * 2 * , 2111 ( 1990 ) . r. evans in d. henderson ed . , _ fundamentals of inhomogeneous fluids _ , ( marcel dekker , new york , 1992 ) . j. chihara , prog . theor . phys . * 59 * , 76 ( 1978 ) . b. j. jesson and p.a . madden , j. chem . phys . * 113 * , 5924 ( 2000 ) , _ ibid _ , * 113 * , 5935 ( 2000 ) . r. kubo , rep . * 19 * , 255 ( 1966 ) . n. w. ashcroft and d. stroud , solid state physics * 33 * , 1 ( 1978 ) . hansen and i. r. mcdonald , _ theory of simple liquids , 2nd ed . _ , ( academic press , london ( 1986 ) ) . j. a. anta and a. a louis , phys . b * 61 * , 11400 ( 2000 ) . j. chihara , _ j. phys . c. : solid state phys _ * 18 * , 3103 ( 1985 ) . j. chihara , phys . a * 40 * , 4507 ( 1989 ) ; m. ishitobi and j. chihara , _ j. phys . : condens . matter _ * 4 * , 3679 ( 1992 ) . j. k. percus , phys . * 8 * , 462 ( 1962 ) ; , see also the appendix of j. chihara , j. phys . : condens . matter * 3 * , 8715 ( 1991 ) . in principle one could also define @xmath62 for all the electrons , including the core - electrons , but since the core electron density changes very little , they are not plotted for the sake of clarity ) . y. rosenfeld and n.w . ashcroft , phys . a * 20 * , 1208 ( 1979 ) . j. hafner , _ from hamiltonians to phase diagrams _ , ( springer verlag , berlin , ( 1987 ) ) . in this paper we used the form described in s. ichimaru and k. utsumi , phys . b. * 24 * , 7385 ( 1981 ) . a. a. louis and n. w. ashcroft , phys . * 81 * , 4456 ( 1998 ) ; see also , a. a. louis and n. w. ashcroft , j. non - cryst . solids , * 250 - 252 * , 9 ( 1999 ) . w.a . curtin and n.w . ashcroft , phys . . lett . * 59 * , 2385 ( 1987 ) . a.r . denton and n.w . ashcroft , phys . a * 39 * , 426 ( 1989 ) . ramakrishnan and m. yussouff , phys . b * 19 * , 2775 ( 1979 ) . a.d.j . haymet and d.w . oxtoby , j. chem . phys . * 74 * , 2559 ( 1981 ) . h. xu and j .- p . hansen , phys . e * 57 * , 211 ( 1998 ) . h. xu , j.p . hansen , and d. chandler , europhys . lett . * 36 * , 419 ( 1994 ) . w. j. nellis , a. a. louis , n. w. ashcroft , phil . a. * 356 * 119 ( 1998 ) . a. de kuijper , w. l. vos , j.l . barrat , j.p . hansen , and j.a . schouten , j. chem . * 93 * , 5187 ( 1990 ) . d.w . marr and a.p . gast , phys . e * 47 * , 1212 ( 1993 ) . a.r . denton , g. kahl , and j. hafner , j. non - cryst . solids * 250 - 252 * 15 ( 1999 ) . j. a. anta , b. j. besson , and p. a. madden , phys . b * 58 * , 6124 ( 1998 ) . j. a. anta and p. a. madden , j. phys . : condens . matter , * 32 * , 6099 ( 1999 ) . g. a. de wijs , b. pastore , a. selloni , and w. van der lugt , phys . lett . * 75 * , 4480 ( 1995 ) .

we find that the full one - loop corrected decay width @xmath3 is very sensitive to the mssm qfv parameters . in a scenario with large @xmath4 mixing , @xmath3 can differ up to @xmath5 from its sm value . after estimating the uncertainties of the width , we conclude that an observation of these qfv susy effects is possible at a future @xmath6 collider such as ilc . hephy - pub 950/15 + uwthph-2015 - 08 +

c

1504.07792

we compute the decay width of @xmath0 in the mssm with quark flavor violation ( qfv ) at full one - loop level in the @xmath1 renormalization scheme . we study the effects of @xmath2 mixing , taking into account the constraints on qfv from the b meson data . we find that the full one - loop corrected decay width @xmath3 is very sensitive to the mssm qfv parameters . in a scenario with large @xmath4 mixing , @xmath3 can differ up to @xmath5 from its sm value . after estimating the uncertainties of the width , we conclude that an observation of these qfv susy effects is possible at a future @xmath6 collider such as ilc . hephy - pub 950/15 + uwthph-2015 - 08 +

in this article , we have shown that the full one - loop corrected decay width @xmath3 is very sensitive to the qfv parameters in the mssm . in a scenario with large @xmath58 mixings , the width can differ up to @xmath85 from its sm value . after estimating the uncertainties of the width , we conclude that an observation of these mssm qfv effects is possible at ilc . therefore , we have a good opportunity to discover the qfv susy effect in this decay @xmath0 at ilc . 99 g. aad _ et al . _ [ atlas collaboration ] , phys . b * 716 * ( 2012 ) 1 . s. chatrchyan _ _ [ cms collaboration ] , phys . b * 716 * ( 2012 ) 30 . et al . _ , d * 91 * ( 2015 ) 015007 [ arxiv:1411.2840 [ hep - ph ] ] . k. a. olive _ et al . _ ( particle data group ) , chin . c * 38 * ( 2014 ) 090001 . l. g. almeida _ et al . _ , d * 89 * ( 2014 ) 033006 . j. tian and k. fujii , proc . eps - hep 2013 , stockholm , sweden , pos(eps - hep2013)316 [ arxiv:1311.6528 [ hep - ph ] ] .

we consider a communication network consisting of nodes and directed edges that connect the nodes . the network may contain cycles . the communications are slotted where the duration of each time slot is equal to the maximum propagation delay experienced by the edges . the edges with negligible delays are allowed to be operated before the other edges in each time slot . for any pair of adjacent edges @xmath0 and @xmath1 where @xmath2 terminates at node @xmath3 and @xmath1 originates from node @xmath3 , we say @xmath2 _ incurs zero delay _ on @xmath1 if @xmath2 is operated before @xmath1 ; otherwise , we say @xmath2 _ incurs a unit delay _ on @xmath1 . in the classical model , every edge incurs a unit delay on every adjacent edge and the cut - set bound is a well - known outer bound on the capacity region . in this paper , we investigate the multimessage multicast network ( mmn ) consisting of independent channels where each channel is associated with a set of edges and each edge may incur zero delay on some other edges . multimessage multicast networks , zero - delay edges , independent channels , cut - set bounds

i

1506.00490

we consider a communication network consisting of nodes and directed edges that connect the nodes . the network may contain cycles . the communications are slotted where the duration of each time slot is equal to the maximum propagation delay experienced by the edges . the edges with negligible delays are allowed to be operated before the other edges in each time slot . for any pair of adjacent edges @xmath0 and @xmath1 where @xmath2 terminates at node @xmath3 and @xmath1 originates from node @xmath3 , we say @xmath2 _ incurs zero delay _ on @xmath1 if @xmath2 is operated before @xmath1 ; otherwise , we say @xmath2 _ incurs a unit delay _ on @xmath1 . in the classical model , every edge incurs a unit delay on every adjacent edge and the cut - set bound is a well - known outer bound on the capacity region . in this paper , we investigate the multimessage multicast network ( mmn ) consisting of independent channels where each channel is associated with a set of edges and each edge may incur zero delay on some other edges . our result reveals that the capacity region of the mmn with independent channels and zero - delay edges lies within the classical cut - set bound despite a violation of the unit - delay assumption . multimessage multicast networks , zero - delay edges , independent channels , cut - set bounds

paper studies time - slotted communications over networks consisting of nodes and directed edges that connect the nodes , and the networks may contain cycles . each edge receives a symbol from a node and outputs a symbol to a node in each time slot , where the duration of a time slot is set to be the maximum propagation delays experienced by the edges . in practical communication networks , propagation delays of different links may vary significantly due to different distances and different transmission medium ( e.g. , optical fiber , air , water , etc . ) across different links . for example , links with relatively short distances have shorter propagation delays compared to those with relatively long distances , and links established through the optical fiber medium generally experience negligible propagation delays compared to links established through the water medium . in order to characterize the scenario where the propagation delays experienced by some edges are negligible compared to the delays experienced by the other edges , we allow the edges with negligible delays to be operated before the rest of the edges in each time slot . since the symbols transmitted on earlier - operated edges may depend on the symbols output from latter - operated edges , we say that an edge @xmath2 terminating at node @xmath3 _ incurs zero delay _ on an edge @xmath1 originating from node @xmath3 if @xmath2 is operated before @xmath1 ; otherwise , we say @xmath2 _ incurs a unit delay _ on @xmath1 . similarly , the network is said to _ contain zero - delay edges _ if there exists an edge that incurs zero delay on another edge ; the network is said to _ contain no zero - delay edge _ if every edge incurs a delay on every other edge . under the classical model , every discrete memoryless network ( dmn ) ( * ? ? ? 15 ) is assumed to contain no zero - delay edge because all the edges are operated at the same time . a well - known outer bound on the capacity region of the dmn that contains no zero - delay edge is the _ classical cut - set bound _ it is easy to construct a network with zero - delay edges whose capacity region is strictly larger than the cut - set bound . one such network is the binary symmetric channel with correlated feedback ( bsc - cf ) considered in ( * ? ? ? vii ) , which will be introduced in the next subsection . consider a network that consists of two nodes denoted by @xmath4 and @xmath5 respectively and two edges denoted by @xmath6 and @xmath7 respectively . node 1 and node 2 want to transmit a message to each other . this is a two - way channel @xcite . in each time slot , node 1 and node 2 transmit @xmath8 and @xmath9 respectively , and they receive @xmath10 and @xmath11 respectively . all the input and output alphabets are binary , and the channel associated with edge @xmath6 is a binary symmetric channel ( bsc ) while the channel associated with edge @xmath7 is a discrete memoryless channel ( dmc ) whose output may depend on the output of channel @xmath6 . in this network , channel @xmath6 incurs zero delay on channel @xmath7 , i.e. , node @xmath5 can receive @xmath11 before encoding and transmitting @xmath9 . we call this network the _ bsc with dmc feedback _ ( bsc - dmcf ) , which is illustrated in figure [ bscfb](a ) . when @xmath12 , the bsc - dmcf is also referred to as the bsc - cf in ( * ? ? ? it has been shown in ( * ? ? ? vii ) that the capacity region of the bsc - cf is strictly larger than the classical cut - set bound , where the classical cut - set bound is obtained under the assumption that the network contains no zero - delay edge while the capacity region of the bsc - cf is achieved when edge @xmath6 incurs zero delay on edge @xmath7 . consequently , we have the following conclusion : ( @xmath13 ) : : _ the capacity region of some bsc - dmcf with zero - delay edges is strictly larger than the classical cut - set bound_. however , statement ( @xmath13 ) is based on an important assumption : the outputs of the two channels can have correlation given their inputs . in other words , the noises of the two channels can be correlated given the channel inputs . if the noises are assumed to be independent given the channel inputs , i.e. , @xmath14 for all @xmath15 , then it is not clear whether statement ( @xmath13 ) still holds . to facilitate discussion , we call the bsc - dmcf which satisfies the _ bsc with independent feedback _ ( bsc - if ) , which is illustrated in figure [ bscfb](b ) . indeed , the bsc - if with zero - delay edges always lies within the classical cut - set bound due to the fact that the two channels are independent and the well - known fact that the presence of instantaneous feedback does not increase the capacity of a point - to - point channel ( * ? ? ? * sec . 7.12 ) . consequently , statement ( @xmath13 ) does not hold for the bsc - if . this motivates us to investigate a general network with zero - delay edges under the assumption that the channels are independent , and compare its capacity region with the cut - set bound . consider a two - relay network ( trn ) illustrated in figure [ 2relaynetwork ] , which consists of a source denoted by @xmath4 , two relays denoted by @xmath5 and @xmath16 respectively , and a destination denoted by @xmath17 . the source wants to send information to the destination with the help of the two relays . suppose all the input and output alphabets are binary . in each time slot , @xmath18 is transmitted on edge @xmath1 by node @xmath3 and @xmath19 is received from edge @xmath1 by node @xmath20 for each edge @xmath1 in the relay network . in addition , suppose @xmath21 @xmath22 and @xmath23 where @xmath24 and @xmath25 are two independent bernoulli random variables with @xmath26 to facilitate discussion , we call the trn described above the _ two - relay network with correlated noises ( trn - cn)_. it can be easily seen that if edge @xmath6 incurs zero delay on edge @xmath27 and edge @xmath28 incurs zero delay on edge @xmath29 , then node 4 can receive one bit per time slot from node 1 with the help of nodes @xmath5 and @xmath16 sending @xmath24 and @xmath25 respectively ( cf . ) . on the contrary , if either edge @xmath6 incurs a delay on edge @xmath27 or edge @xmath28 incurs a delay on edge @xmath29 , then node 4 can not receive any information from node 1 because the independent uniform bits @xmath24 and @xmath25 can not be completely cancelled simultaneously and @xmath25 generated in different time slots are assumed to be independent . ] . consequently , the capacity of the trn - cn with zero - delay edges is strictly larger than the classical cut - set bound , i.e. , @xmath30 . consider another trn with the same topology as illustrated in figure [ 2relaynetwork ] and specified by @xmath31 for all @xmath32 and @xmath33 where @xmath34 s are independent bernoulli random variables . to facilitate discussion , we call the trn described above the _ two - relay network with independent noises ( trn - in)_. it can be easily seen that the capacity of the trn - in , which is equal to the capacity of channel @xmath35 specified in , coincides with the cut - set bound even when zero - delay edges are present . in this paper , we consider the multimessage multicast network ( mmn ) ( * ? ? ? 18 ) consisting of independent channels , where the destination nodes want to decode the same set of messages transmitted by the source nodes . two simple examples of the mmn with independent channel are the following two networks introduced in section [ sectionmotivating ] the bsc - if ( where both nodes want to decode all the messages ) and the trn - in , which belong to the class of mmns consisting of independent discrete memoryless channels ( dmcs ) @xcite . note that the bsc - cf , unlike the bsc - if , does not belong to the class of mmns with independent dmcs because the forward and reverse channels of the bsc - cf are correlated ( cf . figure [ bscfb](a ) ) . similarly , the trn - cn , unlike the trn - in , does not belong to the class of mmns with independent dmcs because the noises among the channels of the trn - cn are correlated ( cf . figure [ 2relaynetwork ] , , and ) . we propose an edge - delay model for the discrete memoryless mmn ( dm - mmn ) with independent channels and zero - delay edges . in our model , each channel is associated with a set of directed edges ( e.g. , a channel characterized by @xmath36 is associated with @xmath37 ) and the channels are operated in a predetermined order so that the output random variables generated by earlier - operated channels are available for encoding the input random variables for latter - operated channels . therefore , an edge may incur zero delay on another edge under our model . our edge - delay model can be used to investigate the practical situation when some edges with negligible propagation delays are allowed to be operated before the rest of the edges in each time slot ( for instance , in a cellular network , edges that connect the mobile users to their closest relays may experience negligible propagation delays compared to those that connect the relays to the base stations ) . the channels of the mmn are assumed to be _ independent _ , meaning that the outputs among the channels are independent given their inputs , but the outputs within a channel are allowed to correlate with each other . the main contribution of this paper is twofold : first , we establish an edge - delay model for the mmn consisting of independent channels which may contain zero - delay edges . our model subsumes the classical model which assumes that every edge incurs a unit delay on every adjacent edge . second , we prove that for each dm - mmn consisting of independent channels with zero - delay edges , the capacity region always lies within the classical cut - set bound despite a violation of the classical unit - delay assumption . combining our cut - set bound result with existing achievability results from network equivalence theory @xcite and noisy network coding ( nnc ) @xcite , we establish the tightness of our cut - set bound under our edge - delay model for the mmn with independent dmcs , and hence fully characterize the capacity region . more specifically , we show that the capacity region is the same as the set of achievable rate tuples under the classical unit - delay assumption . the capacity region result is then generalized to the mmn consisting of independent additive white gaussian noise ( awgn ) channels with zero - delay edges . the mmn with independent dmcs has been investigated in @xcite under the _ node - delay _ model proposed in @xcite for general discrete memoryless networks . the precise definition of zero - delay nodes in ( * ? ? ? iv ) can be expressed under our edge - delay model as follows : a node _ incurs no delay _ if and only if every incoming edge of the node incurs no delay on every outgoing edge of the node . in @xcite , it was shown that the capacity region of the mmn with independent dmcs is equal to that under the classical unit - node - delay assumption even when zero - delay nodes are present . under the node - delay model , all the outgoing edges of each zero - delay node must be operated simultaneously after all the incoming edges of the node have been operated ( cf . * definitions 1 and 2 ) ) while under our edge - delay model , the incoming and outgoing edges of a node can be operated in some predetermined order ( cf . definition [ deforderedpartition ] , [ defdiscretenetwork ] and [ defchanneloperationsequence ] ) . for example , for the trn - cn described in section [ subsectrn ] , edge @xmath28 can be operated before edge @xmath27 under our edge - delay model but not under the node - delay model . in this work , we strengthen the main result in @xcite under our edge - delay model for the mmn with independent dmcs and show that the capacity region remains unchanged even when zero - delay edges are present . it was shown by effros @xcite that under the positive - delay assumption is a function of @xmath38 . ] in the classical setting , the set of achievable rate tuples for the mmn with independent channels does not depend on the amount of positive delay incurred by each edge on each other edge . our capacity result for the mmn with independent dmcs ( as well as awgns ) complements effros s finding as follows : the set of achievable rate tuples for the mmn with independent dmcs ( as well as awgns ) does not depend on the amount of delay incurred by each edge on each other edge , even with the presence of zero - delay edges . from a practical point of view , the capacity region of the mmn with independent dmcs ( as well as awgns ) is not affected by the way of handling delays among the channels or how the channels are synchronized , even when zero - delay edges are present . the rest of the paper is organized as follows . section [ notation ] presents the notation . section [ sectionformulation ] formulates our edge - delay model for the dm - mmn with independent channels and zero - delay edges and state our cut - set bound result , whose proof is contained in section [ sectioninnerouterbound ] . in section [ sectionmmnwithindepdmcs ] , we use our cut - set bound to prove the capacity region of the mmn with independent dmcs and zero - delay edges . section [ sectiongaussianchannels ] generalizes our cut - set bound result to the mmn consisting of independent awgn channels with zero - delay edges and characterizes its capacity region . section [ sectionconclusion ] concludes this paper .

we consider a point particle moving in a random distribution of obstacles described by a potential barrier . we show that , in a weak - coupling regime , under a diffusion limit suggested by the potential itself , the probability distribution of the particle converges to the solution of the heat equation . the diffusion coefficient is given by the green - kubo formula associated to the generator of the diffusion process dictated by the linear landau equation .

r

1307.2157

we consider a point particle moving in a random distribution of obstacles described by a potential barrier . we show that , in a weak - coupling regime , under a diffusion limit suggested by the potential itself , the probability distribution of the particle converges to the solution of the heat equation . the diffusion coefficient is given by the green - kubo formula associated to the generator of the diffusion process dictated by the linear landau equation .

consider a point particle of mass one in @xmath8 , moving in a random distribution of fixed scatterers whose center are denoted by @xmath20 . the equation of motion are @xmath21 where @xmath22 denote position and velocity of the test particle , @xmath23 the time and , as usual , @xmath24 indicates the time derivative for any time dependent variable @xmath25 . + finally @xmath26 is a given spherically symmetric potential . + to outline a kinetic behavior of the particle , we usually introduce a scale parameter @xmath27 , indicating the ratio between the macroscopic and the microscopic variables , and rescale according to @xmath28 with @xmath29 $ ] . then eq.ns become @xmath30 we assume the scatterers @xmath31 distributed according to a poisson distribution of intensity @xmath32 , where @xmath33 . this means that the probability density of finding @xmath34 obstacles in a bounded measurable set @xmath35 is given by @xmath36 where @xmath37 . + now let @xmath38 be the hamiltonian flow solution of eq.n with initial datum @xmath22 in a given sample @xmath31 of obstacles ( skipping the @xmath39 dependence for notational simplicity ) and , for a given initial probability distribution @xmath40 , consider the quantity @xmath41,\ ] ] where @xmath42 is the expectation with respect to the measure @xmath43 given by . + in the limit @xmath44 we expect that the probability distribution solves a linear kinetic equation depending on the value of @xmath45 . more precisely if @xmath13 ( low - density or boltzmann - grad limit ) then @xmath46 converges to @xmath47 , the solution of the following linear boltzmann equation @xmath48 where @xmath49 and where @xmath50 here we are assuming @xmath9 of range one i.e. @xmath51 if @xmath52 , and @xmath53 is the unit vector obtained by solving the scattering problem associated to @xmath9 . this result was proven and discusses in @xcite,@xcite,@xcite,@xcite . + on the other hand , if @xmath14 , the corresponding limit , called weak - coupling limit , yields the linear landau equation ( see @xcite and @xcite ) @xmath54 where @xmath55 and @xmath56 note that @xmath57 is real and spherically symmetric . in the present paper we want to investigate the limit @xmath15 , in case @xmath16 sufficiently small , when the diffusion coefficient @xmath6 given by is diverging . actually we consider the specific example @xmath58 namely a circular potential barrier . + for a potential of the form a simple computation shows that @xmath6 defined in diverges logarithmically . therefore we are interested in characterizing the asymptotic behavior of @xmath59 , given by , under the scaling illustrated above . the main result of the present paper can be summarized in the following theorem . [ th : main th ] suppose @xmath60 a continuous , compactly supported initial probability density . suppose also that @xmath61 , where @xmath62 is any partial derivative with respect to @xmath63 and @xmath64 . finally assume @xmath65 . the following statements hold 1 . if @xmath66 , for all @xmath67 $ ] , @xmath68 , @xmath69 the convergence is in @xmath70 . 2 . if @xmath71 , for all @xmath67 $ ] , @xmath68 , @xmath72 where @xmath47 solves the landau equation with a renormalized diffusion coefficient @xmath73 the convergence is in @xmath70 . + 3 . if @xmath66 , defining @xmath74 , for all @xmath75 , @xmath68 , @xmath76 where @xmath77 solves the following heat equation @xmath78 with @xmath79 given by the green - kubo formula @xmath80\,dt , \ ] ] where @xmath81 is the stochastic process dictated by the generator of the landau equation starting from @xmath82 and @xmath83 $ ] denotes the expectation with respect to the invariant measure on @xmath84 . the convergence is in @xmath70 . some comments to theorem [ th : main th ] are in order . as we shall prove in section 4 , the asymptotic behavior of the mechanical system we are considering is the same as the markov process ruled by the linear landau equation with a diverging factor in front of @xmath85 . this is equivalent to consider the limit in the euler scaling of the linear landau equation , which is trivial . the system quickly thermalizes to the local equilibrium just given by @xmath86 . this is point 1 ) . to detect something non - trivial we have to exploit longer times in which the local equilibrium starts to evolve ( according to the diffusion equation ) , see point 3 ) . note however that , rescaling differently the density of the poisson process , we can recover the kinetic picture given by landau equation ( with a renormalized diffusion coefficient @xmath6 ) as in @xcite , see point 2 ) . we finally remark that this picture is made possible because the recollisions set ( see below for the precise definition ) is negligible , as established in section 4 . we believe that the present result could be recovered also in high - density regimes @xmath87 $ ] , namely also when the recollisions are not negligible anymore . however in this case different ideas and techniques are indeed necessary . the plan of the paper is the following . in the next section we illustrate our strategy and establish some preliminary results . in section 3 we prove theorem 1.1 . finally in section 4 we prove a basic lemma showing that our non - markovian system can indeed be approximated by a markovian one , easier to handle with .

are performed . the critical scaling operator distributions are obtained and their scaling with particle number found to be consistent with the proposed behaviour . the relative merits of employing the constant - npt and grand canonical ( constant-@xmath0vt ) ensembles for simulations of fluid criticality are also discussed .

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cond-mat9606017

we consider the application of finite - size scaling methods to isothermal - isobaric ( constant - npt ) simulations of pure continuum fluids . a finite - size scaling _ ansatz _ is made for the dependence of the relevant scaling operators on the particle number . to test the proposed scaling form , constant pressure simulations of the lennard - jones fluid at its liquid - vapour critical point are performed . the critical scaling operator distributions are obtained and their scaling with particle number found to be consistent with the proposed behaviour . the forms of these scaling distributions are shown to be identical to their ising model counterparts . the relative merits of employing the constant - npt and grand canonical ( constant-@xmath0vt ) ensembles for simulations of fluid criticality are also discussed .

the study of the phase behaviour of simple and complex fluids by computer simulation is a subject of much current research activity @xcite . of particular interest are the critical point properties of such systems @xcite . in the vicinity of a critical point , the correlation length grows extremely large and may exceed the linear size of the simulated system . when this occurs , the singularities and discontinuities that characterise critical phenomena in the thermodynamic limit are shifted and smeared out @xcite . unless care is exercised , such finite - size effects can lead to serious errors in computer simulation estimates of critical point parameters . to cope with these problems , finite - size scaling ( fss ) techniques have been developed @xcite . fss methods enable one to extract accurate estimates of infinite - volume thermodynamic quantities from simulations of finite - sized systems . to date , their application to fluid criticality has been principally in conjunction with simulations in the constant-@xmath0vt or grand - canonical ensemble ( gce ) . the principal merit of this ensemble is that the particle density fluctuates on the scale of the system as a whole , thus enabling direct measurement of the large - scale density fluctuations that are the essential feature of fluid criticality . the gce has proven its worth in fss studies of criticality in a variety of fluid systems including the lennard - jones ( lj ) fluid @xcite and a 2d spin fluid model @xcite . notwithstanding its wide utility , however , there exist many complex fluids for which use of the gce ensemble is by no means efficient . systems such as semi - dilute polymer solutions are difficult to simulate in the gce due to excluded volume effects which hinder chain insertions . while smart insertion techniques go some way to ameliorating this difficulty , the long chain lengths of greatest interest are currently inaccessible @xcite . similarly , electrolyte models such as the restricted primitive model show very poor acceptance rates for particle insertions due to the formation of bound ion clusters @xcite . thus it is interesting to ask whether one can deal with the near - critical density fluctuations in such systems _ without _ having to implement inefficient particle transfer operations . the approach we consider here , is to employ an ensemble wherein the total particle number is fixed , but the density is allowed to fluctuate by virtue of _ volume _ transitions . specifically , we consider how the fss ideas , hitherto only applied to systems with constant volume , may be generalised to an isothermal - isobaric ( npt - ensemble ) simulation . since finite - size scaling usually rests on the idea of comparing the correlation length with the ( fixed ) linear dimensions of the systems , the generalisation to systems whose linear dimensions are dynamically fluctuating is not completely obvious . we make a scaling _ ansatz _ for the near - critical scaling operator distributions and scaling fields , expressed in terms of powers of the particle number . this is then tested via a simulation study of the critical lennard - jones fluid , in which it found that the fss predictions are indeed consistent with the simulation results . finally we discuss the relative merits of the npt- and @xmath0vt- ( gce ) ensembles for simulation studies of fluid criticality .

we consider the application of finite - size scaling methods to isothermal - isobaric ( constant - npt ) simulations of pure continuum fluids . a finite - size scaling _ the forms of these scaling distributions are shown to be identical to their ising model counterparts .

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cond-mat9606017

we consider the application of finite - size scaling methods to isothermal - isobaric ( constant - npt ) simulations of pure continuum fluids . a finite - size scaling _ ansatz _ is made for the dependence of the relevant scaling operators on the particle number . to test the proposed scaling form , constant pressure simulations of the lennard - jones fluid at its liquid - vapour critical point are performed . the critical scaling operator distributions are obtained and their scaling with particle number found to be consistent with the proposed behaviour . the forms of these scaling distributions are shown to be identical to their ising model counterparts . the relative merits of employing the constant - npt and grand canonical ( constant-@xmath0vt ) ensembles for simulations of fluid criticality are also discussed .

the aim of this work was to develop a fss formalism for simulations of near - critical fluids at constant pressure . a scaling form was proposed and tested for the lennard - jones fluid , whose critical point parameters are known to high precision . good consistency with the scaling prediction was found . additionally , it was shown that the forms of the critical scaling operator distributions are the _ same _ as those for the @xmath0vt - ensemble ( and hence the canonical ensemble of the critical ising model ) , despite the very different nature of the simulation ensembles . as is well known , finite - size effects _ may _ differ in various ensembles of statistical mechanics : the microcanonical ensemble , canonical and grand canonical ensembles of fluids are known to have distinct finite - size properties , and are characterized by different scaling functions . our interpretation of the equivalence of the constant - npt and constant-@xmath70 ensemble scaling functions , is that in the thermodynamic limit , @xmath71 , and therefore it is immaterial whether one uses @xmath72 or @xmath73 as the pair of given intrinsic thermodynamic variables . all that matters is that both ensembles have a single extensive variable ( @xmath2 or @xmath30 ) . different scaling properties are obtained when two extensive variables are used , such as in the constant - nvt ( canonical ) ensemble of fluids . it follows that the gce - based fss techniques developed in reference @xcite for accurately locating fluid critical point parameters , carry over directly to the npt - ensemble . it is hoped that use of this latter ensemble will prove beneficial in situations where the gce is highly inefficient , such as for long - chain polymer or electrolyte models . we add the further comment that finite - size scaling with @xmath2 rather than @xmath30 is well known in mean - field spin systems , when every spin interacts with every other spin , and geometry and space have no meaning @xcite . while use of the npt - ensemble is likely to be much more efficient than the gce in cases where particle insertions have a low acceptance probability , we believe that for simple fluids , use of the grand canonical ensemble is much to be preferred . the present study of the lj fluid consumed circa @xmath74 hours cpu time on a cray - ymp , using a vectorized program . by contrast , the previous gce study of the same model was performed with considerably less computational effort using workstations . moreover , it was possible to study much larger systems ( comprising up to @xmath75 particles ) , with considerably greater statistical accuracy than attainable here . the reasons for this difference in efficiency seem to be manifold . owing to the fluctuating volume , it is not possible to easily implement a cell structure for efficiently locating neighbouring particles within the cutoff range . a calculation of all particle separations prior to a trial volume transition involves an @xmath76 operation , which can only be avoided if no potential cutoff is employed @xcite . by contrast , use of a cell structure in the gce leads to a @xmath77 growth in computational complexity . a second disadvantage of the npt - ensemble , is that both volume changes and particle moves must be performed . for each particle move , two partial energy calculations are required , while for a volume change ( with finite interaction cutoff ) , a total energy calculation is required . by contrast , only particle insertions need be implemented in a gce scheme @xcite , each of which requires only a single partial energy calculation . additionally it seems likely that for a given @xmath78 the random walk in @xmath30 required to pass from one phase to the other at coexistence is longer than that in @xmath2 for the gce , even if one employs a dynamically adjusting volume step size such as that of reference @xcite . consequently the correlation time in the npt - ensemble is considerably greater than that of the gce . finally we note that another recent study has also attempted to apply finite - size scaling methods to the lj fluid in the npt - ensemble @xcite . in this study the authors focused on the distribution of the specific volume @xmath79 and attempted to locate the critical point by requiring scale invariance in @xmath80 , subject to the requirement that @xmath80 has two peaks of _ equal _ height at coexistence . however , as we have shown in this work , the volume distribution is not the scaling counterpart for fluids of the ising magnetisation , rather it is the operator @xmath23 . moreover , the limiting ( large @xmath2 ) critical point form of @xmath80 does not have two peaks of equal heights , and is in fact highly asymmetic in form , as figure [ fig : pv ] shows . we therefore ascribe the rather low accuracy in the estimates for @xmath81 and the difficulties in obtaining the surface tension exponent in reference @xcite to this incorrect choice of the scaling operator .

this result leads us to a number of possible algorithms for detecting community structure , as well as several other results , including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong .

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physics0605087

we consider the problem of detecting communities or modules in networks , groups of vertices with a higher - than - average density of edges connecting them . previous work indicates that a robust approach to this problem is the maximization of the benefit function known as `` modularity '' over possible divisions of a network . here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix , which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations . this result leads us to a number of possible algorithms for detecting community structure , as well as several other results , including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong . the algorithms and measures proposed are illustrated with applications to a variety of real - world complex networks .

in this paper , we have studied the problem of detecting community structure in networks . there is already a substantial body of theory supporting the view that community structure can be accurately quantified using the benefit function known as modularity and hence that communities can be detected by searching possible divisions of a network for ones that possess high modularity . here we have demonstrated that the modularity can be succinctly expressed in terms of the eigenvalues and eigenvectors of a matrix we call the modularity matrix , which is a characteristic property of the network and is itself independent of any division of the network into communities . using this expression we have derived a series of further results including several new and competitive algorithms for identifying communities , a method for detecting bipartite or @xmath134-partite structure in networks , and a new community centrality measure that identifies vertices that play a central role in the communities to which they belong . we have demonstrated a variety of applications of our methods to real - world networks representing social , technological , and information networks . these , however , are intended only as illustrations of the potential of these methods . we hope that readers will feel encouraged to apply these or similar methods to other networks of scientific interest and we look forward to seeing the results . the author thanks luis amaral , alex arenas , roger guimer , edward ionides , and david lusseau for useful and enjoyable conversations , and valdis krebs and david lusseau for providing network and other data used in the examples . this work was funded in part by the national science foundation under grant number dms0405348 and by the james s. mcdonnell foundation . g. p. garnett , j. p. hughes , r. m. anderson , b. p. stoner , s. o. aral , w. l. whittington , h. h. handsfield , and k. k. holmes , sexual mixing patterns of patients attending sexually transmitted diseases clinics . _ sexually transmitted diseases _ * 23 * , 248257 ( 1996 ) . s. o. aral , j. p. hughes , b. stoner , w. whittington , h. h. handsfield , r. m. anderson , and k. k. holmes , sexual mixing patterns in the spread of gonococcal and chlamydial infections . _ american journal of public health _ * 89 * , 825833 ( 1999 ) . a. capocci , v. d. p. servedio , g. caldarelli , and f. colaiori , detecting communities in large networks . in s. leonardi ( ed . ) , _ proceedings of the 3rd workshop on algorithms and models for the web graph _ , number 3243 in lecture notes in computer science , springer , berlin ( 2004 ) . h. zhou and r. lipowsky , network brownian motion : a new method to measure vertex - vertex proximity and to identify communities and subcommunities . in _ lecture notes in computer science _ , volume 3038 , pp . 10621069 , springer , new york ( 2004 ) . p. pons and m. latapy , computing communities in large networks using random walks . in _ proceedings of the 20th international symposium on computer and information sciences _ , volume 3733 of _ lecture notes in computer science _ , pp . 284293 , springer , new york ( 2005 ) . o. goldschmidt and d. s. hochbaum , polynomial algorithm for the @xmath134-cut problem . in _ proceedings of the 29th annual ieee symposium on the foundations of computer science _ , pp . 444451 , institute of electrical and electronics engineers , new york ( 1988 ) . m. bern , d. eppstein , and j. gilbert , provably good mesh generation . in _ proceedings of the 31st annual ieee symposium on the foundations of computer science _ , pp . 231241 , institute of electrical and electronics engineers , new york ( 1990 ) . wei and c .- k . cheng , toward efficient hierarchical designs by ratio cut partitioning . in _ proceedings of the ieee international conference on computer aided design _ , pp . 298301 , institute of electrical and electronics engineers , new york ( 1989 ) . p. k. chan , m. d. f. schlag , and j. y. zien , spectral @xmath134-way ratio - cut partitioning and clustering . in _ proceedings of the 30th international conference on design automation _ , pp . 749754 , association of computing machinery , new york ( 1993 ) . s. white and p. smyth , a spectral clustering approach to finding communities in graphs . in h. kargupta , j. srivastava , c. kamath , and a. goodman ( eds . ) , _ proceedings of the 5th siam international conference on data mining _ , society for industrial and applied mathematics , philadelphia ( 2005 ) . t. uczak , sparse random graphs with a given degree sequence . in a. m. frieze and t. uczak ( eds . ) , _ proceedings of the symposium on random graphs , pozna 1989 _ , pp . 165182 , john wiley , new york ( 1992 ) . d. lusseau , k. schneider , o. j. boisseau , p. haase , e. slooten , and s. m. dawson , the bottlenose dolphin community of doubtful sound features a large proportion of long - lasting associations . can geographic isolation explain this unique trait ? _ behavioral ecology and sociobiology _ * 54 * , 396405 ( 2003 ) . c. j. alpert and s .- z . yao , spectral partitioning : the more eigenvectors , the better . in b. t. preas , p. g. karger , b. s. nobandegani , and m. pedram ( eds . ) , _ proceedings of the 32nd international conference on design automation _ , pp . 195200 , association of computing machinery , new york , ny ( 1995 ) .

we construct large-@xmath0 motivated approximate chiral @xmath1 amplitudes of next - to - next - to - leading order . the amplitudes are independent of the renormalization scale . the differences between approximate and full amplitudes are required to be at most of the order of n@xmath2lo contributions numerically . applying the approximate expressions to recent lattice data for meson decay constants , we determine several chiral couplings with good precision . in particular , we obtain a value for @xmath3 , the meson decay constant in the chiral @xmath1 limit , that is more precise than all presently available determinations . plus 1pt uwthph-2013 - 28 + * approximating chiral su(3 ) amplitudes * + * g. ecker@xmath4 , p. masjuan@xmath5 and h. neufeld@xmath4 * + @xmath6 university of vienna , faculty of physics , boltzmanngasse 5 , a-1090 wien , austria + @xmath7 institut fr kernphysik , johannes gutenberg - universitt , d-55099 mainz , germany

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1310.8452

we construct large-@xmath0 motivated approximate chiral @xmath1 amplitudes of next - to - next - to - leading order . the amplitudes are independent of the renormalization scale . fitting lattice data with those amplitudes allows for the extraction of chiral coupling constants with the correct scale dependence . the differences between approximate and full amplitudes are required to be at most of the order of n@xmath2lo contributions numerically . applying the approximate expressions to recent lattice data for meson decay constants , we determine several chiral couplings with good precision . in particular , we obtain a value for @xmath3 , the meson decay constant in the chiral @xmath1 limit , that is more precise than all presently available determinations . plus 1pt uwthph-2013 - 28 + * approximating chiral su(3 ) amplitudes * + * g. ecker@xmath4 , p. masjuan@xmath5 and h. neufeld@xmath4 * + @xmath6 university of vienna , faculty of physics , boltzmanngasse 5 , a-1090 wien , austria + @xmath7 institut fr kernphysik , johannes gutenberg - universitt , d-55099 mainz , germany

we summarize the main results of our work . 1 . lattice qcd has become a major source of information for the low - energy constants of chpt . we have argued that the meson decay constants @xmath11 , @xmath109 are especially suited for extracting chiral @xmath1 lecs of different chiral orders . the ratio @xmath10 allows for a precise and stable determination of the nlo lec @xmath36 . in addition , it gives access to some nnlo lecs although the accuracy is of course more limited in that case . phenomenological analyses have had difficulties in determining the lec @xmath3 , the meson decay constant in the chiral @xmath1 limit . we have shown that lattice data for @xmath11 allow for the extraction of @xmath3 together with the nlo lec @xmath13 . the strong anti - correlation between @xmath3 and @xmath13 observed in phenomenological analyses can in principle be lifted by varying the lattice masses . from a fit to the rbc / ukqcd data for @xmath11 , we have obtained a value for @xmath3 that is more precise than other presently available determinations . 2 . confronting present - day lattice data with chiral @xmath1 requires chiral amplitudes to nnlo in most cases . chiral @xmath1 amplitudes are often rather unwieldy and mostly available in numerical form only . we have therefore proposed large-@xmath0 motivated approximate nnlo amplitudes that contain only one - loop functions . unlike simpler approximations as the double - log approximation , our amplitudes are independent of the renormalization scale and can therefore be used to extract lecs with the correct scale dependence . however , approximations of nnlo amplitudes can only be successful if the differences to the full amplitudes are at most of the order of n@xmath2lo contributions . we have checked that this criterion can be fulfilled with our approximate amplitudes both for @xmath11 and @xmath10 . therefore , we expect our results for the different lecs to be as reliable as chpt to nnlo , @xmath17 , permits . although our general criterion is also satisfied for the kaon semileptonic form factor at @xmath14 , the approximate expression for @xmath102 is not precise enough compared to recent lattice data . the main purpose of this work has been to encourage lattice groups to use nnlo amplitudes in chiral @xmath1 that are more user friendly than the full expressions and yet are reliable enough to provide more insight than nlo amplitudes with polynomial corrections . [ [ acknowledgements ] ] acknowledgements + + + + + + + + + + + + + + + + we are grateful to vronique bernard , claude bernard , gilberto colangelo , laurent lellouch , heiri leutwyler , emilie passemar and lothar tiator for helpful comments and suggestions . we are indebted to elvira gmiz for helping us to understand lattice data . special thanks are due to hans bijnens for suggesting several substantial improvements of the original manuscript and for making the full results of ref . @xcite accessible to us . p.m. acknowledges support from the deutsche forschungsgemeinschaft dfg through the collaborative research center `` the low - energy frontier of the standard model '' ( sfb 1044 ) .

the most frequently employed estimators are not quite satisfactory in this respect . the minimum volume ellipsoid ( mve ) and minimum covariance determinant ( mcd ) estimators are known to have a very low efficiency . s - estimators with a monotonic weight function like the bisquare have a low efficiency for small @xmath1 and their efficiency tends to one with increasing @xmath0 . unfortunately , this advantage is paid for by a serious loss of robustness for large @xmath0 . we consider four families of estimators with controllable efficiencies whose performance for moderate to large @xmath0 has not been explored to date : s - estimators with a non - monotonic weight function ( rocke 1996 ) , mm - estimators , @xmath2-estimators , and the stahel - donoho estimator . two types of starting estimators are employed : the mve computed through subsampling , and a semi - deterministic procedure proposed by pea and prieto ( 2007 ) for outlier detection . a simulation study shows that the rocke estimator starting from the pea - prieto estimator and with an adequate tuning , can simultaneously attain high efficiency and high robustness for @xmath3 and the mm estimator can be recommended for @xmath0@xmath415 . keywords : mm - estimator , tau - estimator , s - estimator , stahel - donoho estimator , kullback - leibler divergence .

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1504.03389

we deal with the equivariant estimation of scatter and location for @xmath0-dimensional data , giving emphasis to scatter . it is important that the estimators possess both a high efficiency for normal data and a high resistance to outliers , that is , a low bias under contamination . the most frequently employed estimators are not quite satisfactory in this respect . the minimum volume ellipsoid ( mve ) and minimum covariance determinant ( mcd ) estimators are known to have a very low efficiency . s - estimators with a monotonic weight function like the bisquare have a low efficiency for small @xmath1 and their efficiency tends to one with increasing @xmath0 . unfortunately , this advantage is paid for by a serious loss of robustness for large @xmath0 . we consider four families of estimators with controllable efficiencies whose performance for moderate to large @xmath0 has not been explored to date : s - estimators with a non - monotonic weight function ( rocke 1996 ) , mm - estimators , @xmath2-estimators , and the stahel - donoho estimator . two types of starting estimators are employed : the mve computed through subsampling , and a semi - deterministic procedure proposed by pea and prieto ( 2007 ) for outlier detection . a simulation study shows that the rocke estimator starting from the pea - prieto estimator and with an adequate tuning , can simultaneously attain high efficiency and high robustness for @xmath3 and the mm estimator can be recommended for @xmath0@xmath415 . keywords : mm - estimator , tau - estimator , s - estimator , stahel - donoho estimator , kullback - leibler divergence .

consider a sample @xmath5 we look for substitutes @xmath6 * * and * * @xmath7 of the sample mean vector and covariance matrix , that are resistant to atypical observations . we also want estimators that have a high efficiency for normal samples@xmath8 as a measure of robustness we consider not only the breakdown point but also the maximum expected kullback - leibler divergence between the estimator and the true value . under contamination . the most frequently employed estimators are not quite satisfactory in this respect . the minimum volume ellipsoid ( mve ) and the minimum covariance determinant ( mcd ) estimators ( rousseeuw 1985 ) are known to have a low efficiency . this efficiency can be increased by means of a one - step reweighting . croux and haesbroeck ( 1999 , tables vii and viii ) computed the finite - sample efficiencies of the reweighted mcd ; although they are much higher than for the raw estimator , they are still low if one wants a high breakdown point . s - estimators ( davies 1987 ) with a monotonic weight function like the bisquare have a low efficiency for small @xmath9 rocke ( 1996 ) showed that their efficiency tends to one with increasing @xmath0 ; unfortunately , this advantage is paid for with a serious loss of robustness for large @xmath0 . we restrict ourselves to equivariant estimators . there exist many non - equivariant proposals ; but the comparison between equivariant and non - equivariant estimators is difficult . in particular , a non - equivariant estimator is more difficult to tune for a given efficiency , since the latter depends on the correlations . among the published equivariant proposals , there are four families of estimators with controllable efficiencies : non - monotonic s - estimators ( rocke 1996 ) , mm - estimators ( tatsuoka and tyler 2000 ) , @xmath2-estimators ( lopuhaa 1991 ) and the estimator proposed independently by stahel ( 1981 ) and donoho ( 1982 ) but their behavior for large dimensions has not been explored to date . we compare their behaviors employing different weight functions . a simulation study shows that the rocke and mm estimators , with an adequate weight function and an adequate tuning , can simultaneously attain high efficiency and high robustness . it will be seen below that if we have a good @xmath10 it is easy to find a good equivariant @xmath11 but the converse is not true . for this reason we shall put more emphasis on the estimation of the scatter matrix . since all the considered estimators are based on the iterative minimization of a non - convex function , the starting values are crucial . subsampling is the standard way to compute starting values ; but we shall see that a semi - deterministic equivariant procedure proposed by pea and prieto ( 2007 ) may yield both shorter computing times and better statistical performances . in section [ secmesti ] we describe monotonic m - estimators ; section [ secminscale ] deals with estimators based on the minimization of a robust scale of mahalanobis distances . sections [ secmm ] and [ sec_stadono ] deal with mm and stahel - donoho estimators respectively . in section [ secrho ] we discuss the choice of the @xmath12function for mm- and @xmath13estimators . section [ seccomputing ] deals with computational details . in section [ secsimula ] the estimators are compared through a simulation study . in section [ secreal ] the estimators are applied to a real data set . finally section [ secconclu ] summarizes the results . section [ secappend ] is an appendix containing the full results of the simulations , the approximations for the tuning constants and some details on the rocke and the pea - prieto procedures .

our calculation incorporates the interactions between nucleotides by using the experimentally - determined free energy rules for rna secondary structure and models the polymeric properties of the exterior single - stranded regions explicitly as elastic freely - jointed chains . we find that in spite of complicated secondary structures , force - extension curves are typically smooth in quasi - equilibrium . we identify and characterize two sequence / structure - dependent mechanisms that , in addition to the sequence - independent entropic elasticity of the exterior single - stranded regions , are responsible for the smoothness .

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cond-mat0101250

we describe quantitatively a rna molecule under the influence of an external force exerted at its two ends as in a typical single - molecule experiment . our calculation incorporates the interactions between nucleotides by using the experimentally - determined free energy rules for rna secondary structure and models the polymeric properties of the exterior single - stranded regions explicitly as elastic freely - jointed chains . we find that in spite of complicated secondary structures , force - extension curves are typically smooth in quasi - equilibrium . we identify and characterize two sequence / structure - dependent mechanisms that , in addition to the sequence - independent entropic elasticity of the exterior single - stranded regions , are responsible for the smoothness . these involve compensation between different structural elements on which the external force acts simultaneously , and contribution of suboptimal structures , respectively . we estimate how many features a force - extension curve recorded in non - equilibrium , where the pulling proceeds faster than rearrangements in the secondary structure of the molecule , could show in principle . our software is available to the public through a ` rna - pulling server ' .

in recent years , single - molecule experiments employing optical tweezers , atomic force microscopy , and other techniques have successfully probed basic physical properties of biomolecules through the application of forces in the pn range ( see , e.g. , @xcite ) . both , simple elastic properties of the polymers ( such as persistence length and longitudinal elasticity ) and structural transitions ( e.g. unfolding of protein domains ) were characterized by recording and analyzing force - extension curves ( fec s ) . for nucleic acids , a prominent experiment of the latter type is the ` unzipping ' of double - stranded dna @xcite . the resulting fec s display clear sequence - specific features ( e.g. local maxima ) , which may be attributed to small regions of the sequence that are more strongly bound than their neighbors @xcite . in contrast , long single - stranded dna , which , like rna , may fold into complicated branched structures by forming intra - strand basepairs , showed extremely smooth fec s in a very recent experiment by @xcite . thus , depending on its structure , dna may show a broad range of fec s from very rugged to completely featureless . however , it is unclear _ how _ quantitatively the structure determines the outcome of the fec measurement . here , we address this question theoretically , focusing on the case of rna and restricting ourselves to secondary structure ( i.e. basepairing patterns only instead of full , tertiary structure ) . in this context , rna seems to be a more interesting object than dna , since rna naturally occurs in many different and functionally important structures , while dna is primarily found as a double strand . one may hope that pulling experiments generate new insights into the rna folding problem @xcite , including the folding pathways @xcite . also , force - induced denaturation of rna is currently studied experimentally ( c. bustamante and i. tinoco , private communiation ) . the limitation to secondary structure allows us to draw upon the experimentally determined ` free energy rules ' for rna secondary structure @xcite , which yield minimum free energy structures that agree reasonably well with experimentally and phylogenetically determined ones @xcite . furthermore , it permits us to employ and extend the efficient dynamic programming algorithms @xcite which can compute the exact partition function ( including all possible secondary structures ) and reconstruct the minimal free energy structures in polynomial time . experimentally , the secondary structures may be probed in specific ionic conditions ( e.g. , those with only monovalent ions ) such that the tertiary contacts are strongly disfavored ( due to electrostatic repulsion of the sugar - phosphate backbone ) @xcite . , while the force @xmath0 acting on the beads is measured . the open circles represent the open bases of the exterior single strands , modeled here as elastic freely jointed chains.,width=264 ] the type of experiment that we consider is sketched in fig . [ figsketch ] . the distance @xmath1 between the two ends of an rna molecule is held fixed , e.g. , by attaching them to two beads whose positions are controlled by optical tweezers , and the force @xmath0 acting on the beads is recorded as a function of @xmath1 . as long as the external change in force / extension is applied at a much slower time scale than that of structural transitions of the molecule , the equilibrium fec is measured . in the main part of the present article , we assume that this is always the case . experimentally , this condition is usually checked by retracing the fec ( e.g. , a hysteresis effect is a clear sign of a non - equilibrium situation ) . besides the above - mentioned free energy parameters for rna secondary structure , we need a polymer model for single - stranded rna as input in order to make quantitative predictions of fec s . to that end , we employ an elastic freely jointed chain model , which has been used to fit experimental fec s of single - stranded dna @xcite . this introduces two polymer parameters , the kuhn length characterizing the lateral rigidity , and the longitudinal elasticity , which is determined by the forces needed to stretch the chemical structure of the backbone . we estimate both from the experiments on dna , so that we are left with no free parameters . we find that for different secondary structures with all other parameters ( temperature , sequence length , etc . ) fixed , the fec s of rna vary over a broad range from very rugged to very smooth . apart from the entropic elasticity of the exterior single strand , which smoothens the features in the fec independent of the secondary structure as already discussed by @xcite , there are two additional smoothing mechanisms . the first is a ` compensation effect ' : the increase in the length of the exterior single strand upon opening of a structural element and the associated drop in the tension may be absorbed by rebinding of bases from the exterior single strand in other structural elements . the second is due to thermal fluctuations in the secondary structure , i.e. the contribution of suboptimal structures . we discuss both mechanisms and analyze the fluctuations in the fec quantitatively . the equilibrium fec s of typical ( natural or random ) rna sequences are smooth and display no distinguishable signatures of individual structural elements opening . this is consistent with the experimental result of @xcite for single - stranded dna , but applies even for sequences with only a few hundred nucleotides , i.e. for much shorter sequences than used in their experiment . for the purpose of obtaining information on the structure of rna , the measurement of equilibrium fec s is therefore not very useful . more promising options include the measurement of the fluctuations about the equilibrium and non - equilibrium fec s , where the pulling proceeds faster than ( some of ) the rearrangements in the structure . while the present approach is extended readily to include equilibrium fluctuations ( gerland , u. , r. bundschuh , and t. hwa , in preparation ) , a quantitative treatment of the dynamics of force - induced denaturation of rna presents a challenge to theoreticians . the organization of the paper is as follows . in the next section , we explain the details of our model and the way we calculate the fec s . readers interested in the results only should directly proceed to section iii . the discussion in section iv explores the possibility of using experimental fec s of appropriately designed sequences as an alternative way to determine the rna free energy parameters . in addition , we estimate to what extent features may be expected in non - equilibrium fec s .

we describe quantitatively a rna molecule under the influence of an external force exerted at its two ends as in a typical single - molecule experiment . we estimate how many features a force - extension curve recorded in non - equilibrium , where the pulling proceeds faster than rearrangements in the secondary structure of the molecule , could show in principle . our software is available to the public through a ` rna - pulling server ' .

c

cond-mat0101250

we describe quantitatively a rna molecule under the influence of an external force exerted at its two ends as in a typical single - molecule experiment . our calculation incorporates the interactions between nucleotides by using the experimentally - determined free energy rules for rna secondary structure and models the polymeric properties of the exterior single - stranded regions explicitly as elastic freely - jointed chains . we find that in spite of complicated secondary structures , force - extension curves are typically smooth in quasi - equilibrium . we identify and characterize two sequence / structure - dependent mechanisms that , in addition to the sequence - independent entropic elasticity of the exterior single - stranded regions , are responsible for the smoothness . these involve compensation between different structural elements on which the external force acts simultaneously , and contribution of suboptimal structures , respectively . we estimate how many features a force - extension curve recorded in non - equilibrium , where the pulling proceeds faster than rearrangements in the secondary structure of the molecule , could show in principle . our software is available to the public through a ` rna - pulling server ' .

in the last section , we found that the equilibrium fec s for typical rna molecules ( like the group i intron that served us as an example ) are quite smooth and do not reveal any features that can be associated with the opening of structural elements . the compensation effect is the primary cause for this result , and we expect it to be responsible , in part , also for the experimental observation of extremely smooth fec s for single - stranded dna by @xcite . nevertheless , the measurement of equilibrium fec s for rna or single - stranded dna might still be useful , e.g. for an experimental determination of the rna / dna free energy parameters . usually , these are extracted from melting curves of oligomers @xcite , which requires variation of the temperature away from the temperature of interest up to the melting point of the oligomers , where the free energy and its temperature derivative are determined . the free energy parameters at the temperature of interest are then obtained by extrapolation , which introduces an error inherent to the method . for pulling experiments , the temperature can be kept constant at the value of interest , which is an obvious advantage . here , the limiting factor is only the precision of the force measurement . the quantitative relationship between stacking energy and threshold force expressed by fig . [ figfc ] furnishes the necessary link between force and energy . measuring fec s for periodic hairpins composed of different building blocks , would lead to curves like the dashed line in fig . [ figgroup1]b with different values for the threshold force . from these values , the stacking energies could then be determined , which might lead to more accurate parameters at the desired temperature and salt concentrations . there are ( at least ) two options to obtain fec s with more features , which in turn might allow one to obtain information on rna secondary structure from pulling experiments . one could either record _ non - equilibrium _ fec s or analyze the _ fluctuations _ around the equilibrium curve . for our theoretical investigation , the latter option is not available as long as we work in the fixed - distance ensemble , since the force fluctuations around the thermodynamic average diverge in that ensemble . we will pursue this option in a separate publication by working in a mixed ensemble ( gerland , u. , r. bundschuh , and t. hwa , in preparation ) . here , we briefly consider non - equilibrium fec s , where the rate of external increase in the force / extension is higher than ( some of ) the rates associated with internal rearrangements in the secondary structure . in the case of long _ proteins _ , either naturally occurring as an array of globular domains @xcite or synthesized protein arrays @xcite , mechanical stretching experiments resolved the unfolding of up to 20 individual domains . these experiments were performed under non - equilibrium conditions @xcite with typical pulling speeds of @xmath107 m/s . . a generalized reaction coordinate @xmath108 is plotted along the horizontal axis and the free energy @xmath109 along the vertical axis . the work that has to be exerted against the force in order to pull in the single strand needed for the formation of the stem - loop structure is denoted by @xmath110 . in principle , the entropy difference between the random coil state on the left and the transition state also contributes to the barrier height , however , we assume that at typical stretching forces it is negligible compared to @xmath110.,width=321 ] in order to estimate whether non - equilibrium conditions are attainable for rna with reasonable pulling speeds , we need a rough idea of the timescales involved in secondary structure rearrangements of rna . for this , we again assume that rna and single - stranded dna behave similarly , so that we may draw on an experiment by bonnet , krichevsky , and libchaber @xcite measuring the opening and closing rates of dna stem - loops using fluorescence correlation spectroscopy . from their results , we extract @xmath111 as an estimate for the closing time ( at @xmath54 ) of a stem - loop structure with three basepairs and a loop of four nucleotides , which may be considered as a minimal secondary structure element . we expect that the formation of the stem - loop takes place in a single step whose reaction pathway goes through a transition state where the basepairs of the stem have not yet formed , but the corresponding bases are already closely together ( see fig . [ loop_formation ] ) . in the presence of an external force , the closing time must then be multiplied with an arrhenius factor @xmath112 , where @xmath110 is the work that has to be exerted against the force to pull in the amount of single strand needed for the formation of the stem - loop @xcite . with a typical force of @xmath113 we obtain @xmath114 , which results in a closing time on the order of @xmath115 . this timescale has to be compared to the time it takes to stretch out the stem - loop . at a pulling speed on the order of @xmath107 m/s , the two timescales are comparable and hence , both the formation of new secondary structure elements and the restoration of already opened ones are likely to be suppressed . although it is beyond the scope of this paper , we want to note that in the presence of pseudoknots and/or tertiary interactions , the formation or re - formation of structural elements is expected to be slowed down even further , due to long search times for the interaction partners . to obtain an impression of how many features a non - equilibrium fec might show for the group i intron , we change our equilibrium algorithm , such that the rebinding of bases is disabled once they have been unbound , and include only the contribution of the minimum free energy structures instead of all possible secondary structures . this is clearly a very crude approximation . in a proper treatment , only those kinetic processes whose energy barrier is higher than a certain threshold as determined by the pulling speed should be suppressed . also , we did not account for the fact that the opening of basepairs occurs at higher forces in non - equilibrium as a consequence of kramers theory @xcite . nevertheless , the fec shown in fig . [ fast_intron]c gives an idea of the large number of structural transitions that take place during force - induced denaturation ( for comparison , the equilibrium fec is shown again in fig . [ fast_intron]a ) . we therefore believe that non - equilibrium stretching experiments of rna could lead to interesting and useful results . we made most of the software tools developed for the present work available to the public by creating a ` rna pulling server ' at http://bioinfo.ucsd.edu/rna . we thank d. bensimon , c. bustamante , and j.d . moroz for stimulating discussions . is supported by the hochschulsonderprogramm iii of the daad . r.b . and t.h . acknowledge support by the nsf through grant no . dmr-9971456 , dbi-9970199 , and the beckmann foundation . 99 bockelmann , u. , b. essevaz - roulet , and f. heslot . molecular stick - slip motion revealed by opening dna with piconewton forces . lett . _ 79:44894492 ; dna strand separation studied by single molecule force measurements . _ 58:23862394 . bonnet , g. , o. krichevsky , and a. libchaber . kinetics of conformational fluctuations in dna hairpin - loops . chen , s .- j . and k.a . rna folding energy landscapes . . de gennes , p .- g . 1975 . brownian motion of a classical particle through potential barriers . application to the helix - coil transitions of heteropolymers . _ j. stat . . de gennes , p .- g . 1979 . scaling concepts in polymer physics . cornell university press , ithaca , ny . essevaz - roulet , b. , u. bockelmann , and f. heslot . mechanical separation of the complementary strands of dna . evans , e. , and k. ritchie . dynamic strength of molecular adhesion bonds . _ biophys . flory , p.j . statistical mechanics of chain molecules . interscience pub . , freier , s.m . , r. kierzek , j.a . jaeger , n. sugimoto , m.h . caruthers , t. neilson , and d.h . improved free - energy parameters for predictions of rna duplex stability . natl . acad . gutell , r.r . , s. subashchandran , m. schnare , y. du , n. lin , l. madabusi , k. muller , n. pande , n. yu , z. shang , s. date , d. konings , v. schweiker , b.weiser , and j.j . cannone . 2001 . comparative sequence analysis and the prediction of rna structure , and the web . manuscript in preparation . hofacker , i.l . , w. fontana , p.f . stadler , s. bonhoeffer , m. tacker , and p. schuster . fast folding and comparison of rna secondary structures . _ monatshefte f. chemie _ 125:167188 . isambert , h. and e.d . siggia . 2000 . modeling rna folding paths with pseudoknots : application to hepatitis delta virus ribozyme . _ 97:65156520 . lubensky , d.k . and d.r . nelson . pulling pinned polymers and unzipping dna . _ _ 85:15721575 . maier , b. , d. bensimon , and v. croquette . replication by a single dna polymerase of a stretched single - stranded dna . _ 97:1200212007 . mathews , d.h . , j. sabina , m. zuker , and d.h . turner . 1999 . expanded sequence dependence of thermodynamic parameters improves prediction of rna secondary structure . _ _ 288:911940 . mccaskill , j.s . the equilibrium partition function and base pair binding probabilities for rna secondary structure . _ biopolymers . _ 29:11051119 . mehta , a.d . , m. rief , j.a . spudich , d.a . smith , and r.m . single - molecule biomechanics with optical methods . _ science . _ 283:16891695 ; and references therein . montanari , a. and m. mzard . hairpin formation and elongation of biomolecules . _ 86:21782181 . rief , m. , m. gautel , f. oesterhelt , j.m . fernandez , and h.e . reversible unfolding of individual titin immunoglobulin domains by afm . _ science . _ 276:11091112 . rief , m. , j.m . fernandez , and h.e . elastically coupled two - level systems as a model for biopolymer extensibility . _ 81:47644767 . rief , m. , h. clausen - schaumann , and h.e . gaub . sequence - dependent mechanics of single dna molecules . _ nature struct . _ 6:346349 . smith , s.b . , y. cui , and c. bustamante . 1996 . overstretching b - dna : the elastic response of individual double - stranded and single - stranded dna molecules . _ science . _ 271:795799 . thirumalai , d. and s. a. woodson . 2000 . maximizing rna folding rates : a balancing act . _ _ 6:790794 ; and references therein . thompson , r.e . and e.d . 1995 . physical limits on the mechanical measurement of the secondary structure of biomolecules . _ europhys . _ 31:335340 . tinoco , i. jr and c. bustamante . 1999 . how rna folds . biol . _ 293:271281 ; and references therein . walter , a.e . turner , j. kim , m.h . lyttle , p. muller , d.h . mathews , and m. zuker . coaxial stacking of helixes enhances binding of oligoribonucleotides and improves predictions of rna folding . _ 91:92189222 . yang , g. , c. cecconi , w.a . baase , i.r . vetter , w.a . breyer , j.a . haack , b.w . matthews , f.w . dahlquist , and c. bustamante . 2000 . solid - state synthesis and mechanical unfolding of polymers of t4 lysozyme . usa . _ 97:139144 . zuker , m. and p. stiegler . optimal computer folding of large rna sequences using thermodynamics and auxiliary information . res . _ 9:133148 .

the method is based on the observation that when the lowest energy modes of the bose field operator are highly occupied , they may be treated classically to a good approximation . we derive a finite temperature gross - pitaevskii equation for these modes which is coupled to an effective reservoir described by quantum kinetic theory . we discuss each of the terms that arise in this gross - pitaevskii equation , and their relevance to experimental systems . we then describe a simpler projected gross - pitaevskii equation that may be useful in simulating thermal bose condensates . this classical method could be applied to other bose fields .

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we develop an approximate formalism suitable for performing simulations of the thermal dynamics of interacting bose gases . the method is based on the observation that when the lowest energy modes of the bose field operator are highly occupied , they may be treated classically to a good approximation . we derive a finite temperature gross - pitaevskii equation for these modes which is coupled to an effective reservoir described by quantum kinetic theory . we discuss each of the terms that arise in this gross - pitaevskii equation , and their relevance to experimental systems . we then describe a simpler projected gross - pitaevskii equation that may be useful in simulating thermal bose condensates . this classical method could be applied to other bose fields .

the achievement of bose - einstein condensation ( bec ) in a dilute gas @xcite offers the possibility of studying the dynamics of a quantum field in the laboratory . in principle it presents an opportunity to directly compare computational predictions with experimental results ; however carrying out dynamical calculations of thermal quantum fields is an extremely difficult problem that generally requires severe approximations to be made . the most successful finite temperature theories of bec are based on second - order perturbation theory , and are limited to the case of thermal equilibrium away from the region of critical fluctuations @xcite . these theories have allowed the accurate determination from first principles of quantities such as excitation frequencies and damping rates of bose - condensed systems . however , their extension to dynamical situations is computationally difficult . at very low temperatures when most of the atoms are in the condensate , the gross - pitaevskii equation ( gpe ) has proved remarkably successful in numerically modelling bec experiments . the time - dependent gpe has the form @xmath0 where @xmath1 is the effective interaction strength at low momenta , @xmath2 is the _ s_-wave scattering length , and @xmath3 is the particle mass . @xmath4 is the single particle hamiltonian @xmath5 where @xmath6 is the external confining potential of the system . the gpe can be derived by a number of different approaches ( e.g. a number - conserving approach @xcite ) , but a direct method is to take the mean mean value of the equation of motion for the bose field operator and assume that the quantum fluctuations can be neglected . this procedure effectively assumes that the field is well approximated by a coherent state . it has been argued that the gpe can also describe the dynamics of a bose - einstein condensate at finite temperature @xcite for the reason that in the limit that all the low - lying modes of the system are highly occupied ( @xmath7 ) , the classical fluctuations of the field operator @xmath8 will be much larger than the quantum fluctuations . it is therefore reasonable to neglect the quantum fluctuations , and thus all highly - occupied modes may be well approximated by a coherent wave function . this is analogous to the situation in laser physics where the highly occupied laser modes can be well described by classical equations . despite this proposal appearing in the literature in 1991 @xcite , very few numerical calculations have been performed . the first was by damle _ et al . _ @xcite , who calculated the approach to equilibrium of a near - ideal superfluid using the gpe . subsequently , marshall _ et al . _ @xcite performed two - dimensional simulations of evaporative cooling of a thermal bose field in a trap . more recently , papers by stoof and bijlsma @xcite and sinatra _ et al._@xcite have used classical methods in dynamical calculations of thermal one - dimensional bose - einstein condensates . et al._@xcite have performed dynamical calculations that treat several modes of a 3d homogeneous bose gas classically . their method , while not specifically employing the gpe , is similar to the approach we suggest here and for which we have presented our own numerical results in reference @xcite . classical approximations to other quantum field equations have also been successful in the calculation of the dynamics of the electroweak phase transition @xcite . the major advantage of using the gpe to describe thermal dynamics is simply that , while it is still a major computational task , it is possible to numerically solve the equation for realistic systems in a reasonable amount of time . in addition , the gpe is non - perturbative and it should be possible to study the region of the bec phase transition , where perturbation theory often fails . there are , however , a number of problems associated with the use of the gpe to represent the entire bose field at finite temperature . it is a classical equation , and so in equilibrium it will satisfy the equipartition theorem all modes of the system will have an occupation of @xmath9 . thus , if we couple the gpe to a heat bath and numerically solve the equation with infinite accuracy , we will observe an ultra - violet catastrophe . also , we can see that the higher the energy of any given mode , the lower its occupation will be in equilibrium and at a sufficiently high energy the criterion @xmath10 will no longer be satisfied . for these low occupation modes a form of kinetic equation is more appropriate . the solution to both of these problems is to introduce a _ cutoff _ in the modes represented by the gpe . in this paper we develop an approximate formalism in which the low - lying modes of the system are described non - perturbatively by the gpe , coupled to a thermal bath described by a quantum boltzmann equation . we derive a finite temperature gross - pitaevskii equation ( ftgpe ) , and discuss the terms that couple the part of the field operator represented by a coherent wave function to the thermal bath . in particular we show how a description of loss via elastic collisions arises naturally in the formalism . several other authors have developed formalisms for non - equilibrium dynamics using quite different theoretical methods we mention gardiner and zoller @xcite , proukakis _ et al . _ @xcite , stoof @xcite , zaremba _ et al . _ @xcite , walser _ et al._@xcite , and finally sinatra _ et al . _ the work we present here has elements in common with several of these . in particular , the average of the quantum langevin equation written down in the formalism of stoof @xcite would correspond to the ftgpe we derive in section [ eom ] . this paper is organized as follows . in section [ hamiltonian ] we write down and discuss the hamiltonian which is our starting point . in section [ projection ] we outline how we decompose the field operator into a coherent and incoherent region , and in section [ eom ] we derive a finite temperature gross - pitaevskii equation that forms the main result of this paper . in section [ ftgpe_terms ] we discuss the terms that arise in the ftgpe , their relation to experiments , and their approximate form in terms of occupations numbers of incoherent region modes . we discuss a simple finite temperature equation which we call the projected gpe in section [ pgpe ] and finally conclude in section [ conclusions ] .

we develop an efficient ewald method of molecular dynamics simulation for calculating the electrostatic interactions among charged and polar particles between parallel metallic plates , where we may apply an electric field with an arbitrary size . we present simulation results on boundary effects of charged and polar fluids , formation of ionic crystals , and formation of dipole chains , where the applied field and the image interaction are crucial . for polar fluids

i

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we develop an efficient ewald method of molecular dynamics simulation for calculating the electrostatic interactions among charged and polar particles between parallel metallic plates , where we may apply an electric field with an arbitrary size . we use the fact that the potential from the surface charges is equivalent to the sum of those from image charges and dipoles located outside the cell . we present simulation results on boundary effects of charged and polar fluids , formation of ionic crystals , and formation of dipole chains , where the applied field and the image interaction are crucial . for polar fluids , we find a large deviation of the classical lorentz - field relation between the local field and the applied field due to pair correlations along the applied field . as general aspects , we clarify the difference between the potential - fixed and the charge - fixed boundary conditions and examine the relationship between the discrete particle description and the continuum electrostatics .

in many problems in physics and chemistry , the electrostatic potential and field acting on each constituting particle need to be calculated @xcite . a large number of simulations have been performed to accurately estimate the long - range electrostatic interactions among charged and polar particles @xcite . the ewald method is a famous technique for efficiently summing these interactions using the fourier transformation . it was originally devised for ionic crystals @xcite and has been widely used to investigate bulk properties of charged and polar particles under the periodic boundary condition in three dimensions ( 3d ) @xcite . it has also been modified for filmlike systems bounded by non - polarizable and insulating regions under the periodic boundary condition in the lateral directions @xcite . however , the ewald method has not yet been successful when charged or polar particles are in contact with metallic or polarizable plates and when electric field is applied from outside . such situations are ubiquitous in solids and soft matters . in idealized metallic plates , the surface charges spontaneously appear such that the electrostatic potential is homogeneous within the plates , thus providing the well - defined boundary condition for the potential within the cell @xcite . between two parallel plates , we may control the potential difference to apply an electric field . however , the electrostatic interaction between the surface charges and the particles within the cell is highly nontrivial . on the other hand , such surface changes are nonexistent for the magnetic interaction . each charged particle between parallel metallic plates induces surface charges producing a potential equivalent to that from an infinite number of image charges outside the cell . if a charged particle approaches a metal wall , it is attracted by the wall or by its nearest image . some mathematical formulae including these image charges in the ewald sum were presented by hautman _ et al_.@xcite and by perram and ratner @xcite . in the same manner , for each dipole in the cell , an infinite number of image dipoles appear . a dipole close to a metal surface is attracted and aligned by its nearest image . accounting for these image dipoles , klapp @xcite performed monte carlo simulations of 500 dipoles interacting with the soft - core potential , but without applied electric field , to find wall - induced ordering . the image effect is also relevant in electrorheological fluids between metallic plates @xcite . inclusion of the image effect in molecular dynamics simulations of molecules near a conducting or polarizable surface is still challenging in a variety of important systems including proteins @xcite , polyelectrolytes @xcite , and colloidal particles @xcite . moreover , the effects of applied electric field remain largely unexplored on the microscopic level , while the continuum electrostatics is well established @xcite . for example , the local electric field acting on a dipole is known to be different from the applied electric field in dielectrics and polar fluids @xcite , where the difference is enlarged in highly polarizable systems . in contrast , a number of microscopic simulations have been performed on the effect of uniform magnetic field for systems of magnetic dipoles @xcite . in this paper , we hence aim to develop an efficient ewald method to treat charged and polar particles between parallel metallic plates accounting for the image effect , where we apply an electric field with an arbitrary size . in the ewald sum in this case , we can sum up the terms homogeneous in the lateral @xmath0 plane but inhomogeneous along the normal @xmath1 axis into a simple form and can calculated them precisely . one - dimensional _ part of the electrostatic energy yields _ one - dimensional _ ( laterally averaged ) electric field along the @xmath1 axis for each particle . using our scheme , we present some numerical results under applied electric field , including the soft - core pair interaction and the wall - particle repulsive interaction . we confirm that accumulation of charges and dipoles near metallic walls gives rise to a uniaxially symmetric , homogeneous interior region . we also examine formation of ionic crystals @xcite and that of dipole chains @xcite under electric field . here , we are interested in the mechanisms of dipole alignment near metallic walls , which are caused by the image interaction or by the applied electric field . we shall also see that the classical local field relation @xcite is much violated in our dipole systems because of strong pair correlations along the applied field . the organization of this paper is as follows . in sec.ii , we will extend the ewald scheme for charged particles between metallic plates . in sec.iii , we will further develop the ewald scheme for point - like dipoles between metallic plates . in these two sections , we will present some numerical results . in appendix b , we will clarify the difference between two boundary conditions at a fixed potential difference and at fixed surface charges . in appendix d , we will compare the electrostatics of our discrete particle systems and the continuum electrostatics .

we use the fact that the potential from the surface charges is equivalent to the sum of those from image charges and dipoles located outside the cell . , we find a large deviation of the classical lorentz - field relation between the local field and the applied field due to pair correlations along the applied field . as general aspects , we clarify the difference between the potential - fixed and the charge - fixed boundary conditions and examine the relationship between the discrete particle description and the continuum electrostatics .

i

1305.3503

we develop an efficient ewald method of molecular dynamics simulation for calculating the electrostatic interactions among charged and polar particles between parallel metallic plates , where we may apply an electric field with an arbitrary size . we use the fact that the potential from the surface charges is equivalent to the sum of those from image charges and dipoles located outside the cell . we present simulation results on boundary effects of charged and polar fluids , formation of ionic crystals , and formation of dipole chains , where the applied field and the image interaction are crucial . for polar fluids , we find a large deviation of the classical lorentz - field relation between the local field and the applied field due to pair correlations along the applied field . as general aspects , we clarify the difference between the potential - fixed and the charge - fixed boundary conditions and examine the relationship between the discrete particle description and the continuum electrostatics .

in summary , we have extended the ewald method for charged and polar particles between metallic plates in a @xmath398 cell , aiming to apply electric field @xmath230 to these systems . in this problem , we should account for an infinite number of image charges and dipoles outside the cell . with this method , we have presented some results of molecular dynamics simulation . in the previous papers by hautman _ et al._@xcite , by perram and ratner@xcite , and by klapp @xcite , the conventional 3d ewald method for periodic systems was applied to a doubly expanded @xmath399 cell , where the three axes were formally equivalent . our scheme is essentially the same as theirs , but we have treated the @xmath1 direction differently from the lateral directions . in particular , we have divided the terms in the long - range part of the ewald sum into those inhomogeneous in the @xmath0 plane ( with nonvanishing @xmath400 or @xmath401 ) and those homogeneous in the @xmath0 plane but inhomogeneous along the @xmath1 axis ( with @xmath75 and @xmath402 ) in eqs.(2.26 ) and ( 3.11 ) . the latter one - dimensional terms can be summed into simple forms in eqs.(2.28 ) and ( 3.12 ) , yielding the one - dimensional electric field @xmath132 in eqs.(2.33 ) and ( 3.15 ) . in our simulations , we have calculated @xmath132 very accurately . for dipole systems , @xmath403 far from the walls for thick cells . in applying electric field between metallic plates , we may control the potential difference @xmath404 or the surface charge @xmath58 . the electrostatic energy , @xmath84 or @xmath249 , in the fixed - potential condition is related to that in the fixed - charge condition by the legendre transformation , as shown in appendix b. in the continuum electrostatics in appendix d , we have also introduced the free energies @xmath405 and @xmath406 for these two cases @xcite . some remarks are given below . + ( 1 ) we have assumed stationary applied field , but we may assume a time - dependent field @xmath407 and examine various nonequilibrium phenomena . for example , when @xmath60 was changed from 0 to 100 , we observed complex dynamics of charged particles from the crystal in fig.4(a ) to that in fig.4(a@xmath163 ) . we also mention that melting due to electric field was observed in charged colloidal crystal @xcite . + ( 2 ) we have assumed spherical dipoles , but real molecules are nonspherical and undergo hindered rotations . this feature should be included in future simulations . we should also consider mixtures of ions and nonspherical polar molecules bounded by metallic plates , where the ion - dipole interaction is crucial @xcite . + ( 3 ) the classical result @xmath346 for the local field factor follows for a spherical cavity @xcite , leading to the clausius - mossotti formula for the dielectric constant . however , @xmath376 becomes one of the depolarization factors for an ellipsoidal cavity@xcite , so it is sensitive to the environment around each dipole . in our case , @xmath376 increases due to the pair correlations along the applied field as in eq.(3.36 ) . more systematic simulations are needed on this aspect . + ( 4 ) various systems such as charged colloids , polyelectrolytes , proteins , and water molecules should exhibit interesting behaviors close to metal surfaces without and with applied field @xcite . for polarizable surfaces , a simulation method similar to ours has recently been reported @xcite . + ( 5 ) we may well expect ferroelectric phase transitions in confined dipole systems ( see the sentences below eq.(3.29 ) ) . furthermore , it is of great interest to examine the electric field effects in ferroelectric systems with impurities . we will shortly report on the electric field effect in orientational glass as a continuation of our previous work @xcite . + this work was supported by grant - in - aid for scientific research from the ministry of education , culture , sports , science and technology of japan . k. t. was supported by the japan society for promotion of science . the numerical calculations were carried out on sr16000 at yitp in kyoto university . the last two terms in eq.(2.7 ) arise from the long - range part of the electrostatic energy , written as @xmath408 . we transform it as follows : u_p^&= & _ m _ i , j q_iq_j_(|r_ij + lm| ) + & = & _ k _ ( k ) _ m _ i , j q_iq_j e^ik(r_ij + lm ) , where @xmath409 and @xmath410 is defined in eq.(2.8 ) . in the second line , we perform the summation over @xmath38 introducing a damping factor @xmath411 $ ] , where @xmath137 is a positive small number ( not to be confused with the energy @xmath412 in @xmath136 in eq.(2.36 ) ) . the summation yields @xmath413 , where ( u ) & = & _ m_x=0,1 , [ i m_x u - |m_x| ) + & & /[^2 + 2(1-(u ) ) ] . for @xmath414 , @xmath410 is finite , so we may replace @xmath415 by @xmath416 , where @xmath417 . for @xmath418 , we may set @xmath419 $ ] . thus , @xmath420 becomes u_p^&= & _ k _ ( k ) ( lk_x ) ( lk_y ) ( lk_z ) _ i , j q_iq_j e^ik_ij + & = & _ k _ ( k ) _ i , j q_iq_j e^ik_ij + & & + _ k . the first term coincides with the third term in eq.(2.7 ) with @xmath421 . the second term arises from @xmath422 , where @xmath423- 1 \cong { { \rm i}{{\mbox{\boldmath$k$}}}\cdot { { \mbox{\boldmath$r$}}}_{i}}$ ] and @xmath424- 1 \cong -{{\rm i}{{\mbox{\boldmath$k$}}}\cdot { { \mbox{\boldmath$r$}}}_{j}}$ ] for small @xmath425 . furthermore , @xmath426 may be replaced by @xmath427 from the angle integration of @xmath39 , leading to the fourth term in eq.(2.7 ) . as illustrated in fig.1 , we may fix the surface changes , @xmath58 and @xmath112 , at @xmath43 and @xmath44 @xcite , as well as the potential difference @xmath60 . here , we consider the fixed charge boundary condition , where we assume @xmath428 without ionization on the surfaces . see appendix d for the continuum theory for these two boundary conditions . for charged particles , let @xmath429 be the electrostatic energy appropriate for the fixed - charge condition , which includes the contribution from the excess electrons on the metal surfaces . for infinitesimal changes @xmath88 and @xmath430 , @xmath431 is changed as d u_e= -_i q_i e_i dr_i + he_a dq_0 , where @xmath230 is a dynamic variable at fixed @xmath58 . the expressions for @xmath8 are the same in the two cases at fixed @xmath230 and at fixed @xmath58 . then , from eqs.(2.24 ) and ( b1 ) , @xmath431 and @xmath84 are related by u_e = u_m - hl^2 e_a^2/8+he_a q_0 . for dipoles , the electrostatic energy @xmath432 under the fixed - charge condition satisfies d u_e^d = -_i ( f_i^e dr_i + e_i d_i)+he_a dq_0 , which should be compared with eq.(3.10 ) . as in eq.(b2 ) , @xmath432 and @xmath253 are related by u_e^d = u_m^d - hl^2 e_a^2/8+he_a q_0 . in eq.(2.26 ) , @xmath433 is given by the lateral integral , & & k_0(z , z ) = dxdy_m [ _ ( |r -r + h| ) + & & -_(|r -|r + h| ) ] , where @xmath434 , @xmath435 , @xmath436 , and @xmath272.after the integration , the right hand side becomes a function of @xmath1 and @xmath437 independent of @xmath438 and @xmath439 . we then twice differentiate @xmath433 with respect to @xmath1 and use the relation @xmath440 , where @xmath441 is defined by eq.(2.5 ) . some calculations yield k_0(z , z ) = -(z - z)+(z+z ) , where @xmath98 is defined by eq.(2.29 ) . the above relation is integrated to give eq.(2.28 ) under @xmath442 . furthermore , eqs.(2.19 ) and ( 2.28 ) give & & = _ 0^z du [ ( u+z)+(u - z)]- , + & & = ( z+z)+(z - z)- , where we have used @xmath443=1 $ ] from the periodicity of @xmath444 . we compare the results in the text and those of continuum electrostatics @xcite . we consider charged particles in a polar medium between parallel metallic plates under applied electric field @xmath230 . the system is in the region @xmath272 and @xmath65 . we assume @xmath445 to neglect the edge effect . we do not assume the ( artificial ) periodic boundary condition in the @xmath45 and @xmath46 axes . in this appendix , the physical quantities are smooth functions of space after spatial coarse - graining . in addition to the electrostatic potential @xmath446 , we introduce the charge density @xmath447 and the polarization @xmath448 . the electric field @xmath449 and the electric induction @xmath450 are defined . for simplicity , we assume the overall charge neutrality condition @xmath451 without ionization on the walls . hereafter , the integral @xmath452 is performed within the cell . from the relation @xmath453 , we may define the effective charge density by _ e= - , which satisfies @xmath454 . let @xmath455 be the 2d fourier transformation in the @xmath0 plane , where @xmath456 and @xmath457 . as in eq.(2.16 ) , the excess potential @xmath64 is written as ( r ) = 4_k_0^h dz g_k(z , z)_ek(z ) e^ik _ , where @xmath458 and the green function @xmath459 is given in eq.(2.18 ) . & & |(z)= dxdy /l^2 , _ e(z)= dxdy _ e / l^2 . then , we find @xmath460 and eq.(d2 ) becomes ( z)= 4_0^h du g_0(x , u ) |_e(u ) , where @xmath461 is given in eq.(2.19 ) . the average electric field @xmath462 is calculated as = - 4 @xmath43 is denoted by @xmath58 ; then , that at @xmath107 is @xmath428 . from eq.(d4 ) we obtain @xcite q_0= e_a + dr [ z(r ) + p_z(r ) ] . this formula corresponds to eqs.(2.31 ) and ( 3.17 ) . the above relation itself readily follows if we set @xmath463 in the integral @xmath464 . second , we consider the electrostatic energy @xmath84 in the fixed - potential condition . its discrete versions are in eqs.(2.23 ) and ( 3.9 ) . the continuum version reads u_m= dr [ _ e -e_a(z+ p_z ) ] . for small incremental changes ( @xmath465 , @xmath84 in eq.(d7 ) is changed as u_m= dr [ -e -(z+p_z ) e_a ] , which corresponds to eqs.(2.24 ) and ( 3.10 ) . on the other hand , the electrostatic energy @xmath431 in the fixed - charge condition should satisfy u_e= dr ( -e ) + h e_a q_0 , which is the counterpart of eqs.(b1 ) and ( b3 ) . then , @xmath431 and @xmath84 are related by eq.(b2 ) or ( b4 ) , leading to@xcite u_e= u_m- e_a^2 + he_aq_0 = dr . third , we remark on the polarization @xmath466 . so far it has been treated as an independent variable . without ferroelectric order , @xmath466 is usually related to @xmath467 by @xcite , = , in the linear response regime . from @xmath468 , the electric susceptibility @xmath469 and the dielectric constant @xmath470 are related by @xmath471 in this situation , we may introduce the following free energy contribution , f_p = dr |p|^2 , which is an increase in the free energy due to mesoscopic ordering of the constituting dipoles . the polarization free energy is needed to examine the thermal fluctuations of @xmath472@xcite . we then treat the sum , @xmath473 or @xmath474 , as the electrostatic free energy in the fixed - potential or fixed - charge condition . since its functional derivative with respect to @xmath472 is given by @xmath475 from eqs.(d8 ) , ( d9 ) , and ( d12 ) , its minimization yields eq.(d11 ) . eliminating @xmath472 , we rewrite @xmath405 and @xmath406 as & & f_m= dr(- & & f_e= dr |e|^2 . the second term in @xmath405 in eq.(d13 ) is a constant at fixed @xmath230 , so we may redefine the electrostatic free energy as f_m = f_m - hl^2 e_a^2/8= f_e- q_0(f_e / q_0 ) , which is the legendre transform of @xmath476 . the two expressions , @xmath477 and @xmath406 , have both been used in the literature . in the ginzburg - landau scheme , et al._@xcite used @xmath477 and one of the present authors@xcite used @xmath406 for ions in a mixture solvent , where @xmath470 depends on the local solvent composition and is inhomogeneous . yeh and m. l. berkowitz , j. chem . phys . * 111 * , 3155 ( 1999 ) ; a. arnold , j. de joannis , and c. holm , j. chem . phys . * 117 * , 2496 ( 2002 ) . p. s. crozier , r. l. rowley , e. spohr , d. henderson , j. chem . phys . * 112 * , 9253 ( 2000 ) . j. hautman , j. w. halley , y .- j . rhee , j. chem . phys . , * 91 * , 467 ( 1989 ) . these authors also found that the contribution from @xmath96 vanishes in the long - range ewald sum of the electrostatic energy ( see the appendix in their paper ) . t. c. halsey and w. toor , phys . * 65 * , 2820 ( 1990 ) ; t. c. hasley , science * 258 * , 761 ( 1992 ) . r. tao and j. m. sun , phys . * 67 * , 398 ( 1991 ) . g. l. gulley and r. tao , phys . rev e * 56 * , 4328 ( 1997 ) . r. messina , j. chem . 117 * , 11062 ( 2002 ) ; a. p. dos santos , a. bakhshandeh , and y. levin , j. chem . phys . * 135 * , 044124 ( 2011 ) ; l. lue and p. linse , j. chem . phys . * 135 * , 224508 ( 2011 ) ; z. gan , x. xing , and z. xu , j. chem . phys . * 137 * , 034708 ( 2012 ) . d. wei , phys . rev.e * 49 * , 2454 ( 1994 ) ; m. j. stevens and g. s. grest , phys . rev.e * 51 * , 5976 ( 1995 ) ; v. v. murashov and g. n. patey , j. chem . phys . * 112 * , 9828 ( 2000 ) ; z. wang , c. holm , and h. w. m@xmath479ller , phys . e * 66 * , 021405 ( 2002 ) ; j. jordanovic and s. h. l. klapp , phys . rev.e * 79 * , 021405 ( 2009 ) . j. richardi and j .- j . weis , j. chem . phys . * 135 * , 124502 ( 2011 ) . in the debye - h@xmath479ckel theory of electrolytes , the potential decays as @xmath480 $ ] or @xmath481 $ ] far from the walls for @xmath482 , where @xmath483 is the debye wave number . in this theory the ratio of @xmath484 to @xmath485 is @xmath486 .

our method substantially improves the original proposal [ m. lobino et al . , science * 322 * , 563 ( 2008 ) ] , which uses a filtered glauber - sudarshan decomposition to determine the effect of the process on an arbitrary state . we introduce a new relation between the action of a general quantum process on coherent state inputs and its action on an arbitrary quantum state . we illustrate our formalism with several examples , in which we derive analytic representations of several fundamental quantum optical processes in the fock basis .

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we develop an enhanced technique for characterizing quantum optical processes based on probing unknown quantum processes only with coherent states . our method substantially improves the original proposal [ m. lobino et al . , science * 322 * , 563 ( 2008 ) ] , which uses a filtered glauber - sudarshan decomposition to determine the effect of the process on an arbitrary state . we introduce a new relation between the action of a general quantum process on coherent state inputs and its action on an arbitrary quantum state . this relation eliminates the need to invoke the glauber - sudarshan representation for states ; hence it dramatically simplifies the task of process identification and removes a potential source of error . the new relation also enables straightforward extensions of the method to multi - mode and non - trace - preserving processes . we illustrate our formalism with several examples , in which we derive analytic representations of several fundamental quantum optical processes in the fock basis . in particular , we introduce photon - number cutoff as a reasonable physical resource limitation and address resource vs accuracy trade - off in practical applications . we show that the accuracy of process estimation scales inversely with the square root of photon - number cutoff .

assembling a complex quantum optical information processor requires precise knowledge of the properties of each of its components , i.e. , the ability to predict the effect of the components on an arbitrary input state . this gives rise to a quantum version of the famous black box problem , which is addressed by means of _ quantum process tomography _ ( qpt ) @xcite . in qpt , a set of probe states is sent into the black box ( here an unknown completely - positive , linear quantum process @xmath0 over the set of bounded operators @xmath1 on a hilbert space @xmath2 ) and the output states are measured . from the effect of the process on the probe states it is possible to predict its effect on any other state within the same hilbert space . qpt exploits linearity of quantum process over its density operators . if the effect of the process @xmath3 is known for a set of density operators @xmath4 , its effect on any linear combination @xmath5 equals @xmath6 . therefore , if @xmath4 forms a spanning set within the space @xmath7 of linear operators over a particular hilbert space @xmath2 , knowledge of @xmath8 is sufficient to extract complete information about the quantum process . however , practical implementations of qpt become demanding especially for systems with large hilbert spaces . for @xmath9 , @xmath10 , which implies that at least @xmath11 unknown operators @xmath12 , each with @xmath11 unknown parameters , must be estimated . this procedure requires preparation of at least @xmath13 states , subjecting each to the unknown process @xmath0 , and determining each element of @xmath14 through measurement ( each with @xmath11 unknown elements ) , thereby inferring an overall number of @xmath15 parameters . furthermore , in order to build up sufficient statistics for reliable estimates of the output states , each measurement should be performed many times on multiple copies of the inputs . thus , a large number of realizations and measurements are required for complete tomography of @xmath0 . an additional complication , especially for qpt of quantum _ optical _ processes , is associated with preparation of the probe states . typical optical qpt implementations deal with systems consisting of one or more dual - rail qubits @xcite , which implies that the probe states are highly nonclassical , hence difficult to generate . these difficulties have been partially alleviated in the recently proposed scheme of coherent - state quantum process tomography " ( csqpt ) @xcite . this scheme is based on the observation that the density operator @xmath16 of a generic quantum state of every electromagnetic mode can be expressed in the _ glauber - sudarshan representation _ @xcite , @xmath17 where @xmath18 is a quasi - probability distribution referred to as the quantum state s @xmath19-function and integrated over the entire complex plane @xcite . linearity hence implies that measuring @xmath20 i.e. , determining the effect of the unknown process on _ all _ coherent states enables a prediction of its effect upon any generic state @xmath16 according to @xmath21 the implementation of csqpt is advantageous because ( i ) coherent states are readily available from lasers , ( ii ) coherent states of different amplitudes and phases can be produced without changing the layout of the experimental apparatus , and ( iii ) output - state characterization can be performed using optical homodyne tomography @xcite , which obviates the need for postselection and provides full information about the process in question . moreover , csqpt has been tested experimentally on simple single - mode processes , such as the identity , attenuation , and phase shift operations @xcite . furthermore , csqpt has been used to characterize quantum memory for light based on electromagnetically - induced transparency @xcite . an apparent obstacle to csqpt , however , is that the @xmath19 function for many nonclassical optical states exists only in terms of a highly singular generalized function @xcite . a remedy therefor is provided by klauder s theorem @xcite , which states that any trace - class operator @xmath16 can be approximated , to arbitrary accuracy , by a bounded operator @xmath22 whose glauber - sudarshan function @xmath23 is in the schwartz class @xcite , so integration can be performed . the klauder approximation can be constructed by low - pass filtering of the @xmath19 function , i.e. , by multiplying its fourier transform with an appropriate regularizing function equal to @xmath24 over a square domain of size @xmath25 and rapidly dropping to zero outside this domain . @xcite employs this method to implement csqpt . practical implementation of klauder s procedure is however complicated , because it requires finding the characteristic function of the input state and subsequently its regularized @xmath19 function . this function features high - frequency , high - amplitude oscillations that limit the precision in calculating the output state . furthermore , klauder s approximation is ambiguous in the choice of the particular filtering function as well as the cutoff parameter @xmath26 @xcite . here we improve csqpt to overcome the above problems . specifically , we develop a new method for csqpt that eliminates the explicit use of the glauber - sudarshan representation and thus removes the inherent ambiguity associated with employing klauder s approximation for csqpt . in sec . [ subsec : csqpt - formalism ] , we obtain an expression for the process tensor in the fock ( photon number ) basis that can be directly calculated from the experimental data . using this tensor , the process output for an arbitrary input can be calculated by simple matrix multiplication rather than requiring integration and high - frequency cut - offs . in this way , transformations between the fock and glauber - sudarshan representations , which were necessary in ref . @xcite , can be sidestepped . using our new approach , we easily extend csqpt from its restrictive single - mode applicability to multi - mode processes and even to non - trace - preserving conditional processes . these extensions are particularly relevant for quantum information processing circuits , whose basic components are inherently multi - mode and conditional @xcite . process tomography is successful if , for every input state , the estimate for the process output closely approximates the actual process output state , and the worst - case error of this estimate , given by a distance between the actual and estimated process outputs , is less than a given tolerance . for states over infinite - dimensional hilbert spaces , this concept of error is however not meaningful because the finiteness of sampling implies that the process is necessarily under - sampled , hence can not be determined with bounded error . instead we could consider the process estimation restricted to a finite - dimensional _ subset _ of @xmath27 . this version of process tomography can always be successful with a sufficiently large amount of sampling . of particular practical interest is the subspace @xmath28 defined by an energy cut - off , i.e. , estimating the process without accessing any information about its high - energy behavior . this restriction is naturally consistent with our choice to work in the fock basis , because then the resulting process tensor is of finite size and with many practical settings ( e.g. quantum - information processing with photonic qubits ) . in sec . [ subsec : erroranalysis ] , we provide process error estimates for several input state subsets that extend beyond @xmath29 . many interesting processes are phase symmetric ; that is , an optical phase shift of the input state results in the same phase shift of the output . this property dramatically simplifies the experiment because one needs to collect data only for coherent states whose amplitudes lie on the real axis rather than the entire complex plane . this prompts us to discuss , in sec . [ sec : experimentalapplication ] , how to obtain the process tensor for phase - symmetric processes , which we test on the experimental data from ref . next , in sec . [ sec : examples ] , we illustrate our method by analytically deriving the superoperators for certain fundamental quantum optical processes using the fock basis . the paper is concluded in sec . [ conc ] and is supplemented with two appendices .

we discuss a computationally efficient classical many - body potential designed to model the al - al interaction in a wide range of bonding geometries . comparison of the latter approximation with the reference monte carlo results provides informations on its range of applicability to surface problems at high temperatures . 2

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we discuss a computationally efficient classical many - body potential designed to model the al - al interaction in a wide range of bonding geometries . we show that the potential yields results in properties in excellent agreement with experiment and _ ab initio _ results for a number of bulk and surface properties , among others for surface and step formation energies , and self - diffusion barriers . as an application , free energy calculations are performed for the al ( 100 ) surface by monte carlo thermodynamic integration and the quasi - harmonic approximation . comparison of the latter approximation with the reference monte carlo results provides informations on its range of applicability to surface problems at high temperatures . 2

atomistic simulations are playing an increasingly prominent role in materials science . from studies of crystallization of clusters@xcite to large - scale simulations of fracture@xcite and grain boundary diffusion@xcite , atomistic simulations offer a microscopic physical view that can not be obtained from experiment . predictions resulting from this atomic level understanding are proving increasingly accurate and useful.@xcite the effective interatomic interaction potential is the key ingredient in all atomistic simulation . the accuracy of the potential affects drastically the quality of the simulation result , and its functional complexity determines the amount of computer time required.@xcite much research effort has therefore been devoted to the design of potential energy functions.@xcite this is especially important in classical dynamics which , although quantum mechanical simulations have been progressing at a rapid pace in recent years , remains the most ( sometimes , the only ) affordable way to perform very large scale simulations in materials science . in this paper , we present a new carefully designed al - al interaction model , test its performance , and we apply it to the study of free energies in atomic scale simulations . the ability to compute free energies is essential to understand or predict many physical phenomena , from the stability of crystal structures , to the propensity to form defects or disorder , and to morphology changes and phase transitions . however , the determination of free energies from atomic scale computer simulations is a daunting task . approximate methods , mostly based on the harmonic vibrational properties of the system , are commonly in use to this end . here , we compare several possible versions of the so called quasi - harmonic approximation , using as reference accurate simulation using canonical or constant - pressure monte carlo methods and thermodynamic integration , focusing on the specific case of surface free energies . the goal is to provide a measure of the range of applicability of approximate methods for complex systems using a reliable al interaction model .

we discuss a method to constrain the intrinsic shapes of galaxy clusters by combining x - ray and sunyaev - zeldovich observations . the method is applied to a sample of @xmath0 x - ray selected clusters , with measured sunyaev - zeldovich temperature decrements . the sample turns out to be slightly biased , with strongly elongated clusters preferentially aligned along the line of sight . we also show that identification of multiple gravitationally - lensed images , together with measurements of the sunyaev - zeldovich effect and x - ray surface brightness , can provide a simultaneous determination of the three - dimensional structure of a cluster , of the hubble constant , and the cosmological energy density parameters .

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we discuss a method to constrain the intrinsic shapes of galaxy clusters by combining x - ray and sunyaev - zeldovich observations . the method is applied to a sample of @xmath0 x - ray selected clusters , with measured sunyaev - zeldovich temperature decrements . the sample turns out to be slightly biased , with strongly elongated clusters preferentially aligned along the line of sight . this result demonstrates that x - ray selected cluster samples may be affected by morphological and orientation effects even if a relatively high threshold signal - to - noise ratio is used to select the sample . a large majority of the clusters in our sample exhibit a marked triaxial structure ; the spherical hypothesis is strongly rejected for most sample members . cooling flow clusters do not show preferentially regular morphologies . we also show that identification of multiple gravitationally - lensed images , together with measurements of the sunyaev - zeldovich effect and x - ray surface brightness , can provide a simultaneous determination of the three - dimensional structure of a cluster , of the hubble constant , and the cosmological energy density parameters .

the intrinsic , three - dimensional ( hereafter 3-d ) shape of clusters of galaxies is an important cosmological probe . the structure of galaxy clusters is sensitive to the mass density in the universe , so knowledge of this structure can help in discriminating between different cosmological models . it has long been clear that the formation epoch of galaxy clusters strongly depends on the matter density parameter of the universe @xcite . the growth of structure in a high - matter - density universe is expected to continue to the present day , whereas in a low density universe the fraction of recently formed clusters , which are more likely to have substructure , is lower . therefore , a sub - critical value of the density parameter @xmath1 favors clusters with steeper density profiles and rounder isodensity contours . less dramatically , a cosmological constant also delays the formation epoch of clusters , favoring the presence of structural irregularity @xcite . + an accurate knowledge of intrinsic cluster shape is also required to constrain structure formation models via observations of clusters . the asphericity of dark halos affects the inferred central mass density of clusters , the predicted frequency of gravitational arcs , nonlinear clustering ( especially high - order clustering statistics ) and dynamics of galactic satellites ( see @xcite and references therein ) . + asphericity in the gas density distribution of clusters of galaxies is crucial in modeling x - ray morphologies and in using clusters as cosmological tools . @xcite . assumed cluster shape strongly affects absolute distances obtained from x - ray / sunyaev - zeldovich ( sz ) measurements , as well as relative distances obtained from baryon fraction constraints @xcite . finally , all cluster mass measurements derived from x - ray and dynamical observations are sensitive to the assumptions about cluster symmetry . + of course , only the two - dimensional ( 2-d ) projected properties of clusters can be observed . the question of how to deproject observed images is a well - posed inversion problem that has been studied by many authors @xcite . since information is lost in the process of projection it is in general impossible to derive the intrinsic 3-d shape of an astronomical object from a single observation . to some extent , however , one can overcome this degeneracy by combining observations in different wavelengths . for example , @xcite introduced a model - independent method of image deprojection . this inversion method uses x - ray , radio and weak lensing maps to infer the underlying 3-d structure for an axially symmetric distribution . @xcite proposed a parameter - free algorithm for the deprojection of observed two dimensional cluster images , again using weak lensing , x - ray surface brightness and sz imaging . the 3-d gravitational potential was assumed to be axially symmetric and the inclination angle was required as an input parameter . strategies for determining the orientation have been also discussed . @xcite proposed a method that , with a perturbative approach and with the aid of sz and weak lensing data , could predict the cluster x - ray emissivity without resolving the full 3-d structure of the cluster . the degeneracy between the distance to galaxy clusters and the elongation of the cluster along the line of sight ( l.o.s . ) was thoroughly discussed by @xcite . they introduced a specific method for finding the intrinsic 3-d shape of triaxial cluster and , at the same time , measuring the distance to the cluster corrected for asphericity , so providing an unbiased estimate of the hubble constant @xmath2 . @xcite recently proposed a theoretical method to reconstruct the shape of triaxial dark matter halos using x - ray and sz data . the hubble constant and the projection angle of one principal axis of the cluster on the plane of the sky being independently known , they constructed a numerical algorithm to determine the halo eccentricities and orientation . however , neither @xcite nor @xcite apply their method to real data . + in this paper we focus on x - ray surface brightness observations and sz temperature decrement measurements . we show how the intrinsic 3-d shape of a cluster of galaxies can be determined through joint analyses of these data , given an assumed cosmology . we constrain the triaxial structure of a sample of observed clusters of galaxies with measured x - ray and sz maps . to break the degeneracy between shape and cosmology , we adopt cosmological parameters which have been relatively well - determined from measurements of the cosmic microwave background ( cmb ) anisotropy , type ia supernovae and the spatial distribution of galaxies . we also show how , if multiply - imaging gravitational lens systems are observed , a joint analysis of strong lensing , x - rays and sz data allows a determination of both the 3-d shape of a cluster and the geometrical properties of the universe . + the paper is organized as follows . the basic dependencies of cluster x - ray emission and the sze on geometry are reviewed in [ sec : multi_wave ] . in [ sec : combin_datasets ] , we show how to reconstruct the 3-d cluster structure from these data , presuming cosmological parameters to be known . in passing we note how the addition of suitable strong gravitational lensing data can constrain the cosmological parameters as well , although we do not impose lensing constraints in this paper . we then turn to face the data . our cluster sample is introduced in [ sec : data_samp ] , and in [ sec : morph_2d ] , we present 2-d x - ray surface brightness parameters for each sample member . the triaxial structure of the clusters is then estimated and analyzed in [ sec : tria ] . [ sec : disc ] is devoted to a summary and discussion of the results . in appendix [ sec : triaxial ] , we provide details on the triaxial ellipsoidal @xmath3-model , used to describe the intra - cluster gas distribution , while appendix [ sec : inclination ] is devoted to a discussion of the consequences of our assumption of clusters being triaxial ellipsoids aligned along the line of sight . in appendix [ sec : lensing ] the identifications of multiple sets of images of background galaxies in strong lensing events is discussed . throughout this paper , unless otherwise stated , we quote errors at the @xmath4 confidence level .

we discuss production of two pairs of @xmath0 within a simple formalism of double - parton scattering ( dps ) . both total inclusive cross section as a function of energy and differential distributions for @xmath1 are shown . we discuss a perspective how to identify the double scattering contribution .

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1111.3255

we discuss production of two pairs of @xmath0 within a simple formalism of double - parton scattering ( dps ) . surprisingly very large cross sections , comparable to single - parton scattering ( sps ) contribution , are predicted for lhc energies . both total inclusive cross section as a function of energy and differential distributions for @xmath1 are shown . we discuss a perspective how to identify the double scattering contribution .

in fig . [ fig : single_vs_double_lo ] we compare cross sections for the single and double - parton scattering as a function of proton - proton center - of - mass energy . at low energies the conventional single - parton scattering dominates . for reference we show the proton - proton total cross section as a function of energy as parametrizes in ref . @xcite . at low energy the @xmath0 or @xmath32 cross sections are much smaller than the total cross section . at higher energies the contributions dangerously approach the expected total cross section . this shows that inclusion of unitarity effect and/or saturation of parton distributions may be necessary . the effect of saturation in @xmath33 production has been included e.g. in ref . @xcite but not checked versus experimental data . presence of double - parton scattering changes the situation . the double - parton scattering is therefore potentially very important ingredient in the context of high energy neutrino production in the atmosphere @xcite or of cosmogenic origin @xcite . we leave this rather difficult issue for future studies where the lhc charm data must be included . at lhc energies the cross section for both terms become comparable or @xmath3 was shown the cross section should be multiplied by a factor of two two @xmath2 or two @xmath3 in each event . ] . this is a completely new situation when the double - parton scattering gives a huge contribution to inclusive charm production . in figs . [ fig : double_single1 ] , [ fig : double_single2 ] , we present single @xmath2 ( @xmath3 ) distributions . within approximations made in this paper the distributions are identical in shape to single - parton scattering distributions . this means that double - scattering contribution produces naturally an extra center - of - mass energy dependent @xmath9 factor to be contrasted with approximately energy - independent @xmath9-factor due to next - to - leading order corrections . one can see a strong dependence on the factorization and renormalization scales which produces almost order - of - magnitude uncertainties and precludes a more precise estimation . a better estimate could be done when lhc charm data are published and the theoretical distributions are somewhat adjusted to experimental data . so far we have discussed only single particle spectra of @xmath2 or @xmath3 ( rapidity , transverse momentum distributions ) which due to scale dependence do not provide a clear test of the existence of double - parton scattering contributions . a more stringent test could be performed by studying correlation observables . in particular , correlations between @xmath2 and @xmath3 are very interesting even without double - parton scattering terms @xcite . in fig . [ fig : double_correlations_1 ] we show distribution in the difference of @xmath2 and @xmath3 rapidities @xmath35 ( left panel ) as well as in the @xmath0 invariant mass @xmath36 ( right panel ) . we show both terms : when @xmath0 are emitted in the same parton scattering ( @xmath37 or @xmath38 ) and when they are emitted from different parton scatterings ( @xmath39 or @xmath40 ) . in the latter case we observe a long tail for large rapidity difference as well as at large invariant masses of @xmath0 . such distributions can not be directly measured for @xmath0 but could be measured for mesons ( rapidity difference up to 5 for the main atlas or cms detector ) or electron - positron or @xmath41 . the alice forward muon spectrometer @xcite covers the pseudorapidity interval 2.5 @xmath42 4 which when combined with the central detector means pseudorapidities differences up to 5 . this is expected to be a region of phase space where double - parton scattering contribution would most probably dominate over single - parton scattering contribution . this will be a topic of a forthcoming analysis . next - to - leading order corrections are not expected to give major contribution at large pseudorapidity differences or / and large invariant masses of @xmath41 but this must be verified in the future . the cms detector is devoted especially to measurements of muons . the lower transverse momentum threshold is however rather high , the smallest being about 1.5 gev at @xmath43 ( 2 - 2.4 ) which may be interesting for double - parton scattering searches . this requires special dedicated monte carlo studies . finally in fig . [ fig : double_correlations_2 ] we present distribution in the transverse momentum of the @xmath0 pair @xmath44 , where @xmath45 which is a dirac delta function in the leading - order approximation . in contrast , double - parton scattering mechanism provide a broad distribution extending to large transverse momenta . next - to - leading order corrections obviously destroy the @xmath46-like leading - order correlation . we believe that similar distributions for @xmath47 or / and @xmath48 or @xmath41 pairs would be a useful observables to identify the dps contributions but this requires real monte carlo simultions including actual limitations of experimental apparatus . correlations between outgoing nonphotonic electrons has been studied at much lower rhic energy in ref . @xcite . production of two @xmath0 pairs in the leading order approximation is only a first step in trying to identify dps contribution . in the next step we plan next - to - leading order calculation of the same process . inclusion of hadronization and/or semileptonic decays would be very useful in planning experimental searches .

the mercury edm also gives a strong constraint for the gluino - squark interaction . kek - th-1830 * sensitivity of high - scale susy + in low energy hadronic fcnc * + + _ @xmath14department of physics , niigata university , + niigata 950 - 2181 , japan + @xmath14institute of particle and nuclear studies , + high energy accelerator research organization ( kek ) , + tsukuba 305 - 0801 , japan + _

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we discuss the sensitivity of the high - scale susy at @xmath0-@xmath1 tev in @xmath2 , @xmath3 , @xmath4 and @xmath5 meson systems together with the neutron edm and the mercury edm . in order to estimate the contribution of the squark flavor mixing to these fcncs , we calculate the squark mass spectrum , which is consistent with the recent higgs discovery . the susy contribution in @xmath6 could be large , around @xmath7 in the region of the susy scale @xmath0-@xmath8 tev . the neutron edm and the mercury edm are also sensitive to the susy contribution induced by the gluino - squark interaction . the predicted edms are roughly proportional to @xmath9 . if the susy contribution is the level of @xmath10 for @xmath6 , the neutron edm is expected to be discovered in the region of @xmath11-@xmath12ecm . the mercury edm also gives a strong constraint for the gluino - squark interaction . the susy contribution of @xmath13 is also discussed . kek - th-1830 * sensitivity of high - scale susy + in low energy hadronic fcnc * + + _ @xmath14department of physics , niigata university , + niigata 950 - 2181 , japan + @xmath14institute of particle and nuclear studies , + high energy accelerator research organization ( kek ) , + tsukuba 305 - 0801 , japan + _

the supersymmetry ( susy ) is one of the most attractive theories beyond the standard model ( sm ) . therefore , the susy has been expected to be observed at the lhc experiments . however , no signals of the susy have been discovered yet . the present searches for the susy particles give us important constraints for the susy . since the lower bounds of the superparticle masses increase gradually , the squark and the gluino masses are supposed to be at the higher scale than @xmath15 tev @xcite . on the other hand , the susy model has been seriously constrained by the higgs discovery , in which the higgs mass is @xmath16 gev @xcite . based on this theoretical and experimental situations , we consider the high - scale susy models , which have been widely discussed with a lot of attention @xcite-@xcite . if the squark and slepton masses are at the high - scale @xmath17-@xmath18 tev , the lightest higgs mass can be pushed up to @xmath16 gev , whereas susy particles are out of the reach of the lhc experiment . therefore , the indirect search of the susy particles becomes important in the low energy flavor physics @xcite . the flavor physics is also on the new stage in the light of lhcb data . the lhcb collaboration has reported new data of the cp violation of the @xmath3 meson and the branching ratios of rare @xmath3 decays @xcite-@xcite . for many years the cp violation in the @xmath19 and @xmath2 mesons has been successfully understood within the framework of the standard model ( sm ) , so called kobayashi - maskawa ( km ) model @xcite , where the source of the cp violation is the km phase in the quark sector with three families . however , the new physics has been expected to be indirectly discovered in the precise data of @xmath2 and @xmath3 meson decays at the lhcb experiment and the further coming experiment , belle - ii . there are new sources of the cp violation if the sm is extended to the susy models . the soft squark mass matrices contain the cp violating phases , which contribute to the flavor changing neutral current ( fcnc ) with the cp violation @xcite . therefore , we can expect the susy effect in the cp violating phenomena . however , the clear deviation from the sm prediction has not been observed yet in the lhcb experiment @xcite-@xcite . actually , we have found that the cp violation of @xmath2 and @xmath3 meson systems are suppressed if the susy scale is above @xmath0 tev @xcite . on the other hand , the ckmfitter group presented the current limits on new physics contributions of @xmath10 in @xmath2 , @xmath3 and @xmath4 systems @xcite . they have also estimated the sensitivity to new physics in @xmath2 and @xmath3 mixing achievable with @xmath20 of belle - ii and @xmath21 of lhcb data . therefore , we should carefully study the sensitivity of the high - scale susy to the hadronic fcnc . in this work , we discuss the high - scale susy contribution to the @xmath2 , @xmath3 and @xmath4 meson systems . furthermore , we also discuss the sensitivity to the @xmath5 meson and the electric dipole moment ( edm ) of the neutron and the mercury . for these modes , the most important process of the susy contribution is the gluino - squark mediated flavor changing process @xcite- @xcite . the cp violation of @xmath19 meson , @xmath6 , provides a severe constraint to the gluino - squark mediated fcnc @xcite . in addition , the recent work have found that the chromo - electric dipole moment ( cedm ) is sensitive to the high - scale susy @xcite . it is noted that the upper - bound of the neutron edm ( nedm ) @xcite gives a severe constraint for the gluino - squark interaction through the cedm @xcite-@xcite . it is also remarked that the upper bound of the mercury edm ( hgedm ) @xcite can give an important constraint @xcite . in order to estimate the gluino - squark mediated fcnc of the @xmath19 , @xmath2 , @xmath3 and @xmath5 mesons , we work in the basis of the squark mass eigenstate with the non - minimal squark ( slepton ) flavor mixing . there are three reasons why the susy contribution to the fcnc considerably depends on the squark mass spectrum . the first one is that the gim mechanism works in the squark flavor mixing , and the second one is that the loop functions depend on the mass ratio of squark and gluino . the last one is that we need the mixing angle between the left - handed sbottom and right - handed sbottom , which dominates the @xmath22 decay processes . therefore , we discuss the squark mass spectrum , which is consistent with the recent higgs discovery . taking the universal soft parameters at the susy breaking scale , we obtain the squark mass spectrum at the matching scale where the sm emerges , by using the renormalization group equations ( rges ) of the soft masses . on the other hand , the @xmath23 mixing matrix between squarks and quarks is taken to be free at the low energy . in section 2 , we discuss the squark and gluino mass spectrum and the squark mixing . in section 3 , we present the formulation of the fcnc with @xmath24 in @xmath19 , @xmath2 , @xmath3 and @xmath5 meson systems together with nedm and hgedm . we present numerical results and discussions in section 4 . section 5 is devoted to the summary . the relevant formulations are presented in appendices a , b , c and d.

we discuss the sensitivity of the high - scale susy at @xmath0-@xmath1 tev in @xmath2 , @xmath3 , @xmath4 and @xmath5 meson systems together with the neutron edm and the mercury edm . in order to estimate the contribution of the squark flavor mixing to these fcncs , we calculate the squark mass spectrum , which is consistent with the recent higgs discovery . the susy contribution in @xmath6 could be large , around @xmath7 in the region of the susy scale @xmath0-@xmath8 tev . the neutron edm and the mercury edm are also sensitive to the susy contribution induced by the gluino - squark interaction .

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we discuss the sensitivity of the high - scale susy at @xmath0-@xmath1 tev in @xmath2 , @xmath3 , @xmath4 and @xmath5 meson systems together with the neutron edm and the mercury edm . in order to estimate the contribution of the squark flavor mixing to these fcncs , we calculate the squark mass spectrum , which is consistent with the recent higgs discovery . the susy contribution in @xmath6 could be large , around @xmath7 in the region of the susy scale @xmath0-@xmath8 tev . the neutron edm and the mercury edm are also sensitive to the susy contribution induced by the gluino - squark interaction . the predicted edms are roughly proportional to @xmath9 . if the susy contribution is the level of @xmath10 for @xmath6 , the neutron edm is expected to be discovered in the region of @xmath11-@xmath12ecm . the mercury edm also gives a strong constraint for the gluino - squark interaction . the susy contribution of @xmath13 is also discussed . kek - th-1830 * sensitivity of high - scale susy + in low energy hadronic fcnc * + + _ @xmath14department of physics , niigata university , + niigata 950 - 2181 , japan + @xmath14institute of particle and nuclear studies , + high energy accelerator research organization ( kek ) , + tsukuba 305 - 0801 , japan + _

we discussed the sensitivity of the high - scale susy at @xmath0-@xmath1 tev in the @xmath2 , @xmath3 and @xmath4 meson systems . furthermore , we have also discussed the sensitivity to the @xmath5-@xmath205 mixing , the neutron edm and the mercury edm . in order to estimate the contribution of the squark flavor mixing to these fcnc , we calculate the squark mass spectrum , which is consistent with the recent higgs discovery . the susy contributions in @xmath77 and @xmath78 are at most @xmath162 and @xmath160 at @xmath163 tev , respectively . as @xmath168 increases , the susy contributions of both @xmath77 and @xmath78 decrease approximately with the power of @xmath169 . therefore , the susy scale increases to more than @xmath0 tev , no signal of the susy is expected . on the other hand , the susy contribution in @xmath94 can be comparable to the experimental value in the case of @xmath182 whereas it is suppressed in the case of @xmath177 at @xmath163 tev . furthermore , the susy contribution in @xmath6 could be large , around @xmath7 in the region of the susy scale @xmath0-@xmath8 tev . by considering the effect of the susy contribution @xmath10 in @xmath6 , the tension between @xmath6 and @xmath188 can be relaxed even if the susy scale is @xmath8 tev . the neutron edm and the mercury edm are also sensitive to the susy contribution induced by the gluino - squark interaction . the @xmath191 is expected to be close to the experimental upper bound even if the susy scale is @xmath69 tev . the predicted nedm is roughly proportional to @xmath9 . if the susy contribution is the level of @xmath10 for @xmath6 , the @xmath191 is expected to be discovered in the region of @xmath195-@xmath12 cm . for the @xmath192 , the susy contribution is close to the experimental upper bound up to @xmath198tev , which is much higher than the one of the nedm . if the hgedm is not observed above @xmath199 cm , the susy contribution of @xmath6 is below a few @xmath196 . thus , the mercury edm gives more significant information for the gluino - squark interaction compared with the neutron edm . it may be important to give a comment that these predictions depend strongly on the assumptions of @xmath200 and @xmath201 . the deviation from these relations destroys these correlations . in conclusion , the careful studies of the mixing angle relations are required to test the correlations between edms and @xmath197 . the predicted edms have also the ambiguity with the factor @xmath204 from the hadronic model . since the sm prediction of @xmath13 at the short distance is @xmath206 gev , which is very small compared with the experimental value , it is important to estimate the susy contribution of @xmath13 . in conclusion , the more detailed studies of @xmath4 meson system , the edms of the neutron and mercury are required in order to probe the high - scale susy at @xmath0-@xmath1 tev . * acknowledgment * 0.3 cm this work is supported by jsps grand - in - aid for scientific research , 24654062 and 25 - 5222 .

we find that for disorder strength , @xmath0 5 , the density of states is flat . we , then , make connection , using the mrg approach , with the work of abrahams _ et al . _ and find a very good agreement for disorder strength , @xmath1 = 5 . for low disorder strength , @xmath1 = 2 , we plot the energy - resolved current matrix elements squared for different locations of the fermi energy from the band centre . further studies of current matrix elements versus disorder strength suggests a cross - over from weakly localized to a very weakly localized system . we calculate conductivity using kubo greenwood formula and show that , for low disorder strength , conductivity is in a good qualitative agreement with the experiments , even for the on - site disorder .

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1105.2354

we employ the exact eigenstate basis formalism to study electrical conductivity in graphene , in the presence of short - range diagonal disorder and inter - valley scattering . we find that for disorder strength , @xmath0 5 , the density of states is flat . we , then , make connection , using the mrg approach , with the work of abrahams _ et al . _ and find a very good agreement for disorder strength , @xmath1 = 5 . for low disorder strength , @xmath1 = 2 , we plot the energy - resolved current matrix elements squared for different locations of the fermi energy from the band centre . we find that the states close to the band centre are more extended and falls of nearly as @xmath2 as we move away from the band centre . further studies of current matrix elements versus disorder strength suggests a cross - over from weakly localized to a very weakly localized system . we calculate conductivity using kubo greenwood formula and show that , for low disorder strength , conductivity is in a good qualitative agreement with the experiments , even for the on - site disorder . the intensity plots of the eigenstates also reveal clear signatures of puddle formation for very small carrier concentration . we also make comparison with square lattice and find that graphene is more easily localized when subject to disorder .

graphene has been long studied as a theoretical toy model not only to understand it s appealing physical properties,@xcite but also as a basic building block of various carbon allotropes like graphite,@xcite and more recently fullerenes and nanotubes.@xcite while graphite is the three dimensional allotrope of carbon and could be formed by the bernal stacking of graphene sheets , fullerene and nanotubes are the zero and one dimensional allotropes , formed by introducing pentagonal impurities and rolling the graphene sheets , respectively . after its experimental isolation in 2004,@xcite there has been a renewed interest in studying various properties of graphene sheet , both theoretically and experimentally , as well as due to potential technological applications.@xcite graphene consists of a single sheet of carbon atoms arranged on a honeycomb lattice . basic properties of graphene are well described by a tight - binding model for the @xmath3-orbitals which are perpendicular to the graphene plane at each carbon atom . the effective low - energy theory states that the charge carriers in graphene are massless dirac fermions , characterized by a linear dispersion relation and a linear energy dependence of the density of states which vanishes at the fermi level implying a semi - metallic behaviour for graphene.@xcite graphene has attracted a lot of attention recently not only due to its potential technological applications but also for understanding of physics in 2d systems@xcite . its low energy description mimics ( 2 + 1)-dimensional quantum electrodynamics and hence graphene could act as a testing ground for various relativistic phenomena.@xcite early experiments on graphene have revealed that the conductivity at low temperatures is directly proportional to the carrier concentration ( or gate voltage ) except for very low carrier concentration . for zero gate voltage , the conductivity approaches a robust minimum universal value proportional to @xmath4.@xcite this could not be explained by the born approximation which predicts a conductivity independent of carrier concentration.@xcite other interesting properties include anomalous integral quantum hall effect and suppression of weak localization.@xcite recent experiments , however , show that the dependence of conductivity on carrier concentration could vary from sub linear to superlinear for different carrier concentrations.@xcite it has been argued that presence of impurities in graphene is the main contributor towards its electronic properties.@xcite the importance of disorder in graphene could most easily be emphasized by observing that the universal conductivity suggested by the theoretical studies on defectless graphene sheet is 2 - 20 times smaller than the observed conductivity close to the dirac points.@xcite the boltzmann conductivity for graphene is given by @xmath5 . the observed conductivity rises linearly with carrier concentration in graphene and @xmath6 , where @xmath7 is the density of states at the fermi energy and @xmath8 is the carrier density . this implies that the scattering rate , @xmath9 . on the other hand , for weak local scatterers , born approximation predicts @xmath10 where @xmath11 is the impurity concentration.@xcite in view of this discrepancy , various investigations , both theoretical and numerical , have been carried out in order to understand the behavior of graphene under various types of disorder,@xcite such as vacancies,@xcite charged carriers,@xcite on - site disorder,@xcite long range on - site disorder,@xcite off - diagonal disorder,@xcite off - diagonal disorder with sign change probability in the hopping term.@xcite vacancies have been proposed to induce localized states , extended over many lattice sites , which are sensitive to the electron - hole symmetry breaking@xcite detailed studies in the presence of both compensated and uncompensated defects reveal that they could modify the low energy spectrum in graphene drastically like there could be quasi - localized zero modes and introduction of gap in the dos.@xcite for charged scatterers , nomura _ @xcite have argued on the basis of boltzmann transport theory that the linear dependence of conductivity on carrier concentration could be explained . they find that states close to the dirac point are delocalized leading to @xmath12 . also , one could observe antilocalization if the inter - valley scattering is weak . on the other hand , if inter - vally scattering is large , all states could be localized due to accumulation of berry phases . conductivity in the presence of random charged impurity is also studied by hwang _ _ et al.__@xcite they find linear dependence of conductivity on carrier concentration for high carrier density . however , for low carrier density , they argue , that system develops some inhomogenities ( random electron - hole puddles ) which implies that this domain is dominated by localization physics . they also conclude that change of bias voltage may change the average distance between graphene sheet and the impurity in the substrate which could lead to sub- and super - linear conductivity dependence on carrier concentraion . _ @xcite have argued that there could be a `` critical coupling '' distinguishing strong and weak coupling regimes in the presence of unscreened coulomb charges . they also find bound states and strong renormalization of van hove singularities in the dos . _ @xcitehave argued that the intrinsic conductivity of graphene ( ambipolar system ) is dominated by strong electron - hole scattering . it has a universal value independent of temperature . it is shown that conductivity could be proportional to v or @xmath13 depending on the other scattering mechanisms present like those on phonons by charged defects . in the unipolar system , it is argued that electron - hole scattering is not important and conductivity is proportional to @xmath14 . _ @xcite have reported an analytical calculation for boltzmann conductivity with screened coulomb scatterers and both electron - hole coherent and incoherent solutions . they find that the experimentally observed dependence of conductivity on @xmath8 could be explained by the electron - hole coherent solution . for diagonal disorder , it is found that beyond a certain threshold disorder strength , bound states appear beyond the band continuum and resonant states could appear at low energies . in the infinite disorder strength limit , results match with that of vacancies . in the off - diagonal disorder case , strong low - energy resonances appear . there are , however , no bound states.@xcite localization studies on graphene with on - site disorder carried out by xiong _ _ et al.__@xcite reveal that all states are localized in the case of random diagonal disorder which is consistent with anderson localization . lherbier _ _ et al.__@xcite have also studied the energy dependent elastic mean free path , charge mobilities and semi - classical conductivity in the presence of anderson - type disorder , using real space order n kubo formalism , for both two - dimensional graphene and graphene nano - ribbons ( gnrs ) . it was found that the systems undergo a conventioanl anderson transition in the zero temperature limit . lewenkopf _ et al . _ @xcite have studied long range diagonal disorder ( gaussian scatteres ) at finite concentration . they find that conductivity increases as disorder strength is decreased . it is shown that conductivity depends only on disorder strength and ratio of the system size to disorder correlation length . this dependence could vary between sublinear to superlinear depending on disorder strength . for fixed disorder strength , conductivity increases with doping concentration . in the presence of strong long - range impurities , zhang _ _ et al.__@xcite have shown that states close to the dirac points are localized for sufficiently strong disorder strength and kosterlitz - thouless transition between localized and delocalized states is proposed which is seen in terms of the current flow vector . in the case of random off - diagonal disorder ( hopping disorder ) , localization studies by xiong _ _ et al.__@xcite reveal that states close to the dirac point are delocalized due to chiral symmetry . they find that the off - diagonal disorder leads to a shape - dependent conductivity depending on the length to width ratio . however , if a sign change probability is introduced , they find that the conductivity becomes shape independent _ et al.__@xcite have shown that for disorder strength less than the hopping strength i.e. @xmath15 , there is no localization . disorder @xmath1 slows down the dirac quasi particles but preserves their nature . for @xmath16 , localization sets in for states close to the fermi energy , gap at energy close to the dirac point and for @xmath17 existence of mobility edge is proposed which starts at fermi energy and moves towards the edges . states close to the fermi energy are extended . they also propose the existence of disorder induced gap defined as the distance between the upper and lower mobility edges around the fermi point . it should be noted that in all these works , the inter - valley scattering is assumed to be very small and hence not contributing towards conductivity . however , klos _ _ et al.__@xcite have done a comparative study of conductivity using the tight - binding(tb ) landauer approach and on the basis of the boltzmann theory and find a discrepancy between that results obtained by tb calculation and boltzmann approach . despite all the efforts , the issue of localization in graphene is currently highly debated from a theoretical standpoint . the obsered minimal conductivity @xmath18 over a range of mobilities remains to be fully understod . in view of a recent experiment by ponomarenko _ _ et al.__@xcite and katoch _ _ et al.__@xcite , which explores the dominant scatterers in graphene , and horng__et al.__@xcite , which measures the high - frequency conductivity in graphene , unlike believed so far , the primary reason for the linear rise of conductivity with carrier concentration is also debatable . in the present work , we will investigate the finite - frequency electrical conductivity and localization properties of graphene in the presence of diagonal ( on - site ) disorder for various disorder strengths . our exact - eigenstates approach implicitly takes into account the inter - valley as well as the intra - valley scatterings . this paper is organized into eight sections . in section ii and iii , we introduce the two sub - lattice basis and evaluate the exact single - particle green s function within the t - matrix approach for a single impurity on either sublattice . in section iv , we consider disordered graphene . disorder is introduced via random fluctuation of the on - site energies of the @xmath3-orbitals . in section v , we use the kubo - greenwood formula to calculate the frequency - dependent conductivity for different disorder strengths and for different system sizes . the system - size dependence is employed to perform a renormalization group analysis , and for moderate disorder strength contact is made with the weak localization result of abraham s _ et al._. later on , focus on the weak disorder strength . we study the frequency dependence of the averaged current matrix element squared for different locations in the band ( fermi energies ) and hence calculate conductivity and mobility for low - disordered graphene samples . we also study the dependence of energy resolved current matrix elements squared on system size and disorder strength . in section vi , we study the average current matrix elements squared over a range of disorder strength and for different system sizes in order to gain a better insight into disorder induced localization in graphene . in section vii , we make a comparision between graphene and square lattice . we compare the normalized conductivity between the two . we also show the intensity plots for both the lattices for different values of disorder strength . finally , our conclusions are presented in section viii .

we employ the exact eigenstate basis formalism to study electrical conductivity in graphene , in the presence of short - range diagonal disorder and inter - valley scattering . the intensity plots of the eigenstates also reveal clear signatures of puddle formation for very small carrier concentration . we also make comparison with square lattice and find that graphene is more easily localized when subject to disorder .

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1105.2354

we employ the exact eigenstate basis formalism to study electrical conductivity in graphene , in the presence of short - range diagonal disorder and inter - valley scattering . we find that for disorder strength , @xmath0 5 , the density of states is flat . we , then , make connection , using the mrg approach , with the work of abrahams _ et al . _ and find a very good agreement for disorder strength , @xmath1 = 5 . for low disorder strength , @xmath1 = 2 , we plot the energy - resolved current matrix elements squared for different locations of the fermi energy from the band centre . we find that the states close to the band centre are more extended and falls of nearly as @xmath2 as we move away from the band centre . further studies of current matrix elements versus disorder strength suggests a cross - over from weakly localized to a very weakly localized system . we calculate conductivity using kubo greenwood formula and show that , for low disorder strength , conductivity is in a good qualitative agreement with the experiments , even for the on - site disorder . the intensity plots of the eigenstates also reveal clear signatures of puddle formation for very small carrier concentration . we also make comparison with square lattice and find that graphene is more easily localized when subject to disorder .

in conclusion , we have studied the finite - frequency electrical conductivity in graphene under diagonal ( on - site ) disorder of various strength and in the presence of inter - valley scattering using kubo - greenwood foumula . for moderate disorder strength , we find that for differnt system sizes , fixed @xmath1 , scaling theory is at work . we made contact with the weak localization result of abrahams _ _ et al.__@xcite and found a very good agreement which means that for @xmath74 , logarithmic scaling is obeyed . we compare normalized conductivity of graphene with that of a square lattice and find that graphene is more susceptible to localization when subject to disorder . we have established that , for low disorder strength , @xmath129 , the states away from the band centre are more localized comared to the ones close to the band centre . for low disorder strength , we have calculated the conductivity for low - disordered graphene and have found the results are in disagreement with that of boltzmann conductivity . also , the conductivity and mobility are in qualitative agreement with experiments . also , for weak disorder strength , it is the competition between @xmath130 and dos which gives rise to a universal conductivity minimum . the linear rise of conductivity with carrier concentration is due to a term unaccounted for in the boltzmann expression for conductivity . we have also established that , for low disorder strength , @xmath129 , the states close to the band centre are extended and that there exists a crossover at @xmath1 @xmath110 3 . comparative study of intensity plots for states close to the band centre for graphene with square lattice shows clear signatures of puddle formation in graphene . although we have studied a simple disorder model in graphene , some of the feature studied could be generic . j. w. klos , and i. v. zozoulenko phys . b * 82 * , 081414(r ) ( 2010 ) . l. a. ponomarenko , r. yang , t. m. mohiuddin , s. m. morozov , a. a. zhukov , f. schedin , e. w. hill , k. s. novoselov , m. i. katsnelson , and a. k. geim phys . rev . lett . * 102 * , 206603 ( 2009 ) . jyoti katoch , j - h . chen , ryuichi tsuchikawa , c. w. smith , e. r. mucciolo , and masa ishigami phys . rev . b * 82 * , 081417(r ) ( 2010 ) . jason horng , chi - fan chen , baisong geng , caglar girit , yuanbo zhang , zhao hao , hans a. bechtel , michael martin , alex zettl , michael f. crommie , y. ron shen , feng wang , arxiv:1007.4623

we examine the general nature of nuclear odd - even mass differences by employing neutron and proton mass relations that emphasize these effects . the most recent mass tables are used . the results deviate from previous parametrizations , and in particular found to be significantly superior to a recent two term , @xmath1 dependence .

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1408.6166

we examine the general nature of nuclear odd - even mass differences by employing neutron and proton mass relations that emphasize these effects . the most recent mass tables are used . the possibility of a neutron excess dependence of the staggering is examined in detail in separate regions defined by the main nuclear shells , and a clear change in this dependency is found at @xmath0 for both neutrons and protons . a further separation into odd and even neutron ( proton ) number produces very accurate local descriptions of the mass differences for each type of nucleons . these odd - even effects are combined into a global phenomenological expression , ready to use in a binding energy formula . the results deviate from previous parametrizations , and in particular found to be significantly superior to a recent two term , @xmath1 dependence .

the systematic odd - even mass difference in nuclei was recognized early on , see @xcite for a brief historical overview . several effects will contribute to the experimentally observed differences , in particular pairing and the twofold degeneracy of orbits , see @xcite for an overview of recent work . traditionally the odd - even mass staggering has been parametrized by a power law in the mass number @xmath2 ( both @xmath3 and @xmath4 have been used ) , but other functional forms have been used , e.g. a constant and a @xmath1 term in @xcite . we emphasize that these smoothly varying parametrizations only were meant to reproduce values of staggering averaged over many neighboring nuclei . the odd - even mass differences has traditionally been attributed to nucleon pairing ( the largest part ) and breaking of the time reversal double degeneracy of the single particle levels ( the smallest part ) . other effects may contribute as well . both experimentally and theoretically one observes significant , systematic deviations from the simple laws @xcite and it therefore seems worthwhile to make use of the recently updated , extensive and accurate , nuclear mass table @xcite to look more carefully for trends in the experimental odd - even staggering . we shall in particular reinvestigate the suggestion of an explicit dependence on neutron excess @xcite that was not supported by nuclear pairing models @xcite . our aim is to find an improved phenomenological description of the odd - even mass differences that may be used in combination with semi - empirical mass models , and perhaps reveal trends that could inspire future more basic theoretical work . the relevant theoretical considerations are presented in sec . in particular , the relevant mass relations designed specifically to isolate odd - even effects are introduced . mass relations of this nature were investigated in detail by jensen _ @xcite , but the relations used here are more compact , and are applied with the sole purpose of analyzing odd - even effects in general . section [ sect . sys ] contains the initial examination of odd - even mass differences . the focus is on the general structure of the staggering effects , and to that end the results , free of any manipulations , are presented in this section . to provide a more general overview of this structure sec . e - o ] presents a three dimensional illustration of neutron staggering as a function of both @xmath5 and @xmath6 . also included in sec . sys ] is a short evaluation of the extent of the shell effects . section [ sec . gen ] contains the examination of staggering effects as a function of isospin projection . this includes both a separation according to odd - even neutron and proton configurations , as well as separation into regions defined by nuclear shells . having established the effect of each separation the results are combined into one global expression , which describes the collective odd - even staggering effect and includes neutron - proton pairing explicitly . finally , in the results are compared to a very accurate recent two - term description with an @xmath1 dependency .

we examine whether the mott transition of a half - filled , two - orbital hubbard model with unequal bandwidths occurs simultaneously for both bands or whether it is a two - stage process in which the orbital with narrower bandwith localizes first ( giving rise to an intermediate ` orbital - selective ' mott phase ) . this question is addressed using both dynamical mean - field theory , and a representation of fermion operators in terms of slave quantum spins , followed by a mean - field approximation ( similar in spirit to a gutzwiller approximation ) . in the latter approach , the mott transition is found to be orbital - selective for all values of the coulomb exchange ( hund ) coupling @xmath0 when the bandwidth ratio is small , and only beyond a critical value of @xmath0 when the bandwidth ratio is larger . finally , the orbital - selective mott phase is found , at zero - temperature , to be unstable with respect to an inter - orbital hybridization @xmath2 , and replaced at small @xmath2 by a state with a large effective mass ( and a low quasiparticle coherence scale ) for the narrower band .

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we examine whether the mott transition of a half - filled , two - orbital hubbard model with unequal bandwidths occurs simultaneously for both bands or whether it is a two - stage process in which the orbital with narrower bandwith localizes first ( giving rise to an intermediate ` orbital - selective ' mott phase ) . this question is addressed using both dynamical mean - field theory , and a representation of fermion operators in terms of slave quantum spins , followed by a mean - field approximation ( similar in spirit to a gutzwiller approximation ) . in the latter approach , the mott transition is found to be orbital - selective for all values of the coulomb exchange ( hund ) coupling @xmath0 when the bandwidth ratio is small , and only beyond a critical value of @xmath0 when the bandwidth ratio is larger . dynamical mean - field theory partially confirms these findings , but the intermediate phase at @xmath1 is found to differ from a conventional mott insulator , with spectral weight extending down to arbitrary low energy . finally , the orbital - selective mott phase is found , at zero - temperature , to be unstable with respect to an inter - orbital hybridization @xmath2 , and replaced at small @xmath2 by a state with a large effective mass ( and a low quasiparticle coherence scale ) for the narrower band . # 1i_#1 c#1#2#3#1_#2 # 3 # 1#2#3#1_#2 # 3^+ 0g_0 2o3v@xmath3o@xmath4 2@xmath5 1@xmath6 # 1d_1eff 2effd_2eff

in this article , we have studied whether the mott transition of a half - filled , two - orbital hubbard model with unequal bandwidths occurs simultaneously for both bands or whether it is a two - stage process in which the orbital with narrower bandwidth localizes first ( giving rise to an intermediate ` orbital - selective ' mott phase ) . in order to study this question , we have used two techniques . the first is a mean - field theory based on a new representation of fermion operators in terms of slave quantum spins . this method is similar in spirit to the gutzwiller approximation , and the slave - spin representation has a rather wide range of applicability to multi - orbital models . the second method is dynamical mean - field theory , using exact diagonalization and quantum monte - carlo solvers . the results of the slave - spin mean - field confirms several aspects of previous studies @xcite , and in particular the possibility of an orbital - selective mott transition . however , some of the conclusions differ from those of previous work . specifically , the slave - spin approximation suggests that a critical value of the bandwidth ratio @xmath120 exists , such that the mott transition is orbital - selective for arbitrary value of the coulomb exchange ( hund coupling ) @xmath0 when @xmath212 . when @xmath213 , @xmath0 has to be larger than a finite threshold for an osmt to take place . this suggests that the existence of an osmt is not simply related to the symmetry of the interaction term only . in particular , an intermediate phase is found for @xmath1 at small @xmath115 . we have studied whether dmft confirms these findings , and found that the main qualitative conclusions on the existence of the orbital - selective phase are indeed the same , but that the nature of the intermediate phase at @xmath1 is a rather subtle issue . indeed , the narrow band does not have the properties of a gapped mott insulator in this phase and displays finite spectral weight down to arbitrary low - energy . this is , for example , consistent with a pseudo - gap behaviour but requires further studies to be fully settled ( using e.g low - energy techniques such as the numerical renormalization group ) . we note also that our study emphasizes the key role of the exchange and ( on - site ) inter - orbital pair hopping terms in the coulomb hamiltonian in stabilizing the orbital - selective phase , in agreement with koga et al . @xcite . finally , we found that the orbital - selective mott phase is generically unstable with respect to an inter - orbital hybridization @xmath2 . in the presence of such a term , two possible phases are obtained , depending on the strength of @xmath7 and @xmath2 . either the narrow orbital acquires a large ( but finite ) effective mass , corresponding to a heavy - fermion metallic state . or the system is an insulator with a gap . this insulator differs from the mott insulator at @xmath181 since it has a singlet ground - state . this is due to screening processes , involving both kondo exchange and the formation of an on - site molecular ( bonding ) level . whether one has in fact two different insulating phases separated by a phase transition ( each phase being dominated by one of these screening processes ) -as obtained by slave - spin mean - field- , or whether one has a simple crossover @xcite is an open question which deserves further study . of course , at intermediate temperature ( above the quasiparticle coherence scale of the narrower band , but below that of the wider band ) , a physics similar to the orbital - selective mott phase can be recovered even in the presence of a finite hybridization . this orbital - selective heavy - fermion state might be relevant to the physics of ca@xmath9sr@xmath10ruo@xmath11 . this is indeed supported by the recent angular magnetoresistance oscillations experiments of balicas et al . @xcite . during the completion of this paper , we learned of the work by m. ferrero , f. becca , m. fabrizio and m. capone , reaching similar conclusions . we are grateful to f. becca , m. fabrizio and m. capone for discussions . a.g acknowledges discussions with s. florens and n. dupuis on the slave - spin representation , at an early stage of this work . we are grateful to a. lichtenstein for help with ed calculations in the multi - orbital context . we also thank a. koga , n. kawakami , g. kotliar , t.m . rice and m. sigrist for useful discussions . finally , we thank the referees for their constructive comments . this research was supported by cnrs and ecole polytechnique and by a grant of supercomputing time at idris orsay ( project 051393 ) . b. a. jones , c. m. varma , and j. w. wilkins , _ phys . _ 61 , 125 ( 1988 ) ; b. a. jones and c. m. varma , _ phys.rev . b _ 40 , 324 ( 1989 ) ; i. affleck and a. w. w. ludwig , phys . 68 , 1046 ( 1992 ) ; i. affleck , a. w. w. ludwig , and b. a. jones , phys . b 52 , 9528 ( 1995 ) .

we examined the vsnet light curve of the unusual su uma - type dwarf nova v503 cyg which is known to show a short ( 89 d ) supercycle length and exceptionally small ( a few ) normal outbursts within a supercycle . in 19992000 , v503 cyg displayed frequent normal outbursts with typical recurrence times of 79 d. the behavior during this period is characteristic to an usual su uma - type dwarf nova with a short supercycle length . on the other hand ,

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we examined the vsnet light curve of the unusual su uma - type dwarf nova v503 cyg which is known to show a short ( 89 d ) supercycle length and exceptionally small ( a few ) normal outbursts within a supercycle . in 19992000 , v503 cyg displayed frequent normal outbursts with typical recurrence times of 79 d. the behavior during this period is characteristic to an usual su uma - type dwarf nova with a short supercycle length . on the other hand , v503 cyg showed very infrequent normal outbursts in 20012002 . some of the superoutbursts during this period were observed shorter than usual . the remarkable alternations of the outbursting states in v503 cyg support the presence of mechanisms of suppressing normal outbursts and premature quenching superoutbursts , which have been proposed to explain some unusual su uma - type outbursts . the observed temporal variability of the suppressing / quenching mechanisms in the same object suggests that these mechanisms are not primarily governed by a fixed system parameter but more reflect state changes in the accretion disk .

er uma stars are a still enigmatic small subgroup of su uma - type dwarf novae [ for a review of dwarf novae , see @xcite ] , which have extremely short supercycle lengths ( @xmath0 the interval between successive superoutbursts ) of 1950 d [ for a review , see @xcite ] and regular occurrence of superoutbursts . only five definite members have been recognized up to now : er uma ( @xcite , @xcite , @xcite ) ; v1159 ori ( @xcite , @xcite ) ; rz lmi ( @xcite , @xcite ) ; di uma ( @xcite ) ; and ix dra ( @xcite ) . some helium - transferring cataclysmic variables have become recognized as helium counterparts " of er uma stars [ cr boo : @xcite ; v803 cen : @xcite , @xcite ] . from a theoretical side , er uma stars have been understood as a smooth extension of normal su uma - type dwarf nova toward higher mass - transfer rates ( @xmath1 ) @xcite . the exact origin of such a high mass - transfer rate is still a mystery . even considering a higher mass - transfer rate , the shortest period systems ( rz lmi and di uma ) are difficult to explain without a special mechanism of prematurely quenching a superoutburst @xcite . in recent years , there have been an alternative attempt to explain the er uma - type phenomenon . @xcite tried to explain the er uma - type phenomenon by considering a decoupling between the thermal and tidal instabilities [ see @xcite for details of the thermal - tidal instability model ] under extremely small binary mass - ratio ( @xmath2=@xmath3/@xmath4 ) conditions . @xcite speculated that repeated post - superoutburst rebrightenings in wz sge - type dwarf novae ( hereafter wz sge stars ) or large - amplitude su uma - type dwarf novae ( e.g. @xcite ; see @xcite for a recent observational review of wz sge - type stars ) . @xcite tried to explain er uma - type phenomenon by ( rather arbitrary ) introducing an inner truncation of the accretion disk and irradiation on the secondary star on a numerical model developed by @xcite . @xcite further tried to explain the unification idea by @xcite using the same scheme as in @xcite . although the results partly reproduced the characteristics of er uma stars and wz sge stars , they failed to quantitatively reproduce the light curves of these dwarf novae . from the observational side , the existence of a gap between distributions of er uma stars and usual " su uma - type dwarf novae has been a challenge . the shortest known @xmath0 in usual su uma - type dwarf novae had been 130 d ( yz cnc , see also table 1 in @xcite ) at the time of the initial proposition of er uma stars . although further works have slightly shortened this minimum @xmath0 [ ss umi : 84.7 d , @xcite ; bf ara : 83.4 d , @xcite ] , there still remains a undisputed gap . in addition to these usual su uma - type dwarf novae with the shortest @xmath0 s , there exists a seemingly different population of su uma - type dwarf novae with short @xmath0 s , but with infrequent normal outbursts . v503 cyg [ @xmath0 = 89 d , only a few normal outbursts in a supercycle @xcite ] and ci uma [ @xmath5 140 d , infrequent normal outbursts @xcite ; @xmath0 variable ? @xcite ] are the best - known examples . the relation , however , between these objects and er uma stars ( and short @xmath0 usual su uma - type dwarf novae ) are unknown . in most recent years , some instances of strong @xmath0 variations have been reported in er uma stars ( @xcite , @xcite ) . in this letter , we report on the dramatic changes in the outburst properties in v503 cyg .

v503 cyg showed very infrequent normal outbursts in 20012002 . some of the superoutbursts during this period were observed shorter than usual . the remarkable alternations of the outbursting states in v503 cyg support the presence of mechanisms of suppressing normal outbursts and premature quenching superoutbursts , which have been proposed to explain some unusual su uma - type outbursts . the observed temporal variability of the suppressing / quenching mechanisms in the same object suggests that these mechanisms are not primarily governed by a fixed system parameter but more reflect state changes in the accretion disk .

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astro-ph0209233

we examined the vsnet light curve of the unusual su uma - type dwarf nova v503 cyg which is known to show a short ( 89 d ) supercycle length and exceptionally small ( a few ) normal outbursts within a supercycle . in 19992000 , v503 cyg displayed frequent normal outbursts with typical recurrence times of 79 d. the behavior during this period is characteristic to an usual su uma - type dwarf nova with a short supercycle length . on the other hand , v503 cyg showed very infrequent normal outbursts in 20012002 . some of the superoutbursts during this period were observed shorter than usual . the remarkable alternations of the outbursting states in v503 cyg support the presence of mechanisms of suppressing normal outbursts and premature quenching superoutbursts , which have been proposed to explain some unusual su uma - type outbursts . the observed temporal variability of the suppressing / quenching mechanisms in the same object suggests that these mechanisms are not primarily governed by a fixed system parameter but more reflect state changes in the accretion disk .

in the standard disk instability model , the recurrence time of normal outbursts ( @xmath12 ) is mainly governed by the diffusion process , while @xmath0 represents the increasing rate of net angular momentum in the accretion disk @xcite . if the quiescent viscosity parameter has a fixed value between various su uma - type dwarf novae , both @xmath12 and @xmath0 are unique functions of @xmath1 @xcite . this relation has been observationally confirmed in most of su uma - type stars @xcite . v503 cyg apparently violates this relation in its low frequency of normal outbursts ( figure [ fig : lc ] , upper panel ) , and several other stars ( v344 lyr , sx lmi ) have been proposed to be analogous to v503 cyg ( @xcite , @xcite ) . there must be an unknown suppression mechanism of normal outbursts in these systems . in 19992000 , v503 cyg showed a very frequent occurrence of normal outbursts ( minimum @xmath13 79 d , figure [ fig : lc ] , middle panel ) . this @xmath12 is just what is expected for a @xmath0 = 89 d usual su uma - type dwarf nova @xcite . this fact indicates that the usually outbursting su uma - type state and unusually outbursting ( in the sense of low frequency of normal outbursts ) v503 cyg - type state are interchangeable . since @xmath0 during this period was not appreciably different from the canonical @xmath0 = 89 d , there should have not been an appreciable change in the @xmath1 . the suppression mechanism of normal outbursts must have been somehow unlocked " during this period . in 20012002 , v503 cyg showed another different aspect ( figure [ fig : lc ] , lower panel ) . during this period , the number of normal outbursts in a supercycle dramatically decreased to @xmath141 . there is some hint of alternating occurrence of a superoutburst and a normal outburst with a period of 4080 d. such a sequence of outbursts is only known in rarely outbursting su uma - type dwarf novae [ cf . sw uma , v844 her cf . @xcite for a discussion ] , and is unprecedented in short @xmath0 systems . during this period , some normal outbursts have comparable peak magnitudes to those of superoutbursts . some of superoutbursts showed rather short durations , which seems to be incompatible with a high @xmath1 necessary to reproduce the short @xmath0 @xcite . these findings suggest that premature quenching of superoutbursts , as proposed by @xcite and @xcite , indeed occurred during this period , although v503 cyg ( orbital period = 0.0757 d ) is unlikely to have a small @xmath2 required in @xcite and @xcite . the overall light curve more or less resembles that of ci uma ( @xcite , @xcite ) . although exact mechanisms have not been yet identified , the present remarkable alternations between the outbursting states in v503 cyg support the presence of mechanisms of suppressing normal outbursts and premature quenching superoutbursts . the most important finding is that the effects of these mechanisms are temporarily variable even in the same object , and are not a fixed character of a certain system . this finding suggests that the shortest @xmath0 usual su uma stars and unusual v503 cyg - like stars can represent different aspects of the same system . among er uma stars , di uma can be a similar system with systematic state changes @xcite . the observed temporal variability of the suppressing / quenching mechanisms in the same object suggests that these mechanisms are not primarily governed by a fixed system parameter [ i.e. mass of the white dwarf @xcite ; @xmath2 @xcite etc . ] but more reflect state changes in the accretion disk . we are grateful to many amateur observers for supplying their vital visual and ccd estimates via vsnet . this work is partly supported by a grant - in - aid ( 13640239 , tk ) from the japanese ministry of education , culture , sports , science and technology . part of this work is supported by a research fellowship of the japan society for the promotion of science for young scientists ( mu ) .

we abridge fragmentary parts of the literature of embeddings , putting the campbell magaard theorem into context . we look at the shiromizu maeda we formulate timelike ( brane ) versions of the thin sandwich conjecture . we point out how the braneworld geodesic postulates lead to futher difficulties with the notion of singularities than in gr where these postulates are simpler .

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gr-qc0309063

we explore some foundational issues regarding the splitting of @xmath0-dimensional einstein field equations ( efe s ) with respect to timelike and spacelike ( @xmath0 - 1)-dimensional hypersurfaces , first without and then with thin matter sheets such as branes . we begin to implement methodology , that is well - established for the gr cauchy and initial value problems ( cp and ivp ) , in the new field of gr - based braneworlds , identifying and comparing many different choices of procedure . we abridge fragmentary parts of the literature of embeddings , putting the campbell magaard theorem into context . we recollect and refine arguments why york and not elimination methods are used for the gr ivp . we compile a list of numerous mathematical and physical impasses to using timelike splits , whereas spacelike splits are known to be well - behaved . we however pursue both options to make contact with the current braneworld literature which is almost entirely based on timelike splits . in our study of timelike splits , we look at the shiromizu maeda sasaki braneworld by means of reformulations which emphasize different aspects from the original formulation . we show that what remains of the york method in the timelike case generalizes heuristic bulk construction schemes . we formulate timelike ( brane ) versions of the thin sandwich conjecture . we discuss whether it is plausible to remove singularities by timelike embeddings . we point out how the braneworld geodesic postulates lead to futher difficulties with the notion of singularities than in gr where these postulates are simpler . having argued for the use of the spacelike split , we study how to progress to the construction of more general data sets for spaces partially bounded by branes . boundary conditions are found and algorithms provided . working with ( finitely ) thick branes would appear to facilitate such a study . * pde system approach to large extra dimensions + + * electronic address : eda@maths.qmw.ac.uk , reza@maths.qmul.ac.uk pacs numbers : 04.20ex , 04.50+h

a great deal of effort has recently gone into the study of higher - dimensional models as unified theories of gravity and fundamental matter fields . the original interest in such models in kaluza klein ( kk ) theory @xcite was revived by the important role of dimension 11 in supergravity @xcite and more recently by superstring theory @xcite and m - theory @xcite , which favour spacetimes of dimension 10 and 11 respectively . the usual ( kk ) argument for the apparent 4-dimensionality of spacetime is that the extra dimensions are compactified i.e curled up sufficiently small so as not to conflict with observation . however , recently much attention has been placed instead on string - theory - inspired models with large extra dimensions @xcite in which most of the physics is confined or closely - bound to a lower - dimensional braneworld surrounded by a higher - dimensional bulk . though motivated by superstring and m - theories , many of these models @xcite are in fact formulated within the framework of ( higher - dimensional ) general relativity ( gr ) . among these are : 1 ) the second randall sundrum scenario @xcite in which the graviton is tightly - bound to the brane by the curvature due to the warping of the bulk metric , which is pure anti - desitter ( ads ) . 2 ) a more general scheme of shiromizu , maeda and sasaki ( sms ) @xcite , in which the 4-dimensional einstein field equations ( efe s ) are replaced by 4-d `` braneworld efe s '' ( befe s ) , which are not closed since there is a ` dark energy ' weyl tensor term , knowledge of which requires solving also for the bulk . the interpretational difficulties due to this constitute the ` weyl problem ' . the other main distinctive feature of sms s befe s is the presence of a term quadratic in the braneworld energy - momentum , which arises from the junction condition used @xcite . two important questions arise in consideration of such models . * q1 : * how should such models be built and interpreted consistently within the framework of gr ? this would require a careful underlying choice of conceptually - clear general framework , in the sense we discuss below . * q2 : * what exactly is the connection between such models and the underlying string / m theory ? more precisely , to what extent can the agreements or otherwise of predictions of such models with observations be taken as support or disagreement with such theories ? here we concentrate on the first question and make a comparative study of the general schemes that have been employed in the literature in order to construct the bulks which surround branes . such a comparative study requires a sufficiently general common language . we use that of _ p.d.e problems , which consist of both the p.d.e system to be solved in some region of a manifold , and data prescribed on ( portions of ) the boundary of this region . for ( @xmath1 , @xmath2 ) a spacetime of dimension @xmath3 with @xmath2 time dimensions , we denote the problem involving the addition of an extra dimension by ( @xmath1 , @xmath2 ; @xmath4 ) , where @xmath5 if the new dimension is spacelike or @xmath6 if it is timelike . this is the generalization of the gr cauchy problem ( cp ) @xcite based on the arbitrary ( @xmath1 , @xmath2 ; @xmath4 ) generalization of the arnowitt misner @xcite split of the metric ( sec 2.1 ) and hypersurface geometry ( sec 2.2 ) . its simple signature - independent features are pointed out in sec 2.3 and the crucial dependence of many of the harder features on the usual cp signatures @xmath7 , @xmath8 is discussed in sec 2.4 . as is well - known , the gr cp presupposes the existence of the data . thus one is in fact considering a two - step process , the other step being the construction of the data on the ( @xmath1 , @xmath2 ) manifold i.e the generalization of the gr initial value problem ( ivp ) @xcite . this is discussed in sec 3 . _ our framework permits a profitable look at a number of recent topics . the aim is to consider gr - based models containing thin matter sheets such as branes or domain walls . we shall compare two broad schemes that have been proposed to construct bulks : the ( 3 , 1 ; 1 ) construction @xcite starting from information on a ( 3 , 1 ) spacetime hypersurface ( usually the brane ) and the ( 4 , 0 ; 1 ) construction @xcite starting by the construction of data on a ( 4 , 0 ) spatial hypersurface . however , first we emphasize that one should grasp the fundamental arguments and results which before the specializing to the thin matter sheet models . a few ideas about the general unspecialized framework recently arose in the literature on ( generalizations of ) the campbell magaard arbitrary - signature embedding theorem @xcite ( see sec 2.3 ) . however , we find it far more profitable instead to adopt the generalized gr cp ivp point of view since this literature is by far more developed and thus a far greater source of well - documented pitfalls and carefully thought - out techniques which avoid them . we identify the embedding step of the campbell magaard theorem with the well - known signature - independent parts of the gr cp in sec 2.3 . but the harder @xmath7 , @xmath8 specific parts of the gr cp strongly suggest that ( 4 , 0 ; 1 ) schemes should be favoured over ( 3 , 1 ; 1 ) ones on very general grounds : well - posedness and causality ( sec 2.4 ) . furthermore , magaard s data construction method @xcite ( sec 3.1 ) does not compare favourably with york s data construction @xcite ( sec 3.2 ) , and its application to @xmath9 , @xmath5 has further conceptual difficulties . in this light we look at the extent to which york s method is adaptable to @xmath9 , @xmath5 , and also consider the thin sandwich method @xcite in this context ( sec 3.3 ) . we then introduce thin matter sheets in sec 4 , and study the ( 3 , 1 ; 1 ) schemes with thin matter sheets , recollecting the derivation of the junction conditions ( sec 4.1 ) , and showing how the sms formulation ( sec 4.2 ) may be reformulated in a large number of ways using geometrical identities that interchange which terms are present in the braneworld efe s . this is illustrated by the formulation in sec 4.3 which directly parallels the gr cp formulation and thus makes no explicit use of the weyl term , and by formulations in sec 4.4 in which the quadratic term has been re - expressed entirely in terms of derivatives off the brane . these formulations are used to clarify a number of aspects of the ` weyl problem ' , in particular to argue for the study of the full brane - bulk system . further aspects of such formulations are discussed in sec 4.5 . the implications of sec 2.4 for thin matter sheets , the heuristic use and limitations of the ( 3 , 1 ) york method with thin matter sheets , and formulations of thin matter sheet thin sandwich conjectures are discussed in sec 4.6 . having gathered arguments against using ( 3 , 1 ; 1 ) schemes in secs 2.4 and 3 , we further consolidate this viewpoint by arguing in sec 5 against a suggested virtue of ( 3 , 1 ; 1 ) schemes @xcite : their use to remove singularities . in addition to using the framework of sec 2 , the corresponding study of geodesics is also used here , which presents further conceptual complications relevant to thin matter sheet models . these follow from the ( 3 , 1 ) geodesics not usually being among the ( 4 , 1 ) geodesics . in sec 6 , we continue the study of the ( @xmath10 , 0 ; 1 ) scheme favoured by our arguments , in the presence of both thin and thick ( i.e finitely thin ) matter sheets . we begin in sec 6.1 by providing a hierarchy of very difficult general thin matter sheet problems in which the main difficulties stem from low differentiability and details about the asymptotics . within this class of problems we identify how the far more specific scenarios currently studied emerge as more tractable cases , and thus identify which as - yet unjustified assumptions such studies entail . the ivp step , of use in the study of how braneworld black holes extend into the bulk ( the ` pancake ' versus ` cigar ' debate @xcite ) , involves fewer of such assumptions . thus in this paper we restrict attention to the ( @xmath10 , 0 ) data construction problem ( sec 6.2 ) , which we apply to thin matter sheets in sec 6.3 and more straightforwardly to thick matter sheets in sec 6.4 .. sec 7 discusses * q2 and contains the conclusions of this paper as regards * q1 . * *

we recollect and refine arguments why york and not elimination methods are used for the gr ivp . we show that what remains of the york method in the timelike case generalizes heuristic bulk construction schemes . having argued for the use of the spacelike split , we study how to progress to the construction of more general data sets for spaces partially bounded by branes .

m

gr-qc0309063

we explore some foundational issues regarding the splitting of @xmath0-dimensional einstein field equations ( efe s ) with respect to timelike and spacelike ( @xmath0 - 1)-dimensional hypersurfaces , first without and then with thin matter sheets such as branes . we begin to implement methodology , that is well - established for the gr cauchy and initial value problems ( cp and ivp ) , in the new field of gr - based braneworlds , identifying and comparing many different choices of procedure . we abridge fragmentary parts of the literature of embeddings , putting the campbell magaard theorem into context . we recollect and refine arguments why york and not elimination methods are used for the gr ivp . we compile a list of numerous mathematical and physical impasses to using timelike splits , whereas spacelike splits are known to be well - behaved . we however pursue both options to make contact with the current braneworld literature which is almost entirely based on timelike splits . in our study of timelike splits , we look at the shiromizu maeda sasaki braneworld by means of reformulations which emphasize different aspects from the original formulation . we show that what remains of the york method in the timelike case generalizes heuristic bulk construction schemes . we formulate timelike ( brane ) versions of the thin sandwich conjecture . we discuss whether it is plausible to remove singularities by timelike embeddings . we point out how the braneworld geodesic postulates lead to futher difficulties with the notion of singularities than in gr where these postulates are simpler . having argued for the use of the spacelike split , we study how to progress to the construction of more general data sets for spaces partially bounded by branes . boundary conditions are found and algorithms provided . working with ( finitely ) thick branes would appear to facilitate such a study . * pde system approach to large extra dimensions + + * electronic address : eda@maths.qmw.ac.uk , reza@maths.qmul.ac.uk pacs numbers : 04.20ex , 04.50+h

several methods have been proposed for the data construction step , including the elimination and conformal methods . the former methods are intuitive in that the prescribed quantities are all physical , but have a number of undesirable mathematical features . in contrast , lichnerowicz s conformal method @xcite is counterintuitive , since some of the prescribed quantities are unphysical , but exploits the mathematical properties of the constraint system in order to decouple it . bruhat s argument @xcite was in favour of the latter , however , some of her criticisms need to be elaborated upon to cover magaard s elimination method @xcite . sec 3.1 covers this question and provides further criticisms in the @xmath9 case . in sec 3.2 , we discuss the desirable features of york s development of the conformal method @xcite , paying careful attention to the signature - dependent ones . the thin sandwich and hamiltonian methods are briefly discussed in sec 3.3 . an example of this method of data construction is employed in the last part of the cm result ( `` magaard s method '' @xcite ) . we discuss and compare this method with the standard method used for the gr ivp . magaard s method ( 1963 ) treats the lower - dimensional metric @xmath76 as a known . here we use a more transparent notation than magaard s , in which the gauss constraint ( [ gauss ] ) takes the form g^abcdk_abk_cd + r + 2= 0 where @xmath77 is the ( undensitized ) inverse of dewitt s supermetric @xcite . this is then split w.r.t some coordinate @xmath78 . then @xmath79 can be isolated as the solution of the linear equation 2k_11g^11uwk_uw + g^1u1wk_1uk_1w + g^uwxyk_uwk_xy = - ( r + 2 ) ( where @xmath80 , @xmath74 , @xmath81 , @xmath82 @xmath83 ) , provided that it is possible to divide by @xmath84 . thus @xmath79 is eliminated from the codazzi constraint ( [ cod ] ) , which is then treated as a p.d.e system for unknowns @xmath85 , some @xmath86 component denoted @xmath87}. on the face of it , this system satisfies the criteria for the ck theorem if one treats @xmath88 \{all the components of @xmath89 bar @xmath79 , @xmath90 and @xmath87 } as known functions on @xmath78 and provided that the p.d.es coefficients and the data are analytic . so a unique solution exists . the ( generalized ) cm result @xcite groups this and the local existence of a unique evolution " to form the statement that a ( @xmath1 , @xmath2 ) spacetime with prescribed analytic metric @xmath76 may be embedded with an extra space or time dimension for any analytic functional form of the energy - momentum tensor . this statement suggests an incredibly rich collection of embeddings exist . however , we must point out that this is itself one of many difficulties associated with the cm result and its applicability , that we describe below . bruhat had already considered the above method in 1956 @xcite in the case of the gr ivp and pointed out a limitation on its validity . we find that her argument can be made for any signature or dimension : @xmath91 must be a function of at least one unknown , @xmath87 , so we have no control over whether it is zero . therefore we can not guarantee the validity of the elimination procedure for @xmath79 from the gauss constraint . although magaard @xcite finds a route round this problem , we find that this leads to two prices to pay later on . he starts with prescribed ` data for the data ' i.e values of @xmath92 on some @xmath93-dimensional set @xmath94 . the ` data for the data ' is validly picked so that @xmath95 on @xmath96 , whereupon by continuity there is a thin region @xmath97 within which it is guaranteed that @xmath95 . thus magaard s procedure produces strips of data to be used in the embedding step . the first price to pay is that in general we can not expect to be able to patch such strips together to make extended patches of data . for , since the strip construction ends where @xmath91 picks up a zero for some @xmath98 , while restarting the procedure with @xmath98 in place of @xmath99 is valid , the two data strips thus produced will have a discontinuity across @xmath98 . so what one produces is a collection of strips belonging to different possible global data sets . the evolution of each of these strips would produce pieces of different higher - dimensional manifolds . so one is _ not in fact saying that an empty ( @xmath10 + 1)-dimensional manifold surrounds any @xmath10-dimensional manifold . rather one is saying that any @xmath10-dimensional manifold can be cut up in an infinite number of ways ( choices of the @xmath78 coordinate ) into many pieces , each of which can be separately bent in an infinite number of ways ( corresponding to the freedom in choosing the components of @xmath17 in @xmath100 on each set of ` data for the data ' ) , and for each of these bent regions we can locally find a surrounding ( @xmath10 + 1)-dimensional manifold for every possible analytic function form of @xmath57 ( corresponding to the generalizability of the cm result ) . this apparent excess richness raises the question of physical significance of such a construction . _ magaard s method does not state enough assumptions to make it rigorous . first , how far does ` data for the data ' extend along @xmath99 ? clearly the topology of the @xmath10-dimensional manifold is an important input , for if it is not compact without boundary , there is a missing boundary or asymptotics prescription required . also the topology of the @xmath99 set itself has not been brought into consideration ( for example continuity is not guaranteed were this to contain loops ) . secondly , we specifically consider the ( @xmath10 , 0 ; 1 ) and ( @xmath1 , 1 ; 1 ) problems as separate cases , since we find that there are implicit ways in which signature plays a crucial role even for the cm result . for ( @xmath10 , 0 ; 1 ) one might worry that the data construction for a strip is flawed because the data problem in question is elliptic and hence naively requires a global treatment . however , we are able to dispel this worry once we treat york s method below . for ( @xmath1 , 1 ; 1 ) , the use of the strip @xmath97 as evolutionary " data is generally invalidated by the information leak construction in fig . 5 , unless one has had the luck to construct a full global data set . this would , however , require the building of the data encountering 1 ) no zeros of @xmath91 ( which is thus the second price to pay ) , 2 ) no asymptotic problems . thus in general there is a severe problem with building ( 4 , 1 ) spacetimes from ( 3 , 1 ) ones using the cm method . thirdly , magaard s method lacks any @xmath10-dimensional general covariance since it involves the choice of a coordinate @xmath78 and the elimination of a @xmath101-component of a tensor . the arguments of lichnerowicz @xcite and bruhat @xcite led to the gr ivp taking a very different route from the above sort of brute - force elimination methods . the conformal method of lichnerowicz and york is instead preferred . this leads us to ask to what extent conformal methods can be adapted both to heuristic and to general constructions for e.g ( @xmath1 , 1 ; @xmath4 ) data . therefore our treatment below is as far as possible for the general ( @xmath1 , @xmath2 ; @xmath4 ) case . in the conformal method , one chooses to treat @xmath102 as a known metric which is moreover not the physical metric but rather only conformally - related to it by _ ij = ^h_ij . we work in terms of @xmath103 and @xmath104 , and permit @xmath105 , @xmath106 and @xmath34 to conformally transform according to ^ij = ^- 2k^ij , ^i = ^ , = ^ , whilst crucially demanding the constant mean curvature ( cmc ) condition k = holds and is conformally - invariant . one then demands that the ( raised ) codazzi constraint ( [ acod ] ) is to be conformally - invariant . since _ = ^- 2 one requires that - = - 2= . [ twiddle ] furthermore one demands that the conformally - transformed gauss equation r - ( n - 1 ) + ( n - 1 ) ( 1 - ) + ( m^2- - ^2^ + 2^+ ) = 0 [ prolich ] ( where @xmath107 and @xmath108 is some york extrinsic dynamical variable " proportional to @xmath104 ) is simplified by being made to contain no @xmath109 term , so that @xmath110 , @xmath111 and @xmath112 [ by making use of ( [ twiddle ] ) ] . now , regardless of ( @xmath1 , @xmath2 ; @xmath4 ) , provided that the ( @xmath10 + 1)-dimensional dec is to be preserved by the conformal transformation , @xmath113 must conformally - transform like @xmath114 , implying @xmath115 . then ( [ prolich ] ) becomes the ( @xmath1 , @xmath2 ; @xmath4 ) version of the lichnerowicz equation d^2= - ( -r - m^-4 + ^2^ - 2 ^ -2 ) [ ndlich ] for the conformal factor @xmath116 . we observe that a number of the very attractive features of the york method are ( @xmath1 , @xmath2 ; @xmath4)-independent . first , it decouples the solution of the codazzi constraint from the solution of the gauss constraint . the former proceeds by a traceless - transverse ( tt)traceless - longitudinal ( tl ) splitting @xcite k^ij = k^ij + k^ij , d_ik^ij 0 , k^ij = 2(d^(iw^j ) - h^ijd_cw^c ) ( for some vector potential @xmath117 ) , which along with the trace - tracefree split is conformally - invariant and thus unaffected by the solution of the latter , which has become the p.d.e ( [ ndlich ] ) for the conformal factor . the simplest case is @xmath118 , @xmath119 which at most requires solution of a first - order linear equation . second , the choice in using the scale - scalefree decomposition of the metric and the trace - tracefree and tt tl decompositions of @xmath89 are all decompositions into irreducibles and thus @xmath10-dimensionally generally - covariant choices , a decided advantage over the magaard method . third , one can attempt to preserve the cmc condition away from the ` initial ' hypersurface @xmath11 , which can be done provided that the equation d^2 + ( k^2 - r - ) = can be solved for the lapse @xmath120 . this choice of lapse is the cmc slicing gauge . this deliberately defocusses geodesics , thus by definition preventing the breakdown of the coordinate system due to caustic formation @xcite , and so enhancing the practical longevity of the evolution . however , york s method is not absolutely general , for some spacetimes have no cmc slice to identify with @xmath11 in the first place , and in others the cmc slicing can not be maintained to cover the whole spacetime . furthermore , these results depend on the asymptotics assumed . however , in the usual ( 3 , 0 ; 1 ) case , this method ( and its variants ) is widely accepted as a practical method by the numerical relativity community , for example in the study of colliding compact astrophysical objects @xcite . of importance for the viability of this method in this application , recent evidence suggests that problems involving gravity wave emission can be treated thus @xcite . however , some of the other attractive features used to gain control in the york method are only known to occur for the @xmath7 case and have mainly been studied in depth for the compact without boundary and asymptotically - flat cases of ( 3 , 0 ) data construction . first , the study of the usual ( 3 , 0 ; 1 ) lichnerowicz equation has been based on its ellipticity ( and elliptic methods are absolutely not generalizable to the ` hyperbolic ' equations ) . the ( 3 , 0 ; 1 ) lichnerowicz equation is well - studied , including with most fundamental matter fields @xcite , and for sobolev spaces matching those then used in the gr cp @xcite . second , the study of the cmc slicing equation has been based on its ellipticity , so the theory of existence of cmc slicings @xcite is likely to be signature - dependent . third , the method depends on the asymptotics used and has only been studied in the ( 3 , 0 ) compact without boundary @xcite and asymptotically flat @xcite cases . fourth , for @xmath7 there is the useful property that certain local data patches can be proved to suffice for the treatment of an astrophysical problem , by building on the notion of dod . as mentioned , this sort of technique is also applicable to protect pieces of local data obtained by magaard s method on a ( @xmath1 , 0 ) hypersurface . investigation of whether the @xmath9 ` wave lichnerowicz equation ' has good existence and uniqueness properties could be interesting . the natural setting for this is as a cauchy problem ( for even the 2-dimensional wave equation is ill - posed as a dirichlet problem ) . assuming that there exists a cauchy surface in the ( 3 , 1 ) spacetime sense , one can attempt forward and backward evolution to produce a global data set ( assuming also that the decoupled procedure for finding @xmath121 also yields a global solution ) . one must remember however that the next stage is still to be a sideways cauchy problem . whilst this suggested procedure for the data could conceivably produce global data sets in some subcases and thus avoid the information leak problem , the other difficulties we described in sec 2.4 remain . therefore in our view the ` wave lichnerowicz equation ' is unlikely to be suitable as a general method . we favour instead the ( 4 , 0 ; 1 ) approach in sec 6 . that said , the ` wave lichnerowicz equation ' may still serve as the basis of a useful heuristic method . we consider this in sec 4.7 . we finally discuss the thin sandwich method and why we do not provide an ( @xmath1 , @xmath2 ; @xmath4 ) hamiltonian formulation . in gr the lapse may be _ algebraically eliminated from the action by use of its own variational equation to form a reduced baierlein sharp wheeler action @xcite . suppose that ( @xmath102 , @xmath122 ) is prescribed on a hypersurface along with @xmath34 and @xmath123 . the thin sandwich conjecture @xcite is that in reasonably general circumstances there exists a unique solution to solving the variational equation for the shift ( this equation replaces the codazzi constraint ) , as a differential equation for the shift itself . once this is done , the lapse may be reconstructed from the equation used to eliminate it , and the extrinsic curvature then follows from its definition . the lapse may then be reconstructed from the equation used to eliminate it , and the extrinsic curvature then follows from its definition ( [ ecd ] ) . _ we note that this procedure is ( @xmath1 , @xmath2 ; @xmath4)-independent . thus we pose the conjecture for general ( @xmath1 , @xmath2 ; @xmath4 ) . this is also considered for thin matter sheets in sec 4.7 . to date we are only aware of ( 3 , 0 ; 1 ) papers @xcite treating this conjecture , which contain some favourable and unfavourable results obtained mostly by use of elliptic methods . in fact , there are two variants of the conjecture : i ) the thick sandwich conjecture in which lower - dimensional metrics are prescribed on two nearby hypersurfaces . ii ) the thin sandwich conjecture proper , as stated above . a ( 3 , 1 ; 1 ) hamiltonian formulation is not provided because although it is insensitive to @xmath4 @xcite , it is sensitive to @xmath2 through the intimate involvement of the space of geometries . whilst the usual hamiltonian formulation is based on the space of riemannian geometries ( superspace ) @xcite , the space of semi - riemannian geometries is reported to be not even hausdorff @xcite .

sasaki braneworld by means of reformulations which emphasize different aspects from the original formulation . boundary conditions are found and algorithms provided . working with ( finitely ) thick branes would appear to facilitate such a study . * pde system approach to large extra dimensions + + * electronic address : eda@maths.qmw.ac.uk , reza@maths.qmul.ac.uk pacs numbers : 04.20ex , 04.50+h

m

gr-qc0309063

we explore some foundational issues regarding the splitting of @xmath0-dimensional einstein field equations ( efe s ) with respect to timelike and spacelike ( @xmath0 - 1)-dimensional hypersurfaces , first without and then with thin matter sheets such as branes . we begin to implement methodology , that is well - established for the gr cauchy and initial value problems ( cp and ivp ) , in the new field of gr - based braneworlds , identifying and comparing many different choices of procedure . we abridge fragmentary parts of the literature of embeddings , putting the campbell magaard theorem into context . we recollect and refine arguments why york and not elimination methods are used for the gr ivp . we compile a list of numerous mathematical and physical impasses to using timelike splits , whereas spacelike splits are known to be well - behaved . we however pursue both options to make contact with the current braneworld literature which is almost entirely based on timelike splits . in our study of timelike splits , we look at the shiromizu maeda sasaki braneworld by means of reformulations which emphasize different aspects from the original formulation . we show that what remains of the york method in the timelike case generalizes heuristic bulk construction schemes . we formulate timelike ( brane ) versions of the thin sandwich conjecture . we discuss whether it is plausible to remove singularities by timelike embeddings . we point out how the braneworld geodesic postulates lead to futher difficulties with the notion of singularities than in gr where these postulates are simpler . having argued for the use of the spacelike split , we study how to progress to the construction of more general data sets for spaces partially bounded by branes . boundary conditions are found and algorithms provided . working with ( finitely ) thick branes would appear to facilitate such a study . * pde system approach to large extra dimensions + + * electronic address : eda@maths.qmw.ac.uk , reza@maths.qmul.ac.uk pacs numbers : 04.20ex , 04.50+h

first , we present a simple instance common in the higher - dimensional literature to which sec 2.1 - 3 is applicable . the _ warpfactor split @xcite g_cd = ( _ ll ^2(x^ , z ) & 0 + 0 & w(x^ , z)f_(x^ ) ) , w(x^ , 0 ) = 1 [ wan ] is a simple subcase of the @xmath23-dynamics scheme , in which the metric is allowed to @xmath23-evolve only in its scale , away from the @xmath124 hypersurface where it is taken to be known . then ( [ ecd ] ) leads to @xmath125 which gives the equation = - [ wftr ] for the warpfactor . for example , using the ansatz @xmath126 in ( [ wftr ] ) gives an exponential randall sundrum type warpfactor . whereas the split ( [ wan ] ) does not cover very many cases , our scheme exhibits generalizations for it : to permit the whole metric to evolve and to recognize the gauge freedom in @xmath127 , which should ideally be used to separate coordinate effects from true physics in the spirit of @xcite . full , overtly @xmath23-dynamical schemes are used in particular examples for domain walls @xcite , braneworld black holes ( such as for the pancake or cigar bulk horizon shape problem @xcite ) and for braneworld stars @xcite . whereas in the randall sundrum model the higher and lower - dimensional cosmological constants balance out leaving vacuum ( minkowski ) on the brane , more generally a brane would consist of a thin sheet of matter a junction . we study such [ shiromizu maeda sasaki ( sms)-type ] braneworlds below , starting first however with a careful recollection of where the underlying israel junction conditions come from . assume that we have a ( @xmath0 1)-dimensional thin matter sheet in a @xmath0-dimensional bulk . in all cases considered , the bulk s extra dimension is spatial ( @xmath5 ) . our discussion follows @xcite most closely whilst keeping the unraised index positions of israel s original work @xcite . whereas the requirement of well - defined geometry dictates that the metric is continuous across the thin matter sheet yielding the junction condition ( j.c ) ^+_- f_^+ - f_^- = 0 , [ jcf ] discontinuities in certain derivatives of the metric are permissible . consider then the 3 projections of the einstein tensor @xmath128 . we use the @xmath5 cases of the codazzi and gauss constraints ( [ cod ] ) and ( [ gauss ] ) for @xmath129 and @xmath130 respectively . for @xmath131 , the following construction is used . one begins by writing down the contracted gauss equation ( [ contg ] ) and subtracts off @xmath132 times the doubly - contracted gauss equation ([gpp ] ) : c r _ + - f _ c - + + c r _ = + r_f _ c r _ + -f _ c - + + c k k _ + k _ ^k _ + f_. [ bfbwefes ] the following steps are then applied . step 1 : the ricci equation ( [ thirdproj ] ) is used to remove all the @xmath133 . step 2 : the contracted ricci equation ( [ tpcont ] ) is used to remove all the @xmath55 . thus ( c r _ + - f _ ) c - + + c + f _ = ( c r _ + -f _ ) c - + + c k k _ + k _ ^k _ + f_. [ step0 ] this is then rearranged to form the `` gr cp '' geometrical identity _ = g _ - k k _ + 2 k _ ^k _ + f _ + . [ grcpid ] @xmath134 _ -^+ = 0 , [ g_]_-^+ = 0 , [ jc0 ] _ -^+ = [ k _ - f_k]^+_- . [ primjn ] the derivation of this last equation makes use of normal coordinates ( in which case the hypersurface derivative @xmath135 becomes the normal derivative @xmath136 ) and the rearrangement to the ` israel ' geometrical identity _ = g _ + k k _ + 2 k _ ^k _ + f _ + ( k _ - f_k ) [ israel ] via the definition of extrinsic curvature ( [ ecd ] ) to form the complete normal derivative @xmath137 . step 3 : one then further assumes that the ( 4 , 1)-dimensional efe s @xmath138 hold . if one then additionally @xmath139 0 = y _ , 0 = y _ , [ jc0 m ] _ -^+ = ( y _ - f _ ) [ prez2 ] ( performing a trace - reversal to obtain the last equation ) . we next recall the method sms use to obtain their befe s @xcite . they begin by forming the ( 3 , 1)-dimensional einstein tensor @xmath140 just like we obtain ( [ bfbwefes ] ) above . sms then apply three steps to this equation . step s1 : using the definition of the weyl tensor , @xmath141 is replaced by the electric part of the weyl tensor , @xmath142 and extra terms built from the projections of @xmath143 . step s2 ( = step 3 of the above subsection ) : the ( 4 , 1)-dimensional efe s are then assumed , which permits one to exchange all remaining projections of @xmath143 for ( 4 , 1)-dimensional energy - momentum terms . only when this is carried out does ( [ bfbwefes ] ) become a system of field equations rather than of geometrical identities . we refer to the field equations at this stage as `` timelike hypersurface efe s '' ( thefe s ) , as opposed to the braneworld efe s which arise at the next stage . step s3 : a special subcase of thefe s are braneworld efe s ( befe s ) , which are obtained in normal coordinates by choosing the ( thin ) braneworld energy - momentum tensor ansatz _ ab = y_ab(z ) - g_ab , _ ab ( t_ab - f_ab ) , t_abz^a = 0 , [ bwem ] where @xmath144 is the energy - momentum of the matter confined to the brane . this is a specialization due to the specific presence of ( 3 , 1 ) and ( 4 , 1 ) cosmological constants @xmath33 and @xmath145 , and by @xmath145 being the only bulk contribution . a more precise formulation of this , and generalizations , are the subject of sec 4.5 . one then adopts the j.cs ( [ jcf ] ) , ( [ jc0 ] ) , and ( [ prez2 ] ) with the additional supposition of @xmath146 symmetry : - k _ _ ^+ = - k_^- _ = - ( y _ - f _ ) = - ( t _ - f _ ) , [ 41jc ] where the 5-dimensional gravitational constant @xmath147 has been made explicit . then sms s befe s read g _ = l^ _ + q^ _ - e _ , where @xmath148 and @xmath149 are the terms quadratic in , and linear together with zeroth order in @xmath150 respectively , given by q^ _ = _ 5 ^ 4 [ befe ] l_^ = -(+ ^2)f _ + t_. as opposed to the ( 3 , 1)-dimensional efe s , sms s befe s are not closed since they contain the unspecified electric part of the weyl tensor @xmath151 . although it also contains 15 equations , the sms befe gauss codazzi system is not equivalent to the ( 4 , 1)-dimensional efe s : indeed sms write down further third - order equations for the `` evolution '' away from the timelike brane of @xmath151 , by use of the @xmath23-derivative of the contracted gauss equation ( [ contg ] ) , bianchi identities and the ricci equation ( [ thirdproj ] ) . this then involves the magnetic part of the weyl tensor @xmath152 , the evolution " of which follows from further bianchi identities . this full brane - bulk sms system is then closed . step 4 : in practice , however , instead of the difficult treatment of this third - order system , other practitioners have often worked on the sms befe s alone . this involves either the ad hoc prescription of the functional form of @xmath151 ( sometimes taken to be zero ) . in fact it is often first decomposed according to a standard procedure @xcite . because the original functional form is unknown , the functional forms of each of the parts defined by the decomposition is also unknown . some of these parts are set equal to zero whereas other parts are taken to have other functional forms ( in particular a radiation fluid term ) . these terms are then argued to be small in the circumstances arising in the inflationary @xcite and perturbative @xcite treatments . however other interpretations may be possible . having dealt with @xmath151 in one of the above ways , the form ( 53 ) of @xmath153 is then often taken to be uniquely defined and the starting - point of many works on brane cosmology @xcite . however , sms s procedure is far from unique . it turns out that there are many reformulations of the befe arising from geometrical identities . each has a distinct split of the non - einsteinian befe terms into ` bulk ' and ` brane ' terms . whereas all these formulations are clearly equivalent , their use helps clarify how to interpret sms s braneworld . were one to truncate the ` bulk ' terms in each case ( in direct analogy with the usual practice of throwing away the weyl term ) , then the befe s obtained in each case would generally be inequivalent . the weyl term in sms s befe s has been the subject of much mystery . how should it be interpreted ? is it right to throw it away and if so under which circumstances ? we emphasize that our stance is broader than merely about what functional form is allocated to the weyl term ( e.g whether it is zero everywhere ) . it is about how formulations can be chosen in which the befe s are not explicitly formulated in terms of a weyl term . we first remove some misconceptions as to how sms s procedure leads to a befe containing a weyl term . does it have anything to do with the modelling of braneworld scenarios ? no , for the weyl term is already in the sms thefe before the braneworld energy - momentum ansatz is invoked . furthermore , all the procedures used in sms s method are independent of signature and dimension . thus this issue of a weyl term must have already arisen long ago in the study of the gr cp . so why is there no manifest weyl term piece in the gr cp formulation of the efe s ? the answer is simple . indeed , we have already seen the answer in sec 4.1 since it is fundamentally tied to how the crucial junction condition ( [ prez2 ] ) is obtained in the first place!. in the `` gr cp '' and israel procedures , _ one uses the ricci equation ( [ thirdproj ] ) to remove the @xmath154 term . if there is no early use of the ricci equation , one is left with @xmath151 in the thefe s , which requires later use of the ricci equation to `` evolve '' it . _ so there is a choice as to whether one formulates the befe s with or without an explicit weyl term . in the usual treatment of the split of the efe s ( sec 2.2 ) , one does not use an explicit weyl term . in the ( 4 , 1)-d case , this gives a well - understood system of 15 p.d.es in the variables @xmath155 . the option of using an explicit weyl term gives a considerably larger , more complicated system of p.d.es with variables @xmath155 , @xmath151 and @xmath156 . in fact a similar scheme known as the _ threading formulation @xcite is sometimes used in the usual ( 3 , 0 ; 1 ) application . the idea behind this formulation is to treat as primary the geodesic congruences perpendicular to the foliation rather than the foliation itself . one then uses only that information on the hypersurfaces that arrives along the impinging geodesic congruence , on the grounds that this is the physically - significant information . thus it is a ` deliberately incomplete system ' from the foliation perspective . whereas this and the sms formulation are similar in their use of weyl variables , the sms system does not appear to be a threading formulation . also , in any case the idea of having a deliberately partial system in the threading formulation is clearly tied to signature - specific physical reasons which do not carry over to the signature relevant to sms s equations . we also note that some other third - order reformulations of the @xmath157 split of the efe s are sometimes used to seek to cast the efe s into hyperbolic forms that manifestly have theorems associated with them @xcite . whereas this is precisely the sort of result that is spoiled by considering instead a sideways split , it serves to illustrate that what at first seems a ` mere reformulation ' of a set of equations can in fact be used to prove highly nontrivial theorems . so , whereas similar complicated formulations have been used elsewhere in the gr literature , sms s unstated motivation to have a complicated formulation does not coincide with the motivation elsewhere in the literature . below we bring attention to many reformulations of sms s system , so we ask : what is the motivation for the original sms formulation ? should the use of some simpler second - order formulation be preferred ? is sms s formulation or any other third- or second - order formulation singled out by good behaviour , either in general or for some particular application ? _ also , from first principles the sms procedure to obtain their befe is quite complicated . for , since they use the j.c obtained by the israel procedure , their procedure actually entails beginning with the whole israel procedure ( steps 1 to 3 of sec 4.1 ) , and then choosing to reintroduce @xmath158 and @xmath55 by reverse application of steps 1 and 2 . this is followed by the weyl rearrangement ( step s1 ) , the use of the efe s ( step s2 ) and the substitution of the j.c into the extrinsic curvature terms in the braneworld ansatz ( step s3 ) . however , despite being complicated , all is well with sms s scheme since any befe s obtained by other such combinations of careful procedures will always be equivalent because the different steps are related by geometrical identities . step 4 however is not an instance of being careful as it is a truncation . our first point is that whereas in sms s formulation the non - einsteinian terms in the befe might be regarded as a bulk - like @xmath151 and a term quadratic in the brane energy - momentum , in other formulations the content of these two terms can be mixed up . in general , befe s contain a group of non - einsteinian ` bulk ' terms we denote by @xmath159 ( which include both weyl terms and normal derivatives of objects such as the extrinsic curvature ) , and a group of non - einsteinian ` brane ' terms that depend on the brane energy - momentum . thus any temptation to discard the weyl term in the sms formulation ( on the grounds that it involves the unknown bulk over which one has no control ) should be seen in the light that if one considered instead a reformulation , then there would be a similar temptation to discard the corresponding ` bulk ' term , which would generally lead to something _ other than the weyl term being discarded . thus for each formulation , the corresponding truncation of the ` bulk term ' would result in inequivalent residual ` braneworld physics ' . this is because there are geometrical identities that relate ` bulk ' and ` brane ' terms , so that the splits mentioned above are highly non - unique and thus not true splits at all . we take this as a clear indication that any such truncations should be avoided in general . instead , the full system must be studied . _ our second point is that each possible bulk spacetime may contain some hypersurface on which a given @xmath159 vanishes . then if one identifies this hypersurface with the position of the brane , one has a solution of the full brane - bulk system and not a truncation . for example , in any conformally - flat bulk , by definition @xmath160 and therefore @xmath161 on all hypersurfaces . thus any of these could be identified as a brane to form a genuine ( rather than truncated ) @xmath162 braneworld . from this , we can see that _ the sms formulation is particularly well adapted for the study of conformally - flat bulks such as pure ads . this motivates sms s formulation as regards this common application . however , also consider repeating the above procedure with some @xmath163 . this would correspond to a genuine ( rather than truncated ) braneworld model with distinct braneworld physics from that given by sms s particular quadratic term . note that given a model with some @xmath164 , the befe formulation for which @xmath159 is the bulk term is particularly well adapted for the study of that model . thus different formulations may facilitate the study of braneworlds with different braneworld physics . in the context of conformally - flat spacetimes , it is probably true that the @xmath162 braneworlds outnumber the braneworlds for which any other ( or even all other ) @xmath164 since these other conditions are not automatically satisfied on all embedded hypersurfaces . rather , each of these other conditions constitutes a difficult geometrical problem , somewhat reminiscent of the question of which spacetimes contain a maximal ( k = 0 ) or cmc slice @xcite . however , generic spacetimes are not conformally - flat . for a generic spacetime , we see no difference between the status of the condition ` @xmath162 on some hypersurface ' and the condition ` any other particular @xmath164 on some hypersurface ' . because braneworlds constructed in each of these cases have a different residual quadratic term and thus a propensity to have distinct braneworld physics , and because we do not know how frequently each of these cases occur , we question whether anything inferred from conformally - flat models with the sms quadratic term need be typical of the full sms brane - bulk system . confirmation of this would require study of the full range of difficult geometrical problems @xmath164 , and the construction of concrete examples of non - sms quadratic term braneworld models together with the assessment of whether their braneworld physics is conceptually and observationally acceptable . _ for the moment we study what is the available range of reformulations and thus of @xmath159 . to convince the reader that such reformulations exist , we provide a first example before listing all the steps which are available for reformulating the befe s . assume we do not perform all the steps implicit within sms s work but rather just the israel steps to obtain the j.c and then use it in the field equation ( [ israel ] ) that gave rise to it ( as done in @xcite ) , or ( as done below ) use it in the `` gr cp '' field equation following from ( [ grcpid ] ) . in other words , why not apply the braneworld ansatz to e.g the israel or `` gr cp '' formulations rather than to the sms formulation ? in the `` gr cp '' case we then obtain g _ = l _ + q _ + b _ [ cpbefe ] q _ = - [ qcp ] l _ = ( t - 2 ^ 2 ) f _ + _ 5 ^ 2[t _ - ( + ) f _ ] [ lcp ] b _ = f _ - . [ bcp ] this example serves to illustrate that choosing to use a different formulation can cause the ` brane ' quadratic term @xmath148 to be different . also note that this formulation makes no explicit use of the weyl term . thus this befe , along with the gauss and codazzi constraints , forms a small second - order system , in contrast with the much larger third - order sms system . now we further study the list of steps @xcite which may be applied in the construction of befe s . steps s1 and 3 together mean that the weyl ` bulk ' term @xmath151 is equivalent to the riemann ` bulk ' term together with matter terms . this swap by itself involves no terms which are quadratic in the extrinsic curvature . step 1 says that the riemann ` bulk ' term is equivalent to the hypersurface derivative of the extrinsic curvature together with a @xmath165 term . steps s1 and 3 together say that the hypersurface derivative of the trace of the extrinsic curvature is equivalent to a matter term together with a @xmath166 term . furthermore , one can use both steps 2 - 3 and step 1 , on arbitrary proportions ( parametrized by @xmath108 and @xmath167 ) of @xmath168 and of @xmath55 : ll g _ & = g _ - ( 1 + ) r_+ ( 1 - ) r_f _ + + & + k k _ + ( - 1 ) k_^ k _ - f _ + ( - ) k f _ [ 2param ] this introduces freedom in the coefficients of the @xmath165 and @xmath166 contributions to the quadratic term @xmath169 in the thefe s . we next find further freedom in @xmath170 by choice of the objects to be regarded as primary . we are free to choose a ` bulk ' term described by hypersurface derivatives @xmath171 ( which are partial derivatives @xmath136 in normal coordinates ) of objects related to the extrinsic curvature @xmath172 by use of the metric tensor ( including its inverse and determinant @xmath173 ) . the underlying reason for doing this is that it is just as natural to treat such an object , rather than the extrinsic curvature itself , as primary ( see below for examples ) . upon careful consideration , there are three separate ways such objects can be related to the extrinsic curvature : raising indices , removing a portion of the trace by defining @xmath174 , and densitizing by defining @xmath175 . the hypersurface derivatives of these objects are related to those of the extrinsic curvature by _ k _ = _ ( f_k^ _ ) = f _ _ k^ _ - 2_k^ _ , [ i ] _ k _ = _ k^ _ + ( _ kf _ - 2 _ ) , [ 64 ] _ k _ = ( f)^-_1_(f^_1k _ ) + 2_1kk_. [ 65 ] further useful equations arise from the traces of these : _ k = f^ _ k _ + 2 , [ 63 ] _ k = [ f^ _ _ _ - 2(k^2 - k ) ] , [ new ] _ k = ( f)^-_2_(f^_2k ) + 2_2k^2 , [ 66 ] where the @xmath176 in ( [ new ] ) and ( [ new ] ) has been obtained via ( [ 66 ] ) . the following examples of @xmath177 illustrate that the use of such objects is entirely natural : @xmath178 is the @xmath121 commonly used in the ivp literature , and @xmath179 appears in the guise of forming the complete normal derivative in the israel procedure . also , the `` gravitational momenta '' are @xmath180 . the above thorough consideration of possible ` bulk ' terms permits all four thefe terms homogeneously quadratic in the extrinsic curvature to be changed independently . one may think that we have a redundancy in providing 8 ways to change only 4 coefficients . however , one can afford then to lose some of the freedoms by making extra demands , of which we now provide four examples of relevance to this paper . first , one could further demand that there is no weyl term in the thefe s ( as discussed in sec . second , unequal densitization of @xmath172 and @xmath181 ( @xmath182 ) corresponds to interpreting the fundamental variable to be some densitization of the metric rather than the metric itself . whereas this is again a common practice ( for example the scale - free metric of the ivp literature is @xmath183 in dimension @xmath10 ) , the use of such an object as fundamental variable does appear to complicate the isolation of the ( 3 , 1 ) einstein tensor truly corresponding to this fundamental variable . thus this option is not pursued in this paper . third , one may start by declaring that one is to use particular well - known primary objects ( such as the `` gravitational momenta '' ) and still desire to be left with much freedom of formulation . fourth , one could declare that one is to use the raised objects given by ( [ 63 ] ) , in which case the further ability to change coefficients by use of ( [ 64 ] ) is lost , since moving a kronecker delta rather than a metric through the derivative clearly generates no terms quadratic in the extrinsic curvature . as a consequence of the above freedoms , there are many formulations in which all four coefficients vanish , and hence @xmath184 . from this it follows that @xmath148 is zero [ and it is easy to show that all instances of @xmath185 follow from @xmath184 ] . thus it suffices to seek for cases of thefe s with @xmath184 to obtain all cases of befe formulations that have no quadratic term . we now motivate these formulations and then choose to exhibit three that comply with some of the extra demands in the previous paragraph . the diversity of ` brane'-`bulk ' splits ensures that truncations such as step 4 produce all possible combinations of quadratic terms as residual ` braneworld physics ' . alternatively , one may suspect that there might be solutions to the full brane - bulk system that just happen to have a particular @xmath164 on some hypersurface which is then identified as a brane . we speculate that each of these situations will often lead to different answers to questions of physical interest . whereas most friedmann lematre robertson walker ( flrw ) perfect fluid models with equation of state @xmath187 arising thus will be similar , differences will be more salient in models with more complicated equations of state , in perturbations about flrw ( as started in @xcite in the sms - adapted case ) and in anisotropic models ( as started by @xcite in the sms - adapted case ) . these in turn constitute natural frameworks to seriously justify the late - time emergence of flrw behaviour and the likelihood of inflation @xcite as well as the study of singularities @xcite on the brane . we emphasize that , for a satisfactory study of whether any particular full brane - bulk ( as opposed to truncated ) case leads to any differences from the hitherto - studied @xmath162 case , one would require a full brane - bulk solution explicitly constructed to satisfy some @xmath164 on some hypersurface within a particular given bulk spacetime . since we currently have no such example , our arguments currently only support the far simpler idea that truncation should be avoided . we illustrate that in different formulations , the truncation of the corresponding ` bulk ' terms can lead to big differences in the residual ` braneworld physics ' , without any of the above lengthy calculations . we do this by formulating the ` bulk ' part so that there is no corresponding @xmath188 term at all . thus these truncations give the ` @xmath34 ' of standard flrw cosmology rather than the ` @xmath34 and @xmath113 ' of brane cosmology @xcite . as a result whether we have a ` @xmath34 and @xmath113 ' brane cosmology depends on the choice of formulation . so we argue that since the sms procedure followed by truncating the weyl term is a hitherto unaccounted - for choice out of many possible procedures , then adopting the particular homogeneous quadratic term of sms ( often taken as the starting - point of brane cosmology ) appears to be unjustified . rather , we conclude that no particular truncation should be privileged as the act of truncation imprints undesirable arbitrariness into the study of the truncated system . whereas the ( 3 , 1)-dimensional trace of @xmath151 happens to be zero ( including use of antisymmetry ) and thus might phenomenologically look like pure radiation fluid to observers on the brane , other bulk characterizations would typically not look like a pure radiative fluid . this may open up phenomenological possibilities . also , before further study of sms s full ( untruncated , third - order ) system is undertaken , some of the reformulations along the lines suggested in sec 4.4 might turn out to be more tractable . in particular those reformulations which fully eliminate @xmath168 by the early use of the ricci equation are already closed as second - order systems . these include the israel formulation in @xcite , the `` gr cp '' formulation ( [ cpbefe][bcp ] ) , and our second and third examples below , which contain neither a weyl term nor a quadratic term . for our first example , we take as the primary object the antidensitized extrinsic curvature @xmath189 so that the ` bulk ' term is ( partly ) a combination of this object s normal derivatives . the corresponding befe s are : g _ = l _ + b _ l _ = + ( 5 t _ - t)f _ , b _ = -2e _ + ( - f^ f _ ) ( where we have chosen to remove all projections of @xmath143 by the efe s ) . to derive this , take ( [ 2param ] ) in normal coordinates . choose to convert all of the @xmath190 into @xmath191 by ( [ 63 ] ) : ll g _ & = g _ - ( 1 + ) r _ + ( 1 - ) r_f _ + ( + f _ ) + & + k k _ + ( - 1 ) k_^ k _ - f _ + ( + ) k f _ now choosing the primary object to be some densitized @xmath192 by ( [ 65 ] ) we have ll g _ = & g _ - ( 1 + ) r _ + ( 1 - ) r _ f _ + ( + f^ ) + & + ( 1 + 2)kk _ + ( - 1 ) k_^ k _ + ( 2- ) k^2f _ + ( + ) k f _ , so clearly @xmath193 , @xmath194 and the antidensitization choice of weighting @xmath195 ensure that @xmath184 the following examples arose from asking if it is possible to find examples in which neither @xmath148 nor @xmath151 feature . we found the following befe s : g _ = l _ + b _ l _ = t _ + ( t_- ) f _ , b _ = ( f _ - f _ ) by considering as our primary object the densitized extrinsic curvature with one index raised , @xmath196 . we obtained these befe s by arguing as follows . in order for the befe s to contain no weyl term , @xmath167 is fixed to be @xmath197 . then the only control over @xmath165 is from raising by ( [ i ] ) . it is easy to show that this raising must be applied to the whole @xmath198 in order for the coefficient of @xmath165 to be zero . then using @xmath199 does not change any terms quadratic in the extrinsic curvature . also , use of distinct densities for @xmath181 and @xmath200 does not appear to make sense since both quantities are related to @xmath172 by a single use of the inverse metric . although all these restrictions make the outcome unlikely , the use of ( [ 65 ] ) and ( [ 66 ] ) alone suffices to obtain the above example : ll g _ & = g _ + ( 1 - ) r_f _ + f^- ( - + f _ ) + & + ( 1 -2 ) k k _ + ( 2- ) k^2f _ + ( - ) k f _ which has no quadratic terms if @xmath201 and @xmath202 ( ` densitization ' weight ) . another possibility is to replace @xmath203 by @xmath204 . although this does not immediately do anything about the quadratic terms , if we also convert a portion @xmath205 of @xmath206 into @xmath207 we obtain ll g _ & = g _ + ( 1 - ) r_f _ + f^- ( - + ( - ) f _ ) + & + ( 1 -2 ) k k _ + ^2f _ + f _ , which requires @xmath208 , whereupon the two remaining equations become identical : @xmath209 , which clearly has many solutions . a particularly neat one is to take @xmath210 so that the primary objects are ` gravitational momenta ' and @xmath211 so that only two normal derivative terms appear in the ` bulk ' term . then @xmath212 so the befe s read g _ = l _ + b _ , l _ = t _ + f _ , b _ = ( f _ - f^ f _ ) . of course , it would make sense to particularly investigate the difficult geometrical problem ` @xmath164 on some embedded hypersurface ' for such @xmath164 corresponding to no quadratic terms , since by the same arguments as above , such a model would be sure to give braneworld physics distinguishable from that hitherto studied . first , so far we have talked in terms of the @xmath213 split of the matter contribution to relate our work as clearly as possible to its predecessors in the literature . however , from the outset @xcite it was pointed out that this split is not unique . on these grounds we would prefer to work with the unique trace - tracefree split in which all the @xmath214 contributes to the trace part . the ( 4 , 0 ) version of this split is used in sec 6 . second , given a fixed type of bulk energy - momentum such as the @xmath56 of nkk or the @xmath215 , then establishing an embedding requires the existence of a suitable compensatory characterization of the bulk geometry . the gr line of thought would be to only take results within such schemes seriously if they are robust to the addition of bulk matter fields . of course privileged choices of bulk could arise from further theoretical input . we argue below that the theoretical arguments behind some privileged choices in the literature for the bulk energy - momentum are not convincing enough to anchor strongly credible physical predictions . one would rather require rigorous and general theoretical input following directly from some fundamental theory such as string theory . the vacuum choice of bulk of the induced matter nkk approach is always possible given the premises of the cm result . then @xmath216 is claimed to be a complete geometrization of matter @xcite . however , the cm result holds equally well for any other analytical functional form of the energy - momentum . furthermore , this approach considers only 1-component ( ` induced ' ) matter ; counting degrees of freedom shows that it can not be extended to many important cases of fundamental matter . whereas allowing for more extra dimensions could improve similar situations @xcite , unification requires geometrization of the fundamental matter laws themselves , whilst this ` induced matter ' approach only geometrizes solutions of the efe s coupled to matter of unspecified field dependence . the @xmath215 choice of bulk ( an example of which is pure ads ) is clearly also always possible given the premises of a particular case of the generalized cm result . however , the motivation we wish to discuss is the argument for pure ads bulks from string theory . this is not generally justifiable since firstly , bulk gravitons are permitted so the bulk geometry would generically contain gravity waves . secondly , bulk scalars ought to be permitted since they occur along with the graviton in the closed string spectrum @xcite . the content of the closed string spectrum thus places interesting restrictions on bulk matter rather than completely abolishing it . from the perspective of 5d gr , evidence for the stability of vacuum or ads bulks ( and of any resulting physical predictions ) to the introduction of suitable bulk fields would constitute important necessary support for such models and their predictions . finally note that use of arbitrary smooth bulk @xmath57 does not affect the form of the junction conditions since only the thin matter sheet contribution to @xmath57 enters these . the conclusion of our second point is that there is no good reason not to explore at least certain kinds of bulk matter in order to have a more general feel for how these thin matter sheet models behave @xcite . first we explain how our criticism of ( 3 , 1 ; 1 ) methods in general in sec 2.4 are applicable to the case with thin matter sheets . as regards the evolution " w.r.t @xmath23 , the issue of causality holds regardless of whether thin matter sheets are present , and the issue of well - posedness not being known will become particularly relevant in the study of sufficiently general situations in which rough function spaces would become necessary to describe the evolution of thin matter sheets ( see sec 6.1 ) . the campbell magaard scheme is of limited use in models with thin matter sheets not only because analytic functions are undesirable ( and definitely inapplicable to sufficiently general situations ) but also because the junction condition imposes restrictions on @xmath172 which prevents these being subdivided into the knowns and unknowns of magaard s method . these restrictions remain even if one considers suitably well - behaved thick matter sheet models . in the next paragraph we outline how much we expect can be achieved with the ( 3 , 1 ) version of the york method applied on the thin matter sheet , but recall that even if this does provide data sets , one is next confronted with the difficulties of the ( 3 , 1 ; 1 ) evolution " scheme . the main message is that the choice of methods which properly respect the difference between space and time is absolutely crucial . thus , although at the simplest level ( 3 , 1 ; 1 ) methods which build higher - dimensional bulks about the privileged ( 3 , 1 ) worlds may look tempting , general attempts at proceeding thus are hampered by the required mathematical tools simply not being available and by these attempts not being in accord with the usual notion of causality . to date ( 4 , 1 ) worlds built from ( 3 , 1 ) ones have relied on very simple specialized anstze , such as \a ) @xmath23-symmetric surfaces @xmath217 with known metric @xmath155 , whereupon the vacuum codazzi equation is automatically satisfied and then @xmath218 is required from the gauss constraint . \b ) @xmath126 with known @xmath155 , for example to obtain the randall sundrum bulk @xcite or slightly more general solutions @xcite . now the maximal subcase @xmath219 of the cmc condition is a generalization of a ) , whereas the full cmc condition itself is a generalization of b ) . moreover , now the metric is to be treated as only known up to scale . thus one would generally only know the full metric of each model s ( 3 , 1 ) world once the ` wave lichnerowicz equation ' for the embedding of this world into the ( 4 , 1 ) world is solved . so one loses the hold from the outset on whether each model will turn out to contain an interesting ( 3 , 1 ) world . nevertheless , some of the ( 3 , 1 ) worlds will turn out to be of interest . furthermore , one should question the sensibleness of any ideas involving the prescription of full ( 3 , 1 ) metrics if the most general technique available fails to respect such a prescription . this point is more significant for ( 3 , 1 ) data than for ( 3 , 0 ) data because conformally - related metrics have different non - null geodesics . for ( 3 , 0 ) data no physical significance is attached to spatial geodesics , but for ( 3 , 1 ) there are timelike geodesics which are physically interpreted as paths of free motion of massive particles . so a @xmath220 spacetime which is conformally related to @xmath221 is different physically ( for example one could violate energy conditions the other one does not violate ) . one can get out of this problem by either attaching no physical significance to one s inspired guesses for @xmath221 or by hoping for unobservably tiny deviations between the geodesic curves of the two geometries . in the specific case of thin matter sheets , by the j.cs , a ) implies that @xmath222 , whilst b ) implies that @xmath223 is a hypersurface constant . the maximal condition implies that @xmath224 whilst the cmc one implies that @xmath223 is a hypersurface constant . so whereas the maximal and cmc ans@xmath225tze are more general than a ) and b ) respectively , they are nevertheless restricted in this braneworld application . notice , however , that a number of interesting cases are included : vacuum , radiative matter and electromagnetic matter are all among the @xmath224 spacetimes . it is important to note that unlike the usual gr application , the choice of a hypersurface to be a brane is not a choice of slicing because localized energy momentum is to be pinned on it . almost all reslicings would fail to isolate this energy - momentum on a single slice . we know of no good reason why the brane should be cmc nor what value the cmc should take on it . however , at least this is a well - defined notion and it is substantially simpler to solve for than in general because of the decoupling of the gauss and codazzi constraints . as regards possible use of either of the two forms of the thin sandwich conjecture to treat branes , we first distinguish between thin sandwiches between 2 nearby branes and thin sandwiches which have a brane on one side and an undistinguished hypersurface on the other . one should be aware that non - intersection requirements may be different in these two cases , and also different from that of the original tsc setting of 2 unprivileged spacelike hypersurfaces . second , one would have to take @xmath226 as unknown until it can be deduced from the @xmath172 evaluated from the ts procedure . finally we caution that tsc schemes need not always exist . they require the `` lapse '' to be algebraically - eliminable , which for example is not the case for the analogous @xmath22 of the kk split .

parts of the classical phase space can be manipulated in a controllable manner . a directed current of an ensemble of particles can be created through locally breaking the spatiotemporal symmetries of the time - driven potential . magnitude and direction of the current are tunable .

i

1004.3894

we explore the dynamics of non - interacting particles loaded into a phase - modulated one - dimensional lattice formed by laterally oscillating square barriers . tuning the parameters of the driven unit cell of the lattice selected parts of the classical phase space can be manipulated in a controllable manner . we find superdiffusion in position space for all parameters regimes . a directed current of an ensemble of particles can be created through locally breaking the spatiotemporal symmetries of the time - driven potential . magnitude and direction of the current are tunable . several mechanisms for transient localization and trapping of particles in different wells of the driven unit cell are presented and analyzed .

time - driven systems represent a major focus in several versatile research fields , such as the physics of atoms , molecules or mesoscopic systems @xcite . generally , they are evoked by the occurrence of time - periodic forces . as an example , the dipole interaction of atoms exposed to laser fields gives rise to several interesting phenomena like laser stabilization , high harmonic generation or above barrier ionization . another example is the coherent control of quantum molecular dynamics by means of shaped femtosecond laser pulses . among the most prominent mesoscopic systems are the various driven lattice setups , i.e. particles in an one - dimensional static potential are acted upon additionally by external time - dependent forces of zero mean . experimentally they have been realized in condensed matter @xcite and cold atomic systems ( see @xcite and refs . therein ) . a remarkable observation is that these systems can show directed transport for an ensemble of particles , although there exists no net force . therefore , they are called ratchets . originally the generation of ratchet effects has been addressed by employing external noise @xcite . similarly , the role of dissipation has been studied thoroughly . in ref . @xcite it has been shown that directed transport occurs for underdamped particles in a sinusoidally rocked spatially asymmetric periodic potential . moreover , as the amplitude of the external driving is varied , the current flow is reversed several times . the underlying mechanism responsible for the existence of directed currents and the reversal of the transport has been identified in refs . @xcite . due to dissipation transporting attractors in phase space emerge and by choosing the initial conditions appropriately it is possible to populate them selectively . the ratchet effect can also be generated in systems without dissipation and noise . in this case one speaks of `` ( deterministic ) hamiltonian ratchets '' . recently , in ref . @xcite the directed transport of atoms in a bec loaded into a flashing ratchet potential was demonstrated . the current flow appears only if certain temporal and spatial symmetries of the driven potential , which have been identified in ref . @xcite , are broken . the occurrence of directed transport in hamiltonian systems has been reported for the case of fully chaotic dynamics @xcite and for systems with mixed phase space @xcite . for the latter case @xcite a sum rule for the transport velocity of a classical ensemble of particles has been derived . additionally , these authors have shown that in the semi - classical limit the quantum and the classical transport velocity coincide . as an extension in ref . @xcite the impact of avoided crossing between different transporting floquet states has been considered . tuning the control parameters leads to an enhancement or suppression of the current flow . moreover , in ref . @xcite the influence of an additional dc bias on the directed transport of a hamiltonian ratchet has been studied . the authors have found the persistence of transporting invariant submanifolds like regular islands . in their vicinity trajectories can get sticky , such that they perform ballistic - like motion . remaining chaotic trajectories are accelerated by the bias field getting separated very fast from the ballistic type dynamics . for all previous setups the static potential is exposed to a so - called global driving law @xcite , i.e. the force acting upon the particles can be separated into two parts , which depend only on the spatial coordinate and the time , respectively . for the systems we explore in the present work this is not true anymore . each potential barrier of the underlying lattice will be equipped with its own characteristic driving law , which gives rise to several new intriguing phenomena and the possibility to `` locally engineer '' the classical phase space . by adjusting carefully the parameters of the barriers and accordingly their driving laws specific parts of the phase space can be manipulated in a controllable manner , whereas the remaining portion stays mainly unaffected . moreover , the symmetries derived in @xcite can be broken by imposing spatially dependent phase shifts to the driving laws of the barriers , which will be called a `` phase - modulated lattice '' in the following . thereby , a directed transport of an ensemble of particles is evoked and both the direction and the magnitude of the current flow can be tuned easily . importantly , for specific ranges of the barriers potential height the particles show different localization behavior depending on their location within the unit cell of the lattice . the paper is organized as follows . in sec . [ ch : setup ] we give a detailed description of our model and define the setups which will be studied . in sec . [ ch : pss ] the phase space is analyzed by means of stroboscopic poincar surfaces of section ( pss ) . in this regard the desymmetrization of the phase space , meaning the loss of symmetry with respect to @xmath0 , is explored . furthermore , we study the occurrence of regular elliptic islands in the pss , present an approximation for the velocity regime of the last stable torus and discuss the impact of cantori on the dynamics of trajectories . section [ ch : trans_loc ] is devoted to the transport and localization properties of the setups and how they originate from the phase space properties of the considered system . finally , a conclusion and outlook is given in sec . [ ch : sum ] .

we extend the homogeneous modified chaplygin cosmologies to large - scale perturbations by formulating a zeldovich - like approximation . we then study how the large - scale inhomogeneities evolve and compare the results with cold dark matter ( cdm ) , @xmath0cdm and generalized chaplygin scenarios .

c

astro-ph0411068

we extend the homogeneous modified chaplygin cosmologies to large - scale perturbations by formulating a zeldovich - like approximation . we show that the model interpolates between an epoch with a soft equation of state and a de sitter phase , and that in the intermediate regime its matter content is simply the sum of dust and a cosmological constant . we then study how the large - scale inhomogeneities evolve and compare the results with cold dark matter ( cdm ) , @xmath0cdm and generalized chaplygin scenarios . interestingly , we find that like the latter , our models resemble @xmath0cdm .

using a zeldovich - like approximation , we have studied the evolution of large - scale perturbations in a recently proposed theoretical framework for the unification of dark matter and dark energy : the so - called modified chaplygin cosmologies @xcite , with equation of state @xmath70 with @xmath71 . this model evolves from a phase that is initially dominated by non - relativistic matter to a phase that is asymptotically de sitter . the intermediate regime corresponds to a phase where the effective equation of state is given by @xmath72 plus a cosmological constant . we have estimated the fate of the inhomogeneities admitted in the model and shown that these evolve consistently with the observations as the density contrast they introduce is smaller than the one typical of cdm scenarios . on general grounds , the pattern of evolution of perturbations follows is similar to the one in the @xmath0cdm models and in generalized chaplygin cosmologies , and therefore our represent plausible alternatives alternatives as usual , in modified chaplygin cosmologies , the equation of state parameter @xmath44 can be expressed in terms of the scale factor and a free parameter @xmath29 , and the value of the latter can be chosen so that the model resembles as much as desired the @xmath0cdm model . it would be very interesting to deepen in the comparison between modified and generalized chaplygin models , particularly from the observational point of view ( as already done in @xcite ) . it would also be worth generalizing our study by going beyond the zeldovich approximation , to incorporate the effects of finite sound speed . this can be done by generalizing the spherical model to incorporate the jeans length as in @xcite . alternatively , following @xcite one could investigate whether the modified chaplygin admits an unique decomposition into dark energy and dark matter , and if that were the case then study structure formation and show that difficulties associated to unphysical oscillations or blow - up in the matter power spectrum can be circumvented . we hope this will be addressed in future works . is partially funded by the university of buenos aires under project x224 , and the consejo nacional de investigaciones cientficas y tcnicas under proyect 02205 . is supported by the university of the basque country through research grant upv00172.310 - 14456/2002 and by the spanish ministry of education and culture through research grant fis2004 - 01626 . b. ratra and p.j.e . peebles , ( 1988 ) 3406 ; ( 1988 ) 117 ; c. wetterich , ( 1988 ) 668 ; j. a. frieman , c. t. hill , a. stebbins and i. waga , phys . rev . * 75 * ( 1995 ) 2077 ; k. coble , s. dodelson and j. a. frieman , phys . d * 55 * ( 1997 ) 1851 ; m. s. turner and m. j. white , phys . d * 56 * ( 1997 ) 4439 ; p. g. ferreira and m. joyce , phys . * 79 * ( 1997 ) 4740 ; p. g. ferreira and m. joyce , phys . d * 58 * ( 1998 ) 023503 ; e. j. copeland , a. r. liddle and d. wands , phys . d * 57 * ( 1998 ) 4686 ; r.r . caldwell and r. dave , p.j . steinhardt , ( 1998 ) 1582 ; p.g . ferreira and m. joyce , ( 1998 ) 023503 ; l. m. wang and p. j. steinhardt , astrophys . j. * 508 * ( 1998 ) 483 ; i. zlatev , l. wang , and p.j . steinhardt , ( 1999 ) 986 ; p. j. steinhardt , l. m. wang and i. zlatev , phys . d * 59 * ( 1999 ) 123504 ; i. zlatev and p. j. steinhardt , phys . b * 459 * ( 1999 ) 570 ; p. bintruy , ( 1999 ) 063502 ; j.e . kim , 9905 ( 1999 ) 022 ; m.c . bento and o. bertolami , ( 1999 ) 1461 ; j.p . uzan , ( 1999 ) 123510 ; t. chiba , ( 1999 ) 083508 ; l. amendola , ( 1999 ) 043501 . y. fujii , ( 2000 ) 023504 ; a. masiero , m. pietroni and f. rosati , ( 2000 ) 023504 ; m.c . bento , o. bertolami , and n. santos , ( 2002 ) 067301 . r. r. caldwell , phys . b * 545 * ( 2002 ) 23 ; a. e. schulz and m. j. white , phys . d * 64 * ( 2001 ) 043514 ; b. mcinnes , jhep * 0208 * ( 2002 ) 029 ; r. vaas , bild . * 2003n8 * ( 2003 ) 52 ; r. r. caldwell , m. kamionkowski and n. n. weinberg , phys . * 91 * ( 2003 ) 071301 ; j. g. hao and x. z. li , phys . d * 67 * ( 2003 ) 107303 ; g. w. gibbons , hep - th/0302199 ; x. z. li and j. g. hao , phys . d * 69 * ( 2004 ) 107303 ; s. nojiri and s. d. odintsov , phys . b * 562 * ( 2003 ) 147 ; s. nojiri and s. d. odintsov , phys . b * 565 * ( 2003 ) 1 ; a. yurov , astro - ph/0305019 ; p. singh , m. sami and n. dadhich , phys . d * 68 * ( 2003 ) 023522 ; j. g. hao and x. z. li , phys . d * 68 * ( 2003 ) 043501 ; p. f. gonzlez - daz , phys . d * 68 * ( 2003 ) 021303 ; s. nojiri and s. d. odintsov , phys . b * 571 * ( 2003 ) 1 ; m. p. dabrowski , t. stachowiak and m. szydlowski , phys . d * 68 * ( 2003 ) 103519 ; d. j. liu and x. z. li , phys . d * 68 * ( 2003 ) 067301 ; l. p. chimento and r. lazkoz , * 91 * ( 2003 ) 211301 ; j. g. hao and x. z. li , phys . d * 70 * ( 2004 ) 043529 ; e. elizalde and j. q. hurtado , mod . a * 19 * ( 2004 ) 29 ; h. stefancic , phys . b * 586 * ( 2004 ) 5 ; v. b. johri , phys . d * 70 * ( 2004 ) 041303 ; j. m. cline , s. y. jeon and g. d. moore , phys . d * 70 * ( 2004 ) 043543 ; m. sami and a. toporensky , mod . . lett . a * 19 * ( 2004 ) 1509 ; h. q. lu , hep - th/0312082 ; h. stefancic , eur . j. c * 36 * ( 2004 ) 523 ; p. f. gonzlez - daz , phys . b * 586 * ( 2004 ) 1 ; y. s. piao and y. z. zhang , astro - ph/0401231 ; p. f. gonzlez - daz , phys . d * 69 * ( 2004 ) 063522 ; m. szydlowski , w. czaja and a. krawiec , astro - ph/0401293 ; e. babichev , v. dokuchaev and y. eroshenko , phys . * 93 * ( 2004 ) 021102 ; j. m. aguirregabiria , l. p. chimento and r. lazkoz , phys . rev . d * 70 * ( 2004 ) 023509 ; j. cepa , astro - ph/0403616 ; j. g. hao and x. z. li , phys.lett . b*606 * ( 2005 ) 7 ; z. k. guo , y. s. piao and y. z. zhang , phys . b * 594 * ( 2004 ) 247 ; m. bouhmadi - lopez and j. a. jimnez madrid , astro - ph/0404540 ; v. faraoni , phys . rev . d * 69 * ( 2004 ) 123520 ; e. elizalde , s. nojiri and s. d. odintsov , phys . d * 70 * ( 2004 ) 043539 ; j. e. lidsey , phys . d * 70 * ( 2004 ) 041302 ; m. g. brown , k. freese and w. h. kinney , astro - ph/0405353 ; l. p. chimento and r. lazkoz , astro - ph/0405518 ; p. f. gonzlez - daz and j. a. jimnez - madrid , phys . b * 596 * ( 2004 ) 16 ; p. f. gonzlez - daz , hep - th/0408225 ; a. vikman , phys.rev . d * 71 * ( 2005 ) 023515 ; r. koley and s. kar , mod . a * 20 * ( 2005 ) 363 ; p. f. gonzalez - daz and c. l. siguenza , nucl . b * 697 * ( 2004 ) 363 ; p. x. wu and h. w. yu , astro - ph/0407424 ; w. fang , h. q. lu , z. g. huang and k. f. zhang , hep - th/0409080 ; l. amendola , phys.rev.lett . * 93 * ( 2004 ) 181102 ; y. h. wei , gr - qc/0410050 ; s. nesseris and l. perivolaropoulos , phys.rev . d * 70 * ( 2004 ) 123529 ; r. j. scherrer , phys . rev . d * 71 * ( 2005 ) 063519 ; w. hu , phys . d * 71 * ( 2005 ) 047301 ; e. majerotto , d. sapone and l. amendola , astro - ph/0410543 ; z. k. guo , y. s. piao , x. zhang and y. z. zhang , phys . b * 608 * ( 2005 ) 177 . v. k. onemli and r. p. woodard , class . * 19 * ( 2002 ) 4607 ; v. k. onemli and r. p. woodard , phys . d * 70 * ( 2004 ) 107301 . m. c. bento , o. bertolami and a. a. sen , phys . d * 66 * ( 2002 ) 043507 . a. kamenshchik , u. moschella , v. pasquier , ( 2001 ) 265 . l. p. chimento , phys . d * 69 * ( 2004 ) 123517 . @xcite t. barreiro and a. a. sen , phys . d * 70 * ( 2004 ) 124013 . g. r. dvali , g. gabadadze and m. porrati , phys . b * 485 * ( 2000 ) 208 ; c. deffayet , phys . b * 502 * ( 2001 ) 199 . k. freese and m. lewis , phys . b * 540 * ( 2002 ) 1 ; p. gondolo and k. freese , phys . d * 68 * ( 2003 ) 063509 . g. dvali and m. s. turner , astro - ph/0301510 . t. barreiro and a. a. sen , phys . d * 70 * ( 2004 ) 124013 . m. c. bento , o. bertolami and a. a. sen , phys . d * 67 * ( 2003 ) 063003 ; phys . lett . b * 575 * ( 2003 ) 172 ; gen . * 35 * ( 2003 ) 2063 ; d. carturan and f. finelli , phys . d * 68 * ( 2003 ) 103501 ; l. amendola , f. finelli , c. burigana and d. carturan , jcap * 0307 * ( 2003 ) 005 . m. c. bento , o. bertolami , n. m. c. santos and a. a. sen , phys . d * 71 * ( 2005 ) 063501 ; o. bertolami , a. a. sen , s. sen and p. t. silva , mon . not . * 353 * ( 2004 ) 329 ; r. j. colistete and j. c. fabris , astro - ph/0501519 ; r. j. colistete , j. c. fabris and s. v. b. goncalves , astro - ph/0409245 ; r. j. colistete , j. c. fabris , s. v. b. goncalves and p. e. de souza , int . j. mod . d * 13 * ( 2004 ) 669 ; m. biesiada , w. godlowski and m. szydlowski , astro - ph/0403305 ; m. makler , s. quinet de oliveira and i. waga , phys . lett . b * 555 * ( 2003 ) 1 ; j. c. fabris , s. v. b. goncalves and p. e. d. souza , astro - ph/0207430 ; a. dev , d. jain and j. s. alcaniz , phys . d * 67 * ( 2003 ) 023515 ; v. gorini , a. kamenshchik and u. moschella , phys . d * 67 * ( 2003 ) 063509 j. s. alcaniz , d. jain and a. dev , phys . d * 67 * ( 2003 ) 043514 ; r. bean and o. dore , phys . d * 68 * ( 2003 ) 023515 . p. t. silva and o. bertolami , astrophys . j. * 599 * ( 2003 ) 829 ; a. dev , d. jain and j. s. alcaniz , astron . astrophys . * 417 * ( 2004 ) 847 .

we extend the results of a previous analysis of ours showing that , when both heavy and light flavour effects are taken into account , successful minimal ( type i + thermal ) leptogenesis with @xmath0-inspired relations is possible . barring fine tuned choices of the parameters , these relations enforce a hierarchical rh neutrino mass spectrum that results into a final asymmetry dominantly produced by the next - to - lightest rh neutrino decays ( @xmath1 dominated leptogenesis ) . we present the constraints on the whole set of low energy neutrino parameters . allowing a small misalignment between the dirac basis and the charged lepton basis as in the quark sector it is confirmed that for normal ordering ( no ) there are two allowed ranges of values for the lightest neutrino mass : @xmath3 and @xmath4 . for @xmath5 the allowed region in the plane

i

1012.2343

we extend the results of a previous analysis of ours showing that , when both heavy and light flavour effects are taken into account , successful minimal ( type i + thermal ) leptogenesis with @xmath0-inspired relations is possible . barring fine tuned choices of the parameters , these relations enforce a hierarchical rh neutrino mass spectrum that results into a final asymmetry dominantly produced by the next - to - lightest rh neutrino decays ( @xmath1 dominated leptogenesis ) . we present the constraints on the whole set of low energy neutrino parameters . allowing a small misalignment between the dirac basis and the charged lepton basis as in the quark sector , the allowed regions enlarge and the lower bound on the reheating temperature gets relaxed to values as low as @xmath2 . it is confirmed that for normal ordering ( no ) there are two allowed ranges of values for the lightest neutrino mass : @xmath3 and @xmath4 . for @xmath5 the allowed region in the plane @xmath6-@xmath7 is approximately given by @xmath8 , while the neutrinoless double beta decay effective neutrino mass falls in the range @xmath9 for @xmath10 . for @xmath11 , one has quite sharply @xmath12 and an upper bound @xmath13 . these constraints will be tested by low energy neutrino experiments during next years . we also find that inverted ordering ( io ) , though quite strongly constrained , is not completely ruled out . in particular , we find approximately @xmath14 , that will be fully tested by future experiments . c i u # 1 # 1#1 # 1 # 1#2#3phys . lett . * b # 1 * ( # 2 ) # 3 # 1#2#3nucl . phys . * b # 1 * ( # 2 ) # 3 # 1#2#3phys . rev . lett . * # 1 * ( # 2 ) # 3 # 1#2#3phys . rev . * d # 1 * ( # 2 ) # 3 # 1#2#3z . phys . * c # 1 * ( # 2 ) # 3 # 1#2#3class . and quantum grav . * # 1 * ( # 2 ) # 3 # 1#2#3commun . math . phys . * # 1 * ( # 2 ) # 3 # 1#2#3j . math . phys . * # 1 * ( # 2 ) # 3 # 1#2#3ann . of phys . * # 1 * ( # 2 ) # 3 # 1#2#3phys . rep . * # 1c * ( # 2 ) # 3 # 1#2#3progr . theor . phys . * # 1 * ( # 2 ) # 3 # 1#2#3int . j. mod . phys . * a # 1 * ( # 2 ) # 3 # 1#2#3mod . phys . lett . * a # 1 * ( # 2 ) # 3 # 1#2#3nuovo cim . * # 1 * ( # 2 ) # 3 # 1#2#3_ibid . _ * # 1 * ( # 2 ) # 3

with the discovery of neutrino masses and mixing in neutrino oscillation experiments , leptogenesis @xcite has become the most attractive model of baryogenesis to explain the observed matter - antimatter asymmetry of the universe . this can be expressed for example in terms of the baryon - to - photon number ratio and is very well measured by cmb observations @xcite to be [ etabobs ] _ b^cmb = ( 6.2 0.15)10 ^ -10 . leptogenesis originates from the see - saw mechanism @xcite that is based on a simple extension of the standard model where right - handed ( rh ) neutrinos with a majorana mass matrix @xmath15 and yukawa couplings @xmath16 to leptons and higgs are added . within @xmath0 models , three rh neutrinos @xmath17 ( @xmath18 ) are nicely predicted and for this reason they are traditionally regarded as the most appealing theoretical framework to embed the seesaw mechanism . however , within the simplest set of assumptions inspired by @xmath0 models @xcite , barring strong fine - tuned degeneracies in the rh neutrino mass spectrum and using the experimental information from neutrino oscillation experiments , the traditional @xmath19-dominated leptogenesis scenario predicts an asymmetry that falls many orders of magnitudes below the observed one @xcite . this is because , within @xmath19-dominated leptogenesis , where the spectrum of rh neutrinos is hierarchical and the asymmetry is produced from the decays of the lightest ones , successful leptogenesis implies a stringent lower bound on their mass @xcite , @xmath20 . on the other hand , @xmath0 grand - unified theories typically yield , in their simplest version and for the measured values of the neutrino mixing parameters , a hierarchical spectrum with the rh neutrino masses proportional to the squares of the up - quark masses , leading to @xmath21 and therefore to a final asymmetry much below the observed one . however , it has been shown @xcite that , when the production from the next - to - lightest rh neutrinos @xcite and lepton flavour effects @xcite are simultaneously taken into account @xcite , the final asymmetry can be generated by the decays of the next - to - lightest rh neutrinos and allowed regions in the low energy neutrino parameter space open up . in this paper we proceed with the analysis of @xcite and present the resulting constraints on all low energy neutrino parameters . the paper is organized as follows . in section 2 we discuss the current experimental status on low energy neutrino parameters , we set up the notation and describe the general procedure to calculate the the asymmetry and find the constraints . in section 3 we first consider the case already studied in @xcite , when the dirac basis and the charged lepton basis coincide and then , in section 4 , we allow for a misalignment between the two bases not larger than that one described by the ckm matrix in the quark sector . finally , in section 5 we present a global scan in the space of parameters where all possible cases between the case of no misalignment and the case of a misalignment at the level of the ckm matrix are taken into account . we also discuss two scenarios , one at small @xmath22 and one at large @xmath22 , and show how , within @xmath0-inspired models , minimal leptogenesis could be tested in future low energy neutrino experiments . notice that our discussion is made within a non - supersymmetric framework . recently a study of @xmath0-inspired models within a supersymmetric framework has also enlightened interesting potential connections with lepton flavour violating decays and dark matter @xcite . an analysis of leptogenesis within left - right symmetric models , where a type ii seesaw contribution to the neutrino mass matrix is also present , has been performed in @xcite . within these models , the minimal type i scenario considered here represents a particular case recovered under specific conditions .

c i u # 1 # 1#1 # 1 # 1#2#3phys * b # 1 * ( # 2 ) # 3 # 1#2#3nucl . * b # 1 * ( # 2 ) # 3 # 1#2#3phys . # 1 * ( # 2 ) # 3 # 1#2#3phys . * d # 1 * ( # 2 ) # 3 # 1#2#3z . * c # 1 * ( # 2 ) # 3 # 1#2#3class . and quantum grav . * # 1 * ( # 2 ) # 3 # 1#2#3commun . math . # 1 * ( # 2 ) # 3 # 1#2#3j . math . # 1 * ( # 2 ) # 3 # 1#2#3ann . of phys . * # 1 * ( # 2 ) # 3 # 1#2#3phys . rep . * # 1c * ( # 2 ) # 3 # 1#2#3progr . # 1 * ( # 2 ) # 3 # 1#2#3int . phys . * a # 1 * ( # 2 ) # 3 # 1#2#3mod . lett . * a # 1 * ( # 2 ) # 3 # 1#2#3nuovo cim . * # 1 * ( # 2 ) # 3 # 1#2#3_ibid . _ * # 1 * ( # 2 ) # 3

r

1012.2343

we extend the results of a previous analysis of ours showing that , when both heavy and light flavour effects are taken into account , successful minimal ( type i + thermal ) leptogenesis with @xmath0-inspired relations is possible . barring fine tuned choices of the parameters , these relations enforce a hierarchical rh neutrino mass spectrum that results into a final asymmetry dominantly produced by the next - to - lightest rh neutrino decays ( @xmath1 dominated leptogenesis ) . we present the constraints on the whole set of low energy neutrino parameters . allowing a small misalignment between the dirac basis and the charged lepton basis as in the quark sector , the allowed regions enlarge and the lower bound on the reheating temperature gets relaxed to values as low as @xmath2 . it is confirmed that for normal ordering ( no ) there are two allowed ranges of values for the lightest neutrino mass : @xmath3 and @xmath4 . for @xmath5 the allowed region in the plane @xmath6-@xmath7 is approximately given by @xmath8 , while the neutrinoless double beta decay effective neutrino mass falls in the range @xmath9 for @xmath10 . for @xmath11 , one has quite sharply @xmath12 and an upper bound @xmath13 . these constraints will be tested by low energy neutrino experiments during next years . we also find that inverted ordering ( io ) , though quite strongly constrained , is not completely ruled out . in particular , we find approximately @xmath14 , that will be fully tested by future experiments . c i u # 1 # 1#1 # 1 # 1#2#3phys . lett . * b # 1 * ( # 2 ) # 3 # 1#2#3nucl . phys . * b # 1 * ( # 2 ) # 3 # 1#2#3phys . rev . lett . * # 1 * ( # 2 ) # 3 # 1#2#3phys . rev . * d # 1 * ( # 2 ) # 3 # 1#2#3z . phys . * c # 1 * ( # 2 ) # 3 # 1#2#3class . and quantum grav . * # 1 * ( # 2 ) # 3 # 1#2#3commun . math . phys . * # 1 * ( # 2 ) # 3 # 1#2#3j . math . phys . * # 1 * ( # 2 ) # 3 # 1#2#3ann . of phys . * # 1 * ( # 2 ) # 3 # 1#2#3phys . rep . * # 1c * ( # 2 ) # 3 # 1#2#3progr . theor . phys . * # 1 * ( # 2 ) # 3 # 1#2#3int . j. mod . phys . * a # 1 * ( # 2 ) # 3 # 1#2#3mod . phys . lett . * a # 1 * ( # 2 ) # 3 # 1#2#3nuovo cim . * # 1 * ( # 2 ) # 3 # 1#2#3_ibid . _ * # 1 * ( # 2 ) # 3

after spontaneous symmetry breaking , a dirac mass term @xmath23 , is generated by the vacuum expectation value ( vev ) @xmath24 gev of the higgs boson . in the see - saw limit , @xmath25 , the spectrum of neutrino mass eigenstates splits in two sets : three very heavy neutrinos , @xmath26 and @xmath27 respectively with masses @xmath28 almost coinciding with the eigenvalues of @xmath15 , and three light neutrinos with masses @xmath29 , the eigenvalues of the light neutrino mass matrix given by the see - saw formula @xcite , m_= - m_d1d_mm_d^t , that we wrote in a basis where the majorana mass matrix is diagonal defining @xmath30 . the symmetric light neutrino mass matrix @xmath31 is diagonalized by a unitary matrix @xmath32 , @xmath33 with @xmath34 , that , in the basis where the charged lepton mass matrix is diagonal , can be identified with the lepton mixing matrix . neutrino oscillation experiments measure two neutrino mass - squared differences . for no one has @xmath35 and @xmath36 . the two heavier neutrino masses can therefore be expressed in terms of the lightest neutrino mass @xmath22 as [ m2m3nor ] m_2 = , m_3 = , where we defined @xmath37 and @xmath38 @xcite . recently , a conservative upper bound on the sum of neutrino masses , @xmath39 , has been obtained by the wmap collaboration @xcite combining wmap 7 years data plus baryon acoustic oscillations observations and the latest hst measurement of @xmath40 . considering that it falls in the quasi - degenerate regime , it straightforwardly translates into [ upperbound ] m_1 < 0.19ev ( 95% cl ) . we will adopt the following parametrization for the matrix @xmath32 in terms of the mixing angles , the dirac phase @xmath41 and the majorana phases @xmath42 and @xmath43 @xcite @xmath44 and the following @xmath45 ranges for the three mixing angles @xcite [ twosigma ] _ 12= ( 31.3 ^ -36.3^ ) , _ 23= ( 38.5 ^ -52.5^ ) , _ 13= ( 0 ^ -11.5^ ) . in the case of io the expression of @xmath46 in terms of @xmath22 becomes [ m2m3inv ] m_2 = , while the expression for @xmath47 does not change . with the adopted convention for the light neutrino masses , @xmath48 , the case of io corresponds to relabel the column of the leptonic mixing matrix performing a column cyclic permutation , explicitly @xmath49 the predicted baryon - to - photon ratio @xmath50 is related to the value of the final @xmath51 asymmetry @xmath52 by @xcite [ etab ] _ b 0.9610 ^ -2 n_b - l^f , where @xmath53 is the @xmath54 number in a co - moving volume that contains on average one rh neutrino @xmath55 in thermal ultra - relativistic equilibrium abundance ( @xmath56 ) . the dirac mass matrix can be diagonalized by a bi - unitary transformation m_d = v_l^d_m_du_r , where @xmath57 . the matrix @xmath58 can be obtained from @xmath59 , @xmath32 and @xmath60 , considering that it provides a takagi factorization @xcite of @xcite m^-1 d^-1_m_dv_lud_mu^tv_l^td^-1_m_d , explicitly [ takagi ] m^-1 = u_rd_m^-1u_r^t . for non degenerate @xmath61 , the matrix @xmath58 can be determined noticing that it diagonalizes @xmath62 , i.e. m^-1(m^-1)^ = u_rd_m^-2u_r^ . this relation determines @xmath58 unless a diagonal unitary transformation , since any @xmath63 is also a solution . however , given a @xmath64 , one can fix @xmath65 from the eq . ( [ takagi ] ) , [ dphi ] d _ = and in doing so @xmath58 is unambiguously determined . inspired by @xmath0 relations , we can parameterize the eigenvalues of @xmath66 in terms of the up quark masses as [ so(10 ) ] _1= _ 1m_u , _2= _ 2 m_c , _3= _ 3m_t . within @xmath0 models one can expect @xmath67 and we will refer to this case . the reader is invited to read ref . @xcite for a more comprehensive discussion about these @xmath0-inspired relations . notice however that our results will be valid for a much broader range of values , since , quite importantly , it turns out that they are independent of @xmath68 and @xmath69 provided @xmath70 and @xmath71 . with the parametrization eq . ( [ so(10 ) ] ) and barring very special choices of parameters where the rh neutrino masses can become degenerate @xcite , and @xmath72 . this is clearly a conservative condition , since the asymmetry gets enhanced when @xmath73 or @xmath74 . however , in this way , we only neglect very special points in the parameter space yielding @xmath75 and @xmath76 . we will comment again later on this point . ] the rh neutrino mass spectrum is hierarchical and of the form ( for generic expressions in terms of the low energy parameters , see ref . @xcite ) [ alpha ] m_1:m_2:m_3=(_1m_u)^2:(_2m_c)^2:(_3m_t)^2 . as we said , the values of @xmath77 and @xmath78 are actually irrelevant for the determination of the final asymmetry ( unless @xmath77 is unrealistically large to push @xmath79 from @xmath80 above the lower bound @xmath81 gev to achieve successful @xmath19 leptogenesis ) . on the other hand , the value of @xmath82 is relevant to set the scale of the mass @xmath83 ( valid for @xmath84 ) of the next - to - lightest rh neutrino mass , but it does not alter other quantities crucial for thermal leptogenesis , such as the amount of wash - out from the lightest rh neutrinos . defining the flavoured @xmath85 asymmetries as _ 2-_2-_2 _ 2+_2 , these can be calculated using @xcite [ eps2a ] _ 2 \ { im+ } , where ( x)=x and @xmath86 is the decay rate of the rh neutrino @xmath1 into the flavor @xmath87 with couplings given by the yukawa s matrix @xmath16 . we will assume an initial vanishing @xmath1-abundance instead of an initial thermal abundance as in @xcite . in this way , a comparison of the results in the two analyses gives a useful information about the dependence of the final asymmetry on the initial @xmath1 abundance when successful leptogenesis is imposed . let us now define the flavored decay parameters as k_i = = , where @xmath88 is the hubble rate , m_= 1.0810 ^ -3ev , @xmath89 is the number of the effective relativistic degrees of freedom and @xmath90 is the planck mass . the total decay parameters are then just simply given by @xmath91 . it is also convenient to introduce the quantities @xmath92 . from the decay parameters one can then calculate the efficiency factors that are the second needed ingredient , together with the @xmath85 asymmetries , for the calculation of the final asymmetry . these can be well approximated by the following analytical expression @xcite at the peak for @xmath93 . for @xmath94 , the difference is below @xmath95 . ] ( k_2,k_2 ) = _ -^f(k_2,k_2)+ _ + ^f(k_2,k_2 ) , where the negative and the positive contributions are respectively approximately given by [ k- ] _ -^f(k_2,k_2)-2p_2 ^ 0 e^-3k_2 8 ( e^p_2 ^ 02n_n_2(z_eq ) - 1 ) , @xmath96 and [ k+ ] _ + ^f(k_2,k_2 ) ( 1-e^-k_2z_b(k_2)n_n_2(z_eq)2 ) , where z_b(k_2 ) 2 + 4k_2 ^ 0.13e^-2.5k_2=o(110 ) . the @xmath0-inspired conditions @xmath97 , yield a rh neutrino mass spectrum with @xmath98 , though , as we already noticed , this spectrum is obtained for a broader range of @xmath99 values . in this situation , the asymmetry is dominantly produced from @xmath1 decays at @xmath100 in a two flavour regime , i.e. when final lepton states can be described as an incoherent mixture of a tauon component and of coherent superposition of a an electron and a muon component . therefore , at the freeze - out of the @xmath1 wash - out processes , the produced asymmetry can be calculated as the sum of two contributions , [ nbmltm2 ] n_b - l^t~m_2 _ 2(k_2,k_2)+ _ 2e+(k_2,k_2e+ ) , where @xmath101 stands for @xmath102 and @xmath103 . more precisely , notice that each flavour contribution to the asymmetry is produced in an interval of temperatures between @xmath104 $ ] and @xmath105 $ ] , with @xmath106 . at @xmath107 the coherence of the @xmath108 quantum states breaks down and a three flavour regime holds , with the lepton quantum states given by an incoherent mixture of @xmath109 , @xmath110 and @xmath111 flavours . the asymmetry has then to be calculated at the @xmath19 wash - out stage as a sum of three flavoured contributions . the assumption of an initial vanishing @xmath1-abundance allows to neglect the phantom terms in the muon and in the electron components @xcite so that the final asymmetry can be calculated using the expression n_b - l^f _ 2e+(k_2 e+ ) e^-38k_1 e+ p^0_2p^0_2e+_2e+(k_2 e+ ) e^-38k_1 + _ 2 ( k_2 ) e^-38k_1 . notice that successful leptogenesis relies on points in the parameter space where one out of the three @xmath112 . from this point of view the constraints on low energy neutrino experiments that we will obtain should be quite stable against effects that could enhance the asymmetry such as a resonant enhancement for special points where @xmath113 . such effects are however still able to relax the lower bound on @xmath114 and on the @xmath115 , since the @xmath116 s do not depend on @xmath114 .

these constraints will be tested by low energy neutrino experiments during next years . we also find that inverted ordering ( io ) , though quite strongly constrained , is not completely ruled out . in particular , we find approximately @xmath14 , that will be fully tested by future experiments . . lett . phys . rev . lett . * rev . phys . phys . * phys . * theor . phys . * phys .

i

1012.2343

we extend the results of a previous analysis of ours showing that , when both heavy and light flavour effects are taken into account , successful minimal ( type i + thermal ) leptogenesis with @xmath0-inspired relations is possible . barring fine tuned choices of the parameters , these relations enforce a hierarchical rh neutrino mass spectrum that results into a final asymmetry dominantly produced by the next - to - lightest rh neutrino decays ( @xmath1 dominated leptogenesis ) . we present the constraints on the whole set of low energy neutrino parameters . allowing a small misalignment between the dirac basis and the charged lepton basis as in the quark sector , the allowed regions enlarge and the lower bound on the reheating temperature gets relaxed to values as low as @xmath2 . it is confirmed that for normal ordering ( no ) there are two allowed ranges of values for the lightest neutrino mass : @xmath3 and @xmath4 . for @xmath5 the allowed region in the plane @xmath6-@xmath7 is approximately given by @xmath8 , while the neutrinoless double beta decay effective neutrino mass falls in the range @xmath9 for @xmath10 . for @xmath11 , one has quite sharply @xmath12 and an upper bound @xmath13 . these constraints will be tested by low energy neutrino experiments during next years . we also find that inverted ordering ( io ) , though quite strongly constrained , is not completely ruled out . in particular , we find approximately @xmath14 , that will be fully tested by future experiments . c i u # 1 # 1#1 # 1 # 1#2#3phys . lett . * b # 1 * ( # 2 ) # 3 # 1#2#3nucl . phys . * b # 1 * ( # 2 ) # 3 # 1#2#3phys . rev . lett . * # 1 * ( # 2 ) # 3 # 1#2#3phys . rev . * d # 1 * ( # 2 ) # 3 # 1#2#3z . phys . * c # 1 * ( # 2 ) # 3 # 1#2#3class . and quantum grav . * # 1 * ( # 2 ) # 3 # 1#2#3commun . math . phys . * # 1 * ( # 2 ) # 3 # 1#2#3j . math . phys . * # 1 * ( # 2 ) # 3 # 1#2#3ann . of phys . * # 1 * ( # 2 ) # 3 # 1#2#3phys . rep . * # 1c * ( # 2 ) # 3 # 1#2#3progr . theor . phys . * # 1 * ( # 2 ) # 3 # 1#2#3int . j. mod . phys . * a # 1 * ( # 2 ) # 3 # 1#2#3mod . phys . lett . * a # 1 * ( # 2 ) # 3 # 1#2#3nuovo cim . * # 1 * ( # 2 ) # 3 # 1#2#3_ibid . _ * # 1 * ( # 2 ) # 3

we start from the case @xmath117 that has been studied already in @xcite deriving constraints in the plane @xmath118 for no . here we show constraints on all low energy neutrino parameters , including the case of io . let us first discuss the case of no . in fig . 1 we plotted the final asymmetry @xmath50 for the same three sets of values of the involved parameters as in the fig . 4 of ref . @xcite , where these three choices were corresponding to three different kinds of solutions for successful leptogenesis . + + + + this time the third solution ( right panel ) , is suppressed and successful leptogenesis is not attained . in @xcite , this was the only solution corresponding to a final asymmetry dominantly in the muon flavour instead than in the tauon flavour ( as for the first two ) . the suppression that we find now is explained partly because we are adopting a correct determination of the phases in the @xmath58 matrix ( cf . ( [ dphi ] ) ) and partly because we are now assuming an initial vanishing @xmath1-abundance instead than an initial thermal one . we will see however that , allowing for @xmath119 , this kind of solution will again yield successful leptogenesis in some allowed regions of the parameter space , characterized in particular by large values of @xmath120 . the solution in the central panel is also partly suppressed and successful leptogenesis is not attained . however , in a parameter scan , we find that this kind of solution can still give successful leptogenesis for slightly different values of the parameters than those indicated in the figure caption . in this case the difference with respect to the results in @xcite is explained just in terms of the different assumption on the initial abundance . this dependence on the initial conditions is due to the fact that @xmath121 , i.e. the solution falls in the weak wash - out regime at the production . finally , the first solution ( left panel ) is fully unchanged . it therefore exhibits a full independence of the initial conditions and this is in agreement with the fact that it respects all the necessary conditions for the independence on the initial conditions found in @xcite . notice that these conditions also enforce an efficient wash - out of a possible pre - existing asymmetry . a scan in the space of parameters confirms that these three solutions obtained for special sets of values are actually representative of the three general kinds of solutions that come out and , therefore , the drawn conclusions apply in general . in the panels of figure 2 we show the results of such a scan that highlight the allowed regions in the parameter space projected on different two - parameter planes . + + the scatter plots have been obtained scanning the three mixing angles @xmath122 and @xmath6 over the @xmath123 ranges eqs.([twosigma ] ) , the three phases @xmath124 over the ranges @xmath125 $ ] and the absolute neutrino mass scale for @xmath126 . these ranges also coincide with those shown in the plots , except for @xmath22 where the plots are for @xmath127 simply because no allowed solutions have been found for lower values . the shown results have been obtained in two steps . a first scan of @xmath128 points has yielded a first determination of the allowed regions . with a second scan of additional @xmath129 points , restricted to the excluded regions , we have then more robustly and sharply determined the contours of the allowed regions . notice that these regions have no statistical significance and the random values of the parameters have been generated uniformly . in the top left panel the three rh neutrino masses are plotted versus @xmath22 . we have also plotted the lower bound on the reheating temperature calculated as [ trhmin ] t_rh^min . this calculation relies on the fact that in the case @xmath117 the solutions , as we commented , always fall in a tauon @xmath1-dominated scenario . it can be seen that the lowest bound is given by @xmath130 that in a supersymmetric version , if unchanged , would be marginally reconcilable with the upper bound from the gravitino problem @xcite . this is another reason to extend our investigation to cases with @xmath119 in next sections . in the top central panel we have then plotted the allowed region in the @xmath118 plane that can be compared with an analogous figure in @xcite . here , however , we show only those points that respect the condition @xmath131 but for 2 different values of @xmath132 ( in @xcite we were only showing points for @xmath133 ) . the ( red ) star represents a point found for a minimum value @xmath134 . this point basically roughly indicates where the maximum of the asymmetry occurs in the parameter space for a fixed value of @xmath135 . we will continue to use this convention ( yellow circles for @xmath133 , green squares for @xmath136 and red stars for minimum found @xmath135 value ) throughout the next figures . the structure of the allowed region in the @xmath118 plane can be understood as follows . since @xmath137 and @xmath138 , we immediately deduce that a large lepton asymmetry in the tau flavor may be produced only for sufficiently large values of @xmath22 . this is rather easy to understand . if @xmath22 tends to zero , we go into the so - called decoupling limit , @xmath139 . as the @xmath85 asymmetry needs ( at least ) two heavy states to be generated at the one - loop level , and disregarding the contribution from the @xmath19 , @xmath140 must vanish . the wash - out parameter @xmath141 is @xmath142 @xcite and therefore the final baryon asymmetry may be estimated to be _ b510 ^ -3_2 5 ( ) 10 ^ -10 , which requires m_1()^210 ^ -3ev , for no . this estimate holds if the wash - out from the interaction with @xmath19 is negligible , _ i.e. _ @xmath143 . of course , the smaller is @xmath22 , the smaller @xmath144 needs to be . for @xmath145 ev , the only possibility is that @xmath144 is significantly below unity . extending the analysis of ref . @xcite , one finds [ pp ] s_13(-2 ) > 0.04 . to get the feeling of the figures involved , we may set @xmath146 and find that the wash - out mediated by the @xmath19 s vanishes for an experimentally allowed value of the mixing between the first and the third generation of lh neutrinos , @xmath147 in agreement with our numerical results . if @xmath22 is larger than @xmath148 ev , then @xmath149 is allowed and @xmath6 can be taken to be vanishing . notice also that the lower bound eq . ( [ pp ] ) on @xmath6 increases with @xmath150 . this nicely reproduces the linear dependence emerging from the numerical results in the _ left column middle panel _ for the plane @xmath151 and that is described , roughly for @xmath133 and more accurately for @xmath136 , by [ linear ] _ 2344^+4(_13 - 7^ ) , represented with a dashed line in the panel . in the _ top right panel _ we show the allowed region in the plane @xmath152 . the @xmath85 non conserving terms in neutrino oscillation probabilities can be expressed in terms of the _ jarlskog invariant _ @xmath153 given by @xcite j_cp & = & im[u_3u_e 2u_2^u_e3^ ] + & = & c_12s_12c_23s_23c^2_13s_13 , such that p___-p_|_|_= 4j_cp_k > js_;kj(m^2_kjl2e ) , where @xmath154 . in the bottom left panel we show the allowed points in the plane @xmath155 . it can be noticed that a non zero value of @xmath153 is not crucial . looking at the bottom - central panel , it is interesting to notice that the allowed regions for the majorana phases are centered approximately around @xmath156 and @xmath157 . these play a role in the determination of the _ effective majorana mass _ of @xmath158 in @xmath159 decays that is given by m_ee & = & |_im_iu_ei^2 | + & = & | m_1c_12 ^ 2c_13 ^ 2e^2i+m_2s_12 ^ 2c_13 ^ 2 + m_3s^2_13e^2i(- ) | . in the bottom - right panel one can see how there is a precise relation between @xmath160 and @xmath22 , given approximately by @xmath12 . it can be also noticed that there is quite a strict lower bound @xmath161 . lowest values @xmath162 are the most favoured ones in this case . though current planned experiments will not be able to test the full allowed range , it is still interesting that they will test it partially , tightening the constraints on the other parameters as well . we have also made an interesting exercise . we determined the constraints without making use of any experimental information on the mixing angles and letting them just simply variate between @xmath163 and @xmath164 . the results are shown in fig . [ thijarb ] . first , notice that the lower bound on @xmath22 relaxes of a few orders of magnitude ( see left panel ) . then notice quite interestingly that small values @xmath165 are well allowed for @xmath166 but values @xmath167 would have been very marginally consistent . therefore , the current bound @xmath165 seems to match quite well with successful @xmath0-inspired leptogenesis on the other hand , values @xmath168 would have been more optimal for @xmath165 than the current experimental large atmospheric values ( see the central panel in the figure ) . however , they are still allowed thanks to the observed range of values of the solar neutrino mixing angle ( see the right panel ) . for the solar neutrino mixing angle there is no real favourite range of values for @xmath165 . let us now discuss the results for io . it has been shown @xcite that in grand unified models with conventional type i seesaw mechanism one can always find , for any no model satisfying the low energy neutrino experimental constraints , a corresponding io model . therefore , though they exhibit some unattractive features that quite strongly disfavour them ( e.g. instability under radiative corrections ) , io models within grand unified theories are not unequivocally excluded . it is therefore legitimate to check whether the requirement of successful leptogenesis can somehow provide some completely independent information . we repeated the same scan performed in the case of no and the results are shown in figure [ constrio ] , the analogous of the figure [ constrno ] for the no case . one can see that io is only very marginally allowed . for @xmath133 , there is only a small region at large values of @xmath169 . extending the analysis in ref . @xcite , this is explained by the fact that the wash - out parameter @xmath144 turns out to be k_110 ^ 3evm_atm , while in the no case @xmath144 was proportional to @xmath170 . this constrains @xmath171 to be as large as possible , thus ruling out small values of @xmath22 . it is interesting to notice that in this case the allowed values for @xmath7 lie in the second octant and correspond to the largest ones compatible with the current experimental limits . the allowed values of the effective neutrino mass fall in a narrow range , @xmath172 . + + therefore , io will be in any case fully tested from cosmology and @xmath159 experiments during next years . we will see that this conclusion will hold also allowing @xmath119 . as usual , in the plots the red star corresponds to the minimum value of @xmath135 for which we have found a solution , @xmath173 . the corresponding set of values indicates approximately where the asymmetry has a maximum for a fixed @xmath135 value . for this choice of values , in figure [ io ] , we show the plots of the rh neutrino masses , of the asymmetry @xmath50 , of the @xmath85 asymmetries @xmath174 , @xmath175 , of @xmath176 and of @xmath177 versus @xmath22 . + one can see how the heaviest rh neutrino mass @xmath178 decreases with @xmath22 much faster and at @xmath179 one has @xmath180 . therefore , as one can see from the central top panel , the @xmath85 asymmetries are this time strongly suppressed at @xmath181 . on the other hand , in the range @xmath182 the @xmath85 asymmetries are large enough that successful leptogenesis is still possible . notice , that this kind of solutions are a sort of modification of the solution obtained at large @xmath22 values for no , simply shifted at somehow larger values . the asymmetry is therefore strongly depending on the initial conditions ( @xmath183 ) . the first kind of solution , at small @xmath22 values , is completely absent . therefore , though io is strongly disfavoured , it is not completely ruled out , a conclusion somehow very similar to that one obtained from completely independent arguments @xcite . in this case , however , leptogenesis provides quite a precise quantitative test . we can conclude this section saying that these results confirm and complete those shown in @xcite . in particular it is confirmed that there are viable solutions corresponding to the different points shown in the figures falling in the currently experimentally allowed ranges of the parameters , . the model is therefore not ruled out . a further step is now to understand whether the model is predictive , excluding regions of the parameter space that future experiments can test . from the figures , as we have discussed , it is clear that assuming @xmath117 such excluded regions exist and therefore one obtains interesting constraints . however , it is important to go beyond the simple condition @xmath117 in order to test the stability of the constraints for variations of @xmath59 . this is the main objective of the next sections .

this form of generalized ( gravitational ) uncertainty principle ( gup ) agrees with various theories of quantum gravity and predicts a minimal length uncertainty proportional to @xmath0 and a maximal momentum proportional to @xmath1 , where @xmath2 is the deformation parameter . _ keywords _ : quantum gravity ; generalized uncertainty principle ; quantum bouncer . _ pacs _ : 04.60.bc

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1309.7284

we find exact energy eigenvalues and eigenfunctions of the quantum bouncer in the presence of the minimal length uncertainty and the maximal momentum . this form of generalized ( gravitational ) uncertainty principle ( gup ) agrees with various theories of quantum gravity and predicts a minimal length uncertainty proportional to @xmath0 and a maximal momentum proportional to @xmath1 , where @xmath2 is the deformation parameter . we also find the semiclassical energy spectrum and discuss the effects of this gup on the transition rate of the ultra cold neutrons in gravitational spectrometers . then , based on the nesvizhevsky s famous experiment , we obtain an upper bound on the dimensionless gup parameter . _ keywords _ : quantum gravity ; generalized uncertainty principle ; quantum bouncer . _ pacs _ : 04.60.bc

the existence of a minimal length uncertainty is one of the common aspects of various theories of quantum gravity such as string theory , loop quantum gravity , quantum geometry , and black - hole physics . all these proposals predict a minimum measurable length of the order of the planck length @xmath3 where @xmath4 is the newton s gravitational constant . in recent years , many papers have appeared in the literature to address the effects of the minimal length on various physical systems in the framework of the generalized uncertainty principle ( gup ) @xcite . recently , several approaches have been developed for testing the effects of quantum gravity which range from astronomical observations @xcite to table - top experiments @xcite . we can mention the proposal by amelino - camelia and lammerzahl that explains puzzling observations of ultrahigh energy cosmic rays in the framework of ( quantum gravity ) modified laws for particle propagation @xcite . the usage of high intensity laser projects for quantum gravity phenomenology is also suggested by magueijo in the context of deformed special relativity @xcite . have proposed a direct measurement scheme to experimentally test the existence of a minimal length scale using a quantum optical ancillary system @xcite . they probed possible deviations from ordinary quantum commutation relation at the planck scale within reach of current technology . these progresses could shed light on possible detectable planck - scale effects . on the other hand , doubly special relativity ( dsr ) theories essentially require the existence of a maximal momentum @xcite . a gup proposal which is consistent with these theories is discussed in refs . moreover , another gup scenario which agrees with the seminal proposal by kempf , mangano and mann ( kmm ) @xcite to first order of the gup parameter is recently proposed in refs . the latter gup model implies the noncommutative geometry , i.e. @xmath5\ne 0 $ ] , and predicts both a minimal length uncertainty and a maximal momentum proportional to @xmath0 and @xmath1 respectively , where @xmath2 is the gup parameter . various problems such as the free particle , particle in a box , harmonic oscillator , black body radiation , cosmological constant , maximally localized states , and hydrogen atom have been previously studied in this framework @xcite . the quantum stationary solutions of the schrdinger equation that describes particles bouncing vertically and elastically above a horizontal reflecting mirror in the earth s gravitational field is well - known theoretically . however , the experimental realization of this phenomenon is so difficult due to two main reasons . first , for the macroscopic objects the gravitational quantum effects are negligible . also , the electromagnetic interaction has the dominate role for the charged particles . thus , we need to perform the experiment using neutral elementary particles with a long lifetime such as neutrons . this famous experiment has been demonstrated a few years ago by nesvizhevsky et al . using a high precision neutron gravitational spectrometer @xcite . notice that , the perturbative effects of the minimal length and/or maximal momentum on the quantum bouncer spectrum are studied in refs . @xcite . in the context of the kmm gup where there exists just a minimal length uncertainty this problem is exactly solved in ref .

we find that the total spectrum of electron states in a bounded 2d electron gas with spin - orbit interaction contains two types of evanescent states lying in different energy ranges . they are described by a pure imaginary wavevector . the states of second type lie in the forbidden band . they are described by a complex wavevector . these states give rise to unusual features of the electron transmission through a lateral potential barrier with spin - orbit interaction , such as an oscillatory dependence of the tunneling coefficient on the barrier width and electron energy . but of most interest is the spin polarization of an unpolarized incident electron flow . the polarization efficiency is an oscillatory function of the barrier width . spin filtering is most effective , if the fermi energy is close to the barrier height .

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0710.2689

we find that the total spectrum of electron states in a bounded 2d electron gas with spin - orbit interaction contains two types of evanescent states lying in different energy ranges . the first - type states fill in a gap , which opens in the band of propagating spin - splitted states if tangential momentum is nonzero . they are described by a pure imaginary wavevector . the states of second type lie in the forbidden band . they are described by a complex wavevector . these states give rise to unusual features of the electron transmission through a lateral potential barrier with spin - orbit interaction , such as an oscillatory dependence of the tunneling coefficient on the barrier width and electron energy . but of most interest is the spin polarization of an unpolarized incident electron flow . particularly , the transmitted electron current acquires spin polarization even if the distribution function of incident electrons is symmetric with respect to the transverse momentum . the polarization efficiency is an oscillatory function of the barrier width . spin filtering is most effective , if the fermi energy is close to the barrier height .

the spin - orbit interaction ( soi ) in low - dimensional structures attracts a great deal of interest since it opens up the possibility to manipulate the electron spin in nonmagnetic structures using electrical means . @xcite in this view , semiconductor heterostructures with 2d electrons are very promising since the rashba soi is effectively controlled @xcite by varying applied bias or gate voltages . in recent years , predominant interest was paid to effects appearing when the soi modifies propagating electron modes with energy above the conduction band bottom . suffice it to mention the spin - hall effect , @xcite or spin manipulation in strained semiconductors @xcite . in this paper we show that interesting effects of the soi arise also when the electron energy is lower than or near to the conduction band bottom and evanescent states are involved . these states determine electron tunneling . they are important in 2d structures with laterally inhomogeneous potential landscape . we find that such structures can effectively polarize the transmitted electron current . 3d tunnel structures , in which spin polarization arises due to the soi , were considered in a number of recent works . zakharova et al @xcite studied the interband tunneling , voskoboynikov et al @xcite considered a tunnel structures with the rashba soi at the interfaces . in these cases the electron flow acquires a spin polarization if the structure is asymmetric . in symmetric tunnel structures the spin polarization arises , if the barrier material is noncentrosymmetrical . @xcite the polarization mechanism , proposed by perel et al @xcite , consists in a spin - dependent renormalization of the electron effective mass owing to the dresselhaus soi in the barrier . however , all these structures have a common property restricting their capability to generate spin polarization . the polarization is absent if the electron current is perpendicular to the barrier . in other words , for the spin polarization to appear the momentum distribution function of incident electrons must be asymmetric with respect to the momentum component parallel to the barrier . the effective mass renormalization occurs if the hamiltonian of the soi is quadratic in longitudinal momentum . however , the dispersion relation of electrons in the presence of the soi is generally much more complicated and therefore a more careful analysis of the complex band structure and evanescent states should be carried out to study the spin - dependent tunneling . in the 3d case , such calculations were recently carried out for some specific materials and qualitatively new features were found . @xcite 2d tunnel structures are scantily studied to date . in particular , as far as we know , even the complex band structure of 2d electrons was not explored . though the presence of evanescent states is obvious , only a few of works touched upon these modes . usaj , reynoso and balseiro @xcite attracted evanescent states to study the electron scattering at the edges of 2d samples , but the total spectrum of evanescent states was not considered . the importance of evanescent modes in quasi - one - dimensional systems in the presence of the soi was pointed out in a number of works . @xcite khodas , shekter , and finkelstein @xcite studied the electron beam propagation in 2d electron gas with spatially inhomogeneous soi . they considered the transmission through a strip , in which the soi strength differs from that in the rest of the 2d electron gas , to show that an initially unpolarized beam splits into two beams with different spin polarizations propagating in different directions . the consideration was restricted by propagating states since only the case of uniform potential landscape was studied . spin - dependent reflection of electrons from a lateral barrier in 2d system was observed in insb / inalsb heterostuctures @xcite and described theoretically in ref . . silvestrov and mishchenko @xcite demonstrated the possibility to achieve spin - polarized currents in a 2d system with smooth potential barrier and spatially - uniform soi by considering propagating modes within semiclassical approach . in this paper we show that strong polarization effect appears in 2d structures when electrons pass through a lateral potential barrier , in which the soi is stronger than in the outside 2d electron gas regions ( reservoirs ) . the polarization arises even if the electric current is normal to the barrier . the highest polarization is attained when the electron energy is close to the conduction band bottom in the barrier . in this case the fact becomes important that the soi effectively splits the barrier height so that some part of electrons passes through the barrier via propagating states while others do this via the evanescent modes . since the spin and orbital degrees of freedom are coupled , rather strong spin filtering occurs . we study the total spectrum of electron states in 2d bounded system with soi to find that there are two type of evanescent states . the first - type states are characterized by an imaginary longitudinal wavevector . they fill in a gap in the propagating state spectrum . the states of the second type lie in the forbidden gap . they are described by a complex wavevector . the electron tunneling through a lateral barrier with soi via these evanescent states exhibits unusual features , such as an oscillatory behavior of the transmission coefficient with the barrier width . but of most interest is the spin polarization of the electron current . the polarization efficiency is high enough even if the distribution function of incident electrons is symmetric with respect to the transverse momentum . we explore the polarization efficiency in a wide range of electron energy to find that most effective spin filtering occurs if the fermi energy is close to the barrier height . the paper is organized as follows . in sec . [ complexstructure ] we describe the complex band structure and total spectrum of electron states . sec . [ tunneling ] is devoted to the tunneling through a barrier with soi . in sec . [ polarization ] the electric and spin currents through the barrier with soi are considered for a wide range of the fermi energy in the reservoirs . the results obtained for the rashba soi are generalized to the dresselhaus soi in sec . [ dresselhaus ] . we summarize and conclude in sec . [ conclude ] .

we have analyzed all the archival x - ray data of 134 unidentified ( unid ) gamma - ray sources listed in the first _ in these analysis , we target all the 1fgl unid sources , using updated data from the second _ fermi / lat _ ( 2fgl ) catalog on their lat position and spectra . we found several potentially interesting objects , particularly three sources , 1fglj0022.2 - 1850 , 1fglj0038.0 + 1236 and 1fglj0157.0 - 5259 , which were then more deeply observed with as a part of an ao7 program in 2012 . we discuss the possible nature of these three sources observed with , together with the x - ray identification results and seds of all 134 sources observed with _ swift_/xrt .

i

1307.5581

we have analyzed all the archival x - ray data of 134 unidentified ( unid ) gamma - ray sources listed in the first _ fermi / lat _ ( 1fgl ) catalog and subsequently followed up by _ swift / xrt_. we constructed the spectral energy distributions ( seds ) from radio to gamma - rays for each x - ray source detected , and tried to pick up unique objects that display anomalous spectral signatures . in these analysis , we target all the 1fgl unid sources , using updated data from the second _ fermi / lat _ ( 2fgl ) catalog on their lat position and spectra . we found several potentially interesting objects , particularly three sources , 1fglj0022.2 - 1850 , 1fglj0038.0 + 1236 and 1fglj0157.0 - 5259 , which were then more deeply observed with as a part of an ao7 program in 2012 . we successfully detected an x - ray counterpart for each source whose x - ray spectra were well fitted by a single power - law function . the positional coincidence with a bright radio counterpart ( currently identified as agn ) in the 2fgl error circles suggests these are definitely the x - ray emission from the same agn , but their seds show a wide variety of behavior . in particular , the sed of 1fglj0038.0 + 1236 is difficult to be explained by conventional emission models of blazars . the source 1fglj0022.2 - 1850 may be in a transition state between a low - frequency peaked bl lac and a high - frequency peaked bl lac object , and 1fglj0157.0 - 5259 could be a rare kind of extreme blazar . we discuss the possible nature of these three sources observed with , together with the x - ray identification results and seds of all 134 sources observed with _ swift_/xrt .

since the successful launch of the _ fermi _ gamma - ray space telescope in 2008 june , we now have a new opportunity to study gamma - ray emission from different types of high energy sources with much improved sensitivity and localization capabilities than with the egret instrument onboard the _ compton gamma - ray observatory _ ( cgro ) . with the field of view covering 20% of the sky at every moment ( five times larger than egret ) , and its improved sensitivity ( by more than an order of magnitude with respect to egret ) , the large area telescope ( lat ; * ? ? ? * ) aboard _ fermi _ surveys the entire sky each day down to photon flux levels of @xmath0 @xmath1 few @xmath2 . the number of detected gamma - ray sources has increased , with the 2nd catalog ( 2fgl ; * ? ? ? * ) containing 1873 gamma - ray sources in the 100 mev to 100 gev range , while 271 objects were previously listed in the 3rd egret catalog ( 3eg ; * ? ? ? more than 1,000 gamma - ray sources included in the 2fgl are proposed to be associated with active galactic nuclei ( agns ) and 87 sources with pulsars ( psrs ; * ? ? ? * ) , including 21 millisecond pulsars ( msps ) . other associations included supernova remnants ( snrs ; * ? ? ? * ) , low - mass / high - mass x - ray binaries @xcite , pulsar wind nebulae @xcite , normal and starburst galaxies @xcite , and the giant lobes of a radio galaxy @xcite . however , no obvious counterparts at longer wavelength have been found for as much as 31% of the 2fgl objects so that several hundreds of gev sources currently remain unassociated with any known astrophysical systems . in other words the nature of unassociated gamma - ray sources are still one of the major puzzles , and the mystery has never been solved yet . fortunately , an improved localization capabilities of the ( typical 95% confidence radii @xmath3 , and even 0@xmath4.005 - 0@xmath4.01 for the brightest sources ; @xcite ) , when compared to that of egret ( typical @xmath5 ) , enables more effective follow - up studies at radio , optical , and x - ray frequencies , which can help to unravel the nature of the unid gamma - ray emitters . indeed for example , a lot of _ fermi _ sources were identified using wise ir data @xcite . in this context , we started a new project to investigate the nature of unid objects through x - ray follow - up observations with the xis sensor onboard the x - ray satellite ( see section 2 ) . for example , the results of the first - year campaign conducted in ao-4 ( 2009 ) were presented in @xcite . in this campaign , the x - ray counterpart for one of the brightest unassociated objects , 1fglj1231.1 - 1410 ( also detected by egret as 3egj1234 - 1318 and egrj1231 - 1412 ) , was discovered for the first time . the x - ray spectrum was well fitted by a blackbody with an additional power - law component , supporting the recent identification of this source with a msp . in the second - year campaign ( ao-5 ) , another seven unid sources were subsequently observed with @xcite . in particular , this paper presented a convenient method to classify the objects into `` agn - like '' and `` psr - like '' by comparing their multiwavelength properties with those of known agns and pulsars . in the third - year ( ao-6 ) , 1fglj2339.7 - 0531 ( yatsu et al . 2013 in prep ; also romani & shaw 2011 ) and 1fglj1311.7 - 3429 @xcite were intensively monitored with a total exposure time of 200 ksec . both sources are now suggested to be `` black widow '' msp systems and newly categorized as `` radio - quiet '' msps . as these projects show , the x - ray follow - up observations especially using provided various fruitful results to clarify the nature of unassociated gamma - ray sources , and was able to find a new type of gamma - ray emitter . to complete a series of x - ray follow - up programs described above , we further carried out the analysis of all the archival x - ray data of 134 unid gamma - ray sources in the 1fgl catalog of point sources ( 1fgl ; * ? ? ? _ swift_/xrt . note that , all these 134 sources have been detected in the 2fgl catalog , hence the updated data on there lat position and spectra were available from the 2nd @xmath6/lat catalog so are used throughout this work . this allowed us to construct the seds ( seds ) of each objects from radio to gamma - rays ( see section2 and appendix ) for the first time . note that we target all the 1fgl unid sources that satisfy our selections ( see section2 ) , using updated / improved information from the 2fgl catalog on their lat positions and spectra in this paper . moreover , three sources that displayed potentially interesting seds , 1fglj0022.2 - 1850 ( or 2fgl j0022.2 - 1853 ) , 1fglj0038.0 + 1236 ( or 2fgl j0037.8 + 1238 ) and 1fglj0157.0 - 5259 ( or 2fgl j0157.2 - 5259 ) , were deeply observed with as a part of ao7 campaign in 2012 . in the 2fgl catalog , both 1fglj0022.2 - 1850 and 1fglj0157.0 - 5259 are categorized as active galaxies of uncertain type ( agu ) , while 1fglj0038.0 + 1236 was classified as a bl lac type of blazar ( bzb ) based on the positional coincidences to sources observed at another wavelength . but as we see below , the unique seds of these three objects are not well understood as conventional blazars . in section2 we first describe the analysis of the 134 1fgl unid sources with _ swift_. subsequently in section3 , deep follow - up observations of the selected three sources , 1fglj0022.2 - 1850 , 1fglj0038.0 + 1236 and 1fglj0157.0 - 5259 are shown . the results of the analysis are given in section4 . the discussion and summary are presented in section5 and 6 , respectively .

the positional coincidence with a bright radio counterpart ( currently identified as agn ) in the 2fgl error circles suggests these are definitely the x - ray emission from the same agn , but their seds show a wide variety of behavior . in particular , the sed of 1fglj0038.0 + 1236 is difficult to be explained by conventional emission models of blazars . the source 1fglj0022.2 - 1850 may be in a transition state between a low - frequency peaked bl lac and a high - frequency peaked bl lac object , and 1fglj0157.0 - 5259 could be a rare kind of extreme blazar .

c

1307.5581

we have analyzed all the archival x - ray data of 134 unidentified ( unid ) gamma - ray sources listed in the first _ fermi / lat _ ( 1fgl ) catalog and subsequently followed up by _ swift / xrt_. we constructed the spectral energy distributions ( seds ) from radio to gamma - rays for each x - ray source detected , and tried to pick up unique objects that display anomalous spectral signatures . in these analysis , we target all the 1fgl unid sources , using updated data from the second _ fermi / lat _ ( 2fgl ) catalog on their lat position and spectra . we found several potentially interesting objects , particularly three sources , 1fglj0022.2 - 1850 , 1fglj0038.0 + 1236 and 1fglj0157.0 - 5259 , which were then more deeply observed with as a part of an ao7 program in 2012 . we successfully detected an x - ray counterpart for each source whose x - ray spectra were well fitted by a single power - law function . the positional coincidence with a bright radio counterpart ( currently identified as agn ) in the 2fgl error circles suggests these are definitely the x - ray emission from the same agn , but their seds show a wide variety of behavior . in particular , the sed of 1fglj0038.0 + 1236 is difficult to be explained by conventional emission models of blazars . the source 1fglj0022.2 - 1850 may be in a transition state between a low - frequency peaked bl lac and a high - frequency peaked bl lac object , and 1fglj0157.0 - 5259 could be a rare kind of extreme blazar . we discuss the possible nature of these three sources observed with , together with the x - ray identification results and seds of all 134 sources observed with _ swift_/xrt .

in the uniform analysis of archival _ swift _ data , we found several objects which seemed to display anomalous seds that are not typical of agns or psrs . then we performed x - ray follow - up observations of three such sources to more accurately determine the seds of each object ( figures 7 , 8 , and 9 ) . different fluxes between _ swift_/xrt and /_xis _ seen in these seds indicate that these objects should have temporal variability that was not seen within the individual shorter exposures . moreover , thanks to the good sensitivity and long exposure of the data , we have additional hints to reveal the nature of each source as discussed below . an x - ray source found within the updated 2fgl error ellipse of 1fglj0022.2 - 1850 is positionally consistent with the radio source nvssj00209 - 185332 found in the nvss catalog @xcite ( see table2 ) . moreover , infrared counterpart source wisej002209.25 - 185334.7 located at ( ra , dec)=(5@xmath4.5385563 , -18@xmath4.8929772 ) was found in the wide field infrared survey explorer ( wise ) all - sky release @xcite . the sed of 1fglj0022.2 - 1850/wisej002209.25 - 185334.7/nvssj00209 - 185332 , including our _ suzaku_/xis data and derived xrt and uvot fluxes from _ swift _ , are shown in figure7 . from the relatively high radio flux and flat x - ray spectrum obtained with _ swift_/xrt , this object is likely to be a low - frequency peaked bl lac ( lbl ) . however , during our observation , the x - ray spectrum was observed to be substantially steeper , more typical of a high - frequency peaked bl lac ( hbl ) . moreover , the flat gev gamma - ray spectrum is typical of hbls like mrk 421 and mrk 501 , rather than a lbl . considering the cherenkov telescope array ( cta ) which is an initiative to built a next generation observatory for very - high energy gamma - rays will have an improved sensitivity by an order of magnitude with respect to current instruments ( @xmath51 above a few tev ) , the upward shape of the spectrum suggests the source could be detected also in tev energy in the near future . in the case of 1fglj0038.0 + 1236 , the location of a x - ray counterpart discovered in our observations is consistent with nvssj003750 + 123818 described in table2 , and each optical counterpart sdssj003750.88 + 123819.9 ( classified as galaxy ) located at ( ra , dec)=(9@xmath4.462 , 12@xmath4.638875 ) and infrared counterpart wisej003750.87 + 123819.9 located at ( ra , dec)=(9@xmath4.4619958 , 12@xmath4.6388878 ) , were also found in the sloan digital sky survey ( sdss ) catalog @xcite and wise catalog respectively . the constructed radio to x - ray sed together with the _ swift _ xrt / uvot and the lat spectrum is shown in figure8 . since the x - ray spectrum appears very steep , this source seems to be associated with a hbl , while the steep gamma - ray spectrum observed with favors a fsrq origin of this source . while optical and ultraviolet fluxes are extremely bright , this could be due to a contribution of soft photons from the host galaxy as seen in some blazar spectra ( see e.g. , the sed of mrk 501 ; @xcite ) . these results show that this source is difficult to be explained by conventional leptonic models of blazars ( i.e. , ssc or external compton models ) . in the case of 1fglj0157.0 - 5259 , our _ suzaku_/xis observations revealed the presence of a quite bright x - ray counterpart in the lat error circle , and since the hard x - ray fluxes of this source are very high , we could also obtain data from _ suzaku_/hxd . at the position of this x - ray source , the radio counterpart sumss j015657 - 530157 was found in the sumss catalog @xcite(table2 ) . the broad - band sed of 1fglj0157.0 - 5259/sumssj015657 - 530157 with our _ suzaku_/xis , hxd and derived _ swift_/xrt , uvot data is presented in figure9 . since the x - ray fluxes are connected by a straight line with the radio fluxes , these fluxes are seemed to be explained by synchrotron radiation . the peak frequency of the synchrotron spectrum is very high ( @xmath810 kev ) suggesting that the source could be one a rare type of `` extreme '' blazar like mrk 501 in the historical high state @xcite . if this source is an `` extreme '' blazar , observations at tev energies or more deep observations with may detect significant signal in the future . finally , we made the similar figure described in takahashi et al . ( 2012 ) for the 1fgl 134 unid objects in which we performed follow - up observations with _ swift_/xrt ( figure10 ) . this figure presents a comparison of the agns ( aqua ) , psrs ( green ) , and unassociated sources ( red ) which classified in the 2fgl catalog in the x - ray to gamma - ray flux ratios versus radio to gamma - ray ratios plane . the three sources we observed with in this paper are shown in black stars . apparently , that these sources are situated in the typical agn region of this diagnostic plane . it is noteworthy that , 1fglj0157.0 - 5259 is at the right edge of this typical agn region , and this means the x - ray and gamma - ray flux ratios of this source is quite high , such that @xmath52 2 , which is consistent with our speculation that the source is an extreme hbl - type blazar .

we have begun a survey of the structure of the milky way halo , as well as the halos of other local group galaxies , as traced by their constituent giant stars . these giant stars are identified via large area , ccd photometric campaigns . here , we verify the primary dependence of the @xmath4 color on luminosity , and demonstrate the secondary sensitivity to metallicity among giant stars . our empirical results are found to be generally consistent with those from analysis of synthetic spectra by paltoglou & bell [ 1994 , mnras , 268 , 793 ] .

i

astro-ph0006411

we have begun a survey of the structure of the milky way halo , as well as the halos of other local group galaxies , as traced by their constituent giant stars . these giant stars are identified via large area , ccd photometric campaigns . here we present the basis for our photometric search method , which relies on the gravity sensitivity of the mg i triplet + mgh features near 5150 in f - k stars , and which is sensed by the flux in the intermediate band @xmath0 filter . our technique is a simplified variant of the combined washington / ddo51 four filter technique described by geisler [ 1984 , pasp , 96 , 723 ] , which we modify for the specific purpose of efficiently identifying distant giant stars for follow - up spectroscopic study : we show here that for most stars the washington @xmath1 color is correlated monotonically with the washington @xmath2 color with relatively low scatter ; for the purposes of our survey , this correlation obviates the need to image in the @xmath3 filter , as originally proposed by geisler . to calibrate our ( @xmath2 , @xmath4 ) diagram as a means to discriminate field giant stars from nearby dwarfs , we utilize new photometry of the main sequences of the open clusters ngc 3680 and ngc 2477 and the red giant branches of the clusters ngc 3680 , melotte 66 and @xmath5 centauri , supplemented with data on field stars , globular clusters and open clusters by doug geisler and collaborators . by combining the data on stars from different clusters , and by taking advantage of the wide abundance spread within @xmath5 centauri , we verify the primary dependence of the @xmath4 color on luminosity , and demonstrate the secondary sensitivity to metallicity among giant stars . our empirical results are found to be generally consistent with those from analysis of synthetic spectra by paltoglou & bell [ 1994 , mnras , 268 , 793 ] . finally , we provide conversion formulae from the ( @xmath6 , @xmath2 ) system to the ( @xmath7 , @xmath8 ) system , corresponding reddening laws , as well as empirical red giant branch curves from @xmath5 centauri stars for use in deriving photometric parallaxes for giant stars of various metallicities ( but equivalent ages ) to those of @xmath5 centauri giants .

understanding the nature of the milky way halo its shape , extent , density distribution , kinematics , abundance distribution and origin has long been a central topic in astronomy . the importance of this endeavor has increased substantially with the growing , pervasive connections to a number of other astronomical enterprises bearing on such wide ranging astrophysical problems as , for example , the magnitude and distribution of dark matter and the frequency of microlensing events , the origin of the second parameter problem of horizontal branch morphology in globular clusters , the nature of high velocity hi clouds , the interaction of galaxies with their environment , and , of course , the origin and evolution of the milky way . in spite of the pressing need for a detailed picture of the halo , at present we still have only the most rudimentary prescriptions of , for example , the phase space distribution of halo stars . unfortunately , for many applications we no longer can be satisfied with elementary analytical models of the halo . indeed , the very suitability of such simple descriptions may now be questioned . a number of new lines of evidence indicate that the halo of the milky way has not achieved a dynamically relaxed state . confirmation of this rather old idea is a long time in coming . studies of candidate `` moving groups '' of metal - poor stars with halo kinematics in the solar neighborhood were made long ago by eggen and collaborators @xcite , and the idea of a halo with significant structure in the form of intermingling `` tube - like swarms '' was a viable theoretical description at least 35 years ago @xcite . however , apart from consistent attention to the subject of halo `` moving groups '' by @xcite ( @xcite , and references therein ) , until recently the subject of halo substructure has received little other interest , in deference to more prosaic descriptions of the galactic halo those easily described by relatively simple analytical prescriptions . this state of affairs was influenced perhaps , in part , by a growing emphasis on computer models of galactic structure that relied on analytical density laws ( * ? ? ? * ; * ? ? ? * _ et seq . _ ) , coupled with the lack of _ systematic _ observational efforts toward uncovering even first order global laws ( e.g. , density relations , amount of flattening , kinematical and chemical trends with position ) along more than a small number of lines of sight , let alone _ deviations _ from these simple global descriptions . moreover , the rather smoother phase space distributions of the `` flattened halo '' and intermediate population ii ( which may or may not be parts of one continuous population ; see @xcite ) , locally dominate the more extended halo component what @xcite refers to as the `` pure races of the halo population ii '' . indeed , that these flattened galactic populations contain stars with chemodynamical properties ( `` high velocity '' and low metallicity ) that are typically considered `` halo - like '' has long vexed understanding of the true `` mixture ratios '' and individual chemodynamical properties of the various overlapping stellar populations ( see , for example * ? ? ? the more relaxed dynamical state of the locally more dominant , flattened metal - poor components of the galaxy may have long distracted attention from an unrelaxed halo population filled with _ substructure_. with the latter point as preface , it is worthwhile , therefore , to clarify our own working conception of the `` halo '' that galactic component we aim to explore in the present survey since the very definition of `` halo '' has taken on such a diversity of connotations . presently fashionable `` dual halo '' models of the milky way those containing both flattened , prograde rotating and spherical , slow to non- ( or even retrograde ) rotating metal - poor components @xcite bear a resemblance to the commonly accepted galactic descriptions at the 1957 vatican conference @xcite , when one appreciates that the properties of the intermediate population ii ( ipii ) discussed there parallel properties assigned to the `` new '' flattened , contracted halo / thick disk components in today s models . in the present survey , we are concerned with oort s `` pure race '' of population ii : the extended , more or less spherical distribution of stars with the most extreme kinematics in the galaxy , where growing theoretical and observational work suggests evidence of past galactic accretion events may be fossilized . the intermediate population ii , `` low '' or `` flattened '' halo which may all be the same thing @xcite we address more fully in our parallel astrometric survey ( e.g. , * ? ? ? * ; * ? ? ? * _ et seq . _ ) . in the last decade or so , a number of developments have spawned intense interest in the interaction of milky way - like galaxies with each other and with their satellites and clusters : e.g. , ( 1 ) the popularity of cold dark matter models of the universe , with the concomitant `` bottom up '' growth of structure from the collection of smaller subunits ( e.g. , * ? ? ? * ) , ( 2 ) the realization of the prevalence of gravitationally interacting galactic systems in the nearby universe ( demonstrated of course by @xcite ; and explored more recently by , for example , @xcite ) and at high redshifts by @xcite , ( 3 ) the discovery of the formation of globular clusters @xcite and dwarf satellites @xcite in the course of such gravitational interactions , ( 4 ) the discovery of new galactic satellites @xcite , possibly associated galactic neighbors @xcite , and distant globular clusters ( e.g. , * ? ? ? * ; * ? ? ? * ) and the fact that some of these systems have complex star formation histories ( e.g. , * ? ? ? * ; * ? ? ? * ) , and ( 5 ) the recognition of the complexities of the dynamics of the local group and the implications for the size of galactic dark matter components and the cosmological density , @xmath9 @xcite . new computer studies of galaxy interactions ( @xcite , but all predated by @xcite ) confirm long - held notions ( @xcite ; see also the related results of @xcite ) that satellite galaxies , when experiencing tidal disruption by a larger galactic potential , can leave behind long - lived structures oort s `` tube - like swarms '' along the satellite orbit . the idea that these _ satellites themselves _ may not be dynamically relaxed systems @xcite has also played an important role in the debate on the existence of substantial dark matter halos in these systems ( cf . discussion in * ? ? ? * hereafter paper ii ) . hints of substructure in the galactic halo that may be the `` swarms '' that are the hallmark of accretion of smaller stellar systems have been suggested in several surveys of halo stars undertaken since the concentrated effort of eggen to find halo ( and other ) `` moving groups '' among stars in the solar neighborhood . this more recent evidence has most often been found in surveys of the more distant , `` pure '' halo , and most typically as clusterings of stars in distance and radial velocity e.g. , the clumps of distant blue horizontal branch stars in @xcite , @xcite , and @xcite . one very notable radial velocity - distance clump in the survey of distant stars by @xcite is now recognized as the structural paradigm of the type of tidal events sought here an extremely elongated , tidal structure forming through the destruction of the sagittarius dwarf galaxy . indeed , the sgr galaxy was first identified through the clustering of radial velocities in distant _ giant stars _ , a technique we intend to exploit in the present survey . earlier evidence for possible tidal debris recognized as families of associated outer halo clusters and dwarf spheroidals was discussed by @xcite , @xcite and @xcite , and has received an increase in interest more recently @xcite . one `` family '' of clusters ( including arp 2 , terzan 7 and 8 , m54 , and pal 12 ) is apparently associated with the paradigm tidal event , sagittarius @xcite . phase space clumpings of more nearby , dwarf stars have also been identified by @xcite , @xcite , @xcite ( @xcite ) , and @xcite , with the clumps in the latter three works delineated in all three dimensions of motion very clearly being identified as halo members on the basis of both kinematics and abundance . a surprising implication of @xcite is that the more distant halo appears to be _ dominated _ by phase space structure i.e. , very little `` random '' , dynamically relaxed halo field population exists outside of the ipii . this empirical result would appear to echo theoretical suggestions that a large fraction of the halo might contain substructure @xcite . detailed surveys of the halo including both precision proper motions and radial velocities , like the @xcite analysis , may be needed to understand the full spectrum of structure in halo phase space , and that particular survey continues to pursue that question . however , to cover any significant amount of area in this detailed manner presents a formidable and improbable task at present . moreover , to carry out this kind of work to distances as large as those of the present retinue of galactic satellites possibly major contributors to the overall halo field star population will need to await new generations of microarcsecond astrometry instruments , such as the space interferometry mission . in the meantime , questions regarding the existence of halo substructure , its extent , filling factor , size spectrum , etc . may be approached even when full kinematical data may not be obtainable . the survey we describe here is aimed at divining and defining physical substructure in the halo when that substructure is coherent and has reasonable contrast above any well - mixed background in the occupied volume . a primary aim of the present survey is to probe to large galactic distances with ease , and so provide a complement to the more detailed , but more confined , @xcite proper motion - radial velocity survey of the halo and ipii . the greater distances probed in the giant survey described here lend certain advantages over a survey of more nearby stars , even one replete with full , 3-d kinematical information . while perhaps decreasing sensitivity to subtle , more diffuse , structures requiring a full analysis of phase space , exploring at great distances from the galactic midplane unfetters the data and analysis from contamination by stars in the same survey volume having similar chemodynamical properties to , but coming from stellar populations ( e.g. , ipii , or the `` lower halo '' ) other than , the `` pure '' halo . from the standpoint of uncovering detailed information on the history of the galaxy from phase space substructure , surveys of distant halo stars also have the added benefit that remote tidal structures are longer lived in the softer gradient of the galactic potential at large radii . debris closer to the galactic center becomes phase - mixed rather quickly , and loses spatial coherence that would otherwise be easily identifiable ( although _ velocity _ coherence is _ increased _ distance also increases the contrast of strongly coherent structures against the background , because the linear width of a given structure subtends a smaller area on the sky , and the magnitude spread in the color - magnitude diagram from depth effects is decreased ( see @xcite ) , and because any smooth background of stars should have a rather steep density fall - off with galactocentric radius ( going as , say , @xmath10 ) . recent work by @xcite and @xcite makes it evident that kinematic substructure in the halo would be difficult to see with simple starcounting techniques . the densities of `` star swarms '' from dissociated galactic satellites are simply too low to be detectable above the foreground curtain of disk and ipii dwarfs a problem especially confounded when the swarms are at distances where the _ much smaller _ volume density of their luminous , evolved stars is the only signal likely to be observable . to make tidal streams in the outer halo more evident , it clearly would be beneficial to be able to reduce , or completely filter out , foreground disk contamination , to which main sequence stars make the greatest contribution redward of the field main sequence turnoff . the signal - to - noise of a systematic search could be increased substantially if one were able _ a priori _ to key on stars of a set absolute luminosity because then disk and ipii stars with this luminosity would be easily differentiated from outer halo stars simply by their substantially brighter apparent magnitudes . for example , halo rr lyrae stars and horizontal branch stars , which have a relatively limited range of absolute magnitudes , are rather easy to identify on the basis of variability or color and have been used as tracers of halo structure ( e.g. , * ? ? ? * ; * ? ? ? on the other hand , horizontal branch stars are sufficiently rare that , while they can point to the _ presence _ of halo substructure , they may not be able to trace subtle or more _ tenuous _ halo substructure convincingly and/or thoroughly , as the rather small , candidate `` moving groups '' found by @xcite , @xcite , and @xcite would suggest . unevolved , main sequence stars would , of course , make up the bulk of any stellar stream , but it is too difficult at present to explore dwarf stars to very great distances over large areas , though this technique has been used to study deep , pencil beam surveys with large telescopes in small numbers of strategically placed directions ( see , e.g. , * ? ? ? * ; * ? ? ? * ) . for exploring halo substructure , giant stars may provide a reasonable compromise between the problems associated with the readily identifiable , but less numerous horizontal branch stars and the more common , but intrinsically faint dwarf stars . giant stars are generally a few times more populous than horizontal branch stars in a given stellar population and provide the distinct advantage that they are bright enough to be imaged to great distances even with small telescopes . with giant stars large volumes of the outer galaxy may be explored efficiently with small telescopes ( where larger blocks of observing time are easier to come by ) if a reasonable means can be found by which to pick out the giants from the foreground dwarfs . there have been several k giant studies at high galactic latitude @xcite from which we can infer expected densities of population ii giants . @xcite found @xmath11 1 giant deg@xmath12 in a survey complete for the magnitude range @xmath13 covering @xmath14 deg@xmath15 at the sgp . in several high galactic latitude fields covering a total area of @xmath16 deg@xmath15 , @xcite found a mean density for population ii giants of order 2 deg@xmath12 in the magnitude range @xmath17 . with an expected mean radial fall - off of the halo with galactocentric radius as @xmath18 we obtain a flat differential count of giants with magnitude ( ) and we may extrapolate that to @xmath19 ( distances of @xmath20 kpc , for typical @xmath21 halo metallicity giants ) we should expect approximate mean densities of halo giants of @xmath22 deg@xmath12 . thus , it is clear that a survey for giant stars must cover large areas of the sky in order to garner reasonably large statistical samples . the requirement for large sky coverage drives the criteria to make our survey as efficient as possible at identifying giant stars . it has long been known that the strength of the mgh + mgb triplet feature at 5100 is strongly dependent on surface gravity ( see figure 1 ; * ? ? ? * ; * ? ? ? * ) , and it is a common technique to identify giants by their weak absorption in this part of the spectrum @xcite . @xcite ( @xcite ) showed that discrimination of k giants and dwarfs by this feature was possible with low resolution ( 20 ) objective prism plates from schmidt telescopes , while @xcite and @xcite had already devised a technique by which to identify giants _ photometrically _ with a pair of intermediate band filters , centered at 4880 ( @xmath23 `` continuum '' ) and 5150 ( @xmath0 `` mg '' ) . this filter system has been applied to the giant surveys of @xcite . later , @xcite ( @xcite , _ et seq . _ ) showed that good photometric luminosity classification was still possible with the @xmath0 filter ( see figure 1 ) when the continuum was measured with an appropriate broad band filter , in this case the @xmath6 filter of the washington system @xcite , at considerable savings in telescope time . note that @xcite actually proposed the use of just such an intermediate band filter located around 5000 to allow luminosity classification . the washington system itself was designed as a more efficient broadband system than @xmath24 for the study of the temperatures and abundances of g and k giants ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? geisler s work has demonstrated the efficacy of separating g - k dwarfs and giants in the ( @xmath1 , @xmath4 ) color - color diagram ( where @xmath6 , @xmath3 , and @xmath25 are in the washington system ) for a sample of stars spanning a broad range of metallicity . geisler pointed out additional features of his technique that are beneficial to a survey as described here : ( 1 ) the @xmath4 index is insensitive to surface gravity variations among g giants , ( 2 ) the reddening vector in the ( @xmath1 , @xmath4 ) diagram is such that more reddened , more distant giants will be even _ more _ separated from less - reddened foreground dwarfs ( see figure 4 ) , and ( 3 ) the metallicity sensitivity of the @xmath4 index is a second order effect , and in the sense that metal - poor giants have even _ smaller _ mg absorption . the latter feature makes geisler s system even more useful , since there is additional discriminating power for our typically expected situation of selecting metal - poor population ii giants from among foreground metal - rich dwarfs . * pb94 hereafter ) demonstrated the gravity discrimination of geisler s system using a grid of synthetic spectra over a range of surface temperatures , gravities and abundances appropriate to both population i and ii stars , and including realistic sequences of atmospheres for red giant branch isochrones . their work provides a useful demonstration of the effects of gravity and abundance on the ( @xmath4 ) index : gravity dominates the color but there is a secondary sensitivity to abundance . this is illustrated in figure 2 where the @xcite synthetic colors are translated to loci in washington / ddo51 color - color planes for dwarfs and giants of different [ fe / h ] . we note here one possible shortcoming of the @xcite curves : as noted by @xcite , @xcite used filter passbands which differ slightly from the adopted standard washington filters , and furthermore , they have used an unpublished grid of model spectra , which are now somewhat out of date . this probably gives rise to the blueward translation and small rotation in the color - color plane that we find necessary in 3.6 ( figure 12b and table 2 ) . @xcite themselves point out that their isochrones are systematically redder than observed globular cluster giant branches . unfortunately , @xcite did not include the @xmath0 filter when they produced their own ( more accurate ) synthetic colors . this leaves @xcite as the only source for synthetic photometry with which we can compare our own photometry . we emphasize that any problems with the @xcite colors appear to be quite small ( again , see 3.6 ) , in as much as they relate to our data . two important and relevant effects fall out of this interplay of gravity and abundance as illustrated in figure 2 . the first is that weakened absorption lines in metal - poor dwarfs that mimic the suppression of mg absorption from low gravity in giants becomes a problem only for subdwarfs with [ fe / h]@xmath26 . main sequence stars more metal - rich than this , presumably all of those in the disk components and the majority in the halo as well , are not , in general , confused with giants , even giants as metal - rich as the sun . the second relevant effect is that , for stars on the giant branch , the ( @xmath4 ) color provides a reasonably good abundance indicator [ @xmath27})\sim 0.13 $ ] at ( @xmath28 ) ] from solar [ fe / h ] down to [ fe / h]@xmath29 . both of these effects are critical to our enterprise here . first , the metallicity sensitivity of ( @xmath4 ) we expect to be useful for an initial sorting of faint giant stars we encounter . for example , the appearance of an apparent excess of giant stars of a single ( @xmath4)-based abundance would be an expected signal for a tidal tail from a mono - metallic parent object ( a commonly expected paradigm ) . such an excess is clearly seen , for example , in our study of extratidal stars near the carina dwarf spheroidal galaxy in ( see , e.g. , figures 79 in that paper ) . in the case of very metal - poor subdwarfs , we should not encounter an overwhelming number of contaminants in a sample of giants selected by ( @xmath4 ) techniques , based on the very small fraction of galactic stars with metallicities this poor . from the interim model of @xcite , the number of halo intermediate population ii / thick disk stars expected in the @xmath30 color range down to @xmath31 is about 200 deg@xmath12 at a galactic pole . approximately half of these stars would be dwarfs and only about 8% of _ these _ would be expected to have metallicities [ fe / h ] @xmath32 , according to @xcite and @xcite . this leaves an expected level of contamination of @xmath33 metal - poor subdwarfs deg@xmath12 , comparable to an expected density of giants of @xmath34 deg@xmath12 down to @xmath31 . this is , of course , in the ideal situation of high galactic latitude . on the other hand , because of the rapid decline in the metallicity distribution function below [ fe / h]@xmath29 , it is possible , with only slightly more conservative giant selection in the color - color plane , to reduce the subdwarf contamination to practically nothing . for example , if one were interested in selecting for [ fe / h]@xmath35 giants , one would only be concerned with about two [ fe / h]@xmath36 subdwarfs per square degree ( see figure 2 ; @xcite ) . we believe this level of contamination in our initial photometric catalogues to be tolerable . in any case , when such stars are encountered , they will be identifiable by followup spectra ( or , for the brighter stars , by their proper motion from such catalogues as the nltt ; ( * ? ? ? * _ et seq . _ ) ) . moreover , these metal - poor stars are interesting in their own right , and worthy of discovery for further exploration of the galaxy s evolution . for our survey , we have adopted a variant of the geisler technique that balances the goals of covering large areas as efficiently as possible with the desire to obtain as much information about identified giant stars as possible . we have adopted a _ three filter _ photometric system that provides dwarf / giant separation capability , a surface temperature indicator , and a rough gauge of stellar abundance in giant stars . in @xcite , the @xmath1 color serves as a surface temperature index , while the @xmath4 is used as the luminosity index . however , as we shall show ( 2.1 ) , the @xmath2 color is monotonically correlated to the @xmath1 color . thus , @xmath2 can serve as a suitable temperature index ( as has also been demonstrated by @xcite ) , with the advantage that one less filter is needed in the observations with no loss in information a useful improvement in efficiency . in this paper , we explore and calibrate the ( @xmath2 , @xmath4 ) diagram for discriminating dwarf and giant stars for a range of metallicities ( 2 ) . we note that the washington @xmath37 filter is designed specifically for photometric abundance measurement in giant stars , and use of this filter would provide a much more accurate [ fe / h ] for our survey giants ( particularly metal - poor ones ) than relying on the secondary dependence of ( @xmath4 ) on abundance . however , observations in the @xmath37 filter are rather expensive ( requiring 3 times the exposure time of the @xmath6 filter to reach an equivalent depth since we already require a large investment in observing time for the @xmath0 filter , and our primary imaging goal is to identify giants with as great efficiency as possible , we have dispensed with using the @xmath37 filter in most of what we do . our rationale is two - fold : ( 1 ) we believe that the coarse abundances afforded by the ( @xmath4 ) color are sufficient for tidal tail / halo substructure searches in our photometry , and ( 2 ) it is our intention to back up our photometrically identified giant candidates with spectroscopy as much as possible . spectroscopy is needed not only as a check on our giant candidates , but also as a means to obtain dynamical information from their radial velocities . much better abundances may be obtained from moderate resolution spectra ( sufficient for a radial velocity measure ) than from @xmath37 filter photometry . typical spectra of the type we are using for this followup work are shown in figure 1 , where several spectroscopic indicators of surface gravity , including the mgb , mgh , and nad features , may be seen . we will discuss our spectroscopic work for this survey further in future contributions . the selection of fields for our survey reflects two distinct , but complementary , strategies . the first is predicated on the paradigm afforded by the example of the sgr dwarf galaxy as well as by dynamical models of tidal effects on satellite galaxies , both which suggest that a non - negligible mass loss rate in the form of stripped stars may be discernible around presently known satellite galaxies . thus , it makes sense to start a search for tidal tails in the galactic halo at the most obvious potential sites for their creation . we have therefore begun a systematic search for giant stars beyond the tidal radii of the galactic dwarf satellite galaxies , as well as a sample of globular clusters . we have already reported successful searches for extended , coherent stellar structures around our first two targets , the magellanic clouds @xcite and the carina dwarf spheroidal ( ) . as the example of the sgr galaxy illustrates , the tidal debris of satellite galaxies may stretch to substantial lengths ( @xcite ) , and perhaps completely encircle the sky @xcite . tracing substantially lengthy tails continuously outward from the parent could be an extremely time - consuming enterprise , and should be weighed against the potential for tracking the path of the debris with more disparate , strategically placed , pencil beam probes around the sky . another problem that may be addressed with a series of probes is the existence of debris from objects that no longer exist with any recognizable , gravitationally intact core . in terms of the formation history of the milky way halo , it is obviously of great interest to assess the net contribution of disrupted bodies to the halo . finally , in order to understand the distribution of any `` smooth background '' of halo stars the magnitude of which affects the contrast of any superimposed substructure @xcite it makes sense to perform a more systematic survey that can address the global distribution of giant stars . for all of these reasons , and others , we have also embarked on the grid giant star survey ( ggss ) . the ggss is a program to observe 1303 isotropically spaced ( mean field spacing @xmath38 ) galaxy pencil - beam probes , each of area 0.40.7 deg@xmath15 , to find giant and hb stars to explore galaxy structure . the details and results of this systematic survey will be presented elsewhere . the `` all - galaxy '' ggss has similar goals and strategy to the `` spaghetti survey '' described by @xcite . this survey also adopts a ( @xmath39 ) photometric search phase to identify giants and hb stars for spectroscopic followup , and has presented initial findings and discussion of strategy in @xcite . together , the spaghetti and ggss surveys should provide a wealth of new information on the outer galaxy . in 2 we determine transformations from our ( @xmath6 , @xmath25 ) system to both the ( @xmath6 , @xmath3 , @xmath25 ) and ( @xmath7 , @xmath40 ) systems . in 3 we calibrate the ( @xmath2 , @xmath4 ) color - color diagram for discriminating dwarfs and giants , and explore the metallicity trends for giant stars in this diagram . we obtain good agreement in our empirical calibration of this two - color plane with that given by synthetic spectra . finally , by way of @xmath5 centauri giants as templates , we determine a rough calibration of giant star absolute magnitudes as a function of photometric abundance ( i.e. , position in the two - color diagram ) , which can be used for photometric parallaxes .

we have developed an automatic search procedure to identify low - energy spectral features in grbs . we have searched 133,000 spectra from 117 bright bursts and have identified 12 candidate features with significances ranging from our threshold of @xmath0 5e@xmath15 to @xmath0 1e@xmath17 . the evidence for spectral features appears good ; however , the features have not conclusively been shown to be narrow lines .

c

astro-ph9712096

we have developed an automatic search procedure to identify low - energy spectral features in grbs . we have searched 133,000 spectra from 117 bright bursts and have identified 12 candidate features with significances ranging from our threshold of @xmath0 5e@xmath15 to @xmath0 1e@xmath17 . several of the candidates have been examined in detail , including some with data from more than one batse spectroscopy detector . the evidence for spectral features appears good ; however , the features have not conclusively been shown to be narrow lines . = = = 1=1=0pt = 2=2=0pt

since our last report @xcite , we have completed the automatic search for bright bursts through may 1996 . we have identified 12 line candidates and have begun detailed analysis . because the 12 candidates appear as expected in the small fraction of spectra with high snr , their probability of appearing in the ensemble by chance is low . for all except one of the 12 candidates , the best line fit is an emission line with a centroid near 40 kev . our simulations show that we have useful sensitivity to _ ginga_-like absorption lines at 40 kev @xcite , so the lack of detections of absorption lines gives a constraint on their frequency . however , with the small number of bright bursts seen by batse and _ ginga _ , there is no significant discrepancy between the two instruments @xcite . observations made with multiple detectors have the strong advantage of redundantly verifying the existence of the features . we have now carefully investigated several candidate features , including some observed with multiple detectors . so far the evidence appears good for the existence of spectral features , however we do not want to make a blanket statement that batse has observed spectral features until we have carefully examined all 12 candidates . note that we are stating that the evidence appears good for the existence of _ spectral features . _ in the cases examined so far , we have not been able to demonstrate that the spectral features must be narrow lines an alternative explanation is possible : a low - energy break in addition to the normal break in the few 100 kev to 1 mev region .

we have measured , using a custom setup , the emissivity of metallic wire - grids , suitable for polarimeters and interferometers at mm and far infrared wavelengths . we find that the effective emissivity of these devices is of the order of a few @xmath0 , depending on fabrication technology and aging . we discuss their use in astronomical instruments , with special attention to martin puplett interferometers in low - background applications , like astronomical observations of the cosmic microwave background . polarizers , interferometers , cosmic microwave background

i

1212.3969

we have measured , using a custom setup , the emissivity of metallic wire - grids , suitable for polarimeters and interferometers at mm and far infrared wavelengths . we find that the effective emissivity of these devices is of the order of a few @xmath0 , depending on fabrication technology and aging . we discuss their use in astronomical instruments , with special attention to martin puplett interferometers in low - background applications , like astronomical observations of the cosmic microwave background . polarizers , interferometers , cosmic microwave background

wire - grid ( wg ) polarizers are widely used at mm - wavelengths as efficient polarization analyzers in polarimeters ( see e.g. @xcite ) , or as beamsplitters in martin - puplett interferometers ( mpi , see @xcite ) . in fact , an array of metallic wires with diameter and spacing much smaller than the wavelength performs as an almost ideal polarizer at mm wavelengths ( see e.g. @xcite ) , providing an almost ideal beamsplitter for mpis . in the case of astronomical observations , low - background operation is required , to observe the faintest sources . in general , fourier transform spectrometers ( fts ) like the mpi can measure a very wide frequency range , often covering up to two decades in frequency . this is an evident advantage with respect to dispersion and fabry - perot spectrometers , but comes at the cost of a higher radiative background on the detector , which is constantly illuminated by radiation from the whole frequency range covered . for this reason the best performing instruments are cooled at cryogenic temperatures , and are operated aboard of space carriers to avoid the background and noise produced by the earth atmosphere . a noticeable example was the cobe - firas fts @xcite , which was cooled at t=1.5k . firas measured the spectrum of the cosmic microwave background with outstanding precision @xcite , with negligible contributions from instrumental emission . intermediate performance can be obtained , quickly and cheaply , using stratospheric balloons . in this case , the residual atmosphere provides a non - negligible background , and the polarimeter / mpi can be operated at room temperature , provided that its background is kept under control . this means that the emissivity of all the optical elements of the instrument has to be as low as possible , to obtain an instrument - produced background lower than the background produced by the residual atmosphere . in figure [ fig1 ] we provide a quantitative comparison between photon noise produced by the earth atmosphere ( quantum fluctuations only ) and photon noise produced by low - emissivity metal surfaces ( assuming a dependence on wavelength as @xmath1 , as expected for bulk metal using the hagen - rubens formula @xcite ) . as evident from the figure , the constraint on the emissivity of the wire - grid is not very stringent for ground based observations , while it is very stringent for balloon - borne observations at mm wavelengths . the two dashed lines refer to a metal surface at the same temperature as the atmosphere , with emissivity 0.02 and 0.001 ( top to bottom ) at @xmath2=2 mm . [ fig1 ] , height=226 ] while measurements of the emissivity of metallic mirrors in this frequency range are readily available , and for clean aluminum or brass surfaces are of the order of 0.3@xmath0 at @xmath2=2 mm ( see e.g. @xcite ) , the emissivity of metallic wire - grids has not been measured systematically . photon noise is not the only problem induced by emissive optical components . the average level of background radiation can saturate sensitive detectors , or seriously limit their responsivity . for this reason in figure [ fig2 ] we provide a quantitative comparison similar to fig.1 but based on the integrated background power , over the range from 15 ghz to the frequency of interest . the background power values from this figure must be used to compute the background power over the frequency coverage of the instrument , and compared to the saturation power of the detector . in the case of tes bolometers for ground based measurements in the mm atmospheric windows , bolometers are designed for a saturation power ranging from @xmath3 1 pw ( balloon - borne experiments , low frequencies ) to @xmath4 10 nw ( ground based experiments , high frequencies ) . the two dashed lines refer to a metal reflector surface at the same temperature as the atmosphere , with emissivity 0.02 and 0.001 ( top to bottom ) at @xmath2=2 mm . [ fig2 ] , height=226 ] at variance with metallic mirrors , where the surface can be cleaned , and high conductivity bulky metal pieces can be used , wire grids are built either with thin free - standing tungsten wires or with gold strips evaporated on a thin dielectric substrate . in both cases we do not expect that the effective emissivity is the same as for bulk metal . and we also expect that aging and oxidization can be an important effect , increasing the emissivity of the device with time . from the discussion around figs . [ fig1 ] and [ fig2 ] and from the considerations above , it is evident that reliable measurements of wire - grid emissivity are in order to properly design sensitive polarimeters and mpis for astronomical use , and decide the operation temperature of the optical components . in this paper we describe a measurement setup we have developed to measure the effective emissivity of wire grids , at temperatures close to room temperature , at mm - wavelengths . we discuss the instrument design , report the results of measurements of different wire - grids , and discuss their application in the case of balloon - borne mpis for mm - wave astronomy .

the star appears much bluer during outburst due to an increased emission of a hot continuum . this is accompanied by a strong increase of the veiling of photospheric lines . we observe inverse p cygni profiles of many emission lines over a large brightness range of ex lup . 2.5 cm # 1to -1.5pt#1

r

astro-ph9506066

we have observed an outburst of the t tauri star ex lup in march 1994 . we present both photometric ( bvr ) and spectroscopic ( low and medium resolution ) observations carried out during the decline after outburst . the star appears much bluer during outburst due to an increased emission of a hot continuum . this is accompanied by a strong increase of the veiling of photospheric lines . we observe inverse p cygni profiles of many emission lines over a large brightness range of ex lup . we briefly discuss these features towards the model of magnetospherically supported accretion of disk material . 2.5 cm # 1to -1.5pt#1

spectroscopic observations in the blue spectral range were carried out during the first few nights in march 1994 on the eso-1.52 m telescope using the boller & chivens spectrograph at 1.2 resolution . after the decline of ex lup we obtained post - outburst spectra in the same wavelength region at resolutions of 1.5 and 12 at the 3.5m - ntt with emmi in august 1994 . all spectra have been reduced with the ctioslit package in iraf . observations of spectrophotometric standards and nightly extinction curves allowed for a flux calibration . + in fig.3 we present two spectra of ex lup : one close to the outburst maximum and the other at low activity almost half a year after the eruption . some of the emission lines of h , caii , feii , hei , and heii are indicated . under the assumption that the total light can be decomposed into an underlying t tauri star photosphere , a continuum source , and superimposed emission lines , we now discuss the different spectral components and their variability . a powerful method to determine the continuum excess emission is to determine the veiling by comparison with spectra of stars of the same spectral type and luminosity class but lacking any disk signature ( hartigan et al . 1989 , 1991 ) . the accuracy of the veiling determination decreases rapidly when the emission component exceeds the photospheric luminosity . in the case of ex lup during its eruption we therefore did not intend to derive the veiling and the true excess emission spectrum by comparison with spectral type standards , but we could examine the spectral variability caused by the outburst . + no photospheric absorption features are seen during the outburst ( upper spectrum in fig.3 ) but they appear in the post - outburst spectrum . thus the major source of variability presumably is a featureless continuum . therefore , a difference spectrum between outburst and post - outburst spectra should be a good measure of the continuum emission spectrum . in fig . 4 we plot two difference spectra at low resolution . the first shows the difference between an outburst ( march 3 ) and a post - outburst ( august 16 ) spectrum , while the second shows the difference between two post - outburst ( august 18 and 16 ) spectra which displays normal low - level variability . the continuum emission spectrum displaying the normal low - level activity is bluer than the continuum emission present during outburst . the most intriguing features in the spectra of ex lup are strong emission lines . the balmer series can be seen up to h15 especially during times of minimum activity . equivalent widths and fluxes of individual lines are given in table 1 . essentially all strong emission lines have increasing fluxes as the star brightens . however due to the steep rise of the continuum the equivalent widths decrease , which is also evident in the data from patten ( 1994 ) at h@xmath3 , h@xmath4 , and h@xmath5 during the maximum . obviously the caii lines have a larger flux amplification during the outburst than the balmer lines . there is some indication that line fluxes of metals do not increase while the star goes into outburst ( cai , feii , srii ) . + lrrrr & & & & + identification & w@xmath6 & w@xmath7 & flux@xmath8 & flux@xmath9 + & & & @xmath10 & @xmath10 + & & & & + & & & & + h11 3771 & -1.0 & -4.2 & 16 & 6 + h10 3798 & -1.5 & -7.0 & 25 & 9 + h 9 3835 & -1.2 & -12.1 & 20 & 16 + h 8 3889 & -2.7 & -13.0 & 44 & 18 + sii 3906 & -0.2 & -0.8 & 3 & 1 + caii 3934 & -7.7 & -12.0 & 123 & 15 + .comparison of selected emission lines at different levels of activity . equivalent widths and line fluxes during the outburst measured on march 3 ( @xmath8 ) and in the post - outburst spectrum on august 16 ( @xmath9 ) [ cols= " < " , ] @xmath11 & -0.4 & -1.7 & 8 & 3 + heii 4686 & -0.3 & -0.9 & 6 & 2 + h@xmath4 4861 & -9.4 & -16.8 & 196 & 30 + feii 4924 & & -1.5 & & 2 + the presence of inverse p cygni profiles in the strongest emission lines during outburst , as first noted by herbig ( 1950 ) , is here corroborated . at balmer lines higher than h9 the equivalent width of the redshifted absorption dip is even larger than the width of the emission component . comparing the sequence of spectra between march 3 and 6 we can see a substantial fading of the absorption . the mean velocity displacement of the absorption measured in these spectra is @xmath12 km / s . this absorption component is still visible in our spectrum taken on august 18 ( fig.5a ) . we also plot the difference between the two spectra from august 18 and august 16 to enhance the visibility of the absorption dip and to remove possible contamination due to photospheric lines . the displacement of the absorption dip measured in the post - outburst difference spectrum corresponds to a velocity of @xmath13 km / s . photospheric features of the underlying t tauri star can be seen only in the post - outburst spectra . figure 6 shows the region around cai 4227 , which is the strongest stellar absorption line , in two post - outburst spectra . the difference of these two spectra no longer exhibits the absorption line , and the change of total flux by about 40% is therefore due to continuum emission rather than photospheric variability . + the photospheric lines of the t tauri star are veiled , even at minimum brightness . the superimposed emission line spectrum additionally fills in many absorption lines . the measurement of the veiling is therefore rather difficult . we find a good fit to the observed strength of absorption lines by introducing a flat continuum emission equal to the photospheric continuum of the underlying star ( veiling r=1 , comparison with hd 202560 , spectral type m0v ) at 4200 when the brightness of ex lup is v=13.0 .

we study @xmath1 simple cubic lattices , using @xmath2 values in the range 16 to 64 , and with random anisotropy strengths of @xmath3 = 1 , 2 , 3 , 6 and @xmath4 . there is a well - defined finite temperature critical point , @xmath5 , for each these values of @xmath3 . we present results for the angle - averaged magnetic structure factor , @xmath6 at @xmath5 for @xmath7 . we also use finite - size scaling analysis to study scaling functions for the critical behavior of the specific heat , the magnetization and the longitudinal magnetic susceptibility . good data collapse of the scaling functions over a wide range of @xmath8 is seen for @xmath3 = 6 and @xmath4 . for our finite values of @xmath3

r

0902.4049

we have performed monte carlo studies of the 3d @xmath0 model with random uniaxial anisotropy , which is a model for randomly pinned spin - density waves . we study @xmath1 simple cubic lattices , using @xmath2 values in the range 16 to 64 , and with random anisotropy strengths of @xmath3 = 1 , 2 , 3 , 6 and @xmath4 . there is a well - defined finite temperature critical point , @xmath5 , for each these values of @xmath3 . we present results for the angle - averaged magnetic structure factor , @xmath6 at @xmath5 for @xmath7 . we also use finite - size scaling analysis to study scaling functions for the critical behavior of the specific heat , the magnetization and the longitudinal magnetic susceptibility . good data collapse of the scaling functions over a wide range of @xmath8 is seen for @xmath3 = 6 and @xmath4 . for our finite values of @xmath3 the scaled magnetization function increases with @xmath2 below @xmath5 , and appears to approach an @xmath2-independent limit for large @xmath2 . this suggests that the system is ferromagnetic below @xmath5 .

in this work , we will present results obtained from heat bath monte carlo calculations . the data were obtained from @xmath1 simple cubic lattices with @xmath67 using periodic boundary conditions . the calculations were done for a 12-state clock model , _ i.e. _ a @xmath68 approximation@xcite to the @xmath0 model of eqn . the computer program was an adaptation of the code used recently for the @xmath0 model in a random field,@xcite modified to replace the random field term with the random 2-fold anisotropy term of eqn . ( 2 ) . for any integer value of the quantity @xmath3 one can use a lookup table for the boltzmann factors , because all the energies in the problem are then expressible as sums of integers and integer multiples of @xmath69 . the values of @xmath3 for which data were obtained are 1 , 2 , 3 , 6 , and @xmath4 . the discretization of the phase space of the model has significant effects at very low @xmath8 , but the effects at the temperatures we study here are expected to be negligible compared to our statistical errors . the probability distributions for the local magnetization of equilibrium states which are calculated for the @xmath68 model are found to have very small contributions from the third and higher harmonics of @xmath70 and @xmath71 . this is strong evidence that the 12-state clock model is an accurate approximation to the @xmath0 model within our range of parameters . the @xmath68 model shows equivalent behavior for @xmath51 and @xmath72 , unlike the @xmath73 model used earlier.@xcite the program uses two independent linear congruential pseudorandom number generators , one for choosing the values of the @xmath22 , and a different one for the monte carlo spin flips , which are performed by a single - spin - flip heat - bath algorithm . the code was checked by setting @xmath53 , and seeing that the known behavior of the pure ferromagnetic system was reproduced correctly . each sample was started off in a random spin state at a temperature significantly above the @xmath5 for the pure model , and cooled slowly . thermal averages for @xmath74 were obtained at a set of temperatures spanning the critical region . angle - averaged structure factor for @xmath75 lattices with @xmath76 at @xmath77 . the axes are scaled logarithmically.,width=326 ] angle - averaged structure factor for @xmath75 lattices with @xmath78 at @xmath79 . the axes are scaled logarithmically.,width=326 ] angle - averaged structure factor for @xmath75 lattices with @xmath80 at @xmath81 . the axes are scaled logarithmically.,width=326 ] angle - averaged structure factor for @xmath75 lattices with @xmath82 at @xmath83 . the axes are scaled logarithmically.,width=326 ] angle - averaged structure factor for @xmath75 lattices with @xmath84 at @xmath85 . the axes are scaled logarithmically.,width=326 ] the magnetic structure factor , @xmath86 , for @xmath15 spins is @xmath87 where @xmath88 is the vector on the lattice which starts at site @xmath11 and ends at site @xmath89 . here the angle brackets denote a thermal average . for a ram with @xmath90 , unlike the rbim , the longitudinal part of the magnetic susceptibility , @xmath91 , which is given by @xmath92 where @xmath93 , and @xmath94 . for o(2 ) spins @xmath95 \ , , \ ] ] and @xmath96 thus @xmath97 is not the same as @xmath98 , even above @xmath5 . the scalar quantity @xmath97 is a well - behaved function of the lattice size @xmath2 for finite lattices , which approaches its large @xmath2 limit smoothly as @xmath2 increases , except possibly at a phase transition . the vector @xmath99 , on the other hand , may not be a well - behaved function of @xmath2 for an @xmath0 model in a two - fold random field . knowing the local direction in which @xmath99 is pointing , averaged over some small part of the lattice , may not give us a strong constraint on what @xmath99 for the entire lattice will be . the critical exponent @xmath100 , is defined at @xmath101 by the small @xmath102 behavior @xmath103 where @xmath104 is some constant . for each value of @xmath24 , results for four different @xmath7 configurations of the random anisotropy @xmath22 were averaged . the same four samples of random @xmath22 were used for all values of @xmath8 , and all values of @xmath24 , in order to facilitate the comparison of results for different values of @xmath8 and @xmath51 . all of the data shown in these figures were obtained from monte carlo runs which used hot start initial conditions , starting at at temperature well above @xmath5 . the value of @xmath8 was then lowered in steps . the initial part of the run at each @xmath8 was discarded to allow the system to equilibrate . for these @xmath7 runs with @xmath3 = 1 , at each @xmath8 a sequence of spin states obtained at intervals of 20,480 monte carlo steps per spin ( mcs ) was fourier transformed and averaged . for the larger values of @xmath51 , where the relaxation times are longer , this interval was chosen to be 102,400 mcs . the number of these selected spin states was chosen to be 16 for each of the finite values of @xmath24 , and 32 for @xmath25 . the fourier transformed spin state data were then binned according to the values of @xmath105 = @xmath106 , to give the angle - averaged @xmath6 . finally , a configuration average over the four random samples was performed . both equally weighted and logarithmically weighted averages were tried . no significant differences were found between these two types of weighting , and only the equally weighted averages will be displayed here . the results for @xmath3 = 1 , 2 , 3 , 6 , and @xmath4 are shown in figs . 1 , 2 , 3 , 4 , and 5 , respectively . the values of @xmath8 which are used in these figures are convenient binary fraction approximations to the values of @xmath5 at these values of @xmath3 . the best estimates of @xmath5 were determined later , by the analysis of the data over a range of @xmath2 and @xmath8 . we see from these figures that @xmath6 is only a weakly varying function of @xmath24 , at least for @xmath7 . the values of @xmath107 , as displayed on the figures , were found by least - squares fits to the data points for @xmath108 , where the data are well - approximated by eqn . note that @xmath100 appears to be a slowly varying monotonic function of @xmath24 , and that the extrapolation of @xmath100 down toward @xmath51 = 0 appears to be significantly different from the value of @xmath100 found for the nonrandom @xmath15 ferromagnet.@xcite it is also interesting to note that the value of @xmath100 found for @xmath84 appears to be identical to the value of @xmath100 for the nonrandom system , but the significance of this is unclear . the fact that @xmath100 appears to vary with @xmath24 is an indication that the claim of reed@xcite is too simplistic . he did not calculate a numerical value for @xmath100 , but he argued that the finite - size scaling ( fss ) behavior at @xmath3 = 1 was indistinguishable from that of the nonrandom system . one should not conclude from these data that @xmath100 is varying continuously with @xmath51 , so that there is a line of critical points . another explanation of the data is that for any @xmath51 we have a function @xmath109 , which increases very slowly as @xmath2 increases , up to a value @xmath110 then we will only find @xmath111 when @xmath2 becomes large enough so that @xmath112 . in the cayley tree mean - field approximation,@xcite whether @xmath113 is finite or infinite depends on the value of @xmath33 . ( color online ) finite - size scaling near @xmath5 for @xmath1 lattices with @xmath76 . ( a ) configuration - averaged magnetization vs. temperature . ( b ) @xmath91 vs. temperature . the @xmath114-axis is scaled logarithmically.,title="fig:",width=297](color online ) finite - size scaling near @xmath5 for @xmath1 lattices with @xmath76 . ( a ) configuration - averaged magnetization vs. temperature . ( b ) @xmath91 vs. temperature . the @xmath114-axis is scaled logarithmically.,title="fig:",width=297 ] ( color online ) finite - size scaling near @xmath5 for @xmath1 lattices with @xmath78 . ( a ) configuration - averaged magnetization vs. temperature . ( b ) @xmath91 vs. temperature . the @xmath114-axis is scaled logarithmically.,title="fig:",width=297](color online ) finite - size scaling near @xmath5 for @xmath1 lattices with @xmath78 . ( a ) configuration - averaged magnetization vs. temperature . ( b ) @xmath91 vs. temperature . the @xmath114-axis is scaled logarithmically.,title="fig:",width=297 ] ( color online ) finite - size scaling near @xmath5 for @xmath1 lattices with @xmath80 . ( a ) configuration - averaged magnetization vs. temperature . ( b ) @xmath91 vs. temperature . the @xmath114-axis is scaled logarithmically.,title="fig:",width=297](color online ) finite - size scaling near @xmath5 for @xmath1 lattices with @xmath80 . ( a ) configuration - averaged magnetization vs. temperature . ( b ) @xmath91 vs. temperature . the @xmath114-axis is scaled logarithmically.,title="fig:",width=297 ] ( color online ) finite - size scaling near @xmath5 for @xmath1 lattices with @xmath82 . ( a ) configuration - averaged magnetization vs. temperature . ( b ) @xmath91 vs. temperature . the @xmath114-axis is scaled logarithmically.,title="fig:",width=297](color online ) finite - size scaling near @xmath5 for @xmath1 lattices with @xmath82 . ( a ) configuration - averaged magnetization vs. temperature . ( b ) @xmath91 vs. temperature . the @xmath114-axis is scaled logarithmically.,title="fig:",width=297 ] ( color online ) finite - size scaling near @xmath5 for @xmath1 lattices with @xmath25 . ( a ) configuration - averaged magnetization vs. temperature . ( b ) @xmath91 vs. temperature . the @xmath114-axis is scaled logarithmically.,title="fig:",width=297](color online ) finite - size scaling near @xmath5 for @xmath1 lattices with @xmath25 . ( a ) configuration - averaged magnetization vs. temperature . ( b ) @xmath91 vs. temperature . the @xmath114-axis is scaled logarithmically.,title="fig:",width=297 ] if we make the assumption that the usual critical exponent scaling laws for translation invariant models remain valid for the ram , we can easily obtain values of the exponent combinations @xmath115 and @xmath116 from our computed values of @xmath107 . these combinations are exactly what we need for fss of the magnetization @xmath117 and the magnetic susceptibility@xcite @xmath118 . thus , by making standard fss plots,@xcite we can test the validity of these scaling laws for the ram . in fig . 6(a ) we show a fss plot of the configuration average of @xmath119 on @xmath1 lattices , for @xmath2 between 16 and 64 . the number of sample configurations used for each @xmath120 was 8 for @xmath3 = 1 , 2 , 3 and 6 , and 16 for @xmath84 . for @xmath2 = 64 , the number of samples was 4 for all @xmath51 . 6(b ) shows a similar plot for @xmath91 . figs . 7 , 8 , 9 and 10 show the corresponding plots for @xmath3 = 2 , 3 , 6 and @xmath4 , respectively . since the values of @xmath100 used here were taken from the fits to the small k behavior of @xmath6 , the only two adjustable fitting parameters used in these figures were the values of @xmath121 and @xmath5 , which were required to be identical for parts ( a ) and ( b ) of each figure . in these fss plots , the temperature coordinate scales as @xmath122 . the reader should note that the range of @xmath8 which we cover in these plots is about an order of magnitude larger than the range which one would typically use for a problem where one is already confident about the nature of the phase transition , and one is trying to obtain high precision estimates of @xmath5 and the critical exponents by concentrating on the range of @xmath8 where @xmath123 . as a consequence of this , the spacings between the values of @xmath8 for which we have taken data are rather large . thus we are unable to use histogram reweighting@xcite to obtain essentially continuous values for the thermodynamic functions . from the results given in these figures , we see that the estimates of @xmath121 increase monotonically and the estimates of @xmath5 decrease monotonically as @xmath3 increases . we also see that the peak in @xmath91 is slightly above @xmath5 for finite @xmath2 , which is typical for ferromagnetic critical behavior . the data collapse is good near this peak , which is the range of @xmath8 for which @xmath124 . we do not give estimates of statistical errors for @xmath121 , because we believe that the variation in @xmath121 in the range @xmath3 = 1 to 6 is due to variation in the value of @xmath125 . we will discuss this further in the next section . the errors in the values of @xmath5 are estimated to be less than @xmath126 . ( color online ) finite - size scaling of the difference between @xmath127= 3.00 and the configuration - averaged @xmath128 vs. temperature near @xmath5 for @xmath1 lattices with @xmath76.,width=326 ] ( color online ) finite - size scaling of the difference between @xmath127= 2.65 and the configuration - averaged @xmath128 vs. temperature near @xmath5 for @xmath1 lattices with @xmath78.,width=326 ] ( color online ) finite - size scaling of the difference between @xmath127= 2.40 and the configuration - averaged @xmath128 vs. temperature near @xmath5 for @xmath1 lattices with @xmath80.,width=326 ] ( color online ) finite - size scaling of the difference between @xmath127= 1.94 and the configuration - averaged @xmath128 vs. temperature near @xmath5 for @xmath1 lattices with @xmath82.,width=326 ] ( color online ) finite - size scaling of the difference between @xmath127= 0.81 and the configuration - averaged @xmath128 vs. temperature near @xmath5 for @xmath1 lattices with @xmath84.,width=326 ] fig . 11 shows the difference between an estimate of the specific heat at @xmath5 for an infinite system , @xmath127 , and the calculated specific heat of a finite system at temperature @xmath8 , @xmath128 for @xmath3 = 1 . the only new adjustable fitting parameter here is @xmath127 . 12 , 13 , 14 and 15 show the corresponding plots for @xmath3 = 2 , 3 , 6 and @xmath4 , respectively . the values of @xmath127 decrease monotonically as @xmath3 increases . in all cases , the values of @xmath127 given in the figures are estimated to be accurate to about 1% . as we also saw for @xmath129 and @xmath91 , the fss data collapse is not good below @xmath5 for @xmath130 . the results for @xmath84 are in very good agreement with the earlier results@xcite obtained with the @xmath131 approximation .

our approach is inherently scalable as all photon pulses can have the same pulse shape and carrier frequency such that output signals of one transistor can be input signals for a consecutive transistor . importantly , our approach works for propagating light signals that all have the same carrier frequency and pulse shape , which makes it inherently scalable as the output signals of one transistor can enter as input signals into a consecutive transistor , c.f . figure [ yet we find that the performance of the transistor is increasingly robust against such delays with increasing phase coherence time @xmath40 of the qubits .

i

1211.7215

we introduce a circuit quantum electrodynamical setup for a `` single - photon '' transistor . in our approach photons propagate in two open transmission lines that are coupled via two interacting transmon qubits . the interaction is such that no photons are exchanged between the two transmission lines but a single photon in one line can completely block respectively enable the propagation of photons in the other line . high on - off ratios can be achieved for feasible experimental parameters . our approach is inherently scalable as all photon pulses can have the same pulse shape and carrier frequency such that output signals of one transistor can be input signals for a consecutive transistor . photons are the most suitable carrier for transmitting information over long distances as they are largely immune to environmental perturbations , and can propagate with very low loss and long - lived coherence in a wide range of media @xcite . the use of photons in information processing however still suffers from the inability to realize controlled , strong interactions between individual photons . to make photons a more versatile information carrier , it is therefore of great importance to conceive means of making photonic signals interact with each other @xcite . in vacuum , direct photon - photon interactions are absent . nonetheless , optical signals can influence each other in nonlinear media . yet , the quantum regime with interactions between individual photons only becomes accessible for devices where optical nonlinearities exceed incoherent and dissipative processes . suitable devices therefore require a strong coupling of the photons to the material that mediates the effective photon - photon interactions . since the coupling of light to matter can be enhanced if light fields are confined to small volumes in space , cavities and one - dimensional waveguides are prime candidates for such devices . here we introduce a scheme for a `` single - photon '' transistor , a device that can be considered to form a cornerstone of quantum optical information processing . in our approach individual photons propagate in two one - dimensional waveguides of low transverse dimension and scatter off each other at a localized scattering center formed by two two - level systems ( qubits ) that each couple to one of the waveguides , see figure [ pnse]a . the qubits interact in such a way that no excitations can be exchanged between them and thus ensure that each photon remains in its initial waveguide after the scattering event . nonetheless , as we show below , the presence of a single photon in one waveguide can completely block or enable the propagation of a photon in the other waveguide . importantly , our approach works for propagating light signals that all have the same carrier frequency and pulse shape , which makes it inherently scalable as the output signals of one transistor can enter as input signals into a consecutive transistor , c.f . figure [ pnse]c for an illustration . such scalability is questionable in previous proposals which are based on different technological platforms @xcite . moreover the device we propose is a passive element that does not require any temporal tuning of the qubits . this implies that the arrival time of the photons at the scattering center can be completely unknown . differences between the arrival times of the individual photons do of course matter but the device becomes increasingly insensitive to timing mismatches as qubit dissipation decreases . a technology that is ideally suited for realizing the device we envision is provided by itinerant microwave photons in superconducting circuits @xcite . here , coherent scattering at a superconducting qubit @xcite and entanglement with a qubit @xcite have been demonstrated for individual photons that propagate in open transmission lines . moreover precise shaping of single photon pulses has been shown @xcite very recently . an implementation of our approach in circuit quantum electrodynamics thus requires two superconducting qubits that are coupled to open transmission lines . we show that the desired qubit - qubit interaction can be realized with two transmon qubits @xcite that are coupled via a squid which can be tuned to ensure that no excitations are exchanged between both transmons . importantly , this coupling is not dispersive @xcite and thus strong as both transmons can have the same transition frequency . these rather unique possibilities for qubit - qubit interactions offered by superconducting circuits are very suitable for our aims . moreover , their robustness with respect to dephasing noise make transmons ideal qubits for our device . yet , alternatively one could also use two flux qubits that are coupled via an induction loop @xcite . to demonstrate the capabilities of the `` single - photon '' transistor we propose , we calculate the photon reflection and transmission probabilities for both transmission lines that depend on the incoming photon pulses , under realistic experimental conditions , i.e. taking into account all dissipative processes in our setup . [ [ sec_master_ham ] ] setup + + + + + we consider two interacting qubits that each couple to a one - dimensional waveguide in which the photons propagate . here we focus on a setup for which we can refer to a control and a target photon , where the presence of the control photon influences the target photon s direction of propagation , while the control photon s direction of propagation always changes . a sketch of this setup is shown in figure [ pnse]a . the control photon propagates in the waveguide of subsystem 2 , c.f . figure [ pnse]a , which has a closed end right where it couples to qubit 2 . this arrangement enhances the absorption of photons by qubit 2 and hence its inversion as compared to an open waveguide end . the target photon in turn propagates in the waveguide of subsystem 1 . the qubit - qubit interaction is such that no excitations are exchanged between the two qubits which implies that photons can not tunnel between the waveguides . nonetheless one control photon in waveguide 2 can completely block or enable the propagation of a target photon in waveguide 1 . , c.f . equation ( [ hising ] ) . ] the hamiltonian of the two coupled qubits reads , @xmath0 where the @xmath1 are pauli - operators , @xmath2 and @xmath3 the transition frequencies of the two qubits and @xmath4 the strength of their mutual interaction . this hamiltonian can be implemented with two transmon qubits that are coupled via a squid , see figure [ transmoncircuit ] and supplemental material @xcite , or with two inductively coupled flux qubits @xcite . both transmission lines have a continuous spectrum of photonic modes and can be described by the hamiltonian @xcite , @xmath5 , where @xmath6 ( @xmath7 ) creates a photon in subsystem 1 which travels to the right ( left ) and @xmath8 creates a photon in subsystem 2 . @xmath9 , where @xmath10 is the group velocity and the wave vector @xmath11 is negative ( positive ) for left ( right ) going modes . a semi - infinite transmission line as in subsystem 2 can be described by only one continuum of modes since its incoming and outgoing modes can be mapped to an infinite waveguide where photons only propagate in one direction @xcite . the dispersion relation of a transmission line is linear and the frequency integration can be extended to @xmath12 since we only consider pulses with a frequency width that is much smaller than their carrier frequency . for these narrow linewidth pulses we thus take the photon - qubit coupling to be independent of the photon frequency , @xmath13.\ ] ] here @xmath14 and @xmath15 are the lifetimes of the two level systems associated to their coupling to the transmission lines . figure [ pnse]c shows the level scheme of the two qubits described by @xmath16 and the transitions induced by the photons . the total hamiltonian that includes the transmission lines , the qubits and their couplings thus reads , @xmath17 in a realistic system , the qubits will be subject to dissipation . we thus assume relaxation of excited qubit levels at a rate @xmath18 and pure qubit dephasing at a rate @xmath19 to derive quantum langevin equations @xcite for the photon and qubit operators that describe the unitary dynamics generated by @xmath20 and the dissipative processes associated to @xmath18 and @xmath19 . the explicit forms of these equations are given in the supplemental material @xcite . to investigate the dynamics of `` single - photon '' pulses in this setup , we combine quantum scattering theory @xcite with the input - output formalism @xcite of quantum optics as in @xcite , where the source terms for the input - output relations are provided by the solutions of the mentioned langevin equations , see supplemental material @xcite for details . [ [ photon - photon - interaction ] ] photon - photon interaction + + + + + + + + + + + + + + + + + + + + + + + + + to see the effect of the photon - photon interaction most clearly , we first consider the situation in which only one target photon but no control photon is present . an incoming target photon that travels to the right is described by @xmath21 , where @xmath22 labels the frequency components . we assume for the target photon a pulse with a lorentzian frequency distribution , @xmath23 \}^{-1}$ ] . here @xmath24 is the temporal width of the pulse and @xmath25 its carrier frequency . a pulse of this form would for example describe a photon that was spontaneously emitted into the transmission line from an excited qubit as experimentally realized in @xcite . we here chose to operate the transistor such that the target photon is reflected in the absence but unaffected in the presence of the control photon and choose @xmath25 to be equal to the frequency of the transition @xmath26 ( @xmath27 denotes qubit @xmath28 in the ground / excited state ) , i.e. @xmath29 , see figure [ pnse]c . the reverse mode of operation where the target photon is unaffected in the absence and reflected in the presence of the control photon can be selected by choosing @xmath30 and works equally well . without control photon evidently no photon - photon interaction can take place and the output state reads , @xmath31 , where the transmission amplitude is denoted @xmath32 , the reflection amplitude @xmath33 and the amplitude for the target photon being lost @xmath34 . these amplitudes relate to the initial state via @xmath35 , where the @xmath36 are the s - matrix elements for the different processes @xcite . the resulting transmission probability for the target photon reads , @xmath37 and the reflection probability @xmath38 , where @xmath39 and @xmath40 is the phase coherence time . we note that @xmath41 because the photon can also be lost due to qubit relaxation . importantly , in the regime of @xmath42 , the reflection probability for the target photon approaches unity @xcite . next we consider the case of the same incident target photon but now in the presence of an incoming control photon . as the control photon inverts qubit 2 , the scattering center is in the state @xmath43 and the target photon can only couple to the transition @xmath44 , see figure [ pnse]c . this transition is detuned by @xmath45 from the target photon frequency , and thus the transmission probability for the target photon approaches unity as @xmath4 becomes larger than the linewidths of target pulse and qubit 1 , @xmath46 . our scheme works best if the control photon pulse is chosen such that it maximally inverts qubit 2 . a suitable pulse is thus the time reversed version of a pulse resulting from spontaneous emission of qubit 2 into the transmission line @xcite which is often called an inverting pulse @xcite . the generation of inverting pulses and their release into a transmission line was demonstrated recently @xcite . for the cut transmission line in subsystem 2 an inverting pulse of carrier frequency @xmath47 and temporal width @xmath48 reads @xmath49 with @xmath50 \}^{-1}$ ] . we note that our results do not change if the target photon pulse also has the shape of an inverting pulse . since a target pulse that is transmitted will keep its shape our scheme is thus indeed scalable . due to the coupling to vacuum , the qubit 2 is of course never completely inverted . the output state can be written as , @xmath51 , where the first index in the amplitudes @xmath52 refers to the target photon , which can be reflected ( @xmath53 ) , transmitted ( @xmath54 ) or lost ( @xmath55 ) and the second index refers to the control photon which can be reflected ( @xmath56 ) or lost ( @xmath57 ) . for the probability of the target photon being transmitted in the presence of a control photon we thus get , @xmath58 .\ ] ] we quantify the performance of the `` single - photon '' transistor we propose via the difference @xmath59 and ratio @xmath60 between the transmission probabilities for the target photon in the presence and absence of a control photon , @xmath61 where @xmath62 and @xmath63 are given in equations ( [ pts ] ) and ( [ ptsc ] ) respectively . for @xmath64 the setup would describe an ideal transistor for single photons . figure [ is ] shows the achievable transmission contrast , @xmath65 , and on - off ratio , @xmath60 , for a realistic device with @xmath66 and a qubit - qubit coupling of @xmath67 as a function of the relaxation rate @xmath18 and pure dephasing rate @xmath19 of the qubits . as the plots show , an ideal `` single - photon '' transistor can be realized in the limit of vanishing @xmath68 and @xmath69 whereas very good performance can already be expected for currently realized values of @xmath70mhz , @xmath71 and @xmath72 @xcite , where a single control photon changes the transmission probability for the target photon by a factor 20 . as a function of the rates for qubit relaxation , @xmath18 , and pure dephasing , @xmath19 , for @xmath73 , @xmath29 , @xmath74 , @xmath75 , @xmath67 and @xmath76 . * b : * on - off ratio @xmath77 for the same parameters . * c * and * d : * @xmath78 and @xmath79 for the optimal choices of @xmath24 and @xmath48 as functions of @xmath80 and @xmath81 . ] the performance of the `` single - photon '' transistor we propose depends on the shapes of the target and control photon pulses and the parameters of the hamiltonian ( [ ham ] ) . as expected the best choices for the carrier frequencies of the control and target pulses are equal to the transition frequencies of @xmath82 respectively @xmath26 , i.e. @xmath73 and @xmath29 . for a single transistor @xmath83 and @xmath84 may be chosen arbitrarily . yet to enable concatenation of multiple transistors , we choose @xmath66 . moreover the interaction of the target photon with qubit 1 should be as high as possible . we choose @xmath75 which is compatible with experiments . for a control photon which is an inverting pulse , the optimal choice for its temporal width is obviously @xmath76 . there are thus two remaining parameters , @xmath24 and @xmath48 , which we have optimized numerically . the optimal choices of @xmath24 and @xmath48 as functions of @xmath68 and @xmath69 are shown in figures [ is]b and [ is]c respectively . the results presented in figure [ is ] assume that control and target pulses arrive at the same time . a possible delay between both pulses can be detrimental to the contrast @xmath59 and on - off ratio @xmath60 . yet we find that the performance of the transistor is increasingly robust against such delays with increasing phase coherence time @xmath40 of the qubits . for example for @xmath85 a very good performance of the transistor is retained for delays up to @xmath86 , see supplemental material @xcite for details . a conservative estimate for the effective gain of our transistor is provided by the maximal number of target photons that can be reflected due to the presence of a single control photon . since target photons only generate a very small excitation probability for qubit 1 and thus do not appreciably affect even `` single - photon '' control pulses , the effective gain can be high . it grows with increasing phase coherence time , @xmath40 , of the qubits and for example reaches 70 for @xmath85 , see @xcite . finally , for the fully scalable case where both , control and target photons are inverting pulses with the same carrier frequency , @xmath87 , and pulse length , @xmath88 , we find that the contrast reaches @xmath89 for @xmath90 and a control photon that arrives @xmath91 ahead of the target photon , see @xcite . this strong influence of the control photon on the target photon despite their identical pulse shapes is enabled by the asymmetry of the device with a semi - infinite ( infinite ) transmission line for the control ( target ) photon and @xmath92 . hence the control pulse can be matched to the control qubit with @xmath93 and @xmath76 , while the target photon is not matched to its qubit . [ [ coupled - transmons ] ] coupled transmons + + + + + + + + + + + + + + + + + as stated above , the qubit - qubit interaction in equation ( [ hising ] ) can be realized with two transmon qubits that are coupled via a squid . the circuit we consider is sketched in figure [ transmoncircuit ] . and shunting capacitances @xmath94 . both transmons are coupled via a combination of capacitive and inductive coupling realized with a squid arrangement with josephson energy @xmath95 and shunting capacitance @xmath96 . the transmons are capacitively coupled to transmission lines.,scaledwidth=32.0% ] and described by the lagrangian @xcite , @xmath97 , where the lagrangians of the individual qubits read , @xmath98 and @xmath99 . here @xmath100 is the flux quantum divided by @xmath101 , the @xmath94 and @xmath102 are the capacitances and josephson energies of the individual transmons . @xmath103 and @xmath95 are the capacitance and josephson energy of the capacitively shunted coupling squid . the @xmath104 are the coupling capacitances between the transmission lines and the individual transmons and the @xmath105 are the fully quantum mechanical quadratures of the electric potential of the transmission line fields . all josephson energies of the setup are tunable by threading external fluxes @xmath106 and @xmath107 through the respective squid loops , c.f . figure [ transmoncircuit ] . we write the corresponding hamiltonian of the transmons in terms of creation and annihilation operators @xmath108 and @xmath109 @xcite . by tuning the @xmath102 and @xmath95 such that @xmath110 , all interactions of the form @xmath111 cancel and the leading term of the remaining interactions reads @xmath112 which is equivalent to the interaction in equation ( [ hising ] ) with @xmath113 . within the approximations we use @xcite the achievable qubit - qubit coupling is @xmath114 . in conclusion , we have introduced a scheme for a `` single - photon '' transistor in circuit quantum electrodynamics that is inherently scalable as both photons can have the same carrier frequency and pulse shape . due to its gain the device could also detect single photons that propagate in the control line . moreover it works quantum coherently such that e.g. a control pulse consisting of a superposition of a single photon and the vacuum generates a quantum superposition of the target photon being blocked and transmitted . its performance might be further improved by suppressing losses with multiple , regularly spaced qubit pairs @xcite . moreover , the complexity of a network built with such transistors , c.f . figure [ pnse]b , could be increased further by integrating directional couplers between them @xcite . [ [ acknowledgements ] ] acknowledgements + + + + + + + + + + + + + + + + this work is part of the emmy noether project ha 5593/1 - 1 and the crc 631 , both funded by the german research foundation , dfg . 99 j.l . obrien , a. furusawa , and j. vuckovic , nat . photon * 3 * , 687 ( 2009 ) h.j . kimble , nature ( london ) * 453 * , 1023 ( 2008 ) d.e . chang , a.s . srensen , e.a . demler and m.d . lukin , nat . phys . * 3 * , 807 ( 2007 ) . f .- y . hong and s .- j . xiong , phys . rev . a * 78 * , 013812 ( 2008 ) . r.j . schoelkopf and s.m . girvin , nature ( london ) * 551 * , 664 ( 2008 ) a. wallraff , d. i. schuster , a. blais , l. frunzio , r .- s . huang , j. majer , s. kumar , s. m. girvin and r. j. schoelkopf , nature * 431 * , 162 ( 2004 ) o. astafiev , a. m. zagoskin , a.a . abdumalikov jr . , yu . a. pashkin , t. yamamoto , k. inomata , y. nakamura , j.s . tsai , science * 327 * , 840 ( 2010 ) i .- c . hoi , c.m . wilson , g. johansson , t. palomaki , b. peropadre , and p. delsing , phys . rev . lett . * 107 * , 073601 ( 2011 ) i .- c . hoi , t. palomaki , j. lindkvist , g. johansson , p. delsing , and c.m . wilson , phys . rev . lett . * 108 * , 263601 ( 2012 ) c. eichler , c. lang , j. m. fink , j. govenius , s. filipp , and a. wallraff , phys . rev . lett . * 109 * , 240501 ( 2012 ) . y. yin , y. chen , d. sank , p.j.j . omalley , t.c . white , r. barends , j. kelly , e. lucero , m. mariantoni , a. megrant , c. neill , a. vainsencher , j. wenner , a.n . korotkov , a.n . cleland and j.m . martinis , phys . rev . lett . * 110 * , 107001 ( 2013 ) . j. koch , t.m . yu , j. gambetta , a.a . houck , d.i . schuster , j. majer , a. blais , m.h . devoret , s.m . girvin , and r.j . schoelkopf , phys . rev . a * 76 * , 042319 ( 2007 ) . g. kirchmair , b. vlastakis , z. leghtas , s.e . nigg , h. paik , e. ginossar , m. mirrahimi , l. frunzio , s.m . girvin , and r.j . schoelkopf , nature * 495 * , 205 ( 2013 ) . t. p. orlando , j. e. mooij , l. tian , c. h. van der wal , l. s. levitov , s. lloyd , and j. j. mazo , phys . rev . b * 60 * , 15398 ( 1999 ) j.e . mooij , t. orlando , l. levitov , l. tian , c. van der wal , and s. lloyd , science * 285 * , 1036 ( 1999 ) see supplementary material j.t . shen and s. fan , phys . rev . a * 79 * , 023837 ( 2009 ) j.r . taylor , _ scattering theory : the quantum theory of nonrelativistic collisions _ ( dover , new york , 2006 ) , sec . 9-e and chap . 10 c. w. gardiner and m. j. collett , phys . rev . a , * 31 * , 3761 ( 1985 ) s. fan , s. e. kocabas , j .- t . shen , phys . rev . a * 82 * , 063821 ( 2010 ) c. w. gardiner and p. zoller , _ quantum noise _ , springer - verlag , ( 2000 ) . c. eichler , d. bozyigit , c. lang , l. steffen , j. fink , and a. wallraff , phys . . lett . * 106 * , 220503 ( 2011 ) . j.i . cirac , p. zoller , h.j . kimble , and h. mabuchi , phys . rev . lett . * 78 * , 3221 ( 1997 ) e. rephaeli , j.t . shen , s. fan , phys . rev . a , * 82 * , 033804 ( 2010 ) m. sandberg , m.r . vissers , t. ohki , j. gao , j. aumentado , m. weides , and d.p . pappas , arxiv:1211.2017 c. rigetti , j.m . gambetta , s. poletto , b.l.t . plourde , j.m . chow , a.d . crcoles , j.a . smolin , s.t . merkel , j.r . rozen , g.a . keefe , m.b . rothwell , m.b . ketchen , and m. steffen , phys . rev . b * 86 * , 100506(r ) ( 2012 ) . j.m . fink , m. gppl , m. baur , r. bianchetti , p.j . leek , a. blais , and a. wallraff , nature * 454 * , 315 ( 2008 ) . yong hu , guo - qin ge , shi chen , xiao - fei yang , you - ling chen , phys . rev . a * 84 * , 012329 ( 2011 ) h. zoubi and h. ritsch , europhys . lett . * 90 * , 23001 ( 2010 ) h. s. ku , f. mallet , l. r. vale , k. d. irwin , s. e. russek , g. c. hilton , and k. w. lehnert , ieee transactions on applied superconductivity * 21 * , 452 ( 2011 ) m. p. blencowe and a. d. armour , new j. phys . * 10 * , 095005 ( 2008 ) . c. lang , c. eichler , l. steffen , j. m. fink , m. j. woolley , a. blais , and a. wallraff , nature phys . * 9 * , 345 ( 2013 ) . * supplemental material

in this section we present explicit estimates for the performance of our device for the case where the pulses of the control and target photon have identical shapes . this case is of particular interest for concatenating multiple transistors in a network as an outgoing target photon of one transistor can act as a control photon for a consecutive transistor . the estimates in this section are again obtained with the phenomenological model introduced in section [ sec : delays ] of this supplementary material . figure [ scalable1 ] shows the maximized contrast @xmath158 as a function of @xmath159 for control and target pulses with identical shapes , where the pulse lengths @xmath168 have been optimized . as a function of @xmath159 , where @xmath39 , for optimized pulse lengths @xmath168 and various time delays between the arrival of control and target pulses in cases where the control and target pulses have identical shapes . scenario where the control pulse arrives before the target pulse for delays @xmath160 ( blue ) , @xmath161 ( magenta ) , @xmath162 ( yellow ) and @xmath163 ( green ) . the remaining parameters are as in figure 2 of the main text , @xmath73 , @xmath29 , @xmath74 , @xmath75 , @xmath67 and @xmath76.,width=264 ] for a given coherence time @xmath169 there is thus an optimal choice for the delay @xmath156 between control and target photon and for the lengths @xmath168 of both pulses . in figure [ scalable2 ] we plot the achievable contrast @xmath158 together with the optimal values for the delay @xmath156 between both pulses and their lengths @xmath168 as functions of the inverse coherence time @xmath170 . as a function of @xmath159 for optimized pulse length @xmath168 and delay @xmath156 . * b : * optimal choice for the delay @xmath156 between control and target pulse . * c : * optimal choice for the lengths @xmath168 of both , control and target pulses . the remaining parameters are as in figure 2 of the main text , @xmath73 , @xmath29 , @xmath74 , @xmath75 , @xmath67 and @xmath76 . ] we find that the maximal contrast is rather insensitive to variations in the pulse length . it furthermore becomes less sensitive to imprecisions in the timing of the pulses with increasing phase coherence time @xmath169 of the qubits . as the optimal delay increases with @xmath40 we find that a relative precision of 50% for the timing of the pulses would be sufficient to reach the optimal contrast with good accuracy

we introduce a new model of a stochastic sandpile on a graph @xmath0 containing a sink . when unstable , a site sends one grain to each of its neighbours independently with probability @xmath1 $ ] . for @xmath2 , this coincides with the standard abelian sandpile model . in general , for @xmath3 , the set of recurrent configurations of this sandpile model is different from that of the abelian sandpile model . we give a characterisation of this set in terms of orientations of the graph @xmath0 .

i

1209.2038

we introduce a new model of a stochastic sandpile on a graph @xmath0 containing a sink . when unstable , a site sends one grain to each of its neighbours independently with probability @xmath1 $ ] . for @xmath2 , this coincides with the standard abelian sandpile model . in general , for @xmath3 , the set of recurrent configurations of this sandpile model is different from that of the abelian sandpile model . we give a characterisation of this set in terms of orientations of the graph @xmath0 . we also define the lacking polynomial @xmath4 as the generating function counting this set according to the number of grains , and show that this polynomial satisfies a recurrence which resembles that of the tutte polynomial .

in this paper , we analyse a stochastic generalisation of the abelian sandpile model ( asm ) . informally ( we provide a formal definition later ) , the asm operates on a graph where each vertex has a number of ` grains of sand ' on it . at every unit of time , another grain of sand is added at a random vertex @xmath5 . if this causes the number of grains at @xmath5 to exceed its degree , @xmath5 topples , sending one grain to each of its neighbours . this may cause other vertices to topple , and we continue until the configuration is stable , i.e. no vertex can topple anymore . a special vertex , the sink , can absorb any number of grains and never topples . it is possible to show that eventually this model will be trapped in a set of configurations , called recurrent configurations . this model arose from work by bak , tang and wiesenfeld @xcite and was named and formalised by dhar @xcite . it displays a phenomenon known as self - organised criticality @xcite , in which characteristic length or time scales break down in the ` critical ' steady state . when this happens , the correlation between the number of grains at two vertices obeys a power - law decay , as opposed to an exponential decay often found in models away from criticality . likewise , the average number of topplings that result from a single grain addition also obeys a power - law distribution . in this sense , the model is ` non - local ' , as grains added at a vertex may have an effect on vertices that are far away . physically , this model ( and self - organised criticality in general ) has been used in applications as wide as forest fires @xcite , earthquakes @xcite and sediment deposits @xcite . mathematically , the asm has been heavily studied , and we shall not list out all the references here . we refer interested readers to dhar s papers @xcite and to the excellent review on the subject by redig @xcite . some relevant results to our current work discussed in @xcite include : * the number of recurrent configurations is equal to the number of spanning trees of the graph . * there is an algorithm ( called the _ burning algorithm _ ) which determines if a given configuration is recurrent or not . this finds , or establishes the non - existence of , a subgraph not including the sink on which the configuration is stable . this algorithm constructively establishes a bijection between recurrent configurations and spanning trees . * in the steady state of the model , each recurrent configuration is equally likely . in the asm , the only randomness occurs in the vertices that we add grains to . we introduce a variation on this model , where the topplings themselves are also random . more precisely , we fix a probability @xmath1 $ ] , and when a site is unstable , each neighbour independently has a probability @xmath6 of receiving a grain from the unstable site . in this way , an unstable site may remain unstable after toppling but , as in the original model , the process continues until the configuration is stable . if @xmath2 , this is identical to the asm . although this new model appears similar to the asm , a closer inspection reveals some qualitative differences . in particular , the model will again become trapped in a set of recurrent configurations , but this set is not equal to the set of recurrent configurations in the asm . furthermore , each recurrent configuration is not equally likely , and the steady state measure now depends on @xmath6 . the aim of this paper is to study the behaviour of this new model , particularly in these respects . we prove a characterisation of the recurrent configurations in terms of orientations of the graph edges , and provide a tutte polynomial - like " formula which counts these configurations in terms of their numbers of grains of sand . the stochastic sandpile model ( ssm ) we propose is an appropriate generalisation of the asm , due to the aforementioned relation between the tutte polynomial and a counting of the recurrent configurations . a similar result has been proved by lpez @xcite for the asm ; in this model , the lacking polynomial we define later has an expression using the `` standard '' tutte polynomial if the number of lacking particles is @xmath7 . ] . see also cori and le borgne @xcite and bernardi @xcite for combinatorial explanations of this fact . although several instances of random sandpile models have already been introduced in the literature ( see for example dhar ( * ? ? ? * section 6 ) , kloster _ @xcite , manna @xcite ) , as far as we are aware none of these models have any known link with tutte - like polynomials . variations on the basic sandpile model also include an asymmetric version @xcite , which devised an analogous algorithm to the burning algorithm called the _ script algorithm_. in section [ sec : model ] , we formally define the asm and introduce our stochastic generalisation of it ( the ssm ) . in section [ sec : result ] , we present our results on the ssm , giving detailed proofs in section [ sec : proof ] . finally , we offer a brief conclusion in section [ sec : conclusion ] .

we investigate a possibility of precision measurements for parameters of the littlest higgs model with t - parity at the international linear collider ( ilc ) . the model predicts new gauge bosons which masses strongly depend on the vacuum expectation value that breaks a global symmetry of the model . through monte carlo simulations of production processes of new gauge bosons , , we also discuss the determination of other model parameters at the ilc .

i

0907.0190

we investigate a possibility of precision measurements for parameters of the littlest higgs model with t - parity at the international linear collider ( ilc ) . the model predicts new gauge bosons which masses strongly depend on the vacuum expectation value that breaks a global symmetry of the model . through monte carlo simulations of production processes of new gauge bosons , we show that these masses can be determined very accurately at the ilc for a representative parameter point of the model . from the simulation result , we also discuss the determination of other model parameters at the ilc .

the little higgs model @xcite has been proposed for solving the little hierarchy problem . in this scenario , the higgs boson is regarded as a pseudo nambu - goldstone ( ng ) boson associated with a global symmetry at some higher scale . though the symmetry is not exact , its breaking is specially arranged to cancel quadratically divergent corrections to the higgs mass term at 1-loop level . this is called the little higgs mechanism . as a result , the scale of new physics can be as high as 10 tev without a fine - tuning on the higgs mass term . due to the symmetry , the scenario necessitates the introduction of new particles . in addition , the implementation of the @xmath0 symmetry called t - parity to the model has been proposed in order to avoid electroweak precision measurements @xcite . in this study , we focus on the littlest higgs model with t - parity as a simple and typical example of models implementing both the little higgs mechanism and t - parity . in order to test the little higgs model , precise determinations of properties of little higgs partners are mandatory , because these particles are directly related to the cancellation of quadratically divergent corrections to the higgs mass term . in particular , measurements of heavy gauge boson masses are quite important . since heavy gauge bosons acquire mass terms through the breaking of the global symmetry , precise measurements of their masses allow us to determine the most important parameter of the model , namely the vacuum expectation value ( vev ) of the breaking . furthermore , because the heavy photon is a candidate for dark matter @xcite , the determination of its property gives a great impact not only on particle physics but also on astrophysics and cosmology . however , it is difficult to determine the properties of heavy gauge bosons at the large hadron collider , because they have no color charge @xcite . on the other hand , the ilc will provide an ideal environment to measure the properties of heavy gauge bosons . we study the sensitivity of the measurements to the little higgs parameters at the ilc based on a realistic monte carlo simulation @xcite . we have used madgraph @xcite and physsim @xcite to generate signal and standard model ( sm ) events , respectively . in this study , we have also used pythia6.4 @xcite , tauola @xcite and jsfquicksimulator which implements the gld geometry and other detector - performance related parameters @xcite .

we investigate the approximate quantum state sharing protocol based on random unitary channels , which is secure against any exterior or interior attackers in principle . although the protocol leaks small information for a security parameter @xmath0 , the scheme still preserves its information - theoretic secrecy , and reduces some pre - shared classical secret keys for a private quantum channel between a sender and two receivers . the approximate private quantum channels constructed via random unitary channels play a crucial role in the proposed quantum state sharing protocol

c

1011.3297

we investigate the approximate quantum state sharing protocol based on random unitary channels , which is secure against any exterior or interior attackers in principle . although the protocol leaks small information for a security parameter @xmath0 , the scheme still preserves its information - theoretic secrecy , and reduces some pre - shared classical secret keys for a private quantum channel between a sender and two receivers . the approximate private quantum channels constructed via random unitary channels play a crucial role in the proposed quantum state sharing protocol

we studied that the approximate quantum state sharing schemes are efficient from the classical information cost of view and those are robust to the two kinds of attacks . the proposed aqss protocol basically depends on an approximate private quantum channel , which is constructed via two independent random unitary channels . although the protocol leaks small information corresponding to the security parameter @xmath0 , the scheme preserves its information - theoretic security , and so the aqss and maqss schemes can be interpreted as some high - efficiency state sharing protocols for any bipartite and multipartite quantum states .

we then provide predictions for a variety of diffractive processes . as the propagators have been evaluated entirely from qcd first principles ( although in the quenched approximation ) , our results provide a consistency check of the landshoff - nachtmann model . we address the issue of the possible gauge - dependence of our results , which will be the object of a future study .

c

hep-lat9511031

we investigate the landshoff - nachtmann two - gluon - exchange model of the pomeron using gluon propagators computed in the landau gauge within quenched lattice qcd calculations . we first determine an effective gluon - quark coupling by constraining the pomeron - quark coupling to its phenomenological value @xmath0 . we then provide predictions for a variety of diffractive processes . as the propagators have been evaluated entirely from qcd first principles ( although in the quenched approximation ) , our results provide a consistency check of the landshoff - nachtmann model . we address the issue of the possible gauge - dependence of our results , which will be the object of a future study . edinburgh preprint : 95/559 + liverpool preprint : lth-363 + hep - lat/9511031 the landshoff - nachtmann pomeron on the lattice + _ ukqcd collaboration _ + * d.s . henty , c. parrinello and d.g . richards * + department of physics and astronomy , university of edinburgh , edinburgh eh9 3jz , scotland +

we have demonstrated how the landau - gauge lattice gluon propagator employed in the two - gluon - exchange model of proton - proton scattering provides a highly successful description of the data , where the only parameter that needs to be fixed is an effective quark - gluon coupling . for the first time a genuine qcd quantity , evaluated entirely from first principles , has been inserted in the ln model , providing an important consistency check of the model itself . also , given the fact that in our approximation the effect of quark loops diagrams is absent , our analysis shows the robustness of the ln model , despite its simplicity . although the description of the data appears largely independent both of the volume of the lattice and of the lattice spacing , a more detailed analysis of lattice systematic errors is necessary . we plan to perform such an analysis , together with an investigation of the gauge dependence of our results , in a future publication .

we investigate the magnetotransport properties of a thin graphite wire resting on a silicon oxide substrate . the electric field effect is demonstrated with back and side gate electrodes . we find that the phase coherence length increases linearly with the conductivity suggesting that at 1.7 k dephasing originates mainly from electron - electron interactions .

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cond-mat0702401

we investigate the magnetotransport properties of a thin graphite wire resting on a silicon oxide substrate . the electric field effect is demonstrated with back and side gate electrodes . we study the conductance fluctuations as a function of gate voltage , magnetic field and temperature . the phase coherence length extracted from weak localization is larger than the wire width even at the lowest carrier densities making the system effectively one - dimensional . we find that the phase coherence length increases linearly with the conductivity suggesting that at 1.7 k dephasing originates mainly from electron - electron interactions .

graphite is composed of stacked layers of graphene sheets in which carbon atoms are ordered in a two - dimensional hexagonal lattice . it is a semimetal with equal electron and hole densities in the undoped case . recently , it has been shown that thin graphite flakes of a few nanometers in height exhibit a pronounced electric field effect.@xcite the applied potential is screened on a length scale corresponding to the interlayer distance implying that the back gate electrode only affects the first few graphene layers close to the insulating substrate . a single - layer of graphene ultimately confines the carriers in a sheet of atomic thickness : the electronic bandstructure is , however , modified resembling a gapless semiconductor with a linear energy dispersion relation . well - defined plateaus were measured in the quantum hall effect opening the way to investigate properties observed so far to two - dimensional electron and hole gases at the interfaces of layered semiconductors.@xcite we report low - temperature magnetotransport measurements on a few - layer graphene wire whose conductance is tunable both with back and side gate electrodes . the combined observation of weak localization and magnetoconductance fluctuations shows that the system is mesoscopic , one - dimensional and in the diffusive regime . the extracted phase coherence length varies from 0.5 @xmath0 m up to 2.5 @xmath0 m for estimated carrier densities from zero to 2.5@xmath110@xmath2/@xmath3 . while this regime has been extensively studied in gaas / algaas systems , @xcite very few experiments have been reported for single- and few - layer graphene.@xcite we find the phase coherence length to be proportional to the conductivity suggesting that the main dephasing mechanism at low temperatures is related to electron - electron collisions with small energy transfer.@xcite finally , adding the electric field effect contributions of the back and side gates allows us to vary the disorder configuration at a given fermi level . ( a ) sfm micrograph of a graphite wire resting on a silicon oxide surface with a schematic of the four contacts ( i@xmath4 , i@xmath5 , o@xmath4 , o@xmath5 ) and four side gates ( l@xmath6 , l@xmath7 , r@xmath6 , r@xmath7 ) . inset : optical microscope image of the structure . ( b ) four - terminal resistance as a function of back gate for different temperatures . ( c ) resistance change as a function of the side gates l@xmath6+l@xmath7 ( solid line ) and r@xmath6+r@xmath7 ( dotted line ) at 1.7 k. ( d ) resistance change as a function of back gate for different side gate voltages ( l@xmath6+l@xmath7+r@xmath6+r@xmath7 ) at 1.7 k.,scaledwidth=40.0% ]

we investigate the properties of galaxies between the blue and the red sequence ( i.e. , the transition region , 4.5@xmath06 mag ) by combining ultraviolet ( uv ) and near - infrared imaging to 21 cm hi line observations for a volume - limited sample of nearby galaxies . we confirm the existence of a tight relation between colour and hi - fraction across all the range of colours , although outside the blue cloud this trend becomes gradually weaker .

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0908.3564

we investigate the properties of galaxies between the blue and the red sequence ( i.e. , the transition region , 4.5@xmath06 mag ) by combining ultraviolet ( uv ) and near - infrared imaging to 21 cm hi line observations for a volume - limited sample of nearby galaxies . we confirm the existence of a tight relation between colour and hi - fraction across all the range of colours , although outside the blue cloud this trend becomes gradually weaker . transition galaxies are divided into two different families , according to their atomic hydrogen content . ` hi - deficient ' galaxies are the majority of transition galaxies in our sample . they are found in high density environments and all their properties are consistent with a quenching of the star formation via gas stripping . however , while the migration from the blue cloud is relatively quick ( i.e. , @xmath11 gyr ) , a longer amount of time ( a few gyr at least ) seems required to completely suppress the star formation and reach the red sequence . at all masses , migrating ` hi - deficient ' galaxies are mainly disks , implying that the mechanism responsible for today s migration in clusters can not have played a significant role in the creation of the red sequence at high - redshift . conversely , ` hi - normal ' transition galaxies are a more heterogeneous population . a significant fraction of these objects show star formation in ring - like structures and evidence for accretion / minor - merging events suggesting that at least part of the hi reservoir has an external origin . the detailed evolution of such systems is still unclear , but our analysis suggests that , in at least two cases , galaxies might have migrated back from the red sequence after accretion events . interestingly , the hi available may be sufficient to sustain star formation at the current rate for several billion years . our study clearly shows the variety of evolutionary paths leading to the transition region and suggests that the transition galaxies may not be always associated with systems quickly migrating from the blue to the red sequence . [ firstpage ] galaxies : evolution galaxies : fundamental parameters galaxies : clusters : individual : virgo ultraviolet : galaxies radio lines : galaxies

the last decades have seen the rise and success of the hierarchical paradigm for galaxy formation in a cold dark - matter dominated universe . although very powerful , the concordance model is still far from providing us with a complete and coherent view of how galaxies form and evolve . this is mainly because we still do not understand the physics involving the baryonic component . the current challenge for galaxy formation and evolution studies is thus to improve our knowledge of the astrophysical processes responsible for _ transforming _ simple dark matter halos into the bimodal population of galaxies inhabiting today s universe . it is in fact well established that , when we look at their integrated optical colours , galaxies constitute a bimodal population ( e.g. , @xcite ) composed of a ` red sequence ' , dominated by old stellar populations , and a ` blue cloud ' where the vast majority of new stars in the universe are formed . however , the dichotomy in the colour distribution does not automatically reflect a difference in morphological type ( e.g. , light distribution ) and we now know that the red sequence is not only composed of quiescent early - type galaxies ( e.g. , @xcite ) . for example , while the red sequence accounts for @xmath260 - 85% ( depending on the colour cut used to define star - forming galaxies ) of the total stellar - mass density in the local universe ( e.g. , @xcite ) , stars in late - type galaxies contribute to at least half the local stellar mass budget ( e.g. , @xcite ) . this automatically implies that a significant fraction of massive late - type galaxies lie in the red sequence , whereas high - mass blue ellipticals are extremely rare . moreover , not all red galaxies have stopped forming stars , as revealed by recent ultraviolet ( uv ) investigations ( e.g. , @xcite ) . it thus emerges that , at least at optical wavelength , the red sequence is a heterogeneous family of objects which have likely followed different evolutionary paths . how galaxies end - up in the red sequence is still partly a mystery , but recently high - redshift surveys have made it possible to start tracing the growth of the star - forming and quiescent galaxy population up to @xmath31 and beyond . despite the observational and theoretical uncertainties ( e.g. , @xcite ) , it seems now commonly accepted that the stellar mass of the blue cloud shows very little growth since @xmath31 , while the red sequence has grown by at least a factor @xmath22 ( e.g. @xcite ) . the most popular scenario invoked to explain the growth of red galaxies is a migration of a significant fraction of star - forming systems from the blue cloud . although not always supported @xcite , the possibility of an exchange of galaxies between the two sequences is exciting , and several theoretical and observational studies have started to look for the possible astrophysical processes responsible for such transition . several mechanisms have been proposed so far , among the most popular are different modes of gas accretion @xcite , feedback from active galactic nuclei ( agn , @xcite ) , and environmental effects ( e.g. , @xcite , hereafter hc09 ) . however , whether a population of migrating galaxies does really exist and what causes the quenching of their star formation is still not clear . in this context , the advent of the _ galaxy evolution explorer _ ( galex ) large - area uv surveys is allowing us to tackle this problem from a different angle . thanks to its high sensitivity to low - level star formation activity , uv magnitudes can be used to better discriminate between quiescent and still active ( although optically - red ) galaxies . in fact , contrary to what is observed at optical wavelengths , the uv - optical colour distribution at a given mass is not well fitted by two gaussian distributions @xcite , but it shows a significant excess of objects in the region between the blue and red sequence ( i.e. , the ` so - called ' transition region or ` green - valley ' , @xcite ) . transition galaxies may thus represent the missing link to understand if and how galaxies move from one population to the other . however , it is worth reminding that , despite its potential , uv emission is significantly affected by dust and , only after accurate dust corrections , can the uv - optical colour be used to identify transition galaxies . a significant fraction of galaxies found between the two sequences may in fact be composed of reddened systems @xcite . once transition galaxies are properly identified , a reconstruction of their past evolution is not straightforward . the correct discrimination between various physical mechanisms able to suppress star formation requires , in theory , a detailed investigation of _ all _ the galactic components , i.e. , stars , gas and dust . of particular importance is the atomic gas content ( hi ) , which represents the fuel for the future star formation activity . the mechanism responsible for the migration from the blue cloud must in fact inhibit the condensation of atomic into molecular hydrogen and the onset of star formation . unfortunately , not only is hi astronomy still technically limited to the nearby universe ( e.g. , @xcite ) , but also our knowledge of hi properties of local galaxies is generally restricted to the blue cloud ( e.g. , @xcite ) . the very local universe ( e.g. , up to the distance of the virgo cluster ) is currently the only place where it is possible to investigate the link between hi - content and quenching of star formation in transition galaxies . for all these reasons , we have collected uv to near - infrared imaging and hi 21 cm line data for a volume - limited sample of nearby galaxies covering different environments . in our previous paper ( hc09 ) , we have highlighted the power of a combination of uv and hi observations to understand the properties of transition galaxies . our analysis suggested a strong relationship between uv - near - infrared colour and hi content showing that migrating spirals are mainly hi - deficient objects found in high density environments . this result apparently rules out agn - feedback as the main mechanism responsible for the quenching of the star formation in nearby spirals . however , a number of important questions still remain to be answered . are transition galaxies really migrating from the blue to the red sequence ? what are the time - scales of such migration ? is the quenching followed by a change in morphology ? while in hc09 we have shown that a large fraction of spirals outside the blue cloud is hi - deficient , this is not true for all transition spirals . how have hi - rich systems reached the transition region ? the aim of this paper is thus to extend the analysis presented in hc09 , in order to provide important constraints on the recent mass growth of the red sequence . the paper is arranged as follows . in 2 we briefly describe the sample and discuss possible biases related to the dust extinction correction . in 3 we define the transition region and in 4 discuss the relation between colour and gas content . the properties of transition galaxies are presented in 5 and their evolutionary histories and implications for galaxy evolution studies are discussed in 6 . finally , our main results are briefly summarized in 7 . throughout the paper we use h@xmath470 km s@xmath5 mpc@xmath5 . in the virgo cluster , where peculiar motions are dominant , we use distances as determined in @xcite . star formation rates ( sfrs ) are computed from the nuv luminosities , following the conversions by @xcite .

hi - deficient ' galaxies are the majority of transition galaxies in our sample . they are found in high density environments and all their properties are consistent with a quenching of the star formation via gas stripping . are mainly disks , implying that the mechanism responsible for today s migration in clusters can not have played a significant role in the creation of the red sequence at high - redshift . our study clearly shows the variety of evolutionary paths leading to the transition region and suggests that the transition galaxies may not be always associated with systems quickly migrating from the blue to the red sequence .

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0908.3564

we investigate the properties of galaxies between the blue and the red sequence ( i.e. , the transition region , 4.5@xmath06 mag ) by combining ultraviolet ( uv ) and near - infrared imaging to 21 cm hi line observations for a volume - limited sample of nearby galaxies . we confirm the existence of a tight relation between colour and hi - fraction across all the range of colours , although outside the blue cloud this trend becomes gradually weaker . transition galaxies are divided into two different families , according to their atomic hydrogen content . ` hi - deficient ' galaxies are the majority of transition galaxies in our sample . they are found in high density environments and all their properties are consistent with a quenching of the star formation via gas stripping . however , while the migration from the blue cloud is relatively quick ( i.e. , @xmath11 gyr ) , a longer amount of time ( a few gyr at least ) seems required to completely suppress the star formation and reach the red sequence . at all masses , migrating ` hi - deficient ' galaxies are mainly disks , implying that the mechanism responsible for today s migration in clusters can not have played a significant role in the creation of the red sequence at high - redshift . conversely , ` hi - normal ' transition galaxies are a more heterogeneous population . a significant fraction of these objects show star formation in ring - like structures and evidence for accretion / minor - merging events suggesting that at least part of the hi reservoir has an external origin . the detailed evolution of such systems is still unclear , but our analysis suggests that , in at least two cases , galaxies might have migrated back from the red sequence after accretion events . interestingly , the hi available may be sufficient to sustain star formation at the current rate for several billion years . our study clearly shows the variety of evolutionary paths leading to the transition region and suggests that the transition galaxies may not be always associated with systems quickly migrating from the blue to the red sequence . [ firstpage ] galaxies : evolution galaxies : fundamental parameters galaxies : clusters : individual : virgo ultraviolet : galaxies radio lines : galaxies

our analysis provides definitive evidence that galaxies in the transition region of the @xmath13 colour - mass diagram are a heterogeneous population . this result strongly suggests that galaxies lying between the blue and red sequence have followed different evolutionary paths , not always going towards redder colours . we remind the reader that the difference in number density between hi - deficient and hi - normal transition galaxies must be taken with a grain of salt . although our sample is magnitude- and volume - limited , it might be biased towards high - density environments . nearly half of the galaxies in our sample lies in fact within the virgo cluster , which might not be a fair representation of the local universe . interestingly , external ( i.e. , environmental ) mechanisms are almost always behind the peculiar properties of transition galaxies , both hi - deficient and hi - normal objects . although the majority of high - mass ( @xmath60@xmath4710@xmath29 m@xmath30 ) transition galaxies harbour an agn , feedback from accreting super - massive black holes appears not to be necessary to explain their properties . as discussed in hc09 , the presence of agns in transition galaxies does not automatically imply a physical link between nuclear activity and quenching . moreover , we do not find any direct observational evidence ( e.g. , jets , radio lobes , etc . ) supporting an interaction between the central black hole and the galaxy s gas reservoir . hi - deficient transition galaxies constitute the majority of the transition population in our sample . by extending the analysis presented in hc09 , we have shown that these galaxies not only are mainly found in the virgo cluster but they also are the only population which is clearly migrating from the blue towards the red sequence . while environmental effects are certainly able to strip the gas from the disk , reducing the star formation in just a few hundreds million years and forcing the galaxy to leave the blue cloud , less clear is the last leg of the journey , i.e. the migration from the transition region to the red sequence . the complete suppression of the star formation requires at least a few billion years . this ` two - step ' migration is more dramatic , and perhaps only visible , in a uv - near - infrared colour - mass diagram whereas in optical the first stripping event is sufficient to make the colours almost as red as an early - type galaxy . at this stage , it is very tempting to use our data to quantify the current ` migration ' rate and , consequently , the mass accretion rate of the red sequence . unfortunately , the large uncertainties in both observables and on the typical time - scale of the migration ( at least a factor 2 ) make this exercise not very useful . for example , a quenching time of @xmath23 gyr would suggest that , at the current rate , the red sequence in our sample could have been built by the migration of objects from the blue cloud in a hubble time , consistent with previous works ( e.g. , @xcite ) . however , at the same time , we are not able to reject scenarii in which either the observed rate is able to build - up the red sequence in half a hubble time or the observed migration is not able to explain the growth of the quiescent galaxy population in the last 13 gyr . thus , no additional constraints on the evolution of the colour - stellar mass diagram are imposed by the estimate of the stellar mass accretion rate observed in our sample . a more interesting exercise is to look for any morphological transformation during the migration towards the red sequence . the crucial question here is whether the red sequence is fed with bulge dominated or disk galaxies . the answer is clear from fig . [ c31virgo ] , where we compare the distribution of the concentration index in h - band for galaxies in the virgo cluster . in the transition region , we show only virgo hi - deficient galaxies . overall ( fig . [ c31virgo ] , left panel ) , hi - deficient transition galaxies have a concentration index much more similar to blue than red - sequence systems . however , such difference is only evident at stellar masses higher than @xmath210@xmath29 m@xmath46 ( fig . [ c31virgo ] , central panel ) whereas for smaller galaxies ( right panel ) the distribution of @xmath55 does not significantly vary across the whole range of colours , reflecting the fact that dwarf ellipticals have exponential light profiles like dwarf irregulars ( e.g.,@xcite ) . this result implies that , while hi - deficient transition galaxies are likely the progenitors of cluster low - mass red objects ( see also @xcite ) , this is not completely true at high stellar masses . this is additionally supported by the fact that the vast majority of high - mass transition galaxies are early - type spirals and almost no ellipticals are present ( fig [ typedistr ] and [ trdistr ] ) . the vast majority of galaxies in the process of reaching the red sequence are thus disk systems , significantly different from ellipticals or bulge - dominated galaxies characterizing high - mass , quiescent objects at low redshift . since a significant fraction of hi - deficient transition galaxies appears to have recently infalled into the center of virgo and will likely spend a few gyr in the transition region ( see [ hidef ] ) , it may be possible that a morphological transformation still takes place before reaching the red sequence . although we can not completely exclude this scenario , we consider it unlikely . given the long time required to halt the star formation , galaxies with increased bulge component should be present in our sample . moreover , since gas stripping appears not to significantly increase the bulge component in early type galaxies ( e.g. , @xcite ) , an additional environmental effect ( different from the one responsible for the quenching of the star formation ) must be invoked . thus , the fact that transition galaxies are not morphologically transformed before reaching the red sequence may have two different implications : either 1 ) galaxies are morphologically transformed once already in the red sequence , or 2 ) the mechanism controlling the accretion of stellar mass into the red sequence at @xmath30 is not the one responsible for the creation of the red sequence in the first place . although it is possible that the bulge component is enhanced in some red galaxies via gravitational interactions , such scenario seems unlikely to explain the growth of the red sequence . firstly , the mechanism responsible for the morphological transformation should be efficient only on giants and not on dwarf systems , which seems inconsistent with what known about environmental effects @xcite . secondly , the major mergers required to significantly increase the bulge component are extremely rare in today s clusters of galaxies . thirdly , the presence of red - sequence galaxies in isolation ( e.g. , hc09 ) implies that star formation has been suppressed also outside clusters of galaxies . although our sample could be biased against isolated objects , the fact that we do not find a field population which is clearly migrating from the blue sequence may suggest that in low density environments the red sequence has been mainly populated in the past . finally , if the morphological transformation takes place in the red sequence , the number of bulge - dominated / elliptical galaxies should decrease at increasing redshift , which does not seem to be the case @xcite . thus , the most favourite scenario emerging from our analysis is that the red sequence is currently accreting mass , at all masses , mainly via disk galaxies . no significant structural modification takes place during the journey from the blue cloud to the red sequence . the main process responsible for the suppression of the star formation in nearby galaxies is thus not the same responsible for the formation of the red sequence at high redshift . . the distribution of the h - band concentration index for virgo hi - deficient ( dashed ) and hi - normal transition galaxies . all galaxies and galaxies with @xmath56 m@xmath30 are shown in the left and right panel respectively.,width=321 ] while in the case of hi - deficient objects it seems plausible to associate transition galaxies with objects that are migrating from the blue to red sequence , this is not always the case for hi - normal transition galaxies . the discovery of such systems is probably the most exciting result of this work . they represents @xmath212% of our transition galaxy population , and are only found at high stellar masses ( @xmath6110@xmath29 m@xmath46 ) . as shown in fig . [ c31gasrich ] , these galaxies are mainly disks with a significant bulge component * ( they are in fact all sa or s0 galaxies ) * and , despite the low number statistics , it seems clear that , , contrary to the hi - deficient population , in this family we find very few ` disk - only ' galaxies . despite their different properties , a great fraction of these galaxies show active star - forming regions and hi segregated in one or multiple ring - like structures . the picture emerging from our analysis is quite complex and exciting at the same time , showing that the transition region can be fed with galaxies from both sequences . red sequence galaxies can acquire new gas supply and restart their star formation activity , as predicted by cosmological simulations . however , it is unlikely that the red galaxies in our sample will re - build a significant stellar disk ( see also @xcite ) . merging , accretion of gas - rich satellites and exchange of material during close encounters are among the likely responsible for this rejuvenation . such processes are more frequent in low density environments , where red - sequence galaxies are rarer , perhaps reducing the chances to observe such phenomenon . when a suppression of the star formation is the most likely scenario to explain hi - normal transition galaxies , the process behind such migration is still unclear . in this case , star formation must be reduced by making the hi stable against fragmentation ( e.g. , by decreasing the hi column density below the threshold for star formation ) and not via hi stripping as observed in hi - deficient objects . starvation @xcite by removing any extended gaseous halo surrounding the galaxy , preventing further infall , could be a possibility . this would imply a longer time - scale ( several gyr ) for the migration from the blue cloud @xcite than the one observed in the case of hi stripping ( a few hundreds million years ) . however , the evidence for accretion / interaction in some of these objects may suggest that starvation , if efficient , is not the only mechanism at work . @xcite have recently proposed a ` morphological quenching ' to explain the origin of gas - rich bulge - dominated objects . the idea behind this mechanism is that the presence of a bulge could inhibit the collapse of a gas disk . however , the ` morphological quenching ' appears only to be effective when the disk stellar component is negligible , which is not the case for the majority of the systems in our sample . finally , the fact that the majority of these objects show some level of nuclear activity , might indicate a link between agn activity and their position in the colour stellar mass diagram . however , although we can not exclude that recent accretion events may have triggered the agn , we do not find any direct observational evidence suggesting that agn - feedback is playing a significant role in the recent star formation history of these objects ( see also hc09 ) . thus , the past evolutionary history of hi - normal transition galaxies has still to be unravelled . whatever is the path followed to get to the transition region , hi - normal systems currently have enough fuel to sustain star formation at the current rate for almost another hubble time . this is an unexpected result , implying that such systems could remain in the transition region for a very long time and that the colour range 4.5@xmath06 mag does not automatically correspond to a snapshot in the star formation history of nearby galaxies .

we observed the `` micro - quasar '' four times with _ chandra_. two hrc - i observations were made in 2000 september - october spanning an intermediate - to - hard spectral transition ( identified with _ rxte _ ) . another hrc - i and an acis / hetgs observation were made in 2001 march following a hard - to - soft transition to a very low flux state . the accurate position ( j2000 ) of the source is ra @xmath0 18 01 12.40 , dec @xmath0 @xmath125 44 36.0 ( 90% confidence radius @xmath0 0.6 ) , consistent with the purported variable radio counterpart . all images are consistent with being a point source , indicating that any bright jet is less than 1light - month in projected length , assuming a distance of 8.5kpc . the march spectrum is well - fit with a multi - color disk - blackbody with an inner temperature of @xmath2kev , interstellar absorption of @xmath3 , and ( un - absorbed ) 1@xmath110kev luminosity of @xmath4 .

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astro-ph0107469

we observed the `` micro - quasar '' four times with _ chandra_. two hrc - i observations were made in 2000 september - october spanning an intermediate - to - hard spectral transition ( identified with _ rxte _ ) . another hrc - i and an acis / hetgs observation were made in 2001 march following a hard - to - soft transition to a very low flux state . the accurate position ( j2000 ) of the source is ra @xmath0 18 01 12.40 , dec @xmath0 @xmath125 44 36.0 ( 90% confidence radius @xmath0 0.6 ) , consistent with the purported variable radio counterpart . all images are consistent with being a point source , indicating that any bright jet is less than 1light - month in projected length , assuming a distance of 8.5kpc . the march spectrum is well - fit with a multi - color disk - blackbody with an inner temperature of @xmath2kev , interstellar absorption of @xmath3 , and ( un - absorbed ) 1@xmath110kev luminosity of @xmath4 . no narrow emission lines are apparent in the spectrum and upper limits to line equivalent widths are given . # 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in

during more than 5 years monitoring with the _ rxte _ prior to 2001 march , the hard spectrum was always dominated by a hard power law with photon index @xmath8 @xcite with occasional appearance of a weak thermal component @xcite . as shown in figure [ f_lc ] , made an abrupt state change in 2001 march . the hard flux dropped by an order of magnitude in a few days , leaving the thermal component seen in figure [ f_spec ] . based on relative luminosity , however , the current soft state is not a _ high_/soft state . rather it is significantly less luminous than the low / hard state in this source . this can be contrasted to cyg x-1 and the soft transients , where the _ high_/soft state is more luminous . rather , this seems to be a low - luminosity state which is fading into quiescence ( figure [ f_lc ] ) . finally , we note that the measured column density is consistent with previous measurements @xcite since strong jet ejections are generally associated with the `` very high state '' and transitions from the `` off '' to high / soft states in transients @xcite , it is perhaps not surprising that no jet emission appeared in our low / hard state observations ( sep - oct 2000 ) and the recent transition observation ( mar 2001 ) . perhaps our best opportunity will come when ( if ? ) makes a transition once again to its normal , low / hard state . we have an approved _ chandra_cycle 3 proposal to monitor the morphology of and hope to observe a jet ejection .

we perform large scale simulations of a two dimensional lattice model for amorphous plasticity with random local yield stresses and long - range quadrupolar elastic interactions . we show that as the external stress increases towards the yielding phase transition , the scaling behavior of the avalanches crosses over from mean - field theory to a different universality class . this behavior is associated with strain localization , which significantly depends on the short - range properties of the interaction kernel .

i

1307.2135

we perform large scale simulations of a two dimensional lattice model for amorphous plasticity with random local yield stresses and long - range quadrupolar elastic interactions . we show that as the external stress increases towards the yielding phase transition , the scaling behavior of the avalanches crosses over from mean - field theory to a different universality class . this behavior is associated with strain localization , which significantly depends on the short - range properties of the interaction kernel .

in recent years , strong experimental evidence has emerged that the plastic response of materials is not smooth and continuous as would be expected from classical stress - strain relationships but instead intrinsically subject to fluctuations @xcite , both temporally and spatially . for example , upon application of external stress , plastic strain in micron sized samples increases in avalanches with power law distributions @xcite . such avalanches are also present in bulk materials , as shown by acoustic emission measurements @xcite . furthermore , acoustic emission localization @xcite and surface observations @xcite reveal complex spatial patterns . in crystalline materials , the observed intermittent behavior is related to the dynamics of interacting dislocations @xcite , and it is believed that because interactions between dislocations are long - ranged , the scaling of this intermittent behavior is of a mean - field nature @xcite . at the same time , experiments @xcite and molecular dynamics simulations @xcite show that scale free avalanches and complex strain patterns are also shared by amorphous materials where localized defects are not present . an open question that remains is whether the universality class of amorphous plasticity is the same as that of crystalline plasticity . in two dimensions , amorphous plasticity can be captured by a simple model @xcite with two competing ingredients : ( i ) disorder in the form of randomly distributed local yield thresholds , and ( ii ) a long - range , anisotropic interaction kernel , which in an infinite system is given by the eshelby form @xmath0 @xcite . the build up of plastic strain can be mapped on to the motion of a 2d interface in the transverse direction , driven by external stress . the random yield thresholds represent a landscape of random energy barriers through which the interface moves , so that the model can be thought of as a type of @xmath1 dimensional depinning model that undergoes a transition from the pinned phase to the moving phase as external stress is increased @xcite . in fact , a formally similar model was derived in ref . @xcite as a mesoscale model for crystal plasticity . the similarity derives from the fact that in two dimensions the stress created by moving a dislocation in a crystal is equivalent to the one produced by a localized shear event in an amorphous material . therefore we could expect that crystal and amorphous plasticity share the same critical behavior , at least in two dimensions , where mean field behavior has been observed @xcite . this is , however , contradicted by recent results by talamali _ et al _ @xcite suggesting that at criticality , the amorphous plasticity model is not mean - field , as evidenced by , e.g , avalanche size distributions . to shed some light on the universality class of amorphous plasticity , we present large - scale simulation studies of plasticity in 2d amorphous materials . previous studies of this system have suffered from small system sizes , a consequence of the large computational cost induced by the long - range interactions . by implementing our simulations on the parallel architecture of a graphics processing unit , we are able to access larger system sizes than those previously published , enabling a clearer picture to be built up of the critical behaviour of the model . this paper is organized as follows . first , we examine the strain avalanches of the system away from criticality , and find that depending on the short - range part of the interaction kernel the model can exhibit a nonuniversal crossover from mean - field behavior at small stresses to non mean - field behavior , similar to that observed in a lattice model for ductile fracture @xcite . we then examine the non mean - field behavior at criticality in greater depth , and present evidence that it is indeed universal , depending only on the large - scale nature of interactions . the onset of non mean - field behavior is connected to strain localization , which we find is affected by small changes to short - range interactions . this is especially apparent when weakening is introduced to the model .

we performed the numerical simulation of quantum turbulence produced by thermal counterflow in superfluid @xmath0he by using the vortex filament model . the pioneering work was made by schwarz , which has two defects . et al _ , where thermal couterflow was visualized by solid hydrogen particles .

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0906.3142

we performed the numerical simulation of quantum turbulence produced by thermal counterflow in superfluid @xmath0he by using the vortex filament model . the pioneering work was made by schwarz , which has two defects . one is neglecting non - local terms of the biot - savart integral ( localized induction approximation , lia ) , and the other is the unphysical mixing procedure in order to sustain the statistically steady state of turbulence . we succeeded in making the statistically steady state without the lia and the mixing . this state shows the characteristic relation @xmath1 between the line - length - density @xmath2 and the counterflow relative velocity @xmath3 with the quantitative agreement of the coefficient @xmath4 with some typical observations . we compare our numerical results to the observation of experiment by paoletti _ et al _ , where thermal couterflow was visualized by solid hydrogen particles .

quantum turbulence(qt ) , which consists of a tangle of quantized vortices , has been investigated since the thermal counterflow experiments of vinen [ 1 - 4 ] half a century ago , while the underlying physics is far from being fully understood [ 5,6 ] . the numerical simulations are the useful source of knowledge about qt , because the whole dynamics of this system is too complicated to be described analytically . one of the powerful schemes of the simulation is the vortex filament model based on pioneering works by schwarz [ 7,8 ] . schwarz performed the numerical simulation of counterflow turbulence under the periodic boundary condition by using the localized induction approximation ( lia ) which neglects a non - local term of the biot - savart integral [ 8 ] . however he could not obtain the statistically steady state ( sss ) because the vortices lie in planes normal to @xmath5 to prevent them from reconnecting . therefore the unphysical mixing procedure , in which half of the vortices are randomly selected to be rotated by 90@xmath6 around the axis defined by the flow velocity , was used , and only this method enabled him to obtain the sss . this failure reminds us that the lia is unsuitable through the absence of the interaction between vortices . recently , thermal counterflow in superfluid @xmath7he was visualized by using solid hydrogen particles , and the velocity distribution of particles was observed [ 9 ] . in this experiment , two types of particles appeared . some particles move straight along the normalflow with the approximately same velocity as normalflow . other particles move zigzag along the direction of superfluid and has different velocity from superfluid . in the latter case , particles seem to be trapped in the core of the vortices . we try to apply our numerical results for understanding these observations . section 2 describes the equation of motion of vortices and the method of numerical calculation . in sec.3 we show the typical numerical results of vortex tangle . section 4 studies the validity of the lia by comparing the lia calculation with the full biot - savart calculation . in the section 5 we present the velocity distribution of vortices in the sss of vortex tangle and compare it with that of particles in the experimental observation .