Datasets:

parteeksj

/

scientific_papers_DANCER

like 0

0908.4520

m

similar to the grad s method for deriving higher order continuum systems ( e.g , grad 13-moment equations ) , using the hermite expansion to approximate the boltzmann - bgk equation can lead to the lb equation , i.e. eq.([lbgk ] ) . however , the major difference is that lb models are always staying at the kinetic level , i.e. solving the kinetic equation - eq.([lbgk ] ) , while the grad s method will produce a set of continuum equations . the basic idea of grad s method is to use the truncated hermite polynomials to approximate the full boltzmann ( or boltzmann - bgk ) equation . due to the unique feature of hermite polynomial , the moments of up to the chosen truncation order can be described accurately by the derived macroscopic moments systems . in contrary , the only explicit effect of the truncation on the lb models is on the approximation of the equilibrium distribution function and the body force , while the grad s moment equations do not approximate the equilibrium distribution function . although the order of hermite expansion determines the accuracy level of the moment model , which is not the same for the lb models . essentially , the lb equation i.e. eq.([lbgk ] ) is similar to any model equation which is to simplify the full boltzmann equation . the kinetic process , i.e. gas molecules relaxing to the equilibrium state through collisions , is still the same . therefore , the lb method is very close to the discrete velocity method solving the boltzmann - bgk equation ( especially the linearized - bgk equation ) , which we will discuss in the section below . the above procedure of establishing lb models is similar to the problem solving process of the discrete velocity method , which directly solves the boltzmann - bgk equation . since dvm has been proved to be able to provide accurate results for rarefied gas dynamics , it is helpful to compare two numerical methods in depth . the discrete velocity method is to discretize the velocity space based on quadratures e.g. gauss - hermite quadrature and newton - cotes quadrature ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the first step is to non - dimensionalize the boltzmann - bgk equation and obtain the reduced functions , e.g. @xmath59 and @xmath60 in eqs.([ga ] ) and ( [ gb ] ) , which are important to reduce computational costs . the second step is to apply an appropriate discretization method for the velocity space , which is important but difficult because the velocity space ranges from @xmath3 to @xmath4 and the properties of conservation and dissipation of the entropy should be kept . a typical choice is the gauss - hermite quadrature , which is to be adopted in our simulations . in order to reduce the velocity components which need to be integrated from @xmath3 to @xmath4 , curvilinear coordinates including the polar coordinates for 2d systems may be used for the velocity space . afterwards , the continuous maxwell equilibrium should also be discretized . the last step is to adopt an appropriate numerical scheme for the space and time discretization . therefore , we can see that lb methodology closely resembles the dvm problem solving process . @xcite noticed this similarity and stated * * * * the lb equation is essentially dvm with finite discrete velocities and fully discretized space and time tied to the discrete velocity set**"**. for simulating rarefied gas flows , this similarity is important as we have shown how the lb framework is developed from the boltzmann - bgk equation . for both dvm and lb methods , the most critical task is to discretize the velocity space . when the gauss - hermite quadrature is used in dvm , the discretization of the velocity space in these two methods are the same , which may indicate that the lb models with sufficiently accurate gauss - hermite quadrature can capture the higher - order non - equilibrium effects in the rarefied gas flows . this in deed is confirmed by the simulation results presented in fig.[exm ] , which we will discuss in detail in section 4 . however , an important advantage of the lb models is the `` stream - collision '' mechanism which is mainly inherited from the lattice gas automata . this `` stream - collision '' mechanism makes the lb method easy to understand and simple for computer programming . therefore , the `` stream - collision '' mechanism is an important feature of the lb models which distinguishes them from dvm . the coupled time step and physical space in the lb models will dramatically reduce the computational cost . in addition , dvm relies heavily on mathematical techniques which depend on specific problem , while the lb methodology is straightforward and more suitable for developing a generic simulation package for engineering design . by introducing @xmath61 to denote the unknown perturbed distribution function and assuming the flow is weakly non - equilibrium , @xmath6 can be approximated by @xmath62 where @xmath63 which is the global ( absolute ) equilibrium distribution function . using the taylor series to expand the local equilibrium distribution function and keeping the terms up to the first order , one can obtain the following equation @xmath64 \right\},\ ] ] where we assume the flow is incompressible . using eq.([lsum ] ) , we can obtain the linearized bgk equation : @xmath65= -\frac{1}{kn}\left\{\psi-\left[\bm \xi \cdot \bm u + \frac{1}{2}(t-1)(\xi^2-d)\right ] \right\}.\ ] ] for lattice boltzmann models , one can rewrite eq.([approxf ] ) as @xmath66,\ ] ] where @xmath67 substituting eq.([approxfhermite ] ) into the boltzmann - bgk equation and keeping the first- and second - order expansions of the equilibrium distribution , one can obtain @xmath68= -\frac{1}{kn}\left ( \varphi-\bm \xi \cdot \bm u \right),\ ] ] and @xmath69= -\frac{1}{kn}\left \{\varphi-\bm \xi \cdot \bm u - \frac{1}{2}\left[(\bm \xi \cdot \bm u)^2-u^2+(t-1)(\xi^2-d)\right ] \right\}.\ ] ] because @xmath25 is equal to @xmath70 , we can observe the following interesting facts by comparing eqs.([lbm1 ] ) and ( [ lbm2 ] ) with eq.([generallbgk ] ) . first of all , by keeping the first order hermite expansion , the essential lb model equation is the same with that of the isothermal ( @xmath71 ) linearized bgk equation except the body force term . _ this implies that @xmath72 is indeed equivalent to @xmath61 though @xmath72 is prescribed to include only the finite order terms of the hermite polynomials ( cf . eq.([approxf ] ) and eq.([approxfhermite ] ) ) . therefore , the lb equation with the first order terms should be as good as the linearized bgk equation for isothermal flows_. this indicates that high - order hermite expansion is not necessary for rarefied gas flows . secondly , with the second order hermite expansion , there is an extra velocity term @xmath73 $ ] for the lb equation in comparison to the linearized bgk equation . however , for flows with low mach number , this term is a higher - order small quantity which can be ignored . this is the reason why the hermite expansion order is reported to make negligible difference on the simulation results ( see * ? ? ? in fact , the first order expansion is sufficient to obtain the accurate results for isothermal rarefied flows with low speed . furthermore , the lb equation with the second order expansion can in principle describe thermal problems since the temperature information is included in eq.([lbm2 ] ) , which at least has the same capability as the linearized bgk equation , though the bgk kinetic model gives wrong @xmath74 number . thirdly , the treatment of the body force makes the difference between the lb model and the linearized bgk equation . it is because that the linearized bgk model keeps the full information while the lb model uses the hermite expansion to approximate @xmath75 , i.e. @xmath76 . however , for the problem is not far from equilibrium state , this difference is not important , which will be confirmed by the numerical simulations in section 4 . from the above analysis , we can see that the hermite expansion order does not determine the accuracy of lb models for rarefied gas flows as described by eq.(4.7 ) in . the hermite expansion provides a means to approximate the equilibrium distribution and the body force in the kinetic equation . therefore , the lb equation , similar to the linearized bgk equation , is an approximation of the boltzmann - bgk equation . in contrast to the grad s moment method , lb models include the information of any order moment though it may not be accurate . for instance , with the first order expansion , the lb model equation is as the same as the isothermal linearized bgk equation in the incompressible limit , which will give accurate results for any order velocity moment . when the mach number of flow increases , high - order terms in the hermite expansion become important . therefore , the order of hermite expansion is important to simulate compressible flows rather than rarefied flows . to capture non - equilibrium effects in rarefied flows , the gauss - hermite quadrature is the key as it determines the discretization accuracy to the model equation . with sufficiently high order of the gauss - hermite quadrature , lb models can give excellent numerical results , e.g. the results presented in fig.([exm ] ) where 400 discrete velocities are used are identical to the dvm solution . considering the similarity of the lb equation and linearized bgk equation , insufficient quadrature order should be responsible for the failure on capturing the constitutive relations in the knudsen layer because the kinetic boundary condition have been well accepted in solving the linearized bgk equation . in summary , the lb method is essentially a special discrete velocity model , which approximates the boltzmann - bgk equation with finite discrete velocities and fully discretized space and time tied to the discrete velocity set . the capability of lb equation is similar to the linearized bgk equation for simulating rarefied gas flows . the hermite expansion order determines the model equation and is important for compressible flows . it has no direct effect on the accuracy of capturing high - order non - equilibrium effects . meanwhile , the gauss - hermite quadrature as a discretization technique for the velocity space directly determines whether the lb models can describe rarefied flows accurately .

therefore , when the same gauss - hermite quadrature is used , lb method closely assembles the discrete velocity method ( dvm ) . in addition meanwhile , appropriate gauss - hermite quadrature has the most significant effect on whether lb models can describe the essential flow physics of rarefied gas accurately .

in this work , we have theoretically analyzed and numerically evaluated the accuracy of high - order lattice boltzmann ( lb ) models for capturing non - equilibrium effects in rarefied gas flows . in the incompressible limit , the lb equation is proved to be equivalent to the linearized bhatnagar - gross - krook ( bgk ) equation . therefore , when the same gauss - hermite quadrature is used , lb method closely assembles the discrete velocity method ( dvm ) . in addition , the order of hermite expansion for the equilibrium distribution function is found not to be correlated with the approximation order in terms of the knudsen number to the bgk equation , which was previously suggested by @xcite . furthermore , we have numerically evaluated the lb models for a standing - shear - wave problem , which is designed specifically for assessing model accuracy by excluding the influence of gas molecule / surface interactions at wall boundaries . the numerical simulation results confirm that the high - order terms in the discrete equilibrium distribution function play a negligible role . meanwhile , appropriate gauss - hermite quadrature has the most significant effect on whether lb models can describe the essential flow physics of rarefied gas accurately . for the same order of the gauss - hermite quadrature , the exact abscissae will also modestly influence numerical accuracy . using the same gauss - hermite quadrature , the numerical results of both lb and dvm methods are in excellent agreement for flows across a broad range of the knudsen numbers , which confirms that the lb simulation is similar to the dvm process . therefore , lb method can offer flexible models suitable for simulating continuum flows at navier stokes level and rarefied gas flows at the linearized boltzmann equation level . [ firstpage ]

0908.4520

c

we have theoretically and numerically analyzed the high - order lb models for rarefied gas flows . the lattice boltzmann equation is shown to be equivalent to the linearized bgk equation in the incompressible limit . when the same gauss - hermite quadrature is used , both lb and dvm simulations produce results in excellent agreement across a broad range of the knudsen numbers . this suggests the importance of the gauss - hermite quadrature and the great potential of the lb method for modeling rarefied gas flows . while the gauss - hermite quadrature is of the most importance to capturing non - equilibrium effects , the first - order hermite expansion on the equilibrium distribution function is sufficient to obtain the correct moments for isothermal flows e.g. increasing the hermite expansion order further will not improve the model accuracy . for the same order gauss - hermite quadratures , the chosen abscissae will influence the model accuracy and more discrete velocities may not lead to improved model accuracy . overall , we have demonstrated that lb method offers a computationally efficient approach to solve the bgk equation . we can choose a suitable lb model to meet different requirement on model accuracy and computational efficiency , which offers an ideal flexible engineering design simulation tool to be able to simulate flows in the continuum and transition regimes .

in this work , we have theoretically analyzed and numerically evaluated the accuracy of high - order lattice boltzmann ( lb ) models for capturing non - equilibrium effects in rarefied gas flows . in the incompressible limit , the lb equation is proved to be equivalent to the linearized bhatnagar - gross - krook ( bgk ) equation . for the same order of the gauss - hermite quadrature , the exact abscissae will also modestly influence numerical accuracy . using the same gauss - hermite quadrature , the numerical results of both lb and dvm methods are in excellent agreement for flows across a broad range of the knudsen numbers , which confirms that the lb simulation is similar to the dvm process .

in this work , we have theoretically analyzed and numerically evaluated the accuracy of high - order lattice boltzmann ( lb ) models for capturing non - equilibrium effects in rarefied gas flows . in the incompressible limit , the lb equation is proved to be equivalent to the linearized bhatnagar - gross - krook ( bgk ) equation . therefore , when the same gauss - hermite quadrature is used , lb method closely assembles the discrete velocity method ( dvm ) . in addition , the order of hermite expansion for the equilibrium distribution function is found not to be correlated with the approximation order in terms of the knudsen number to the bgk equation , which was previously suggested by @xcite . furthermore , we have numerically evaluated the lb models for a standing - shear - wave problem , which is designed specifically for assessing model accuracy by excluding the influence of gas molecule / surface interactions at wall boundaries . the numerical simulation results confirm that the high - order terms in the discrete equilibrium distribution function play a negligible role . meanwhile , appropriate gauss - hermite quadrature has the most significant effect on whether lb models can describe the essential flow physics of rarefied gas accurately . for the same order of the gauss - hermite quadrature , the exact abscissae will also modestly influence numerical accuracy . using the same gauss - hermite quadrature , the numerical results of both lb and dvm methods are in excellent agreement for flows across a broad range of the knudsen numbers , which confirms that the lb simulation is similar to the dvm process . therefore , lb method can offer flexible models suitable for simulating continuum flows at navier stokes level and rarefied gas flows at the linearized boltzmann equation level . [ firstpage ]

1103.0732

i

a periodic variation of a system parameter leads to the exponential growth of certain modes of the system . this phenomenon is known as parametric resonance and occurs in a wide variety of systems such as classical oscillators , nonlinear optics , system governed by non - linear schrdinger equations and in hamiltonian chaotic systems . parametric excitations in the form of faraday waves , were observed in a cigar - shaped bose - einstein condensate ( bec ) by periodically modulating the radial trap frequency @xcite . the modulation of the radial trap frequency leads to a periodic modulation of the density of the cloud in time , which in turn leads to a periodic change in the nonlinear interactions . this leads to the parametric excitation of longitudinal sound - like waves ( faraday waves ) in the direction of weak confinement . from the theoretical side , parametric excitations have already been investigated by numerous authors @xcite . a bec in an optical lattice potential exhibits parametric excitations when the depth of the optical lattice potential is periodically modulated in time . these parametric excitations correspond to an exponential growth of the population of counter - propagating bogoliubov excitations @xcite . when the frequency of oscillation of the scattering length is an even multiple of the radial or axial natural oscillation frequency , respectively , the radial or axial oscillation of the condensate exhibits resonance @xcite . parametric resonances in a bec under periodic oscillations of the position of a quadratic plus quartic trap have also been predicted @xcite . experimentally , stferle et al . @xcite measured the excitation spectrum of the condensate in the superfluid regime by time modulating the optical lattice depth . the width of the expanding cloud after it is released from the trap is taken as a measure of the excitation energy . the observed resonances in these experiments were explained by the generation of parametric amplification of bogoliubov states and the subsequent nonlinear dynamics , which leads to the broadening of the momentum distribution @xcite . in this work , we study parametric resonances in an elongated cigar - shaped bec in a combined harmonic trap and a time dependent optical lattice by using numerical and analytical techniques . in order to distinguish the present work from parametric resonances studied earlier , we always consider the case when the frequency of oscillation of the optical lattice depth is not equal to the axial or radial natural oscillation frequency . we show that there exists a relative competition between the harmonic trap which tries to spatially localize the bec and the time varying optical lattice which tries to delocalize the bec . this competition gives rise to parametric resonances ( collapse and revival in the oscillations of the bec width ) . parametric resonances disappear when one of the competing factors i.e strength of harmonic trap or the strength of optical lattice dominates . on one hand , parametric instabilities ( exponential growth of bogoliubov modes ) arise for large variations in the strength of the optical lattice and on the other hand , stable oscillations of the condensate width occurs when the harmonic trap strength dominates . we employ a variational technique @xcite to derive analytical predictions for the parametric resonances . the analytical results qualitatively agree with the numerical results .

in this work , we study parametric resonances in an elongated cigar - shaped bec in a combined harmonic trap and a time dependent optical lattice by using numerical and analytical techniques . we show that there exists a relative competition between the harmonic trap which tries to spatially localize the bec and the time varying optical lattice which tries to delocalize the bec . this competition gives rise to parametric resonances ( collapse and revival of the oscillations of the bec width ) . parametric resonances disappear when one of the competing factors i.e strength of harmonic trap or the strength of optical lattice dominates . parametric instabilities ( exponential growth of bogoliubov modes ) arise for large variations in the strength of the optical lattice .

in this work , we study parametric resonances in an elongated cigar - shaped bec in a combined harmonic trap and a time dependent optical lattice by using numerical and analytical techniques . we show that there exists a relative competition between the harmonic trap which tries to spatially localize the bec and the time varying optical lattice which tries to delocalize the bec . this competition gives rise to parametric resonances ( collapse and revival of the oscillations of the bec width ) . parametric resonances disappear when one of the competing factors i.e strength of harmonic trap or the strength of optical lattice dominates . parametric instabilities ( exponential growth of bogoliubov modes ) arise for large variations in the strength of the optical lattice .

1209.2232

i

observing the behavior of electrons in graphene under high magnetic field has played an important role not only for uncovering new quantum hall states , but also for proving the very existence of massless dirac particles @xcite . affected by the linear dispersion near dirac points , landau levels are formed in graphene such that their energy is scaled as @xmath1 in units of @xmath2 with @xmath3 , the landau level index , allowed for all integers including positive , zero , and negative @xcite . in the above , @xmath4 is the fermi velocity at the dirac point and @xmath5 is the magnetic length . the @xmath0 landau level offers a particularly intriguing departure from the usual quantum hall effect ( qhe ) in that its hall coefficient is shifted by half an integer . with both spin and valley degeneracy taken into account , the consequent hall conductance is predicted to be quantized in the form of @xmath6 in units of @xmath7 , which exhibits beautiful agreement with experiment @xcite . there is , however , a glaring omission in the discussion so far . in the above , the effect of lattice is completely ignored except that the electron dispersion becomes linear near dirac points . the question is how valid this assumption can be . more specifically , will there be any changes in the landau - level structure once the effect of lattice is better incorporated ? navely speaking , since the deviation from the linear dispersion occurs in relatively high energy , one may expect that the landau levels should be more or less the same as before so that they remain as flat bands . in particular , the @xmath0 landau level is then expected to remain as a flat band pinned exactly at zero energy due to the particle - hole symmetry . seemingly innocuous , if true , this expectation gives rise to a very puzzling question : what determines which states within the @xmath0 landau level evolves into the particle ( or the positive energy ) branch and which into the hole ( or the negative energy ) branch at the edge ? a natural resolution of this puzzle is that the @xmath0 landau level is broadened with its bandwidth becoming finite . if so , what would be the nature of such bandwidth - broadened @xmath0 landau level ? the quantum mechanical problem of an electron moving in lattice under magnetic field is generally known as the azbel - hofstadter problem named after azbel @xcite , who originally proposed the model , and hofstadter @xcite , who first obtained a numerical solution in the square lattice and showed the existence of a self - similar fractal structure in energy eigenvalue , dubbed as the hofstadter butterfly . the actual equations , that need to be solved , are known as harper s equations which are in fact nothing but the energy eigenvalue equation for the hamiltonian matrix . by numerically solving harper s equations , the self - similar fractal structure of the azbel - hofstadter model was found also for various other lattices including the triangular and the honeycomb lattice @xcite . in addition to numerical studies solving harper s equation , there have been extensive efforts to obtain analytic solutions @xcite . the reason for such efforts is multifaceted . for one , many researchers have been curious about the very origin of the self - similar fractal structure seen in the hofstadter butterfly and tried to make a connection to other known systems exhibiting similar fractal structures . for another , numerical computations can be performed only in the situation where the magnetic flux per unit cell , @xmath8 , is a rational fraction of the magnetic flux quantum , @xmath9 . therefore , what happens at irrational fractions can be addressed only by the analytic approaches . perhaps , the most important reason in connection with experiment is the fact that the numerical approach can not access the weak - field limit where the size of the matrix that needs to be diagonalized diverges . the weak - field limit is most relevant for experiment since , even in the quantum hall regime , the magnetic flux per unit cell is typically much less than @xmath10 in units of magnetic flux quantum . among various analytic approaches , the bethe - ansatz approach is regarded to be most systematic , where the azbel - hofstader problem is converted into solving the bethe - ansatz equations whose roots are directly connected to the energy eigenvalues as well as eigenstates . despite providing such insightful relationship to an integrable model , the bethe - ansatz approach is proven to be of little practical use since the bethe - ansatz equations are generally insoluble except for special cases . the use of other analytic approaches is also similarly limited . in this paper , we develop a method that can be used to provide an accurate analytic description of the evolution of the @xmath0 landau level as a function of magnetic field ranging from being arbitrarily weak to moderately strong . in this method , it is shown that , for @xmath11 with @xmath12 and @xmath13 being coprime positive integers , the central band of the hofstadter butterfly , which is obtained from the original @xmath14 matrix for harper s equations , is captured extremely accurately by diagonalizing the effective hamiltonian matrix with a much reduced size of @xmath15 in the weak - field regime . the central band of the hofstadter butterfly is connected with the @xmath0 landau level in the continuum limit . actually , this effective hamiltonian matrix works quite well for @xmath16 as large as @xmath17 . one of the most important discoveries of this work is that , no matter how small the magnetic flux per unit cell may become , the central hofstadter band ( chb ) always contains massless dirac particles whose energy dispersion is completely isomorphic to that in the absence of magnetic field . in fact , by combining the self - similar pattern of the central hofstadter band and some analytic as well as numerical results for the zero - energy modes of harper s equations , we conclude that there should be exactly @xmath18 dirac cones in the magnetic brillouin zone ( mbz ) for @xmath11 with arbitrary @xmath12 and @xmath13 . a corollary of this result is that there should also be a self - similar occurrence of landau levels associated with such dirac cones . in order to assess the experimental feasibility of observing such massless dirac particles within the central hofstadter band , we compute the width of the central hofstadter band which , for small @xmath16 , is predicted to scale as @xmath19 in units of the energy level spacing between the @xmath0 and @xmath20 landau level , @xmath2 . here , @xmath21 and @xmath22 is called the clausen function . actually , motivated by an intriguing conjecture proposed by thouless @xcite a while ago , there has been a long history for addressing how the total bandwidth of the hofstadter butterfly scales as a function of magnetic field @xcite . to the best of our knowledge , our result is the first report for the scaling of the hofstadter butterfly bandwidth in the honeycomb lattice . considering difficulties in directly observing the hofstadter butterfly under magnetic field with typically available strength , we believe that a precise measurement of the bandwidth itself can be used to infer the existence of the hofstadter butterfly in addition to the diophantine equation for the quantized hall conductance @xcite . the rest of the paper is organized as follows . in sec . [ section : model ] , we present the azbel - hofstadter model in graphene with a particular choice of gauge called the optimal gauge . in sec . [ section : zero - energy ] , we analyze various properties of the zero - energy solutions for harper s equations , which play a crucial role in our effective hamiltonian method by generating basis wave functions for the central hofstadter band . a precise mathematical form of the effective hamiltonian is presented in sec . [ section : effective_hamiltonian ] , where it is shown that the resulting magnetic band structure provides an excellent agreement with that of the central hofstadter band obtained from the original harper s equations in the weak - field regime . in sec . [ section : self - similar ] , by using such effective hamiltonian method , we carefully analyze the self - similar recursive pattern of the central hofstadter band , which is then combined with analytic as well as numerical results for the zero - energy modes to show that massless dirac particles should occur under arbitrary magnetic field . we conclude in sec . [ section : conclusion ] .

intricate interplay between the periodicity of the lattice structure and that of the cyclotron motion gives rise to a well - known self - similar fractal structure of the energy eigenvalue , known as the hofstadter butterfly , for an electron moving in lattice under magnetic field . evolving from the @xmath0 landau level , one of the most important discoveries obtained in this work is that massless dirac particles always exist inside the central hofstadter band no matter how small the magnetic flux may become . in other words , with its bandwidth broadened by the lattice effect , the @xmath0 landau level contains massless dirac particles within itself . in fact , by carefully analyzing the self - similar recursive pattern of the central hofstadter band , we conclude that massless dirac particles should occur under arbitrary magnetic field . as a corollary , the central hofstadter band also contains a self - similar structure of recursive landau levels associated with such massless dirac particles . to assess the experimental feasibility of observing massless dirac particles inside the central hofstadter band , we compute the width of the central hofstadter band as a function of magnetic field in the weak - field regime .

intricate interplay between the periodicity of the lattice structure and that of the cyclotron motion gives rise to a well - known self - similar fractal structure of the energy eigenvalue , known as the hofstadter butterfly , for an electron moving in lattice under magnetic field . evolving from the @xmath0 landau level , the central band of the hofstadter butterfly is especially interesting since it may hold a key to the mysteries of the fractional quantum hall effect observed in graphene . while the entire hofstadter butterfly can be in principle obtained by solving harper s equations numerically , the weak - field limit , most relevant for experiment , is intractable due to the fact that the size of the hamiltonian matrix , that needs to be diagonalized , diverges . in this paper , we develop an effective hamiltonian method that can be used to provide an accurate analytic description of the central hofstadter band in the weak - field regime . one of the most important discoveries obtained in this work is that massless dirac particles always exist inside the central hofstadter band no matter how small the magnetic flux may become . in other words , with its bandwidth broadened by the lattice effect , the @xmath0 landau level contains massless dirac particles within itself . in fact , by carefully analyzing the self - similar recursive pattern of the central hofstadter band , we conclude that massless dirac particles should occur under arbitrary magnetic field . as a corollary , the central hofstadter band also contains a self - similar structure of recursive landau levels associated with such massless dirac particles . to assess the experimental feasibility of observing massless dirac particles inside the central hofstadter band , we compute the width of the central hofstadter band as a function of magnetic field in the weak - field regime .

astro-ph9803345

i

garcia - lario , manchado , sahu , and pottasch ( 1993 , hereafter gmsp ) present the first detailed analysis of iras 06562@xmath00337 . they argue that it is a proto - planetary nebula ( ppn ) undergoing final mass - loss episodes . their time - series of optical spectra , obtained over a 5 year period , show the onset of forbidden line emission and the possible evolution of the central star toward hotter temperatures . they derive a zanstra temperature of 2@xmath410@xmath5 k , with a slight increase over a two year interval . the effective temperature of the exciting star , t@xmath6 @xmath7 3.6@xmath410@xmath5 k , also showed a slight increase in two years . the h@xmath8 line profile changes in time , which gmsp interpret as variable high velocity winds associated with episodic mass - loss . the appearance of [ ] emission lines in 1990 and the resulting 4363/(4959 + 5007 ) line ratio requires an ionizing region of high electron density , log(@xmath9 ) @xmath7 6.9 . the absence of these lines in spectra obtained before and after 1990 is interpreted as collisional de - excitation due to changing densities in the ionized region effected by violent episodic mass - loss . from co observations gmsp derive @xmath10 = 50 @xmath11 1 km sec@xmath12 , which agrees with the velocity derived from their high resolution optical spectra . adopting a model galactic rotation curve , they estimate a distance of 4 kpc , which compares to a distance of 2.4 kpc estimated from the equivalent width of na d absorption seen in their spectra . the iras colors fit with blackbodies show a trend of decreasing temperature with increasing wavelength which implies a gradient of dust temperatures . gmsp integrated the optical ir spectral energy distribution of iras 06562@xmath00337 , yielding a luminosity of l = 7000 @xmath13 for their preferred distance of 4 kpc . kerber , lercher , and roth ( 1996 , hereafter klr ) describe an additional medium resolution , high s / n spectrum of iras 06562@xmath00337 obtained in early 1996 . [ ] emission is still absent , but a wealth of and [ ] lines are found . these lines confirm the high electron density derived by gmsp from the [ ] lines present in 1990 . klr argue that the spectrum also implies a considerable density gradient in the object , as [ ] lines are collisionally suppressed at densities where lines exist . they maintain the classification of iras 06562@xmath00337 as a candidate ppn , designating it `` the iron clad nebula '' . bachiller , gutierrez , and garcia - lario ( 1998 , hereafter bgg ) present new mm and sub - mm observations of iras 06562@xmath00337 . they derive @xmath10 = 54.0 @xmath11 0.2 km sec@xmath12 and adopt a different model galactic rotation curve than gmsp to estimate a distance of 7 kpc . this distance yields a luminosity of 21000 @xmath13 and a cloud mass m @xmath14 1000 @xmath15 . from the strength of the co emission and the presence of cs emission , bgg surmise that iras 06562@xmath00337 is a `` young stellar object ( or small cluster ) still associated to its parent molecular cloud . '' bgg point out that iras 06562@xmath00337 satisfies the three criteria for a herbig ae / be star ( herbig , 1960 ) and the spectral energy distribution , which rises sharply in the far infrared ( gmsp ) , is similar to group ii herbig ae / be stars ( hillenbrand , 1992 ) . they also note the presence of blue and redshifted wings in the co emission indicating a bipolar outflow . the co outflow may be driven by an eruptive ionized jet , which leads them to suggest the sporadic [ ] emission seen by gmsp originates in a herbig - haro object . we present the first 2@xmath1 image of iras 06562@xmath00337 . our image reveals a compact cluster of stars surrounding a bright , central object . we independently confirm the result also discovered by bgg that iras 06562@xmath00337 is a young stellar object . in section 2 of this paper , we describe our near - infrared observations and stellar census of the iras 06562@xmath00337 cluster . we also compare the co(2@xmath161 ) map of bgg with our image . in section 3 , we describe our new spectroscopic observations and summarize the resulting 1997 epoch emission line data . we make a detailed comparison with the 1996 epoch emission line data of klr . in section 4 , we present our conclusions .

iras 06562@xmath00337 has been the recent subject of a classic debate : proto - planetary nebula or young stellar object ? we present the first 2@xmath1 image of iras 06562@xmath00337 , which reveals an extended diffuse nebula containing approximately 70 stars inside a 30@xmath2 radius around a bright , possibly resolved , central object . we therefore identify iras 06562@xmath00337 as a new young star cluster embedded in its placental molecular cloud . comparison with previously published spectra shows new evidence for time variable permitted and forbidden line emission , including , , [ ] , and [ ] .

iras 06562@xmath00337 has been the recent subject of a classic debate : proto - planetary nebula or young stellar object ? we present the first 2@xmath1 image of iras 06562@xmath00337 , which reveals an extended diffuse nebula containing approximately 70 stars inside a 30@xmath2 radius around a bright , possibly resolved , central object . the derived stellar luminosity function is consistent with that expected from a single coeval population , and the brightness of the nebulosity is consistent with the predicted flux of unresolved low - mass stars . the stars and nebulosity are spatially coincident with strong co line emission . we therefore identify iras 06562@xmath00337 as a new young star cluster embedded in its placental molecular cloud . the central object is likely a herbig be star , @xmath3 , which may be seen in reflection . we present medium resolution , high s / n , 1997 epoch optical spectra of the central object . comparison with previously published spectra shows new evidence for time variable permitted and forbidden line emission , including , , [ ] , and [ ] . we suggest the origin is a dynamic stellar wind in the extended , stratified atmosphere of the massive central star in iras 06562@xmath00337 .

astro-ph9803345

c

the bright central object in iras 06562@xmath00337 is probably a single herbig ae / be class star , with @xmath3 . there is some evidence that it is seen at least partially in reflection . for example , the central star is poorly fit by the stellar point spread function derived from other stars in our k@xmath17 image . in addition , the centroids in the visible and at k@xmath17 are offset by @xmath390.6@xmath2 . a comparison of our 1997 epoch optical spectra to the 1996 epoch spectrum presented by klr has provided new evidence for spectral line variability in iras 06562@xmath00337 that is not easily interpreted as simple changes in temperature or density . this argues against previous suggestions that the already - published spectral data reflect real - time evolutionary changes of the central star . understanding the immediate environs of the central star is an essential first step to better understanding the emission line variability that has been observed . we note that our analysis of the 19961997 spectral variability of iras 06562@xmath00337 using simple zones and changes in one parameter ( such as the electron temperature or electron density ) is only intended as an interpretive tool and should be treated with some caution . the inconsistencies of this analysis suggest the complexity of the actual emission line region . if the central star is analagous to a herbig be star , then its `` fully ionized zone '' should have a very high electron density . thus , the low density derived with the [ ] emission implies a stratification of densities , likely in the extended atmosphere of the central star in iras 06562@xmath00337 . the anti - correlation of [ ] and [ ] emission is not easily understood if they arise from a common partially ionized zone ( perhaps located at the edge of a compact region around the central star ) , but is likely consistent with an origin in a dynamic stratified atmosphere . spectral variability is also consistent with a stellar wind origin . stellar winds from herbig be type stars are highly variable , extremely complex , and poorly understood ( e.g. , they are possibly modulated by magnetic fields or non - radial pulsations ; catala et al . wind line strengths and profiles can show nightly variations , some of which are correlated with temperature changes of the star ( scuderi et al . the appearance of [ ] emission in iras 06562@xmath00337 during 1990 ( gmsp ) can be understood as shocks in stellar jets from a variable stellar wind ( hartigan & raymond 1993 ) . additionally , we emphasize that the size of the ionized region in iras 06562@xmath00337 is small . six cm radio observations yielded a surprising non - detection given the strong h@xmath52 flux , and allow an upper limit angular diameter of @xmath79 arcsec to be set for the ionized region ( gmsp ) . if we assume the 7 kpc distance estimate of bgg , then the ionized region in iras 06562@xmath00337 has an upper limit diameter of 23 au . we conclude that stellar winds in the extended , stratified atmosphere of a very young , @xmath3 star is the most plausible explanation for the puzzling spectral variability of iras 06562@xmath00337 , the `` iron clad nebula . '' a valuable time series of spectra of the central object in iras 06562@xmath00337 , covering a 10 year interval , are now available in the literature . a useful complementary study would obtain more densely sampled spectroscopic observations , to investigate the short timescale behavior of the emission . in particular , correlated line variability and characteristic timescales could be used to constrain the dimensions of the ionized region , which we have suggested is likely to be an extended stellar atmosphere . we emphasize the need for high resolution and high s / n spectroscopic observations in the near - uv , and of the entire balmer series , as these data can be used to study the extended atmospheres of be stars ( burbidge & burbidge 1953 ) . it is important to build a consistent physical picture of the environs around the central star in order to answer questions such as `` is the central star seen in reflection ? '' this problem in particular could be addressed with high resolution imaging and polarization data . lastly , as a young star cluster , iras 06562@xmath00337 is interesting and notable for its richness . multi - color near - infrared photometric observations would allow an accurate measurement of the imf , and an investigation into problems such as mass segregation and star formation efficiencies ( e.g. , barsony et al .

the central object is likely a herbig be star , @xmath3 , which may be seen in reflection . we present medium resolution , high s / n , 1997 epoch optical spectra of the central object . we suggest the origin is a dynamic stellar wind in the extended , stratified atmosphere of the massive central star in iras 06562@xmath00337 .

iras 06562@xmath00337 has been the recent subject of a classic debate : proto - planetary nebula or young stellar object ? we present the first 2@xmath1 image of iras 06562@xmath00337 , which reveals an extended diffuse nebula containing approximately 70 stars inside a 30@xmath2 radius around a bright , possibly resolved , central object . the derived stellar luminosity function is consistent with that expected from a single coeval population , and the brightness of the nebulosity is consistent with the predicted flux of unresolved low - mass stars . the stars and nebulosity are spatially coincident with strong co line emission . we therefore identify iras 06562@xmath00337 as a new young star cluster embedded in its placental molecular cloud . the central object is likely a herbig be star , @xmath3 , which may be seen in reflection . we present medium resolution , high s / n , 1997 epoch optical spectra of the central object . comparison with previously published spectra shows new evidence for time variable permitted and forbidden line emission , including , , [ ] , and [ ] . we suggest the origin is a dynamic stellar wind in the extended , stratified atmosphere of the massive central star in iras 06562@xmath00337 .

1604.00194

r

we have studied the dependence of neutron and proton chemical potentials on both source size and source asymmetry and the results are displayed in fig . 1 . in fig . 1(a ) , the variation of both @xmath73 and @xmath74 with source proton number @xmath75 is shown for two values of the asymmetry parameter @xmath76 0.11 and 0.27 . the source size @xmath77 is varied from 44 to 264 ( @xmath75 from 16 to 96 ) and it is seen that both the neutron and the proton chemical potential remains almost constant as one increases the source size irrespective of the value of @xmath78 . in the same figure results are shown from both the canonical and the grand canonical models and it is seen that the chemical potentials calculated from both the ensembles are almost equal except for the very small sources where they are slightly different . in fig . 1(b ) , the variation of chemical potentials with the asymmetry parameter @xmath78 is shown where @xmath78 is varied from 0 to 0.33 . the source size @xmath77 is kept fixed at 60 whereas @xmath75 varies from 20 ( @xmath78=0.33 ) to 30 ( @xmath78 = 0 ) . the change of @xmath73 and @xmath79 with @xmath78 is almost linear for both the ensembles and also the results from the canonical and the grand canonical ensembles are more or less the same except for higher @xmath78 values where they are slightly different . + ) and neutron chemical potential ( @xmath73 ) with ( a ) source size ( at constant source asymmetry @xmath80 and @xmath81 ) ( b ) source asymmetry ( for fixed source size @xmath82 ) from canonical ( red solid lines ) and grand canonical models ( black dotted lines).,width=268,height=201 ] since it is seen from fig . 1(a ) & 1(b ) that the chemical potentials are almost same for both models for the entire range of source size and source asymmetry , hence for all other results to be presented for these systems , the chemical potentials obtained from grandcanonical model are being used . + ( @xmath71 ) with fragment proton number @xmath0 ( @xmath1 ) for each pair of sources having same isospin asymmetry @xmath83 and @xmath81 but different charges @xmath84 ( black squares joined by solid lines ) , 24 ( red circles joined by dotted lines ) , 32 ( green circles joined by dashed lines ) 48 ( blue stars joined by dash dotted lines ) and 96 ( magenta pentagons joined by short dotted lines ) from canonical [ 2(a ) , 2(b ) ] and grand canonical [ 2(c ) , 2(d ) ] model . 2(e ) and 2(f ) shows the variation of the isoscaling parameters @xmath70 and @xmath71 respectively with source charge ( @xmath75 ) obtained from canonical model ( red solid lines ) , grand canonical model ( black dotted lines ) and that calculated from the formulae @xmath85 and @xmath86 ( blue stars).,width=268,height=326 ] the isoscaling parameters @xmath70 and @xmath71 ( eq . 11 ) depend only on the difference in chemical potentials of more neutronrich and less neutron rich fragmenting systems and on the temperature at freeze - out . for isoscaling studies a pair of sources with same @xmath75 value is required . we have kept the asymmetry value of the more neutron - rich source to be 0.27 and that of the less neutron - rich one to be 0.11 . the study was done for different source sizes ranging from @xmath75 = 16 to @xmath75 = 96 , the y values being the same for each pair . since for a particular pair of reaction the difference in chemical potentials are the same , therefore it is expected that the isoscaling parameters @xmath70 ( @xmath71 ) would remain constant throughout the entire @xmath0 ( @xmath1 ) regime of the fragments . it can also be concluded from fig . 1(a ) that at constant temperature and same @xmath78 value of the fragmenting sources , @xmath79 and @xmath73 are almost independent of the source size . on the contrary , from theoretical calculation by the canonical model it is observed from fig 2(a ) & 2(b ) that @xmath70 increases with the increase of fragment proton number @xmath0 and @xmath71 decreases with increase of fragment neutron number @xmath1 and the change is more for smaller fragmenting sources . on the other hand , @xmath70 and @xmath71 values calculated from the grand canonical model ( fig 2(c ) & 2(d ) ) are independent of the fragment size . the dependence on source size is also very small as compared to the canonical results ( fig 2(a ) & 2(b)).therefore if we take the average of @xmath70 ( or @xmath71 ) in the range of @xmath87 to @xmath88 ( or @xmath89 to @xmath88 ) for each source and compare those with that calculated from the formula @xmath85 or @xmath86 , then it is observed that the average values obtained from canonical and grand canonical model are different for the smaller fragmenting sources and the difference decreases substantially as one increases the source size as seen in fig 2(e ) & 2(f ) ) . the values of the isoscaling parameter @xmath70 and @xmath71 calculated from the slopes of the ratio @xmath67 of the grand canonical model coincides exactly with those calculated from the formula . this is seen from the dotted lines and the stars in fig 2(e ) & 2(f ) . this is what is expected since the formulae connecting the isoscaling parameters with the difference in chemical potentials is deduced from the grand canonical ensemble and hence results from the later exactly coincide with those calculated from the formulae . + $ ] with @xmath90 for sources having same isospin asymmetry 0.27 but different charge @xmath84 ( black squares ) , 24 ( red circles ) , 32 ( green circles ) 48 ( blue stars ) and 96 ( magenta pentagons ) from canonical ( a ) and grand canonical ( b ) model . here the lines connecting the points represent the linear fittings . ( c ) and ( d ) shows variation of the isobaric yield ratio parameters @xmath91 and @xmath92 respectively with source charge ( @xmath75 ) obtained from canonical model ( red solid lines ) , grand canonical model ( black dotted lines ) and that calculated from the formulae @xmath93 and @xmath94 ( blue stars).,width=268,height=268 ] $ ] with @xmath90 for sources having same mass @xmath82 but different isospin asymmetry 0.1 ( black squares ) , 0.17 ( red stars ) , 0.27 ( green circles ) and 0.33 ( magenta triangles ) from canonical ( a ) and grand canonical ( b ) model . here the lines connecting the points represent the linear fittings . ( c ) and ( d ) shows the variation of isobaric yield ratio parameters @xmath91 and @xmath92 respectively with source isospin asymmetry ( @xmath78 ) obtained from canonical model ( red solid lines ) , grand canonical model ( black dotted lines ) and that calculated from the formulae @xmath93 and @xmath94 ( blue stars).,width=268,height=268 ] in fig . 3(a ) & 3(b ) we show the variation of the isobaric yield ratio @xmath95 $ ] with the fragment sizes where each line represents a particular source having different size but same isospin asymmetry 0.27 . in the isobaric yield ratio method , it is observed from eq . 10 that the quantity @xmath95 $ ] calculated for odd @xmath21 nuclei ( since @xmath96 ) , varies linearly with @xmath90 by an equation like @xmath97 with @xmath98 & @xmath93 ( where @xmath43 and @xmath99 ) . the difference @xmath100 is almost independent of the source size ( fig . 1(a ) ) ; hence c s should be almost equal and m s are exactly equal for all the fragmenting sources . therefore the plot of the ratio @xmath95 $ ] originating from all the fragmenting sources ( as used in fig . 1(a ) ) should almost coincide . but from the canonical model , the variation of @xmath95 $ ] with @xmath90 is different for different sources as shown in fig . the slopes of the lines from different sources vary with the source size although the slope should be exactly equal according to the formula . this deviation arises because from eq . 10 the slope @xmath94 is derived from the grand canonical model and the same may not hold true for the canonical results . the results from the grand canonical model are shown in fig . here it is seen that the slopes are exactly equal irrespective of the source size . the calculated values of the slope @xmath92 and the y - intercept @xmath91 obtained from linear fitting of the lines from canonical models ( fig . 3(a ) ) and those calculated from formula @xmath93 and @xmath94 are not same for smaller fragmenting sources , but are close for the larger sources . this is shown in fig . 3(c ) & 3(d ) . the reason for this deviation is that the formulae are derived using the grand canonical ensemble and hence they are in general not true for the canonical model results . for larger sources the fragmentation is more , therefore the particle number fluctuation in grand canonical model is very less @xcite . in canonical model , particle number is strictly conserved and there is no such fluctuation . hence the isoscaling parameters and isobaric yield ratios obtained from canonical and grand canonical model become closer compared to that from the smaller fragmenting sources . the values of @xmath91 and @xmath92 obtained by fitting the lines from the grand canonical model ( fig . 3(b ) ) coincide exactly with the values given by the formula . this is shown by the dashed line and the symbols in fig . 3(c ) and fig . 4 we show the effect of variation of the source asymmetry @xmath78 on the isobaric yield ratio parameters . in fig . 4(a ) we plot the ratio @xmath95 $ ] with @xmath90 where @xmath21 is the mass number of the fragment . the different lines on the plot corresponds to different sources with @xmath78 values ranging from 0.33 to 0 . the slopes of these lines according to eq . 10 is equal to @xmath94 and hence should not depend on its @xmath78 value . the value of the y - intercept @xmath91 of these lines will be different since it is equal to @xmath101 which depend on @xmath78 as seen from fig 1(b ) . it is seen from fig . 4(a ) that the slopes are different for different sources from the canonical model calculation , the deviation being more for the source which is more asymmetric . for the grand canonical model(fig . 4(b ) ) , the slopes are exactly equal for each source as expected from the formulae . the values of the parameters @xmath91 and @xmath92 are plotted in fig . 4(c ) & 4(d ) respectively . it is seen that results from the canonical model differs from that of the formulae for higher values of @xmath78 and they become close as @xmath78 value approaches 0 or in other words the source becomes symmetric . the results from the grand canonical ensemble coincide exactly with that from the formulae . it has been already studied that results from the canonical and grand canonical models converge more as the fragmenting system becomes more symmetric as the particle fluctuation in grand canonical model becomes less in such cases . similar effect is obtained earlier for mass distribution @xcite .

isoscaling and isobaric yield ratio parameters are compared from canonical and grand canonical ensembles when applied to multifragmentation of finite nuclei . source dependence of isoscaling parameters & source and isospin dependence of isobaric yield ratio parameters are examined in the framework of the canonical and the grand canonical models .

isoscaling and isobaric yield ratio parameters are compared from canonical and grand canonical ensembles when applied to multifragmentation of finite nuclei . source dependence of isoscaling parameters & source and isospin dependence of isobaric yield ratio parameters are examined in the framework of the canonical and the grand canonical models . it is found that as the nucleus fragments more , results from both the ensembles converge and observables calculated from the canonical ensemble coincide more with those obtained from the formulae derived using the grand canonical ensemble .

1201.3660

i

what is the final fate of a massive star that has exhausted its internal nuclear fuel and which then undergoes a catastrophic gravitational collapse under the force of its own gravity ? what are the implication of such a phenomenon on our basic understanding of gravitation theory , and what will be the observational implications as far as very high energy astrophysical phenomena are concerned ? this is the arena where we in fact come face to face with the regime of extreme and ultra - strong gravity fields , and the answer must be sought within the framework of a gravitation theory such as the einstein s theory of gravity . this is where the new and unfamiliar universe encompassing the ultra - strong gravity effects actually reveals itself and we must encounter exotic astrophysical objects such as the spacetime singularities , black holes , and other ultra - compact entities in nature . > from such a perspective , considerable work has been done in past years to understand the dynamical gravitational collapse in general relativity , and many new insights have been obtained . at the same time , several basic issues also remain unclear or unanswered , and there is a general consensus that the nature of cosmic censorship , black holes and naked singularities remain one of the most important unresolved issues in gravitation theory and black hole physics today . these issues would necessarily have far - reaching implications and applications for our understanding on fundamental aspects of gravity theories and applications to high energy astrophysics . our purpose here is to discuss several key problems and questions on gravitational collapse , formation of black holes and naked singularities as final state for a continual collapse , and the related issues regarding the nature and structure of spacetime singularities . these problems are closely related to the nature of cosmic censorship hypothesis and our current understanding on black hole physics . the understanding of such questions is also basic to the theoretical developments as well as the modern astrophysical applications of black holes which are being vigorously pursued today . further , we discuss and consider here certain interesting astrophysical implications emerging from the current work on gravitational collapse within the framework of general relativity . an important question would be , if naked singularities , which are hypothetical astrophysical objects , actually formed in gravitational collapse of massive stars , how these would look observationally different from black holes . a lead that is emerging from the recent work is that the accretion discs around these ultra - high gravity objects , namely black holes and naked singularities , would be significantly different from each other providing characteristic signatures . therefore there exists a possibility to distinguish these two different outcomes of collapse observationally . we discuss some of these current developments here . we thus consider and take up below a series of outstanding questions on these topics , where we attempt to clarify what is already known , while separating the issues which remain unanswered as yet , and on which more work still remains to be done . it is our hope that such a treatment will clarify where the research frontiers are moving on these problems and what remain the major outstanding questions where more work is needed . we intend to review here in this manner some of the major challenges in black hole physics today , and the current progress on the same . it is emphasized that to secure a concrete foundation for the basic theory of black hole physics as well as to understand the high - energy astrophysical phenomena , it is essential to gain a suitable insight into these questions . this will be of course from a perspective of what we think are the important problems , mainly within an analytical treatment of the einstein s theory of gravity in the framework of the general relativity field equations , and no claim to completeness is made .

the research of recent years has provided considerable clarity and insight on stellar collapse , black holes and the nature and structure of spacetime singularities . we discuss several of these developments here . these issues have key implications for our understanding on black hole physics today , its astrophysical applications , and for certain basic questions in cosmology and possible quantum theories of gravity . the emerging astrophysical and observational perspectives and implications are dicussed , with particular reference to the properties of accretion discs around black holes and naked singularities , which may provide characteristic signatures and could help distinguish these objects . pnumwidth1.55em tocrmarg2.55em dotsep4.5 @sectiondottedtocline20em1.5em @subsectiondottedtocline21.5em2.3em @subsubsectiondottedtocline33.8em3.2em

it is now known that when a massive star collapses under the force of its own gravity , the final fate of such a continual gravitational collapse will be either a black hole or a naked singularity under a wide variety of physically reasonable circumstances within the framework of general theory of relativity . the research of recent years has provided considerable clarity and insight on stellar collapse , black holes and the nature and structure of spacetime singularities . we discuss several of these developments here . there are also important fundamental questions that remain unanswered on the final fate of collapse of a massive matter cloud in gravitation theory , especially on naked singularities which are hypothetical astrophysical objects and on the nature of cosmic censorship hypothesis . these issues have key implications for our understanding on black hole physics today , its astrophysical applications , and for certain basic questions in cosmology and possible quantum theories of gravity . we consider these issues here and summarize recent results and current progress in these directions . the emerging astrophysical and observational perspectives and implications are dicussed , with particular reference to the properties of accretion discs around black holes and naked singularities , which may provide characteristic signatures and could help distinguish these objects . pnumwidth1.55em tocrmarg2.55em dotsep4.5 @sectiondottedtocline20em1.5em @subsectiondottedtocline21.5em2.3em @subsubsectiondottedtocline33.8em3.2em

1703.03415

i

while a static magnetic field can not change the kinetic energy of charged particles , it affects the direction of their motion due to a lorentz force . this property is widely used in physics and technology . for example , magnetic fields play a crucial role in cyclotrons and particle accelerators , where they keep beams of charged particles on correct trajectories . another application is the mass spectrometry , which utilizes magnetic fields in order to sort charged particles based on their mass - to - charge ratio . magnetic fields can be also used as lenses for deflecting and focusing beams of charged particles . such lenses are utilized , for example , in cathode ray tubes and electron microscopes @xcite . the history of geometric electron optics started from a paper by hans busch in 1926 @xcite , where he suggested that the magnetic field of a short coil can act as a converging lens for electrons . this proposal was instrumental for the construction of the first electron microscope by knoll and ruska @xcite . owing to the fact that the wavelengths of electrons can be much smaller than the wavelengths of the visible light , the resolution of the electron microscope quickly surpassed that of the conventional optical microscope . modern transmission electron microscopes with aberrations correctors achieve a few orders of magnitude better resolution than the usual light microscopes and , therefore , are used to investigate the structure of metals , crystals , large molecules , as well as biological specimens including microorganisms and cells . in geometrical particle optics , the motion of charged particles in macroscopic electromagnetic fields is described analogously to the propagation of the light rays . mathematically , the possibility of such a description stems from the eikonal or wentzel kramers brillouin ( wkb ) approximation @xcite . the eikonal approximation is an appropriate and efficient means to solve wave equations in the case when the de broglie wavelengths of particles are small compared to the characteristic inhomogeneities of the system or external fields . in mathematical physics , the wkb approximation is a well - established method for finding approximate solutions to linear differential equations with coefficients varying slowly in space @xcite . recent experimental discovery of dirac and weyl materials made possible a condensed - matter realization of the systems whose low - energy quasiparticles are massless dirac or weyl fermions ( for reviews , see refs . the corresponding quasiparticles have a well - defined chirality in the vicinity of dirac points or weyl nodes . in this connection it should be noted that a dirac point in the brillouin zone could be viewed as an overlap of two weyl nodes of opposite chirality . according to the celebrated nielsen - ninomiya theorem @xcite , weyl nodes in condensed matter materials , in fact , always come in pairs of opposite chirality . in general , however , the nodes in each pair need not coincide . experimentally , the first three - dimensional dirac materials , i.e. , na@xmath0bi and cd@xmath0as@xmath1 , were discovered only a few years ago @xcite . since then a large number of weyl materials ( i.e. , @xmath2 , @xmath3 , @xmath4 , @xmath5 , @xmath6 , @xmath7 ) were discovered as well @xcite . these discoveries opened a new chapter in studies of numerous effects associated with quantum anomalies and chirality by using simple table - top experiments , rather than accelerator techniques of high - energy physics . in addition to quantum field theoretical methods , there exist a number of very powerful semiclassical techniques for studying condensed matter systems such as weyl and dirac materials in external electromagnetic fields . one of them is the kinetic theory . because of the nontrivial topological properties of weyl fermions @xcite , the corresponding kinetic theory should account for the berry curvature effects @xcite . amazingly , the resulting chiral kinetic theory @xcite can reproduce even the effects due to the quantum chiral anomaly @xcite . note that the latter implies the nonconservation of the chiral charge in the presence of parallel background electric and magnetic fields . the dirac and weyl materials make also possible the investigations of novel quantum phenomena that can not exist in high - energy physics . in particular , a number of such phenomena can be associated with the quasiparticle response to background pseudoelectromagnetic ( axial ) fields . unlike the ordinary electromagnetic fields @xmath8 and @xmath9 , their pseudoelectromagnetic counterparts @xmath10 and @xmath11 couple to the left - handed and right - handed particles with opposite signs . indeed , as shown in refs . @xcite , such fields can be induced by mechanical strains in dirac and weyl materials . a pseudoelectric field @xmath12 , for instance , can be created by dynamically stretching or compressing the sample . a nonzero pseudomagnetic field @xmath13 is generated , e.g. , by applying a static torsion @xcite or bending the sample @xcite . a typical magnitude of the pseudomagnetic field @xmath14 is estimated to be about @xmath15 in the former case and about @xmath16 in the latter case . for the purposes of this study , it will be sufficient to consider only static deformations so that @xmath17 . in addition , we will also assume that the ordinary electric field is also absent @xmath18 . in this study we suggest that the strain - induced pseudomagnetic fields can be utilized for creating pseudomagnetic lenses for deflecting and focusing beams of weyl quasiparticles , depending on the particle chiralities . a general experimental setup that allows a maximum control of chiral beams is given by a combination of the magnetic and pseudomagnetic lenses as shown schematically in fig . [ fig : illustration ] . the system consists of a thin long crystal ( wire ) of a weyl material placed inside a solenoid . in this case , magnetic and pseudomagnetic fields are directed along the @xmath19 axis and are present in the region @xmath20 . ( generically , the sample itself can be longer than @xmath21 . ) the magnetic field is generated by an electric current in the solenoid and the pseudomagnetic one is produced by the torsion of the crystal . since the characteristic scales of spatial variations of the background magnetic and pseudomagnetic fields in the ( pseudo-)magnetic lens are much larger than the de broglie wavelengths of weyl quasiparticles , it is justified to use the eikonal approximation for the description of their motion . because of a nontrivial topology of chiral particles , we will pay a special attention to the berry curvature effects on the corresponding chiral rays . is produced by an electric current @xmath22 in the solenoid , the pseudomagnetic field @xmath11 is created by twisting the crystal of a weyl material.,scaledwidth=50.0% ] the paper is organized as follows . in sec . [ sec : eikonal ] we describe the eikonal approximation in application to weyl quasiparticles . the properties of magnetic and pseudomagnetic lenses for weyl quasiparticles are considered in sec . [ sec : lens ] . the discussion and summary of the main results are given in sec . [ sec : summary - discussions ] .

it is proposed that strain - induced pseudomagnetic fields in weyl materials could be used as chirality sensitive lenses for beams of weyl quasiparticles . the study of the ( pseudo-)magnetic lenses is performed by using the eikonal approximation for describing the weyl quasiparticles propagation in magnetic and strain - induced pseudomagnetic fields .

it is proposed that strain - induced pseudomagnetic fields in weyl materials could be used as chirality sensitive lenses for beams of weyl quasiparticles . the study of the ( pseudo-)magnetic lenses is performed by using the eikonal approximation for describing the weyl quasiparticles propagation in magnetic and strain - induced pseudomagnetic fields . analytical expressions for the locations of the principal foci and the focal length are obtained in the paraxial approximation in the models with uniform as well as nonuniform effective magnetic fields inside the lens . the results show that the left- and right - handed quasiparticles can be focused at different spatial locations when both magnetic and pseudomagnetic fields are applied . it is suggested that the use of the magnetic and pseudomagnetic lenses could open new ways of producing and manipulating beams of chiral weyl quasiparticles .

1703.03415

i

in this study we investigated the conceptual possibility of pseudomagnetic lenses that can be used to focus the beams of chiral quasiparticles in weyl materials . we found that the maximum flexibility in controlling the beams of weyl quasiparticles is achieved when one combines the magnetic and pseudomagnetic lenses , as shown schematically in fig . [ fig : illustration ] . indeed , the presence of both magnetic _ and _ pseudomagnetic fields allows one to achieve different magnitudes of the effective magnetic fields exerted on the left- and right - handed quasiparticles . this provides enough control to manipulate the focal lengths @xmath89 independently for each chirality . in order to obtain the geometric optics description for the beams of weyl quasiparticles in background magnetic and pseudomagentic fields , we used the conventional eikonal approximation for solving the semiclassical wave equation . such an approximation is well justified for weyl materials when the de broglie wavelengths of quasiparticles in the beam are small compared to the spatial scale of the background - field inhomogeneities , as well as the sample size . in this study we argued that , because of the nontrivial topology of weyl fermions , the corresponding eikonal equation is affected by the berry curvature in a nontrivial way . the corrections due to berry curvature effects are rather small when the magnetic and pseudomagnetic fields are much weaker than the reference value @xmath140 , defined in eq . ( [ lens - eikonal - bcrit ] ) , which is the scale set by the quasiparticle energy . this regime seems to be relevant for applications in dirac semimetals such as cd@xmath0as@xmath1 when the effective background field is weaker than about @xmath141 . for stronger fields , or for other types of dirac / weyl materials , it is possible that the berry curvature could lead to substantial corrections in the quantitative description of the ( pseudo-)magnetic lenses . in fact , these corrections may lead to a spatial separation of the beams of chiral quasiparticles even by the ordinary magnetic field alone . in such a case , a more refined analysis using quantum , rather than semiclassical equations would be required . in the framework of a simplified model with a spatially uniform ( pseudo-)magnetic field inside the lens , we derived the explicit general expressions for the principal foci and the focal length . the corresponding results include the effects due to the berry curvature and are reliable only in the case of not too strong background fields . in addition , in order to address the role of inhomogeneous fields , we also studied a simple model with a nonuniform pseudomagnetic field , see eq . ( [ inhom - b - profile ] ) . in this case , we found that the effect of a highly nonuniform field is similar to that of a uniform one , but with the effective length of the lens @xmath142 given by eq . ( [ inhom - b - leff ] ) . it is worth noting that in this study we solved the eikonal equation for weyl quasiparticles by using the paraxial approximation . clearly , this is adequate only when the beam of chiral quasiparticles remains close to the axis of the ( pseudo-)magnetic lens . in practice , of course , this condition may break down and , then , one would have to reanalyze the problem by using numerical methods . in such a regime , optical aberrations will appear and further complicate the situation . while all these issues may be of real importance for making pseudomagnetic lenses in practice , they are beyond the scope of the conceptual study presented here . it is intriguing to suggest that the pseudomagnetic lenses could allow for new and powerful ways of controlling and manipulating the chiral beams of quasiparticles inside dirac and weyl materials . for example , they may open an experimental possibility to control the spatial distributions of the electric current densities due to weyl quasiparticles , depending on their chirality . by focusing the beams of the left- and right - handed quasiparticles in different spatial regions , one could achieve a chiral distillation " and/or steady states of matter with a nonzero chiral asymmetry . this could allow various new applications that utilize the possibility of a _ chiral spectrometer _ , in which spatial separation of chiral charges may be detected via the local probes . the work of e.v.g . was partially supported by the program of fundamental research of the physics and astronomy division of the nas of ukraine . the work of v.a.m . and p.o.s . was supported by the natural sciences and engineering research council of canada . the work of i.a.s . was supported by the u.s . national science foundation under grant no . phy-1404232 . o. vafek and a. vishwanath , ann . condensed matter phys . * 5 * , 83 ( 2014 ) . a. a. burkov , j. phys . : condens . matter * 27 * , 113201 ( 2015 ) . h. b. nielsen and m. ninomiya , nucl . b * 185 * , 20 ( 1981 ) [ erratum : nucl . b * 195 * , 541 ( 1982 ) ] ; nucl . b * 193 * , 173 ( 1981 ) . s. borisenko , q. gibson , d. evtushinsky , v. zabolotnyy , b. buchner , and r. j. cava , phys . rev . lett . * 113 * , 027603 ( 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 , nature commun . * 5 * , 3786 ( 2014 ) . 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 , science * 343 * , 864 ( 2014 ) . c. zhang , z. yuan , s. xu , z. lin , b. tong , m. z. hasan , j. wang , c. zhang , and s. jia , phys . b * 95 * , 085202 ( 2017 ) . s .- y . xu , i. belopolski , n. alidoust , m. neupane , g. bian , c. zhang , r. sankar , g. 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 , 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 , phys . x * 5 * , 031013 ( 2015 ) . x. huang , l. zhao , y. long , p. wang , d. chen , z. yang , h. liang , m. xue , h. weng , z. fang , x. dai , and g. chen , phys . x * 5 * , 031023 ( 2015 ) . i. belopolski , s .- y . xu , y. ishida , x. pan , p. yu , d. s. sanchez , m. neupane , n. alidoust , g. chang , t .- chang , y. wu , g. bian , h. zheng , s .- huang , c .- c . lee , d. mou , l. huang , y. song , b. wang , g. wang , y .- w . yeh , n. yao , j. rault , p. lefevre , f. bertran , h .- jeng , t. kondo , a. kaminski , h. lin , z. liu , f. song , s. shin , and m. z. hasan , arxiv:1512.09099 . s. borisenko , d. evtushinsky , q. gibson , a. yaresko , t. kim , m. n. ali , b. buechner , m. hoesch , and r. j. cava , arxiv:1507.04847 . g. sundaram and q. niu , phys . b * 59 * , 14915 ( 1999 ) . d. xiao , j. shi , and q. niu , phys . lett . * 95 * , 137204 ( 2005 ) [ erratum : phys . lett . * 95 * , 169903 ( 2005 ) ] . c. duval , z. horvath , p. a. horvathy , l. martina , and p. stichel , mod . b * 20 * , 373 ( 2006 ) . y. gao , s. a. yang , and q. niu , phys . b * 91 * , 214405 ( 2015 ) . m. v. berry , proc . a * 392 * , 45 ( 1984 ) . d. xiao , m. c. chang , and q. niu , rev . phys . * 82 * , 1959 ( 2010 ) . d. t. son and n. yamamoto , phys . . lett . * 109 * , 181602 ( 2012 ) . m. a. stephanov and y. yin , phys . * 109 * , 162001 ( 2012 ) . d. t. son and n. yamamoto , phys . d * 87 * , 085016 ( 2013 ) . s. l. adler , phys . rev . * 177 * , 2426 ( 1969 ) ; j. s. bell and r. jackiw , nuovo cim . a * 60 * , 47 ( 1969 ) . m. a. zubkov , annals phys . * 360 * , 655 ( 2015 ) . a. cortijo , y. ferreiros , k. landsteiner , and m. a. h. vozmediano , phys . 115 * , 177202 ( 2015 ) . a. cortijo , d. kharzeev , k. landsteiner , and m. a. h. vozmediano , phys . b * 94 * , 241405 ( 2016 ) . a. g. grushin , j. w. f. venderbos , a. vishwanath , and r. ilan , phys . rev . x * 6 * , 041046 ( 2016 ) . d. i. pikulin , a. chen , and m. franz , phys . x * 6 * , 041021 ( 2016 ) . t. liu , d. i. pikulin , and m. franz , phys . b * 95 * , 041201 ( 2017 ) . e. v. gorbar , v. a. miransky , i. a. shovkovy and p. o. sukhachov , arxiv:1702.02950 .

the results show that the left- and right - handed quasiparticles can be focused at different spatial locations when both magnetic and pseudomagnetic fields are applied . it is suggested that the use of the magnetic and pseudomagnetic lenses could open new ways of producing and manipulating beams of chiral weyl quasiparticles .

it is proposed that strain - induced pseudomagnetic fields in weyl materials could be used as chirality sensitive lenses for beams of weyl quasiparticles . the study of the ( pseudo-)magnetic lenses is performed by using the eikonal approximation for describing the weyl quasiparticles propagation in magnetic and strain - induced pseudomagnetic fields . analytical expressions for the locations of the principal foci and the focal length are obtained in the paraxial approximation in the models with uniform as well as nonuniform effective magnetic fields inside the lens . the results show that the left- and right - handed quasiparticles can be focused at different spatial locations when both magnetic and pseudomagnetic fields are applied . it is suggested that the use of the magnetic and pseudomagnetic lenses could open new ways of producing and manipulating beams of chiral weyl quasiparticles .

1207.1607

i

the present paper investigates the asymptotic distribution of the incomplete gauss sum @xmath0 where @xmath1 , @xmath2 , and @xmath3 ; the weight function @xmath4 is periodic with period one . the case @xmath5 corresponds to the classical gauss sum . the main example of an incomplete gauss sum in the literature is the case when @xmath4 is the characteristic function of a subinterval of the unit interval @xcite . it is natural to assume that @xmath6 and @xmath7 are coprime , i.e , @xmath8 . here @xmath9 is the multiplicative group of integers mod @xmath7 . the order of @xmath9 is denoted by @xmath10 ( euler s totient function ) . if @xmath11 are not coprime , say @xmath12 for some @xmath13 , we set @xmath14 , @xmath15 , and observe that @xmath16 where @xmath17 the case when @xmath11 are not coprime can therefore be reduced to the coprime case . functional equations and pointwise estimates of incomplete gauss sums have been studied extensively by oskolkov @xcite , and the aim of the present paper is to complement his results by establishing limit theorems for their value distribution at random argument . the existence of a limit distribution of the classical theta sum @xmath18 for @xmath19 uniformly distributed in @xmath20 has been proved by jurkat and van horne @xcite ( for its absolute value ) and the second author @xcite ( for its full distribution in the complex plane ) ; we refer the reader also to the recent study by cellarosi @xcite . a striking feature of the limit distribution of theta sums is that it has a heavy tail : the probability that @xmath21 has a value greater than @xmath22 , decays , for large @xmath22 , as @xmath23 . at rational @xmath19 , the theta sum of course reduces to an incomplete gauss sum where @xmath4 is the characteristic function of an interval , and we will see below ( remark [ rem1 ] ) that in this case the limit distribution has compact support the exact opposite of a heavy tail . we denote by @xmath24 the fourier series of @xmath4 . we will focus for the major part of this paper on gauss sums with differentiable weight functions @xmath4 in the space @xmath25 and only later extend our results to general riemann integrable functions , under an additional assumption on @xmath7 . the limit distributions of incomplete gauss sums will be characterized by the following random variables : * @xmath26 takes the four values @xmath27 with equal probability . * @xmath28 takes the values @xmath29 with equal probability . * @xmath30 takes the values @xmath31 with equal probability . * @xmath32 , @xmath33 , @xmath34 are random variables given by the fourier series @xmath35 respectively , with @xmath19 uniformly distributed on @xmath36 . note that , for @xmath37 , the functions in are differentiable and thus continuous . if @xmath4 satisfies the functional relation @xmath38 , then its fourier coefficients are related via @xmath39 , and hence @xmath40 and @xmath41 . if @xmath42 is real - valued for all @xmath43 , then @xmath44 and @xmath45 . hence the probability density describing the distribution of the imaginary part of the random variables @xmath32 , @xmath33 , @xmath34 is symmetric . furthermore , @xmath46 , and thus the real and imaginary part of @xmath34 have the same distribution . we define @xmath47 if @xmath48 , and @xmath49 if @xmath50 . the symbol @xmath51 denotes convergence in distribution . [ thm1 ] fix a subset @xmath52 with boundary of measure zero , and let @xmath37 . for each @xmath1 , choose @xmath53 at random with uniform probability . then , as @xmath54 along an appropriate subsequence as specified below , we have : [ cols="^,^,^",options="header " , ] the following technical estimate allows us to extend theorem [ thm1 ] to non - smooth @xmath4 as long as @xmath7 has a bounded number of divisors @xmath55 . [ rilem ] fix a positive integer @xmath56 . then there exists a constant @xmath57 such that , for every riemann integrable function @xmath58 , we have @xmath59 lemma [ rilem ] is proved in section [ variasec ] . together with chebyshev s inequality it implies the following extension of theorem [ thm1 ] . [ thm2 ] fix a subset @xmath52 with boundary of measure zero , and let @xmath58 be riemann integrable . then the conclusions of theorem [ thm1 ] and corollary [ cor1 ] remain valid for any sequence of @xmath54 with a bounded number of divisors . the proof of theorem [ thm2 ] is supplied in section [ extens ] . [ rem1 ] for @xmath37 , the functions in are continuous and bounded . arkhipov and oskolkov @xcite prove that boundedness ( but not continuity ) still holds even if @xmath4 is the characteristic function of a subinterval of @xmath36 . this implies that the limit distribution has compact support and that therefore corollary [ cor2 ] remains valid in this case , subject to the addtional assumption @xmath60 . [ rem2 ] it seems plausible that the hypothesis on the number of divisors of @xmath7 can be removed from theorem [ thm2 ] , at least in the case of weights @xmath4 of bounded variation or indeed all riemann integrable functions . to illustrate theorem [ thm2 ] , we have computed numerically the value distribution of the real and imaginary parts of incomplete gauss sums for different values of @xmath7 , see figures [ fig5012][fig5014 ] and section [ secnumerics ] . where @xmath4 is the characteristic function of the interval @xmath61 $ ] , @xmath62 and @xmath6 uniformly distributed in @xmath9 . there are thus @xmath63 sample points distributed across 40 bins , which means we have on average 53.4 values in each bin . the histogram seems consistent with fluctuations of the order of the square - root of that number , i.e. , approximately @xmath64 of the height of each bin . the histogram on the right shows the imaginary part of the corresponding quantities . the continuous curves represent a numerical approximation to the real and imaginary part of the probability density of the random variable @xmath65.,title="fig:",scaledwidth=49.0% ] where @xmath4 is the characteristic function of the interval @xmath61 $ ] , @xmath62 and @xmath6 uniformly distributed in @xmath9 . there are thus @xmath63 sample points distributed across 40 bins , which means we have on average 53.4 values in each bin . the histogram seems consistent with fluctuations of the order of the square - root of that number , i.e. , approximately @xmath64 of the height of each bin . the histogram on the right shows the imaginary part of the corresponding quantities . the continuous curves represent a numerical approximation to the real and imaginary part of the probability density of the random variable @xmath65.,title="fig:",scaledwidth=49.0% ] , now for @xmath66 . the number of sample points is now @xmath67 . the continuous curves represent a numerical approximation to the real and imaginary part of the probability density of the random variable @xmath68.,title="fig:",scaledwidth=49.0% ] , now for @xmath66 . the number of sample points is now @xmath67 . the continuous curves represent a numerical approximation to the real and imaginary part of the probability density of the random variable @xmath68.,title="fig:",scaledwidth=49.0% ] with the same @xmath4 as in figure [ fig5012 ] and @xmath69 , @xmath6 uniformly distributed in @xmath9 , where @xmath70 . the histogram on the right shows the imaginary part of the corresponding quantities . the continuous curves represent a numerical approximation to the real and imaginary part of the probability density of the random variable @xmath71.,title="fig:",scaledwidth=49.0% ] with the same @xmath4 as in figure [ fig5012 ] and @xmath69 , @xmath6 uniformly distributed in @xmath9 , where @xmath70 . the histogram on the right shows the imaginary part of the corresponding quantities . the continuous curves represent a numerical approximation to the real and imaginary part of the probability density of the random variable @xmath71.,title="fig:",scaledwidth=49.0% ]

it is well known that the classical gauss sum , normalized by the square - root number of terms , takes only finitely many values . if one restricts the range of summation to a subinterval , a much richer structure emerges . we prove a limit law for the value distribution of such incomplete gauss sums . the limit distribution is given by the distribution of a certain family of periodic functions . our results complement oskolkov s pointwise bounds for incomplete gauss sums as well as the limit theorems for quadratic weyl sums ( theta sums ) due to jurkat and van horne and the second author .

it is well known that the classical gauss sum , normalized by the square - root number of terms , takes only finitely many values . if one restricts the range of summation to a subinterval , a much richer structure emerges . we prove a limit law for the value distribution of such incomplete gauss sums . the limit distribution is given by the distribution of a certain family of periodic functions . our results complement oskolkov s pointwise bounds for incomplete gauss sums as well as the limit theorems for quadratic weyl sums ( theta sums ) due to jurkat and van horne and the second author .

1011.3806

i

in this paper , we have studied how the entanglement among register qubits affects the gate fidelity of the inaccurate ancilla - driven quantum computation . by generalizing the previous result about the entanglement - fidelity relation in the inaccurate one - way quantum computation @xcite , we have shown similar entanglement - fidelity relations for the inaccurate ancilla - driven quantum computation . our results are ( i ) for the ancilla - driven single - qubit rotation , and for the ancilla - driven two - qubit entangling gate with the cz interaction , we obtain the entanglement - fidelity relation as given in eq . ( [ similar ] ) . ( ii ) for the ancilla - driven two - qubit entangling gate with the cz+swap interaction , we obtain the entanglement - fidelity relation eq . ( [ main2 ] ) which is slightly different from eq . ( [ similar ] ) . these relations imply that if the entanglement is strong , the inaccurate measurements make the gate fidelity low in the ancilla - driven quantum computation . as is mentioned in ref . @xcite , the error model considered here is a kind of error that can ultimately be recovered with the quantum error - correcting code . therefore , our entanglement - fidelity relations are of use for studying the stability of a bare quantum computation in order to obtain valuable feedbacks for the study of general fault - tolerant schemes , to develop the made - to - measure error - correcting codes , to estimate the threshold value of the error - correction , and to help experimentalists who want to perform proof - of - principle experiments with few qubits . it is very important to study the difference between the one - way model and the ancilla - driven model from the view point of our entanglement - fidelity relations . although these two models share many similarities , one interesting difference that has been revealed in this paper is that not only the single - qubit entanglement but also the two - qubit entanglement are related to the gate fidelity in the ancilla - driven case . therefore , in addition to the physical constraints come from the specific experimental setups in the laboratory , the amount of the two - qubit entanglement in the register can also be one criterion for choosing the one - way model or the ancilla - driven model . detailed studies according to this direction would be a subject of the future study .

a * 81 * , 060307(r ) ( 2010 ) ] that the gate fidelity of an inaccurate one - way quantum computation is upper bounded by a decreasing function of the amount of entanglement in the register . this means that a strong entanglement causes the low gate fidelity in the one - way quantum computation with inaccurate measurements . in this paper , we derive similar entanglement - fidelity relations for the inaccurate ancilla - driven quantum computation .

it was shown in [ t. morimae , phys . rev . a * 81 * , 060307(r ) ( 2010 ) ] that the gate fidelity of an inaccurate one - way quantum computation is upper bounded by a decreasing function of the amount of entanglement in the register . this means that a strong entanglement causes the low gate fidelity in the one - way quantum computation with inaccurate measurements . in this paper , we derive similar entanglement - fidelity relations for the inaccurate ancilla - driven quantum computation . these relations again imply that a strong entanglement in the register causes the low gate fidelity in the ancilla - driven quantum computation if the measurements on the ancilla are inaccurate .

1411.3095

c

in summary , we have examined the backaction cooling of mesoscopic mechanical resonators in the strong coupling regime . when the rotating - wave approximation is satisfied , the mean phonon number undergoes simple damped rabi - like oscillations with the rabi frequency of @xmath84 and the exponential damping envelope scales as @xmath176 . at the first half oscillation cycle , the minimum mean phonon number is derived as @xmath177 . for large coupling strength where the rotating - wave approximation fails , the mean phonon number oscillates as functions of both the evolution time and the coupling strength , which is a result of frequency mixing . under the frequency matching condition , the optimal coupling strengths are derived as @xmath178 , @xmath179 , @xmath180 ... by employing the dynamic dissipative approach @xcite , the reduced instantaneous - state cooling limits reach the lower bound @xmath181 $ ] . this provides a guideline for achieving the lowest cooling limit , which is reached when the frequency matching condition is satisfied and when the cavity decay rate @xmath91 is small . compared with the steady - state cooling limit , the unique advantage is that it does not require an optimal value for @xmath91 , allowing for long - coherence - time quantum operations deeply in the strong coupling regime . the parameter ranges @xmath182 can be realized in various optomechanical systems , for example , in the microtoroid system studied in ref . @xcite , with the parameters @xmath183 @xmath184 , @xmath185 @xmath184 , @xmath186 @xmath187 and @xmath188 @xmath184 , or in the superconducting aluminium membrane system studied in ref . @xcite , with the parameters @xmath189 @xmath184 , @xmath190 @xmath187 , @xmath191 @xmath192 and @xmath193 . this work is supported by the 973 program ( 2013cb328704 , 2013cb921904 ) , nsfc ( 11004003 , 11222440 , and 11121091 ) , and rfdph ( 20120001110068 ) . y.c.l is supported by the scholarship award for excellent doctoral students granted by the ministry of education . y.f.s was supported by the national fund for fostering talents of basic science ( grants no . j1030310 and no . j1103205 ) @xmath194{ccccc}-{\kappa } & 0 & -ig & ig^{\ast } & ig^{\ast}\\ 0 & -{\gamma } & ig & -ig^{\ast } & ig^{\ast}\\ -ig^{\ast } & ig^{\ast } & -i\left ( \delta^{\prime}+{\omega_{\mathrm{m}}}\right ) -\frac{{\kappa+\gamma}}{2 } & 0 & 0\\ ig & -ig & 0 & i\left ( \delta^{\prime}+{\omega_{\mathrm{m}}}\right ) -\frac{{\kappa+\gamma}}{2 } & 0\\ -ig & -ig & 0 & 0 & i\left ( \delta^{\prime}-{\omega_{\mathrm{m}}}\right ) -\frac{{\kappa+\gamma}}{2}\\ ig^{\ast } & ig^{\ast } & 0 & 0 & 0\\ 0 & 0 & 0 & -2ig & -2ig\\ 0 & 0 & 2ig^{\ast } & 0 & 0\\ 0 & 0 & -2ig & 0 & -2ig^{\ast}\\ 0 & 0 & 0 & 2ig^{\ast } & 0 \end{array } \right . \nonumber\\ & \left . \begin{array } [ c]{ccccc}-ig & 0 & 0 & 0 & 0\\ -ig & 0 & 0 & 0 & 0\\ 0 & 0 & -ig & ig^{\ast } & 0\\ 0 & ig^{\ast } & 0 & 0 & -ig\\ 0 & -ig^{\ast } & 0 & -ig & 0\\ -i\left ( \delta^{\prime}-{\omega_{\mathrm{m}}}\right ) -\frac{{\kappa+\gamma } } { 2 } & 0 & ig & 0 & ig^{\ast}\\ 0 & 2i\delta^{\prime}-{\kappa } & 0 & 0 & 0\\ 2ig^{\ast } & 0 & -2i\delta^{\prime}-{\kappa } & 0 & 0\\ 0 & 0 & 0 & -2i{\omega_{\mathrm{m}}}-{\gamma } & 0\\ 2ig & 0 & 0 & 0 & 2i{\omega_{\mathrm{m}}}-{\gamma}\end{array } \right),\end{aligned}\ ] ] t. j. kippenberg and k. j. vahala , * 321 * , 1172 ( 2008 ) ; f. marquardt and s. m. girvin , * 2 * , 40 ( 2009 ) ; m. aspelmeyer , t. j. kippenberg , f. marquardt , : 1303.0733 ( 2013 ) ; y .- c . liu , y .- w . hu , c. w. wong and y .- f . xiao , * 22 * , 114213 ( 2013 ) . m. d. lahaye , o. buu , b. camarota , k. c. schwab , * 304 * , 74 ( 2004 ) ; g. anetsberger _ et al . _ , * 5 * , 909 ( 2009 ) ; j. d. teufel , r. donner , m. a. castellanos - beltran , j. w. harlow , and k. w. lehnert , * 4 * , 820 ( 2009 ) ; a. g. krause , m. winger , t. d. blasius , q. lin , o. painter , * 6 * , 768 ( 2012 ) ; t. p. purdy , r. w. peterson , and c. a. regal , * 339 * , 801 ( 2013 ) ; y .- d . wang and a. a. clerk , * 108 * , 153603 ( 2012 ) ; l. tian , * 108 * , 153604 ( 2012 ) ; s. barzanjeh , m. abdi , g. j. milburn , p. tombesi , and d. vitali , * 109 * , 130503 ( 2012 ) ; j. t. hill , a. h. safavi - naeini , j. chan , and o. painter , * 3 , * 1196 ( 2012 ) ; c. dong , v. fiore , m. c. kuzyk , and h. wang , * 338 , * 1609 ( 2012 ) ; y. liu , m. davanco , v. aksyuk , and k. srinivasan , * 110 * , 223603 ( 2013 ) . d. vitali _ et al . _ , * 98 * , 030405 ( 2007 ) ; l. tian , * 110 * , 233602 ( 2013 ) ; y .- d . wang and a. a. clerk , * 110 * , 253601 ( 2013 ) ; h .- k li , x .- x ren , y .- c . liu , y .- f . xiao , * 88 * , 053850 ( 2013 ) ; m. c. kuzyk , s. j. van enk , and h. wang : 1307.2844 ( 2013 ) . p. rabl , * 107 * , 063601 ( 2011 ) ; a. nunnenkamp , k. brkje , and s. m. girvin , * 107 * , 063602 ( 2011 ) ; m. ludwig , a. h. safavi - naeini , o. painter , and f. marquardt , * 109 * , 063601 ( 2012 ) ; m .- a . lemonde , n. didier , and a. a. clerk , * 111 * , 053602 ( 2013 ) ; k. brkje , a. nunnenkamp , j. d. teufel , and s. m. girvin , * 111 * , 053603 ( 2013 ) ; y .- c . liu , y .- f . xiao , y .- l . chen , x .- c . yu , and q. gong , * 111 * , 083601 ( 2013 ) ; a. kronwald and f. marquardt , * 111 * , 133601 ( 2013 ) . s. mancini , d. vitali , and p. tombesi , * 80 * , 688 ( 1998 ) ; p .- f . cohadon , a. heidmann , and m. pinard , * 83 * , 3174 ( 1999 ) ; d. kleckner and d. bouwmeester , * 444 * , 75 ( 2006 ) ; t. corbitt _ et al . _ , * 99 * , 160801 ( 2007 ) ; m. poggio , c. l. degen , h. j. mamin , and d. rugar , * 99 * , 17201 ( 2007 ) . f. elste , s. m. girvin , and a. a. clerk , * 102 * , 207209 ( 2009 ) ; m. li , w. h. p. pernice , and h. x. tang , * 103 * , 223901 ( 2009 ) ; a. xuereb , r. schnabel , and k. hammerer , * 107 * , 213604 ( 2011 ) ; t. weiss and a. nunnenkamp , * 88 * , 023850 ( 2013 ) ; m .- y . yan , h .- k . li , y .- c . liu , w .- l . jin , and y .- f . xiao , * 88 * , 023802 ( 2013 ) . m. r. vanner _ _ , * 108 * , 16182 ( 2011 ) ; y. li , l .- a . wu , and z. d. wang , * 83 * , 043804 ( 2011 ) ; j .- q . liao and c. k. law , * 84 * , 053838 ( 2011 ) ; x. wang , s. vinjanampathy , f. w. strauch , and k. jacobs , * 107 * , 177204 ( 2011 ) ; s. machnes _ et al . _ , * 108 * , 153601 ( 2012 ) .

laser cooling of mesoscopic mechanical resonators is of great interest for both fundamental studies and practical applications . , we find that the temporal evolution of mean phonon number oscillates as a function of the optomechanical coupling strength depending on frequency mixing . the further analytical result reveals that the optimal cooling limit is obtained when the system eigenmodes satisfy the frequency matching condition . our study provides a guideline for optimizing the backaction cooling of mesoscopic mechanical resonators in the strong coupling regime .

laser cooling of mesoscopic mechanical resonators is of great interest for both fundamental studies and practical applications . we provide a general framework to describe the cavity - assisted backaction cooling in the strong coupling regime . by studying the cooling dynamics , we find that the temporal evolution of mean phonon number oscillates as a function of the optomechanical coupling strength depending on frequency mixing . the further analytical result reveals that the optimal cooling limit is obtained when the system eigenmodes satisfy the frequency matching condition . the reduced instantaneous - state cooling limits with dynamic dissipative cooling approach are also presented . our study provides a guideline for optimizing the backaction cooling of mesoscopic mechanical resonators in the strong coupling regime .

astro-ph0601465

c

we built the @xmath1 bolometric lc integrating the @xmath0 broadband flux ( see paper i for details ) . a reddening of @xmath65 was corrected for @xcite , and a distance modulus of 29.5 was adopted ( but see @xcite ) . the lc is shown in figure 4 , extending that in paper i to @xmath66 days since explosion . it consists of three independent data sets , which agree with one another . most of the data ( _ filled circles _ ) , tabulated in table 3 ( _ late time _ ) and paper i ( _ early time _ ) , were made from the magnum photometry . we interpolated and extrapolated the observations to estimate the the @xmath38 magnitudes between day 280 and 340 and the @xmath36 and @xmath58 magnitudes at day 520 . for epochs @xmath67 days , the observations of @xcite , @xcite , and @xcite were used for interpolation . bolometric magnitudes at day 407 and 578 ( _ triangles _ ) were converted from @xmath4 magnitudes using approximate bolometric corrections . the other two data sets were based on the @xcite ( _ open circles _ ) and @xcite ( _ crosses _ ) optical photometry , respectively , which was combined with the @xcite and our @xmath21 photometry . the bolometric lc at late time has a shape similar to that of sn 1998bw ( figure 4 ; _ squares _ ) , another hypernova , although the latter was much brighter . the sn 1998bw lc in figure 4 is shifted down by 1.75 mag to match the peak magnitude of sn 2002ap . both lcs show a similar late - time slowing - down . for sn 2002ap , the decline rate changed from @xmath68 mag / day between day 130 and 230 to @xmath69 mag / day between day 270 and 580 . for sn 1998bw , the decline rate was @xmath70 mag / day between day 70 and 220 and @xmath69 mag / day between day 320 and 540 . for comparison , the late - time bolometric lc of another hypernova , sn 1997ef , followed the decay rate of @xmath14co , i.e. , @xmath71 mag / day @xcite . on the other hand , sn 2002ap reached its light maximum @xmath72 days earlier than sn 1998bw did , although their peak widths are actually comparable ( figure 4 ; _ inset _ ) . we show the sed of sn 2002ap at 5 typical late epochs in figure 5 , where the monochromatic fluxes converted from the magnum @xmath0 photometry are connected using spline - fitting curves . the observed upper limits of the @xmath38-band flux at day 393 and 520 are marked by _ arrows_. zero flux was assumed at both the the blue edge of the @xmath33 band and the red edge of the @xmath38 band . we used such seds to obtain the @xmath1 bolometric magnitudes . the seds are dominated by the flux in the @xmath63 and @xmath58 bands before about day 340 - 390 , which was mainly due to strong [ ] , ] , and emissions @xcite . the @xmath33 bump at the three intermediate epochs reflects the contribution of ] @xmath644571 . after about day 340 - 390 , the @xmath34 flux , attributed to [ ] multiplets , increased relative to that in other optical bands , while the @xmath58-band - dominated emissions died away . the nir flux contribution rose rapidly after @xmath5 day 300 ( figure 6 ) . this can been seen in figure 5 as a big @xmath4 bump in the sed and also in figure 2 as a significant flattening of the @xmath4 and @xmath36 lcs . to explain this , we examined the synthesized nir spectra of the models that reproduce the late - time optical spectra of sn 2002ap ( p. a. mazzali et al . 2005 , in preparation ) . the most likely candidates are the strong [ ] 1.646 @xmath6 m and 1.608 @xmath6 m lines , while the 1.099 @xmath6 m line may account for the concurrent @xmath36-band flux increase . the lines were already developed in the day @xmath5 200 nir spectrum of @xcite , although they were still not as strong as a 1.5 @xmath6 m feature , possibly emission . we note in passing that the appearance of the co first - overtone band in that spectrum suggested by those authors seems to coincide with the @xmath38-band lc steepening seen in figure 2 . the late - time @xmath4-band spectra of sn 1983n , taken by @xcite and of very low resolution , showed a strong 1.65 @xmath6 m feature , which was explained by those authors as [ ] lines but was soon , together with an adjacent feature , re - identified as [ ] lines by @xcite . these [ ] nir features can also be found in the synthetic late - time spectra of type ib sne computed by @xcite . in figure 7 we compare the late - time @xmath21 lcs of sn 2002ap with those of other type ib / c sne ( see table 4 ) . sn 1998bw and sn 1984l were 1.52.5 mag brighter than all other sne , indicating a large mass of @xmath14ni ejected . the nir lcs of sn 1984l were relatively slow , as was its late - time optical lc which was modelled using very massive ejecta but with normal kinetic energy @xcite . the few points of sn 1998bw , when shifted down by 1.8 mag ( @xmath36 ) , 1.5 mag ( @xmath4 ) , and 1.7 mag ( @xmath38 ) , respectively , fall on the lcs of sn 2002ap . the lcs of sn 1983n have later and broader peaks than those of sn 2002ap , but they become similar between in the @xmath36-band and @xmath4-band day @xmath5 200 and 350 . on the other hand , the @xmath21 data of sn 1983i and 1982r seem to bridge the lc gap in sn 2002ap data between day 50 and day 140 ( solar conjunction ) . figure 7 contradicts the picture that sne 1983i , 1983n , and 1984l have similar @xmath21 lcs @xcite . type ib / c sne were first established as a new class by those authors , who showed that these sne have similar @xmath21 lcs which are different from those of type ia sne [ and also by @xcite through an analysis of the optical spectra ] . they artificially shifted the data of sn 1983i and sn 1984l in both phase and brightness in order to match the nir lcs of sn 1983n . their sn 1983i data were assigned epochs 20 days later than ours , and sn 1984l 14 days earlier . our epoch estimates are more reasonable because we based them on optical lcs and spectra which are better observed and understood than the nir data . inspecting by eye the only published spectrum of sn 1983i @xcite , we noticed that it resembles those of sn 2002ap between 2002 february 16 and 22 @xcite . the similarity can be seen not only in the overall shape and strongest line features , but also in relatively weak ones , like those near @xmath73 , @xmath74 , and @xmath75 . the spectrum was taken on 1983 may 17 , 5 days after discovery . we estimate the epoch of that spectrum as @xmath76 days since explosion , through this comparison , and hence derive an explosion date of 1983 april 25 . the lcs of sn 1983i seem to match those of sn 2002ap not only in the nir ( figure 7 ) but also in the optical ( figure 8) , if our estimates of the explosion date and the distance modulus are correct . we adopt 31.0 as the distance modulus to the host galaxy of sn 1983i , ngc 4051 in the ursa major cluster @xcite . this value is also close to the average of the distance modulus of the ursa major cluster ( 31.4 , @xcite ) , and that corresponding to its radial velocity corrected for the local group infall onto virgo ( 30.5 , leda ; @xcite ) the late - time bolometric lc of sn 2002ap declines more slowly than that of the 1-dimensional ( 1-d ) model of @xcite that best reproduced the early - time spectra and lc ( see figure 9 ; _ dotted line _ ) . this is expected , since the lc follows that of sn 1998bw closely in terms of the decline rate , as shown in figure 4 . the best - fitting 1-d model for the early - time spectra and lc of sn 1998bw also fails to explain its late - time spectrum and lc @xcite . to mimic the outcome of 2-dimensional jet - induced explosion calculations @xcite , which applies to sn 1998bw and may also apply to sn 2002ap , @xcite introduced a dense core . that core absorbs @xmath77-rays efficiently at late time . using this structure , the slow lc decline of hypernovae was reproduced by those authors using a monte - carlo radiative transfer code but with simplified physics . we tested the dense - core scenario on sn 2002ap using our sophisticated 1-d sn radiation hydrodynamical and @xmath77-ray transfer code @xcite . the best - fitting model ( _ solid line _ ) has @xmath78 ejecta below 3,000 km s@xmath18 , compared with 0.1 @xmath2 in the model without a dense core , and @xmath79 low - velocity @xmath14ni . compared with @xcite , who modelled only the early - time observations , the total ejecta mass has increased from 2.5 @xmath2 to 3 @xmath2 , but with little change in the total @xmath14ni mass ( 0.08 @xmath2 ) and the kinetic energy ( @xmath80 ergs ) . a dense ejecta core is also required in 1-d late - time spectrum models ( p. a. mazzali et al . 2006 , in preparation ) in order to explain the observed sharp line cores of [ ] and ] @xcite . a dense core can not be formed in 1-d explosion simulations for hypernovae @xcite , but it is a natural product of 2-d jet - induced explosions @xcite . this strongly indicates asymmetry in the sn 2002ap explosion , an intrinsic feature also shared by other hypernovae . evidence of asymmetry in sn 2002ap can also be found in spectropolarimetry @xcite , which shows an intrinsic continuum polarization varying around 0.5% , corresponding to an asphericity of @xmath5 10% for the bulk of the ejecta . we thank s. b. pandey , e. nishihara , and r. j. foley for the electronic files of their photometric data . this work has been supported in part by the grant - in - aid for scientific research ( 16540229 , 17030005 , & 17033002 for kn ) and the 21st century coe program ( quest ) from the jsps and mext in japan , and by the national science foundation under grant no . phy99 - 07949 . gerardy , c. l. , fesen , r. a. , marion , g. h. , hflich , p. , wheeler , j. c. , nomoto , k. , & motohara , k. 2004 , in cosmic explosions in three dimensions , ed . p. hflich , p. kumer , & j. c. wheeler ( cambridge : cambridge univ . press ) , 57 llcccccccc jun 12.61 & 52437.61 & & 16.15@xmath81 & & & & & 14.98@xmath82 & clear jun 13.60 & 52438.60 & 16.75@xmath83 & & & & & 14.93@xmath84 & & clear jun 14.60 & 52439.60 & & & 15.43@xmath85 & & 15.75@xmath83 & & & clear jun 16.60 & 52441.60 & & & & 15.10@xmath85 & & & & clear jun 18.60 & 52443.60 & & & & 15.14@xmath85 & & 15.01@xmath84 & & clear jul 3.56 & 52458.56 & 17.07@xmath84 & & 15.70@xmath85 & & 16.17@xmath82 & & 15.49@xmath86 & thin cloud jul 5.60 & 52460.60 & & & 15.72@xmath85 & & & & & thin cloud jul 6.55 & 52461.55 & & & 15.74@xmath85 & & & & 15.53@xmath87 & cloudy jul 19.56 & 52474.56 & & & 15.94@xmath85 & & & & & clear jul 22.56 & 52477.56 & & & 15.98@xmath85 & & & & & clear jul 23.51 & 52478.51 & 17.42@xmath83 & 17.00@xmath85 & 16.01@xmath85 & 15.75@xmath85 & 16.51@xmath83 & 15.74@xmath86 & 15.84@xmath86 & clear aug 7.47 & 52493.47 & 17.71@xmath82 & 17.36@xmath85 & 16.28@xmath85 & 16.04@xmath85 & 16.81@xmath82 & 16.00@xmath88 & 16.03@xmath89 & thin cloud aug 11.59 & 52497.59 & & & 16.34@xmath85 & & 16.80@xmath82 & & & thin cloud aug 17.61 & 52503.61 & & 17.59@xmath85 & & & & 16.14@xmath86 & & thin cloud aug 18.44 & 52504.44 & & & 16.45@xmath85 & 16.24@xmath85 & 17.05@xmath82 & & & clear aug 22.54 & 52508.54 & & 17.64@xmath83 & 16.51@xmath85 & 16.29@xmath85 & 16.87@xmath82 & 16.22@xmath88 & & cloudy sep 2.44 & 52519.44 & 18.16@xmath84 & 17.89@xmath85 & & & & 16.36@xmath88 & 16.74@xmath87 & clear sep 3.61 & 52520.61 & & 17.90@xmath85 & & & & 16.43@xmath88 & & thin cloud sep 5.59 & 52522.59 & & & 16.73@xmath85 & 16.54@xmath85 & 17.22@xmath82 & & & thin cloud sep 7.61 & 52524.61 & & 18.02@xmath85 & & & & 16.56@xmath88 & & cloudy sep 8.41 & 52525.41 & 18.25@xmath84 & & 16.77@xmath85 & & 17.41@xmath88 & & 16.98@xmath90 & cloudy sep 16.54 & 52533.54 & 18.41@xmath84 & 18.15@xmath85 & 16.91@xmath85 & 16.73@xmath85 & 17.42@xmath82 & 16.57@xmath86 & 17.07@xmath91 & clear oct 27.52 & 52574.52 & 19.12@xmath91 & 18.86@xmath83 & 17.59@xmath83 & 17.41@xmath83 & 17.93@xmath88 & 17.08@xmath87 & 18.24@xmath92 & clear oct 30.45 & 52577.45 & 19.11@xmath89 & 18.92@xmath82 & 17.61@xmath85 & 17.46@xmath82 & 17.88@xmath86 & 17.09@xmath87 & 17.96@xmath93 & thin cloud nov 23.22 & 52601.22 & 19.49@xmath90 & 19.31@xmath84 & 17.99@xmath83 & 17.94@xmath82 & & 17.21@xmath88 & & clear dec 1.39 & 52609.39 & 19.67@xmath94 & 19.40@xmath84 & 18.12@xmath83 & 18.06@xmath82 & & 17.29@xmath88 & & clear dec 9.35 & 52617.35 & 19.75@xmath94 & 19.58@xmath86 & 18.26@xmath83 & 18.19@xmath82 & & 17.32@xmath88 & & clear dec 18.37 & 52626.37 & 19.91@xmath93 & 19.66@xmath89 & 18.38@xmath82 & 18.34@xmath84 & 18.55@xmath87 & & & clear dec 30.37 & 52638.37 & 20.03@xmath95 & 19.85@xmath87 & 18.62@xmath83 & 18.47@xmath86 & & 17.38@xmath87 & & clear feb 11.22 & 52681.22 & & & & & & & @xmath96 19.7 & clear feb 23.22 & 52693.22 & 20.99@xmath97 & & & & & & & clear feb 24.23 & 52694.23 & & 20.49@xmath98 & & & & & & clear feb 25.23 & 52695.23 & & & 19.60@xmath86 & & & & & clear feb 26.23 & 52696.23 & & & & 19.50@xmath99 & & & & clear mar 11.21 & 52709.21 & & & & & & 17.89@xmath90 & & clear mar 12.22 & 52710.22 & & & & & 19.16@xmath100 & & & clear jun 27.62 & 52817.62 & & & 21.26@xmath100 & & & & & clear jul 3.60 & 52823.60 & 22.80@xmath101 & & & & & & & clear jul 5.60 & 52825.60 & & 21.75@xmath102 & & & & 18.80@xmath103 & & clear aug 15.49 & 52866.49 & & & & @xmath96 21.5 & & & & thin cloud aug 28.50 & 52879.50 & & & & & @xmath96 21.2 & 19.83@xmath104 & & clear aug 29.50 & 52880.50 & & & & & & & @xmath96 19.9 & clear lccc 52438.5 & 136.5 & -13.53@xmath150.03 & 23% 52458.5 & 156.5 & -13.17@xmath150.03 & 22% 52478.5 & 176.5 & -12.81@xmath150.03 & 22% 52493.5 & 191.5 & -12.52@xmath150.03 & 22% 52504.0 & 202.0 & -12.32@xmath150.03 & 21% 52508.5 & 206.5 & -12.28@xmath150.03 & 23% 52521.0 & 219.0 & -12.04@xmath150.05 & 21% 52525.0 & 223.0 & -11.96@xmath150.03 & 21% 52533.5 & 231.5 & -11.83@xmath150.03 & 22% 52574.5 & 272.5 & -11.15@xmath150.05 & 23% 52577.5 & 275.5 & -11.14@xmath150.05 & 24% 52601.0 & 299.0 & -10.74@xmath150.07 & 25% 52609.5 & 307.5 & -10.62@xmath150.07 & 26% 52617.5 & 315.5 & -10.50@xmath150.07 & 26% 52626.5 & 324.5 & -10.37@xmath150.09 & 29% 52638.5 & 336.5 & -10.23@xmath150.09 & 29% 52695.0 & 393.0 & -9.47@xmath116 & 39% 52709.0 & 407.0 & -9.3@xmath15 0.2 & 52822.0 & 520.0 & -8.06@xmath117 & 54% 52879.5 & 577.5 & -6.8@xmath15 0.5 & cccccc spectroscopic type & ib / c & ic & ib & ib & ic , hypernova distance modulus & 31.2 & 31.0 & 28.25 & 31.5 & 32.76 extinction @xmath118 & 0.5 & 0.04 & 0.2 & 0.09 & 0.1@xmath150.1 explosion date ( ut ) & 1982 september 28 & 1983 april 25 & 1983 july 1 & 1984 august 5 & 1998 april 25.9

the light curve has a late - time shape strikingly similar to that of the hypernova sn 1998bw . the decline rate changes from 0.018 mag / day between day 130 and 230 to 0.014 mag / day between day 270 and 580 . to reproduce the late - time light curve , a dense core must be added to the 1-d hypernova model that best fits the early - time observations , bringing the ejecta mass from 2.5 @xmath2 to 3 @xmath2 without much change in the kinetic energy , which is @xmath3 ergs . this is similar to the case of other hypernovae and suggests asymmetry . a large @xmath4-band bump developed in the spectral energy distribution after @xmath5 day 300 , probably caused by strong [ si i ] 1.646@xmath6 m and 1.608@xmath6 m emissions . the near - infrared flux contribution increased simultaneously from @xmath7 to @xmath8 at day 580 . the near - infrared light curves were compared with those of other type ib / c supernovae , among which sn 1983i seems similar to sn 2002ap both in the near - infrared and in the optical .

late - time @xmath0 photometry of the peculiar type ic sn 2002ap , taken between 2002 june 12 and 2003 august 29 with the magnum telescope , is presented . the light curve decline rate is derived in each band and the color evolution is studied through comparison with nebular spectra and with sn 1998bw . using the photometry , the @xmath1 bolometric light curve is built , extending from before light maximum to day 580 after explosion . the light curve has a late - time shape strikingly similar to that of the hypernova sn 1998bw . the decline rate changes from 0.018 mag / day between day 130 and 230 to 0.014 mag / day between day 270 and 580 . to reproduce the late - time light curve , a dense core must be added to the 1-d hypernova model that best fits the early - time observations , bringing the ejecta mass from 2.5 @xmath2 to 3 @xmath2 without much change in the kinetic energy , which is @xmath3 ergs . this is similar to the case of other hypernovae and suggests asymmetry . a large @xmath4-band bump developed in the spectral energy distribution after @xmath5 day 300 , probably caused by strong [ si i ] 1.646@xmath6 m and 1.608@xmath6 m emissions . the near - infrared flux contribution increased simultaneously from @xmath7 to @xmath8 at day 580 . the near - infrared light curves were compared with those of other type ib / c supernovae , among which sn 1983i seems similar to sn 2002ap both in the near - infrared and in the optical .

1506.02430

i

a non - empty subset @xmath0 of a finite group @xmath1 is called product - free if @xmath11 does not hold for any @xmath12 . equivalently , writing @xmath13 for @xmath14 , we have @xmath15 . product - free sets were originally studied in abelian groups , and therefore they are often referred to in the literature as sum - free ( or sumfree ) sets . if @xmath0 is product - free in @xmath1 , and not properly contained in any other product - free subset of @xmath1 , then we call @xmath0 a locally maximal product - free set ( see @xcite , @xcite and @xcite ) . on the other hand , a product - free set @xmath0 is called maximal if no product - free set in @xmath1 has size bigger than @xmath16 . in the latter direction , see @xcite , @xcite and @xcite . there has been a good deal of work on maximal product - free sets in abelian groups ; for example green and ruzsa in @xcite were able to determine , for any abelian group @xmath1 , the cardinality of the maximal product - free sets of @xmath1 . gowers ( * ? ? ? * theorem 3.3 ) proved that if the smallest nontrivial representation of @xmath1 is of dimension @xmath17 then @xmath1 has no product - free sets of size greater than @xmath18 . much less is known about sizes of locally maximal product - free sets , in particular the minimal size of a locally maximal product - free set . + since every product - free set is contained in a locally maximal product - free set , we can gain information about product - free sets in a group by studying its locally maximal product - free sets . in connection with group ramsey theory , street and whitehead @xcite noted that every partition of a group @xmath1 ( or in fact , of @xmath19 ) into product - free sets can be embedded into a covering by locally maximal product - free sets , and hence to find such partitions , it is useful to understand locally maximal product - free sets . they remarked that many examples of these sets have the additional property that @xmath20 , and with that in mind gave the following definition . a subset @xmath0 of a group @xmath1 is said to _ fill _ @xmath1 if @xmath6 . the group @xmath1 is called a _ filled group _ if every locally maximal product - free set in @xmath1 fills @xmath1 . street and whitehead in @xcite and @xcite classified the abelian filled groups and conjectured that the dihedral group of order @xmath8 is not filled when @xmath9 for @xmath10 . one consequence of our results in this paper is that this conjecture is false . + this paper is aimed at throwing more light on locally maximal product - free sets ( lmpfs for short ) and filled groups in the non - abelian case . in section 2 we look at filled groups . we show ( theorem [ soluble ] ) that all non - abelian finite filled groups have even order , and that all finite nilpotent filled groups of even order are 2-groups . using gap @xcite we have seen that for groups of order up to 31 the only examples of non - abelian filled groups are 2-groups or dihedral ( see table [ table1 ] ) . therefore the dihedral case is of interest . in section @xmath21 , we study lmpfs in finite dihedral groups and classify all lmpfs of sizes @xmath21 and @xmath22 in dihedral groups . ( groups containing a locally maximal product - free set of size 1 or 2 were classified in @xcite . ) in section 4 we look at filled dihedral groups , give a counterexample to the conjecture of street and whitehead and obtain some restrictions on the possible orders of filled dihedral groups . + in the rest of this section we establish the notation we will need and gather together some useful results . all groups in this paper are finite . given a positive integer @xmath23 , we write @xmath24 for the cyclic group of order @xmath23 and @xmath25 for the dihedral group of order @xmath8 ( where @xmath26 ) . in @xmath27 the elements of @xmath28 are called rotations and the elements of @xmath29 are called reflections . for any subset @xmath0 of @xmath27 , we write rot(@xmath0 ) for @xmath30 , the set of rotations of @xmath0 , and ref(@xmath0 ) for @xmath31 , the set of reflections of @xmath0 . let @xmath0 and @xmath32 be subsets of a finite group @xmath1 . we define @xmath33 , @xmath34 , @xmath35 and @xmath36 . the following results will be used repeatedly . [ gh2009l ] let @xmath0 be a product - free set in a finite group @xmath1 . then @xmath0 is locally maximal if and only if @xmath37 . the following result is well - known but we include a short proof for the reader s convenience . [ lemma1.2 ] let @xmath38 be a subgroup of a group @xmath1 . any non - trivial coset of @xmath38 is product - free in @xmath1 . further , if @xmath38 is normal and @xmath39 is product - free in @xmath40 then the set @xmath41 is product - free in @xmath1 . for the first statement , if for some @xmath42 and @xmath43 we have @xmath44 , then @xmath45 . therefore if @xmath46 we have @xmath47 , so @xmath48 is product - free . now suppose @xmath38 is normal with @xmath39 and @xmath0 as defined in the statement of the lemma . then @xmath49 . the fact that @xmath0 is product - free now follows immediately from the fact that @xmath39 is product - free . the following is a straightforward consequence of the definitions . [ ah2015a_pro ] each product - free set of size @xmath50 in a finite group @xmath1 is the non - trivial coset of a subgroup of index 2 . furthermore such sets are locally maximal and fill @xmath1 .

let @xmath0 be a non - empty subset of a group @xmath1 . we say @xmath0 is product - free if @xmath2 , and @xmath0 is locally maximal if whenever @xmath3 is product - free and @xmath4 , then @xmath5 . finally @xmath0 fills @xmath1 if @xmath6 ( where @xmath7 is the set of all non - identity elements of @xmath1 ) , and @xmath1 is a filled group if every locally maximal product - free set in @xmath1 fills @xmath1 . street and whitehead @xcite investigated filled groups and gave a classification of filled abelian groups . in this paper , we obtain some results about filled groups in the non - abelian case , including a classification of filled groups of odd order . street and whitehead conjectured that the finite dihedral group of order @xmath8 is not filled when @xmath9 ( @xmath10 ) . we disprove this conjecture on dihedral groups , and in doing so obtain a classification of locally maximal product - free sets of sizes 3 and 4 in dihedral groups , continuing earlier work in @xcite and @xcite . * on a conjecture of street and whitehead on locally maximal product - free sets * by + chimere s. anabanti and sarah b. hart +

let @xmath0 be a non - empty subset of a group @xmath1 . we say @xmath0 is product - free if @xmath2 , and @xmath0 is locally maximal if whenever @xmath3 is product - free and @xmath4 , then @xmath5 . finally @xmath0 fills @xmath1 if @xmath6 ( where @xmath7 is the set of all non - identity elements of @xmath1 ) , and @xmath1 is a filled group if every locally maximal product - free set in @xmath1 fills @xmath1 . street and whitehead @xcite investigated filled groups and gave a classification of filled abelian groups . in this paper , we obtain some results about filled groups in the non - abelian case , including a classification of filled groups of odd order . street and whitehead conjectured that the finite dihedral group of order @xmath8 is not filled when @xmath9 ( @xmath10 ) . we disprove this conjecture on dihedral groups , and in doing so obtain a classification of locally maximal product - free sets of sizes 3 and 4 in dihedral groups , continuing earlier work in @xcite and @xcite . * on a conjecture of street and whitehead on locally maximal product - free sets * by + chimere s. anabanti and sarah b. hart +

1602.07600

i

the large high altitude air shower observatory ( lhaaso ) project is a new generation instrument , to be built at 4410 meters of altitude in the sichuan province of china , with the aim of studying with unprecedented sensitivity the energy spectrum , the elemental composition and the anisotropy of cosmic rays ( hereafter cr ) in the energy range between 10@xmath4 and 10@xmath1 ev , as well as to act simultaneously as a wide aperture ( @xmath52 sr ) , continuosly - operated gamma ray telescope in the energy range between 10@xmath0 and @xmath6 ev . the remarkable sensitivity of lhaaso in cr physics and gamma astronomy would play a key - role in the comprehensive general program to explore the _ `` high energy universe''_. the first phase of lhaaso will consist of the following major components : * 1 km@xmath2 array ( lhaaso - km2a ) for electromagnetic particle detectors ( ed ) divided into two parts : a central part including 4931 scintillator detectors 1 m@xmath2 each in size ( 15 m spacing ) to cover a circular area with a radius of 575 m and an outer guard - ring instrumented with 311 eds ( 30 m spacing ) up to a radius of 635 m. * an overlapping 1 km@xmath2 array of 1146 underground water cherenkov tanks 36 m@xmath2 each in size , with 30 m spacing , for muon detection ( md , total sensitive area @xmath542,000 m@xmath2 ) . * a close - packed , surface water cherenkov detector facility with a total area of about 78,000 m@xmath2 ( lhaaso - wcda ) . * 12 wide field - of - view air cherenkov telescopes ( lhaaso - wfcta ) . lhaaso will be located at high altitude ( 4410 m asl , 600 g / cm@xmath2 , 29@xmath8 21 31 n , 100@xmath8 0815 e ) in the daochen site , sichuan province , p.r . china . the commissioning of one fourth of the detector will be implemented in 2018 . the completion of the installation is expected by the end of 2021 . + lhaaso will enable studies in cr physics and gamma - ray astronomy that are unattainable with the current suite of instruments : * lhaaso will perform an _ unbiased sky survey of the northern sky _ with a detection threshold of a few percent crab units at sub - tev / tev energies and around 100 tev in one year . this sensitivity grants a high discovery potential of flat spectrum geminga - like sources not observed at gev energies . this unique detector will be capable of continuously surveying the @xmath9-ray sky for steady and transient sources from about 100 gev to 1 pev . + from its location lhaaso will observe at tev energies and with high sensitivity about 30 of the sources catalogued by fermi - lat at lower energy , monitoring the variability of 15 agns ( mainly blazars ) at least . * the sub - tev / tev lhaaso sensitivity will allow to observe agn flares that are unobservable by other instruments , including the so - called tev orphan flares . * lhaaso will study in detail the high energy tail of the spectra of most of the @xmath9-ray sources observed at tev energies , opening for the first time the 1001000 tev range to the direct observations of the high energy cosmic ray sources . _ when new wavelength bands are explored in astronomy , previously unknown sources and unknown types of sources are discovered . lhaaso s wide field of view provides therefore a unique discovery potential . _ * lhaaso will map the galactic _ diffuse gamma - ray emission _ above few hundreds gev and thereby measure the cr flux and spectrum throughout the galaxy with high sensitivity . the measurement of the space distribution of diffuse @xmath9-rays will allow to trace the location of the cr sources and the distribution of interstellar gas . * the high background rejection capability in the 10 100 tev range will allow lhaaso to measure the _ isotropic diffuse flux of ultrahigh energy @xmath9 radiation _ expected from a variety of sources including dark matter and the interaction of 10@xmath10 ev crs with the 2.7 k microwave background radiation . in addition , lhaaso will be able to achieve a limit below the level of the icecube diffuse neutrino flux at 10 100 tev , thus constraining the origin of the icecube astrophysical neutrinos . * lhaaso will allow the reconstruction of the energy spectra of different cr mass groups in the 10@xmath4 10@xmath1 ev with unprecedented statistics and resolution , thus tracing the light and heavy components through the knee of the all - particle spectrum . * lhaaso will allow the measurement , for the first time , of the cr anisotropy across the knee separately for light and heavy primary masses . * the different observables ( electronic , muonic and cherenkov components ) that will be measured in lhaaso will allow a detailed investigation of the role of the hadronic interaction models , therefore investigating if the eas development is correctly described by the current simulation codes . * lhaaso will look for signatures of wimps as candidate particles for dm with high sensitivity for particles masses above 10 tev . moreover , axion - like particle searches are planned , where conversion of gamma - rays to / from axion - like particles can create distinctive features in the spectra of gamma - ray sources and/or increase transparency of the universe by reducing the extragalactic background light ( ebl ) absorption . testing of lorentz invariance violation as well as the search for primordial black holes and q balls will also be part of the scientific programme of the experiment . in the next decade cta - north and lhaaso are expected to be the most sensitive instruments to study gamma - ray astronomy in the northern hemisphere from about 20 gev up to pev .

lhaaso is expected to be the most sensitive project to face the open problems in galactic cosmic ray physics through a combined study of photon- and charged particle - induced extensive air showers in the energy range 10@xmath0 - 10@xmath1 ev . this new generation multi - component experiment will be able of continuously surveying the gamma - ray sky for steady and transient sources from about 100 gev to pev energies , thus opening for the first time the 10@xmath210@xmath3 tev range to the direct observations of the high energy cosmic ray sources . in addition , the different observables ( electronic , muonic and cherenkov components ) that will be measured in lhaaso will allow the study of the origin , acceleration and propagation of the radiation through a measurement of energy spectrum , elemental composition and anisotropy with unprecedented resolution . the installation of the experiment started at very high altitude in china ( daocheng site , sichuan province , 4410 m a.s.l . ) . the commissioning of one fourth of the detector will be implemented in 2018 . the completion of the installation is expected by the end of 2021 . cosmic rays physics , gamma ray astronomy , lhaaso experiment

lhaaso is expected to be the most sensitive project to face the open problems in galactic cosmic ray physics through a combined study of photon- and charged particle - induced extensive air showers in the energy range 10@xmath0 - 10@xmath1 ev . this new generation multi - component experiment will be able of continuously surveying the gamma - ray sky for steady and transient sources from about 100 gev to pev energies , thus opening for the first time the 10@xmath210@xmath3 tev range to the direct observations of the high energy cosmic ray sources . in addition , the different observables ( electronic , muonic and cherenkov components ) that will be measured in lhaaso will allow the study of the origin , acceleration and propagation of the radiation through a measurement of energy spectrum , elemental composition and anisotropy with unprecedented resolution . the installation of the experiment started at very high altitude in china ( daocheng site , sichuan province , 4410 m a.s.l . ) . the commissioning of one fourth of the detector will be implemented in 2018 . the completion of the installation is expected by the end of 2021 . cosmic rays physics , gamma ray astronomy , lhaaso experiment

1107.4694

r

for a fixed mn impurity concentration of @xmath30 in ga@xmath31mn@xmath32as the density of states ( dos ) is shown in fig . [ fig:1 ] . for different values of the effective p - d coupling strength j@xmath14s . empirical tight - binding ( etbm ) density of states for ga@xmath31mn@xmath32as for @xmath30 and different values of j@xmath14s . the dashed lines indicate the chemical potentials for @xmath33 k corresponding to the hole density p = 0.75@xmath23 . ] these results are in perfect agreement with ref.@xcite . the dos is almost unchanged compared to that of the pure system for j@xmath14s @xmath34 ev . this already gives a first indication / hint that this range of parameters corresponds to the perturbative rkky regime , this will be confirmed in what follows . let us proceed further by calculating the zeeman splitting @xmath35 ( @xmath36 is the largest eigenvalue in the corresponding @xmath6 sector ) as a function of the mn concentration . it is depicted in fig . [ fig:2 ] . together with available ab - initio results . zeeman splitting @xmath37 as a function of the mn concentration @xmath23 for ga@xmath31mn@xmath32as calculated within lsda [ i]@xcite [ ii]@xcite and within the v - j model . ] for j@xmath14s = 1.2 ev @xmath38 is found to be in perfect agreement with the mean - field expression @xmath39j@xmath14s , the accordance is still reasonable for j@xmath14s = 3 ev . remark that , it is now widely accepted that j@xmath14 @xmath40 1.2 ev in mn - doped gaas @xcite . thus the realistic value of j@xmath14s should be 3 ev since s = 5/2 for mn@xmath13 . however in ref.@xcite j@xmath14s = 1.2 ev was used , which is almost three times smaller than the realistic value @xcite . from fig . [ fig:2 ] . one can clearly see that for both j@xmath14s = @xmath41 ev the calculated zeeman - splitting largely underestimates that obtained from first - principle studies @xcite . for example , for @xmath42 , one finds @xmath43 and 0.2 ev for j@xmath14 = 1.2 ev and 3 ev respectively , in contrast to 0.65 ev obtained from lsda calculations . thus , even the correct value of j@xmath14s does not lead to an agreement with first - principle results . in addition , experimental studies @xcite and ab - initio lsda calculations @xcite indicate the existence of an acceptor level or bound hybridized mn pd - state at @xmath44 mev above the valence band . this impurity state is absent for both values of j@xmath14s = @xmath41 ev in the limit of @xmath45 . in order to recover the correct zeeman - splitting and impurity acceptor level energy using j@xmath14s = 3 ev , one has to include a finite additional impurity potential scattering term v ( see eq.([eq : hamiltonian ] ) ) @xcite . within a single - band model this term has been shown to be a crucial ingredient to understand magnetism and transport properties in iii - v compounds @xcite . hence , our conclusion contradicts that of ref.@xcite , that a finite v is irrelevant . let us now discuss the nature of the magnetic couplings obtained within our multiband model . the mn - mn exchange couplings @xmath19 are calculated according to eq.([eq : couplings ] ) . in comparison to the mc studies of ref.@xcite our calculations are carried out for much larger systems ( 2048 lattice sites vs. 256 ) and the average over the disorder is performed over up to 800 vs. about 5 configurations in the mc simulations . thus we expect our results to have much less finite size effects and reliable statistics . for different values of j@xmath14s , @xmath46 as a function of @xmath47 is shown in fig . [ fig:3 ] . , where @xmath48 and @xmath49 . our results show clearly a major difference in the range , magnitude and nature of the effective exchange couplings . for small values of j@xmath14s=@xmath50 ev @xmath51 exhibits undamped long range rkky oscillations . hence , the couplings obtained for these values of j@xmath14 are inconsistent with those calculated from first principle studies for which rkky oscillations are absent ( see ref.@xcite ) . this disagreement indicates that either the choice of parameters used to describe the physics of gamnas is incorrect or the model itself is inappropriate . in contrast , in the strong coupling regime j@xmath14s = @xmath52 ev , the exchange integrals appear to be of short - range ferromagnetic type . this regime can be seen as a precursor of the double - exchange regime , j@xmath14s = @xmath53 . both the rkky and exponentially damped nature of the exchange couplings can be clearly seen in fig . [ fig:4 ] . note that for j@xmath14s @xmath54 3 ev the hamiltonian actually describes the physics of ii - vi mn - doped systems as , e.g. or . thus , for j@xmath14s @xmath54 3 ev long - range ferromagnetic order is unlikely @xcite , because of high frustration . instead one would expect a spin glass phase . mean effective exchange couplings @xmath46 as a function of distance @xmath47 ( @xmath55 is the lattice constant ) for several values of j@xmath14s and p = 0.75@xmath23 using @xmath56 . please note the oscillating rkky nature of the couplings for j@xmath14s = @xmath50 ev in contrast to the short - range ferromagnetic couplings for j@xmath14s = @xmath52 ev . ] mean effective exchange couplings @xmath46/(@xmath57 as a function of distance @xmath47 for several values of j@xmath14s and p=0.75@xmath23 using @xmath56 in the [ 110 ] direction . ] finally , in fig . [ fig:5 ] . we present the calculated curie temperatures t@xmath0 obtained by diagonalizing the heisenberg hamiltonian eq.([eq : heisenberg ] ) within the sc - lrpa using different hole densities . for comparison both t@xmath58 ( from ref.@xcite ) and the mean - field virtual - crystal value ( mf - vca ) t@xmath59 are shown . if we first focus on the largest hole density , p = 0.75@xmath23 , we observe that t@xmath58 is surprisingly larger than t@xmath59 . this is in contrast to the expectation that the mf value should overestimate the real critical temperature . even in the region of small j@xmath14s ( @xmath54 3ev ) , the mf value is zero whilst the mc value is always finite and relatively large . e.g. for j@xmath14s = 3 ev the mc value is about 500 k. therefore one can question the reliability of the present mc calculations . on the other hand , the sc - lrpa t@xmath0 is always much smaller than the mf values for the whole parameter range of j@xmath14s . ferromagnetism is possible only for sufficiently large values of j@xmath14s . we find that the critical value is about 5 ev for p = 0.75@xmath23 and about 2 ev for p = 0.3@xmath23 . our calculated t@xmath0 are approximately one order of magnitude smaller than those obtained from mc simulations . for example for j@xmath14s = 12 ev we have obtained 400 k within sc - lrpa whilst the mc simulations value is 2300 k. note that for lower carrier density the critical temperatures are smaller but the ferromagnetism already appears for smaller values of j@xmath14s . this is expected since the effect of disorder is stronger at lower carrier concentration and rkky oscillations will be suppressed for smaller values of j@xmath14s . additionally , at lower density the period of the rkky oscillations is larger thus the frustration effects weaken when carrier concentration is reduced . let us now explain the origin of the disagreement between our calculations and the mc simulations . the system considered in the mc study consists of only 256 lattice sites with typically only 20 localized spins and about 15 carriers / holes in the whole cluster . in addition the statistical average was carried out over about five configurations of disorder only . as it was already pointed out in ref.@xcite , the t@xmath0 is strongly size dependent and huge fluctuations of the critical temperatures distribution were observed for such small system sizes . for j@xmath14s @xmath54 4 ev , the smallness of the cluster used in the mc study does not resolve the asymptotic rkky tail for j@xmath14s = 1.2 ev leading to finite and large curie temperatures . in the large coupling regime , j@xmath14s @xmath60 8 ev the t@xmath58 overestimates the real critical temperatures both due to insufficient statistical sampling and finite size effects . on the other hand , it is clear , that these essential numerical requirements are difficult to fulfill within standard mc calculations . at last , one should underline , crucial differences between the two - step approach and mc simulations concerning the way t@xmath0 is determined . within sc - lrpa t@xmath0 is directly calculated from a semi - analytical expression whilst in the present mc study it is extracted from the temperature variation of the magnetization curve . a more accurate way should be to use binder cumulant in order to avoid additional errors , for the cost of significant computing time and memory needed for the finite size analysis . on the other hand , the sc - lrpa , allows the use of very large systems , typically of the order of @xmath61 thus containing about 10@xmath62 impurities . calculated curie temperature t@xmath0 for ga@xmath31mn@xmath32as with @xmath56 using the v - j model in connection with v = 0 . the sc - lrpa calculations were done with a system of 4@xmath63(22)@xmath64 sites ( 3600 impurities ) and the average was performed over 100 disorder configurations . ]

indeed , it is shown , using identical parameters that ( i ) the calculated zeeman - splitting largely underestimates that obtained from first principle studies , ( ii ) the couplings exhibit strong rkky oscillations , ( iii ) the stability region for ferromagnetism is much narrower than obtained previously and ( iv ) the calculated curie temperatures appear to be at least one order of magnitudes smaller .

magnetic properties of mn - doped gaas are re - investigated within a realistic multiband description of the host valence bands . we explicitely demonstrate that the recent monte carlo ( mc ) simulations performed on a large scale supercomputer suffer from severe shortcomings . indeed , it is shown , using identical parameters that ( i ) the calculated zeeman - splitting largely underestimates that obtained from first principle studies , ( ii ) the couplings exhibit strong rkky oscillations , ( iii ) the stability region for ferromagnetism is much narrower than obtained previously and ( iv ) the calculated curie temperatures appear to be at least one order of magnitudes smaller . we show that the proposed choice of physical parameters can not describe the physics in ( ga , mn)as .

1501.00758

c

mathematical model for hit phenomena is extended to analyze the popularity of weekly tv drama . the equation for each individual consumers is assumed and the equation of social response to each hit subject is derived as stochastic process of statistical physics . the advertisement effect is included as external force and the communication effects are included as two - body and three - body interaction . using the model . we analyze the popularity of drama in japanese market and we include both the realtime viewing and the playback viewing using the digital tv log data of toshiba . we found the high correlation between the tv viewing rate and the strength of the indirect communication strength obtained from the analysis of daily blog posting of each drama using our model .

the equation for each individual consumers is assumed and the equation of social response to each hit subject is derived as stochastic process of statistical physics . the advertisement effect is included as external force and the communication effects are included as two - body and three - body interaction . the applications of this model are demonstrated for analyzing population of weekly tv drama . including both the realtime view data and the playback view data

mathematical model for hit phenomena presented by a ishii et al in 2012 has been extended to analyze and predict a lot of hit subject using social network system . the equation for each individual consumers is assumed and the equation of social response to each hit subject is derived as stochastic process of statistical physics . the advertisement effect is included as external force and the communication effects are included as two - body and three - body interaction . the applications of this model are demonstrated for analyzing population of weekly tv drama . including both the realtime view data and the playback view data , we found that the indirect communication correlate strongly to the tv viewing rate data for recent japanese 20 tv drama .

0705.3199

c

we have taken the consistency constraints that exist in the literature for modified gravity models , and used them to construct a particular modified gravity function @xmath0 . a study of the model has shown that in order to satisfy all constraints , it must act like gr with highly suppressed corrections throughout cosmic history . in addition , we find that even though we do not have a true cosmological constant in our setup , we must still fine - tune the parameters in our @xmath0 function to obtain an acceptable late time accelerating epoch . although we have come to this conclusion for our specific model , we expect our results to hold true for a large class of @xmath0 models which satisfy all of the constraints that we have considered . while we were completing this work we became aware of refs . @xcite , which come to similar conclusions . in ref . @xcite , it was found that in order to satisfy local gravity constraints , the function @xmath55 as defined in section @xmath88 must satisfy @xmath170 for @xmath171 . this places a severe constraint upon @xmath36 , which must be very small in the current epoch of the universe . the model considered in this paper can satisfy the constraint @xmath170 by making the free parameter @xmath70 sufficiently large . however , such a stringent constraint is likely to yield a model that is virtually indistinguishable to gr . was considered , where @xmath59 , @xmath173 , @xmath174 and @xmath175 are free parameters . the model considered in this paper shares many similarities with ( @xmath176 ) ; the condition @xmath177 was imposed in ref . @xcite both at @xmath178 and as @xmath43 . this implies that the function @xmath179 can be expanded as for small @xmath181 , which is valid throughout the cosmic history of the model . we have arrived at a very similar expansion for the @xmath0 function considered in this paper , ( @xmath124 ) . the difference between the two models is that ( @xmath182 ) contains power law corrections to gr , whereas ( @xmath124 ) contains exponentially suppressed corrections .

we study a particular class of @xmath0 functions which satisfy various constraints that have been found in the literature . these models have a late time accelerating epoch , and an acceptable matter era . we calculate the friedmann equation for our models , and show that in order to satisfy the constraints we impose , they must mimic general relativity plus @xmath1 throughout the cosmic history , with exponentially suppressed corrections . we also find that the free parameters in our model must be fine tuned to obtain an acceptable late time accelerating phase .

modified gravity models are subject to a number of consistency requirements which restrict the form that the function @xmath0 can take . we study a particular class of @xmath0 functions which satisfy various constraints that have been found in the literature . these models have a late time accelerating epoch , and an acceptable matter era . we calculate the friedmann equation for our models , and show that in order to satisfy the constraints we impose , they must mimic general relativity plus @xmath1 throughout the cosmic history , with exponentially suppressed corrections . we also find that the free parameters in our model must be fine tuned to obtain an acceptable late time accelerating phase . we discuss the generality of this conclusion .

cond-mat0205642

i

the term polyelectrolyte is employed for the wide field of macromolecules which contain dissociable subunits ( see , e.g. , @xcite and references therein ) . with respect to different dissociation behavior one can distinguish between strong and weak polyelectrolytes @xcite or between quenched and annealed ones @xcite . so - called strong polyelectrolytes , polysalts as e.g. na - polystyrene sulfonate , dissociate completely in the total ph range accessible by experiment . the total charge as well as its specific distribution along the chain is solely imposed by chemistry , i.e. , by polymer synthesis . that is why such polyelectrolytes are also called quenched . on the other hand , weak polyelectrolytes represented by polyacids and polybases dissociate only in a rather limited ph range . the total charge of the chain is not fixed but it can be tuned by changing the ph of the solution . because of dissociation and recombination of ion pairs along the chain one expects spatial and/or temporal fluctuations in the local degree of dissociation . such titrating polyelectrolytes exhibit an annealed inhomogeneous charge distribution . a pronounced charge accumulation appears at chain ends because there are fewer neighbors for the charges to interact with and the penalty in energy is therefore reduced . although , at the level of scaling laws describing the statistical properties of polymer chains , the local charge distribution has only a weak effect on numerical pre - factors @xcite the extra degree of freedom for the charges leads to new and non trivial features . the charge inhomogeneity can have a strong impact on processes dominated by end - effects , such as the self - assembly of weakly charged linear micelles @xcite and adsorption on charged surfaces @xcite . for end - grafted weak polyelectrolytes , a rather unusual regime has been obtained where the chain stretching ( brush thickness ) depends non - monotonously on salt concentration @xcite and grafting density @xcite . this is mainly due to the fact that the net charge of a chain as well as its distribution along the chain is not fixed but depends on its local environment . the dissociation of a low molecular acid ( ha ) in an aqueous medium is given by the equilibrium reaction @xmath1 or more simply by @xmath2 the law of mass action yields the equilibrium constant @xmath3\,\left [ \text{a}^-\right]}{\left [ \text{ha}\right]},\ ] ] where @xmath4 $ ] , @xmath5 $ ] , @xmath6 $ ] are the ( monomolar ) concentrations of dissociated and undissociated acid and dissociated hydrogen , respectively . using the standard notation @xmath7 $ ] , and defining the degree of dissociation by @xmath8}{\left [ \text{ha}\right]\,+\,\left[\text{a}^-\right]},\ ] ] eq . ( [ eq : ka ] ) gives the well - known relation between the ph of the solution and degree of dissociation @xmath9 of a simple acid @xmath10 the dissociation behavior of polyacids can be described in a similar way , but the resulting @xmath11 value is now an apparent one ( in the physico - chemical literature denoted by @xmath12 ) @xcite . in contrast to low - molecular - weight acids , the charged groups of polyacids are linked together along the chain . therefore , the dissociation of one acid group is correlated in a complex way to the position and the number of other charged groups of the chain resulting in a masking of the intrinsic @xmath13 of a ( polyelectrolyte ) monomer . the corresponding relation can be written @xcite @xmath14 with @xmath15 being the electrostatic free energy of the polyelectrolyte chain and @xmath16 is the chain length . introducing the chemical potential @xmath17 eq . ( [ eq : pkapoly ] ) can be written @xmath18 clearly , the chemical potential has two contributions : ( i ) an entropic one related to the mixing of charged and non - charged groups along the chain and ( ii ) an electrostatic one related to the interaction with charged groups forming the local charge environment of an ionizable site . for good and @xmath0 solvents , the electrostatic contribution @xmath19 is an increasing monotonic function of @xmath9 . for poor solvents , raphael and joanny @xcite found a non - monotonic variation of @xmath20 , and thus of @xmath21 , with @xmath9 which results in a first order phase transition from a collapsed weakly charged conformation to an extended strongly charged state . the particular behavior of weak polyelectrolytes has attracted considerable interest in experimental @xcite , theoretical @xcite and simulation @xcite studies . because a usual experimental approach to characterizing weak polyelectrolytes is to perform titration experiments much effort has been done to understand the titration curves , i.e. , the dependence of the degree of ionization ( or the degree of neutralization in the titration experiment ) on the ph of the solution . the inhomogeneous charge distribution has been first studied by numerical simulation @xcite . for not too large mean charge densities @xmath22 and screening lengths @xmath23 , a quite good agreement between simulation data and the predictions of a linearized density functional approach has been obtained in the case of rod - like polyelectrolytes @xcite . recently a generalization of the theory to the case of flexible chains has been given by castelnovo _ qualitatively they found the result obtained in our previous simulations : a charge accumulation at chain ends . however , a quantitative comparison between theory and simulation data was not possible because the chains considered by berghold _ at al . _ @xcite are not in the asymptotic regime where the approach used in theory can be applied . a similar end - effect has been demonstrated in simulations of quenched strongly charged polyelectrolytes with explicit counterions : around the ends the counterion distribution is significantly different from that around the inner part of the chain @xcite . however , although the resulting effective charge looks quite similar to that of an annealed polyelectrolyte a quantitative comparison with the corresponding theoretical predictions is not possible due to some important differences between the two systems . so the theoretical predictions given by castelnovo _ et al . _ are still waiting for a quantitative verification . in the present paper we study the non - uniform charge distribution on annealed weakly charged polyelectrolytes in a @xmath0 solvent by ( semi-)grand canonical monte carlo simulation . to be close to the theoretical model we consider chains where neighboring monomers are bound by harmonic springs . in addition , charged monomers interact with a debye - hckel potential , the screening length of which is tuned over the range where the theory is valid . in this case we observe not only qualitative agreement between simulation data and theory , but indeed a quite good quantitative one . although the theoretical single chain problem and its solution in a restricted parameter range may seem rather academic it is a first step towards a more precise understanding of unusual collective properties of , e.g. , annealed polyelectrolyte brushes and stars . the outline of the paper is as follows . in section [ sec : theory ] we present the main theoretical predictions . the model and the method we use in the simulation are described in section [ sec : simmodel ] . in section [ sec : results ] we discuss the results and compare theory and simulation . finally , a brief summary and our conclusions can be found in section [ sec : conclu ] .

monte carlo simulations are used to study the non - uniform equilibrium charge distribution along a single annealed polyelectrolyte chain under @xmath0 solvent conditions and with added salt . within a range of the order of the debye length charge accumulates at chain ends while a slight charge depletion appears in the central part of the chain . the simulation results are compared with theoretical predictions recently given by castelnovo _ et al_. in the parameter range where the theory can be applied we find almost perfect quantitative agreement .

monte carlo simulations are used to study the non - uniform equilibrium charge distribution along a single annealed polyelectrolyte chain under @xmath0 solvent conditions and with added salt . within a range of the order of the debye length charge accumulates at chain ends while a slight charge depletion appears in the central part of the chain . the simulation results are compared with theoretical predictions recently given by castelnovo _ et al_. in the parameter range where the theory can be applied we find almost perfect quantitative agreement .

1401.4275

i

in ashtekar s theory of gravity , a @xmath2-connection captures the extrinsic curvature of a space - like leaf in a time - transversal foliation , and the intrinsic geometry of the leaf is given by a tetrad @xcite . it is shown that the einstein - hilbert functional and einstein equations can be written in terms of @xmath2-connections and tetrads , thus these variables together recast einstein s theory of gravity . by rewriting einstein s gravity with the connection variables and tetrad variables , one could attempt to quantise gravity via the hamiltonian formalism , and obtain a theory of quantum gravity @xcite . the reader may refer to thiemann s introductory @xcite . this article offers an alternative view of the space of connections to ones that appear in other loop quantum gravity literatures , and proposes a semi - classical limit using strict @xmath1-algebraic deformation quantisation formalism @xcite . to take the connections as dynamic variables in a quantum theory , one studies wave functions , also known as probability amplitudes , on the space of connections . unfortunately , the lack of a measure on such a space poses the first challenge , since in such case probabilities can not be defined . one typical solution to obtain a measure on the connection space comes from spaces of progressively refined cylindrical functions . in another description , one uses a finite set of curves to probe the space of @xmath0-connections to obtain a finite dimensional manifold that depend on the sets of curves . by successively refining the finite sets of curves , such as successive triangulation of the manifold , one obtains a pro - manifold that extends the original space of connections to the so - called space of generalised connections @xcite . as a step to quantising gravity in the ashtekar framework , there are recent developments of describing such an extended space of connections using a spectral triple in noncommutative geometry @xcite , which captures the geometry of the space of generalised connections as operators on a hilbert space . while the geometries of the base manifold and the space of @xmath0-connections on it are in theory retained , the construction of the spectral triple is considered too discrete to practically allow one to recapture the geometry of the base manifold and its @xmath0-connections . to rid the discrete description of using finite sets of embedded curves , this article proposes an alternative approach to smoothly probe the space of connections using the tangent groupoid . and then followed by an application of strict deformation quantisation in @xmath1-algebraic formalism , a possible semi - classical limit of can be obtained . the purposes of this article are to present an alternative idea to the studies of loop quantum gravity with the goal of obtaining a semi - classical limit , which is what loop quantum gravity still lacks today . this article contains six small sections , they are arranged as follows : section [ sec2 ] discusses the traditional way of putting a measure on the space of connections in loop quantum gravity literature , and the short coming of such a method . in section [ sec3 ] , we review the definitions of a lie groupoid , a lie algebroid , and tangent groupoid of a lie groupoid in an elementary way . section [ sec4 ] shows that how one uses the tangent groupoid as a tool to model the space of connections in a smooth way , and discuses the corresponding gauge action . section [ sec5 ] is the first attempt of deforming connections into noncommutating operators acting on a hilbert space . section [ sec6 ] introduces the notion of strict deformation quantisation in @xmath1-algebra formalism , and an important theorem by landsman @xcite , which states that a tangent groupoid defines a strict deformation quantisation . hence , using this formalism , we can deformation quantise @xmath0-connections . finally , section [ sec7 ] is an outlook that summarises the article and the current state of work toward obtaining a semi - classical limit in loop quantum gravity .

motivated by the compactification process of the space of connections in loop quantum gravity literature . a description of the space of @xmath0-connections using the tangent groupoid is given . as the tangent groupoid parameter is away from zero , the @xmath0-connections are ( strictly ) deformation quantised to noncommuting elements using @xmath1-algebraic formalism .

motivated by the compactification process of the space of connections in loop quantum gravity literature . a description of the space of @xmath0-connections using the tangent groupoid is given . as the tangent groupoid parameter is away from zero , the @xmath0-connections are ( strictly ) deformation quantised to noncommuting elements using @xmath1-algebraic formalism . the approach provides a mean to obtaining a semi - classical limit in loop quantum gravity .

1011.3006

c

deep @xmath27 and @xmath31 images obtained with the cfht wircam have been used to explore the stellar content in the outer regions of the nearby starburst galaxy ngc 253 . this is the first panoramic stellar survey of this galaxy . photometrically - selected samples of rsgs , m giants and c stars are used to trace the spatial distribution of stars with young and intermediate ages . stars are assigned to the disk or the extraplanar regions based on their projected location on the sky ( 1 ) to assess population characteristics , and ( 2 ) to investigate spatial trends and search for structures . while there is inevitable contamination between the disk and extraplanar samples , this is only an issue at modest offsets from the disk plane , near the boundary separating the disk and extraplanar regions . the brightest disk stars in the near - infrared are rsgs , and comparisons with isochrones suggest that the youngest of these have ages @xmath7 myr in ngc 253 . rsgs are highly effective probes of recent star formation by virtue of their intrinsic brightness , and the distribution of rsgs in the ngc 253 disk is lop - sided , with many more in the north east quadrant of the galaxy than in the south west quadrant . unfortunately , small number statistics restrict the usefullness of rsgs as stellar content probes in low - density environments . m giants that are evolving on the agb are more plentiful in composite stellar systems than rsgs , and hence provide a better means of tracing diffuse structures . the photometric depth of the wircam data is such that m giants with ages that span the lifetime of the galaxy are present in these data , although the vast majority of m giants detected here probably have ages @xmath129 gyr . while m giants have the merit of being comparatively easy to detect because of their intrinsic luminosity , the ability to use them to identify individual star - forming episodes diminishes towards progressively older ages . this is because the rate of change of agb - tip brightness with time decreases with increasing age , making efforts to isolate individual large - scale star - forming events that occured more than a few gyr in the past difficult . an added complication is that a significant fraction of stars near the agb - tip are lpvs , and photometric variability blurs information in the lfs . because of their comparatively high numbers , m giants have been adopted as the main tracer of structure in this paper . c stars provide insights into the star - forming history of a system that are complementary to those provided by m giants . whereas the brightest m giants have ages @xmath6 gyr , the majority of c stars have ages 1 3 gyr ( e.g. maraston 2005 ) . that c stars are seen over the same spatial intervals as m giants throughout the disk and extraplanar regions of ngc 253 provides direct evidence that the disk and extraplanar regions of this galaxy contain stars that span a wide range of ages . the extent to which ngc 253 can serve as a template for understanding more distant starburst systems depends on its nature prior to the events that sparked the current starburst if ngc 253 has not had a ` typical ' history then it may not be a good comparison object for probing ` typical ' starburst activity . in fact , the properties of the globular cluster system hint that ngc 253 may not be a textbook spiral galaxy in terms of its past evolution . expanding upon the sample of clusters identified by beasley & sharples ( 2000 ) , olsen et al . ( 2004 ) used deep spectra to identify ngc 253 globular clusters and study their kinematics . olsen et al . ( 2004 ) find that the globular clusters system of ngc 253 is remarkable in two respects . first , it appears to be rotationally supported , with a characteristic scale length that is comparable to that of the present - day hi disk , although there are admittedly large uncertainties in this quantity . while ngc 253 is not unique in having a rotationally - supported globular cluster system , it is the best characterized such system ( olsen 2010 , private communication ) . second , the specific frequency of globular clusters in ngc 253 is more than an order of magnitude lower than in other sculptor group spiral galaxies . that the characteristic size of the star - forming disk of ngc 253 has evidently not changed since early epochs is surprising given the evidence for inside - out disk growth in spiral galaxies ( e.g. trujillo & pohlen 2005 ; colavitti et al . if disks form from the inside - out then globular clusters that formed early - on should have a more compact distribution than the present day stellar disk ( at least assuming that the stellar disk of ngc 253 has not been tidally pruned , which appears not to be the case given the large physical extent of the stellar disk defined by m giants see below ) . a core assumption is that all of the clusters formed as part of ngc 253 , and were not accreted by an interaction with a companion . if ngc 253 did accrete clusters then the companion must have been on a coplanar orbit in order to retain a disk - like cluster distribution in the final merged system . in any event , cluster accretion seems unlikely given the low globular cluster specific frequency of ngc 253 . the presence of a spatially - extended disk - like globular cluster system is also surprising given that major mergers can have a highly disruptive effect on the properties of stars in disks prior to the merger . the vast majority of nearby spirals appear to have experienced such an event during the past few gyr ( hammer et al . 2007 ) . hopkins et al . ( 2009 ) investigate the impact of major ( mass ratios @xmath130 ) mergers on gas - rich disks , and find that while the initial disk of the more massive galaxy may be obliterated , it re - forms on a cosmologically short time scale . existing stars are scattered out of the plane of the primary galaxy , and these subsequently virialize to form a pressure - supported system . an old globular cluster system in a disk galaxy that has experienced a major merger should then be pressure - supported , rather than distributed in a disk . the disk - like globular cluster distribution in ngc 253 is counter to this expectation , unless it experienced a major merger with a companion with an orbit that was coplanar with the ngc 253 disk . such a merger geometry is conducive to producing starburst activity and maintaining asymmetries in the disk ( such as those discussed in 4 ) if the companion orbit is prograde ( hopkins et al . 2009 ) . the sculptor group is dynamically unevolved ( karachentev 2005 ) , and ngc 253 may simply be one of the @xmath131 of nearby spirals that have avoided a major merger ( hammer et al . 2007 ) . major mergers involving gas - rich systems produce environments that are conducive to globular cluster formation ( e.g. ashman & zepf 1992 ) . therefore , an uneventful interaction history could explain the low specific frequency of globular clusters in ngc 253 . if ngc 253 has not experienced a major merger for a large fraction of the hubble time then it might have a relatively compact stellar disk when compared with other nearby galaxies , due to a relative deficiency in angular momentum ( hammer et al . m81 has an m@xmath64 that is comparable to that of ngc 253 , and the disk scale length of ngc 253 ( 1.7 kpc ; forbes & depoy 1992 ) is comparable to that measured for m81 from the @xmath74band surface brightness profiles given by jarrett et al . the wircam data also indicate that the physical extent of the ngc 253 disk is not compact . agb stars in the disk are traced out to at least 22 kpc along the major axis ( 4 ) , which corresponds to 13 scale lengths . given the diffuse appearance of the outer disk in figure 3 , it is possible that the stars seen at large r@xmath43 may not be in the classical disk ; rather , they could be the result of tidal interactions . still , that stars are detected out to this distance in both fields 1 and 2 with comparable number densities argues that the majority of these stars are part of a dynamically mature component , which we associate with the disk . the extent of the stellar disk in ngc 253 is thus comparable to the distances out to which stars have been resolved in ngc 247 ( davidge 2006 ) and m81 ( davidge 2009 ) , and exceeds the stellar disk of ngc 2403 ( davidge 2007 ) . we conclude that the stellar disk of ngc 253 is not compact when compared with other nearby galaxies . if , as the other evidence suggests , ngc 253 avoided mergers up to the recent epochs , then ngc 253 may have received angular momentum from torques exerted by ngc 247 ( whiting 1999 ) . in fact , the disk of ngc 253 is likely even more extended than indicated by agb stars . the holmberg radius of ngc 253 is 17.6 arcmin ( puche et al . 1991 ) , or 21 kpc . bright agb stars are relatively rare , and deeper images that sample stars on the upper portions of the rgb , will probably trace the stellar disk of ngc 253 out to even larger radii . blue main sequence stars may also provide a powerful means of plumbing the outer limits of the ngc 253 disk . the main sequence phase of evolution has a much longer duration than the agb phase , so that main sequence stars will occur in much larger numbers than agb stars . moreover , the use of blue stars also results in greater contrast with respect to background galaxies , the majority of which have red colors ( e.g. davidge 2008d ) . the spatial distribution of recent star formation can be used to probe the recent history of the galaxy . starbursts are most commonly associated with galaxy - galaxy interactions and so the disk of ngc 253 might be expected to harbour signatures of a tidal encounter . in fact , evidence for such an interaction is evident in the sub - structure close to the disk plane ( figure 3 ) . if there was an interaction then it evidently produced elevated levels of star formation not only in the inner regions of the galaxy , but also in the disk . indeed , the high density of rsgs in the north east portion of ngc 253 indicates that this was an area of very active star formation within the past few tens of myr . this interpretation is supported by the presence of nuv and fuv emission ( hoopes et al . 2005 ) and intense h@xmath15 emission ( hoopes et al . 1996 ) in this part of the galaxy . the bright h@xmath15 emission indicates that the elevated star - forming activity heralded by the rsgs almost certainly continues up to the current time . while the south west part of the disk is not devoid of h@xmath15 emission and uv - bright objects , the sources there are fainter and less numerous than at the other end of the major axis . the north east portion of the ngc 253 thus appears to have had the highest levels of star formation in the main body of the disk during at least the past few tens of myr . this part of the galaxy also shows an enhancement in the number of bright agb stars with respect to the south east arm of the major axis ( 4 ) , suggesting that excess star formation in this area has occured for hundreds of gyr . while the orbital properties of the supposed interacting galaxy are not known , there are clues to possible trajectories . the distribution of stars in figure 3 is suggestive of an encounter involving a companion with an orbit that was close to the ngc 253 disk plane , and this is consistent with the flattened distribution of extraplanar m giants measured in 5 . dynamically de - coupled material near the galaxy center ( anantharmaiah & goss 1996 ; prada et al . 1998 ) suggests that the encounter may also have involved the central regions of the galaxy . the range of interaction geometries investigated by hopkins et al . ( 2009 ) indicate that the most pronounced asymmetries in the disk result from prograde encounters in which the companion orbit is close to that of the disk plane of the larger galaxy . the lop - sided nature of the ngc 253 disk thus suggests that the galaxy that interacted with ngc 253 was probably not on a retrograde orbit . we are not aware of published studies that investigate an interaction between ngc 253 and a possible companion . however , interactions between m31 , which has an integrated brightness that is similar to that of ngc 253 and is known to be surrounded by tidal features , and a companion have been examined . there is some similarity between the general appearance of m31 with its tidal structures in figure 1 of fardal et al . ( 2007 ) and ngc 253 in figure 3 of the current paper . fardal et al . ( 2007 ; 2008 ) investigate the interaction between a single satellite and the m31 disk . the main emphasis of these studies was to model the tidal features that have been found near m31 , and the orbital pericenter of the companion is a few kpc ( fardal et al . in addition to producing the m31 giant stellar stream , these models produce structures that are close to the observed disk plane . while originating in the satellite , the stars in these structures have a spatial distribution that is defined largely by the m31 gavitational potential . if the extraplanar population in ngc 253 is analogous to that in m31 then the fardal et al . ( 2007 ; 2008 ) simulations indicate that the extraplanar regions of ngc 253 are populated predominantly by stars that originated in a companion galaxy . an interaction with a satellite will also affect the stellar distribution in the m31 disk . block et al . ( 2006 ) consider a companion ( presumably m32 ) that passes through the center of m31 , and that study provides insights into signatures in the disk that such an encounter might produce . the interaction in that model produces a density wave that propogates outwards from the point of impact . this wave spurs star formation as it moves along , and localized regions of star formation in ring- or arm - like structures result ( figure 2 of block et al . 2006 ) . is there evidence for a collisionally - induced propagating density wave in ngc 253 ? galex uv images are examined in an effort to answer this question . the nuv and fuv morphology of ngc 253 , corrected to show the galaxy as it would appear if viewed face - on , is shown in figure 19 . the de - projection involved stretching the image along the minor axis to simulate tilting the line of sight , and then applying a deconvolution filter to correct for distortions introduced by this process . the overall distribution of star - forming regions is not affected by the deconvolution process . no attempt was made to correct for the inherent thickness of the ngc 253 disk , and emission from the outflow blurs the right and left hand edges of the disk in the de - projected images . the position angle and ellipticity measured from 2mass images ( jarrett et al . 2003 ) were adopted , and residual oblateness in the de - projected images suggests that the ellipticity was underestimated by a small amount . the side lobes that bracket bright point sources are artifacts of the deconvolution process . the de - projected @xmath31-band 2mass image of ngc 253 is also shown in figure 19 . this is an interesting comparison dataset as near - infrared light traces mass , whereas uv light mainly traces young stars ; hence , differences between the near - infrared and uv images are expected . the barred morphology of the central regions of the galaxy is clearly evident in the @xmath31 image , as are the two spiral arms that emerge from the ends of the bar . the high dust content of ngc 253 almost certainly affects the appearance of the galaxy in the uv , and the bar that is prominent in the near - infrared is invisible in the uv . dust in the outflow likely produces the streaks in the right half of the southern disk of the uv images as well as the lack of uv emission immediately to the left of the nucleus . the uv sources loosely follow the spiral structure that is conspicuous in the near - infrared . the agreement between the near - infrared arms and uv sources in the northern half of the galaxy is reasonable ; while there is some uv emission along the spiral arm , the brightest sources of uv emission fall along the leading edge of the spiral arm , as expected if the leading edge of the density wave compresses the ism and triggers star formation . there is similar agreement between uv emission and spiral structure in the southern half of the disk . with the caveat that there is substantial extinction throughout the ngc 253 disk , there is no evidence for ring - like distribution of star - forming regions . if a galaxy passed through the ngc 253 disk then it did not leave a signature like that predicted by the encounter modelled by block et al . this might indicate that the companion was not as massive as m32 and/or that the passage had an oblique collision geometry . we close the discussion of the disk by noting that the north east disk of ngc 253 bisects the extraplanar hi found by boomsma et al . ( 2005 ) , suggesting a causal relationship between the elevated sfrs and the gas emission . the high levels of recent star formation in the north east portion of the ngc 253 disk may have an impact on the circumgalactic environment through the formation of chimneys , which are conduits for channeling gas out of the disk plane ( e.g. norman & ikeuchi 1989 ) . significant mass outflow rates do not require large sfrs ( e.g. ceverino & klypin 2009 ) . melioli et al . ( 2009 ) model the impact on the extraplanar environment of sne from a star - forming complex in a milky way - like system . their simulations indicate that the moderately compact concentration of star - forming regions produces a vertical plume of gas that diffuses only modest distances from the chimney axis after one disk rotation ( @xmath132 myr in their model ) . gas is ejected @xmath133 kpc above the disk plane in these models , whereas the extraplanar hi near ngc 253 is traced out to 12 kpc ( boomsma et al . figure 2 of boomsma et al . ( 2005 ) shows extended spurs in the extraplanar hi emission , especially the column that extends to the north west of the disk plane , and this is consistent with the morphology of the chimney outflow predicted by melioli et al . ( 2009 ) . while the arguements presented here are not ironclad , feedback from a ` boiling disk ' ( sofue et al . 1994 ) , of which the concentration of rsgs in the north east disk are the most conspicuous manifestation at near - infrared wavelengths , is a viable mechanism for producing the extraplanar hi in ngc 253 . a diffuse extraplanar stellar component , which comparisons with model lfs in 5 indicate contains stars that formed over gyr or longer timescales , is seen in all three wircam fields . the distribution on the sky of the extraplanar component appears to be flattened , with an ellipticity near 0.4 . it can be anticipated that stars belonging to this extraplanar component should also be found to the north of the galaxy disk . the extraplanar regions of ngc 253 contain clues about the events that triggered the starburst . if the starburst was triggered by a tidal encounter with another galaxy then detritus from the interaction may lurk in the extraplanar regions , and evidence for such material is seen in figure 3 . while the extraplanar stars are widespread , girdling at least the southern part of the galaxy , there are minor field - to - field differences in extraplanar stellar density , indicating that the extraplanar stars are not yet well mixed throughout the halo . smaller scale structures , such as streams and shells , may become better characterised with deeper images that sample larger numbers of objects , such as stars on the rgb . in a related vein , studies of the present - day extraplanar component can also be used to predict the future appearance of the ngc 253 ` halo ' ; for example , will an observer in the distant future find that the halo of ngc 253 contains a complex mix of stellar components , the origins of which can only be identified through extremely deep photometric studies ? to the extent that the simulations run by fardal et al . ( 2007 ; 2008 ) can be applied to ngc 253 , then any tidal streams may have lower surface brightnesses than the morass of stars that surround the ngc 253 disk . selection effects may also come into play , as higher surface brightness tidal structures tend to be associated with material accreted from more metal - rich companions that have been recently accreted ( gilbert et al . hence , the prominence of stellar tidal streams provides clues about the nature of the companion and the time of the encounter . the extraplanar regions of ngc 253 contain a complex mix of stellar populations . ngc 253 is almost certainly surrounded by an old , classical stellar halo , although the spatial distribution and specific frequency of globular clusters hints that the classical halo may be even more poorly populated than the classical halos around other galaxies , and have a highly flattened morphology . comeron et al . ( 2001 ) find stars with young ages near the minor axis of ngc 253 , that presumably are associated with the outflow from the nuclear starburst . the first stars that formed in the outflow ( i.e. at least a few tens of myr in the past ; pietsch et al . 2000 ) may have diffused away from their places of birth by now , and the dominant gravitation influence of ngc 253 will pull the young stars towards the disk plane , where they may ultimately form a more compact , kinematically relaxed distribution . a fraction of stars that formed in the outflow may also obtain relatively high velocities ( e.g. stone 1991 ) , allowing them to move large distances from their places of birth . the diffuse extraplanar component contains stars that are far too young to belong to a classical halo , while the wide age span ( @xmath134 gyr ) deduced from the m giant lf is not consistent with formation in the outflow , which has probably been in place for ( at most ) only a few 100 myr ( i.e. since the interaction with a companion ) . the uniform mix of the extraplanar population over large spatial scales , coupled with a lf that is indicative of an extended star - forming history that is typical of disk systems , is consistent with the stars having formed in an environment other than the extraplanar regions of ngc 253 . while it is argued here that the stars did not form in the extraplanar regions , pockets of star formation in such environments are not without precedent ( e.g. tullmann et al . 2003 ) , and _ in situ _ formation has been suggested as a possible mechanism for the formation of young stellar ensembles near m82 ( davidge 2008e ) . two possible sources of origin for the diffusely distributed extraplanar stars are the disk of ngc 253 or a gas - rich companion galaxy with m@xmath5 . an interaction between ngc 253 and another galaxy could perturb the orbits of stars in the ngc 253 disk , and produce an extraplanar component . as for an origin in a dwarf galaxy , ngc 253 does not have an entourage of companions , and so the companion in question must have been completely destroyed or absorbed by ngc 253 . the chemical composition of stars in the extraplanar regions of ngc 253 will provide obvious clues into their origins . if these stars have near - solar metallicities than this would be indicative of having formed in the disk , whereas a metallicity that is , for example , one - tenth solar would favor formation in a lower luminosity dwarf galaxy . the photometric properties of rgb stars are one means of estimating metallicities , albeit for stars that formed at least a few gyr in the past . the deep cmd discussed by mouchine ( 2006 ) suggests that the majority of stars in the extraplanar regions near the minor axis have a mean [ m / h ] @xmath135 , ostensibly suggesting an origin in a dwarf companion . however , this mean metallicity assumes that the stars are all ` old ' . if the extraplanar regions are populated by stars that formed over a range of ages , then a large fraction may have ages @xmath136 gyr , and the metallicities of these objects will be underestimated if they are assumed to be old . the combination of visible and near - infrared data would provide considerable wavelength leverage for measuring improved metallicities . still , the ability to measure the characteristic metallicity of rgb stars may be complicated by the extensive dust content of the galaxy . differential reddening causes conspicuous blurring of the cmds of ngc 253 in the disk ( e.g. the discussion of the karachentsev et al . 2003 and dalcanton et al . 2009 cmds in 1 of this paper ) . there is also evidence for substantial quantities of dust in the extraplanar regions of the galaxy ( kaneda et al . 2009 ) , which probably was ejected by winds from star - forming regions . the broadening of sequences on the cmds of ngc 253 fields caused by differential extinction may be mistaken for a mixture of ages and/or metallicities . moderate resolution specroscopy provides a means of measuring metallicities that is less susceptible to differential extinction . given the low temperatures of the brightest stars in the extraplanar regions of ngc 253 , coupled with the need for high angular resolutions to resolve sources at small offsets from the disk plane , near - infrared spectra are of obvious interest , and the feasibility of obtaining such data is briefly discussed here . the near - infrared spectral region contains a number of metallicity - sensitive features that can be examined with spectral resolutions of @xmath137 , and the calibration of these has been investigated by frogel et al . the brightest m giants in the extraplanar regions of ngc 253 have @xmath138 , and experience with spectrographs on 8 10 meter telescopes indicates that total on - source exposure times of hundreds of hours would be required to obtain a spectrum with a s / n = 100 of a @xmath50 source with a resolution @xmath139 . however , the exposure time is markedly lower if the observations are conducted with a 30 meter telescope working at the diffraction limit , due to the d@xmath140 advantage . indeed , a simple scaling of the exposure times required for 8 meter telescopes suggests that spectra with a suitable s / n ratio could be obtained with exposure times of only a few hours with a 30 metre telescope . thus , while obtaining spectra of the brightest red stars is not feasible with 8 10 metre telescopes , this is a project that is well within the grasp of a 30 meter telescope . ngc 247 is the nearest large galaxy to ngc 253 . could ngc 253 and ngc 247 have interacted in the not too distant past ? an interaction between ngc 247 and ngc 253 seems unlikely at first blush , as ngc 247 does not show classical signatures of an interaction , such as a central starburst or extended tidal arms . surveys also have not found hi streams near ngc 247 or ngc 253 ( haynes & roberts 1979 ; putman et al . 2003 ) that could be part of a debris trail . still , the disks of these galaxies are oriented in a manner that is consistent with mutual tidal torquing ( whiting 1999 ) . in addition , ngc 247 like ngc 253 has a truncated hi disk ( carignan & puche 1990 ) , a tendency for mean age to increase with radius in the outer disk ( davidge 2006 ) , and what is perhaps most suggestive of a recent encounter an intermediate age extraplanar population ( davidge 2006 ) . if ngc 247 and ngc 253 had a close encounter then tidal fragments may have been removed from one or both galaxies . while there are a number of nearby dwarf irregular and dwarf spheroidal galaxies , these are located to the north west of ngc 253 and are clustered near ngc 247 ( e.g. figure 3 of karachentsev et al . could some of the actively star - forming dwarf galaxies near ngc 247 be tidal dwarfs ? tidal dwarfs have characteristics that are distinct from those of classical galaxies that formed within primordial dark matter halos . the gas and stars that tidal forces displace from a galaxy quickly develop different kinematic properties , as gas is a collisional system that can dissipate energy , while stellar ensembles are collisionless systems . gas may thus form concentrated pockets where star formation may subsequently occur . because tidal dwarfs are not in dark matter dominated halos , they have structural properties that are distinct from those of classical galaxies , and may dissipate on timescales that are significantly less than the hubbble time . in addition , they will not have an underlying concentrated substrate of older stars , of which rgb stars are among the most prominent signature . finally , if the tidal gas came from a massive galaxy then the stars in a tidal dwarf will have a metallicity that differs from that expected from the [ m / h ] m@xmath141 relation defined by classical galaxies . there are two galaxies close to ngc 247 on the sky that have conspicuous blue populations : ddo 6 and ddo 226 . karachentsev et al . ( 2003 ) present @xmath142 cmds of both galaxies that are based on moderately - deep wfpc2 observations . the cmd of ddo 6 has a prominent rgb , indicating that it contains stars with ages of at least a few gyr . a subsequent investigation of the star - forming history of ddo 6 by weisz et al . ( 2006 ) suggests that the majority of stars in ddo 6 formed 12 14 gyr in the past , and that star formation was only rejuventated within the past 0.5 gyr . thus , based on the presence of a large old population , ddo 6 is not a tidal dwarf . the situation might be different for ddo 226 , the cmd of which lacks a prominent rgb . there _ is _ a concentration of red stars in the cmd with @xmath143 , but these do not form a well - defined sequence . working on the assumption that the red stars are on the rgb , karachentsev et al . ( 2003 ) assign ddo 226 a distance modulus of 28.5 , placing it @xmath8 mpc beyond ngc 247 and ngc 253 . deeper images will help establish the nature of ddo 226 . more specifically , the detection of a well - defined rgb would indicate that ddo 6 is not a tidal fragment . the manner and timescale in which a galaxy and its companions evolve depends on initial conditions , such as the orbital characteristics of satellites , and environment , including the distances to the nearest large galaxies . while no two galaxies have the same initial conditions , and hence do not have the same evolutionary histories , the study of resolved stars can be used to identify nearby galaxies that may have experienced similar events , but are in different stages of their evolution and as such may appear to be unrelated . identifying such relationships will lead to a better understanding of galaxy evolution , as it will then be possible to directly probe the influence of for example local environment . m31 is potentially an interesting comparison object for ngc 253 . not only is m31 sufficiently close that it can be studied in considerable detail , but ngc 253 and m31 have similar m@xmath141 and m@xmath64 . the distribution of stars outside of the disk plane in m31 ( e.g. figure 1 of fardal et al . 2007 ) is also reminiscent of that seen in ngc 253 . still , the validity of pairing m31 and ngc 253 may seem dubious , given the obvious differences in overall morphology and environment . indeed , ngc 253 lacks the large bulge that dominates the central regions of m31 , while m31 is not presently experiencing a starburst . ngc 253 also lacks an entourage of companions , whereas m31 has many accompanying galaxies . the extraplanar structure around m31 indicates that it has had an extremely eventful past , and the number of companions in the past was probably even greater than at present . evidence for this comes in the form of conspicuous streams and shells , which are the remnants of one or more satellites that have all but disintegrated ( e.g. fardal et al . 2007 , 2008 ; ibata et al . 2007 ; koch et al . 2008 ) ; tanaka et al . ( 2010 ) distinguish 16 substructures in the outer regions of m31 . the globular cluster system of m31 is also highly inhomogeneous , suggesting a diversity in origins ( beasley et al . 2005 ) . in addition to the well - documented structures in the outer regions of m31 , there is also evidence of a diffuse extraplanar stellar component . some of these stars belong to a classical metal - poor halo ( e.g. chapman et al . 2006 ; kalirai et al . 2006 ; ibata et al . 2007 ; koch et al . 2008 ) . however , the majority of stars in all but the outermost fields have characteristic ages and metallicities that differ substantially from those associated with a classical halo ( e.g. bellazzini et al . 2003 ; brown et al . 2007 ; richardson et al . 2009 ; tanaka et al . 2010 ) . in addition to classical halo stars and tidal debris , brown et al . ( 2007 ) argue that the extraplanar regions of m31 also contain stars that formed in the disk of m31 , and were displaced during intermediate epochs in a merger event . evidence has been presented in this paper that a similar event may have happened in ngc 253 , probably within the past few 100 myr . if ngc 253 evolves in isolation in the future and does not experience another interaction , which seems likely given its isolation , then the diffuse extraplanar component will evolve passively , slowly fading and becoming less conspicuous ; the differences between the old populations that have been in place since the initial formation of ngc 253 and the diffuse extraplanar component that formed recently will thus become less obvious , as the main sequence turn - off of the most recently formed stars dims . the end result will be a mix of old and intermediate age stars smilar to what is seen in the outer regions of m31 today . despite the obvious differences in the evolution of ngc 253 and m31 , the present day ngc 253 may provide a glimpse of a younger m31 .

near - infrared images obtained with wircam on the canada - france - hawaii telescope are used to investigate the recent history of the nearby sculptor group spiral ngc 253 , which is one of the nearest starburst galaxies . a large population of red supergiants is also found in the north east portion of the disk and , with the exception of the central 2 kpc , this area appears to have been the site of the highest levels of star - forming activity in the galaxy during the past @xmath3 gyr . ( 2005 ) may be one manifestation of such activity . bright agb stars , including cool c stars that are identified based on their @xmath4 colors , are detected out to 15 kpc above the disk plane , and these are part of a diffusely distributed , flattened extraplanar component . additional evidence of a diffuse , extraplanar stellar component that contains moderately young stars comes from archival galex images . it is suggested that the disk of ngc 253 was disrupted by a tidal encounter with a now defunct companion . this encounter introduced asymmetries that remain to this day , and the projected distribution of stars in and around ngc 253 suggests that the companion had an orbit that was prograde and moderately inclined to the ngc 253 disk . the star - forming history of the extraplanar stars suggests that they either originated in the ngc 253 disk , or in a gas - rich companion . in the latter case the companion must have had an initial m@xmath5 in order to produce the more - or - less continuous star - forming history that is suggested by the stellar content .

near - infrared images obtained with wircam on the canada - france - hawaii telescope are used to investigate the recent history of the nearby sculptor group spiral ngc 253 , which is one of the nearest starburst galaxies . bright agb stars are traced out to projected distances of @xmath0 26 kpc ( @xmath1 disk scale lengths ) along the major axis . the distribution of stars in the disk is lop - sided , in the sense that the projected density of agb stars in the north east portion of the disk between 10 and 20 kpc from the galaxy center is @xmath2 dex higher than on the opposite side of the galaxy . a large population of red supergiants is also found in the north east portion of the disk and , with the exception of the central 2 kpc , this area appears to have been the site of the highest levels of star - forming activity in the galaxy during the past @xmath3 gyr . it is argued that such high levels of localized star formation may have produced a fountain that ejected material from the disk , and the extraplanar hi detected by boomsma et al . ( 2005 ) may be one manifestation of such activity . diffuse stellar structures are found in the periphery of the disk , and the most prominent of these is to the south and east of the galaxy . bright agb stars , including cool c stars that are identified based on their @xmath4 colors , are detected out to 15 kpc above the disk plane , and these are part of a diffusely distributed , flattened extraplanar component . comparisons between observed and model luminosity functions suggest that the extraplanar regions contain stars that formed throughout much of the age of the universe . additional evidence of a diffuse , extraplanar stellar component that contains moderately young stars comes from archival galex images . it is suggested that the disk of ngc 253 was disrupted by a tidal encounter with a now defunct companion . this encounter introduced asymmetries that remain to this day , and the projected distribution of stars in and around ngc 253 suggests that the companion had an orbit that was prograde and moderately inclined to the ngc 253 disk . the star - forming history of the extraplanar stars suggests that they either originated in the ngc 253 disk , or in a gas - rich companion . in the latter case the companion must have had an initial m@xmath5 in order to produce the more - or - less continuous star - forming history that is suggested by the stellar content . the ages of the youngest extraplanar stars suggests that the event that produced the extraplanar population , and presumably induced the starburst , occured within the past @xmath6 gyr . = 1.0 cm

hep-th0404054

i

there are different examples of noncommutative theories , we here concentrate on the case where noncommutativity is described by a constant parameter @xmath5 . the commutation relations among the coordinates read @xmath6\equiv x^\mu\*x^\nu - x^\nu\ * x^\mu = i\th^{\mu\nu}$ ] , where the star product between functions @xmath7 is given by @xmath8 . we do not claim that spacetime has exactly this noncommutativity , rather we are interested in investigating a mathematically sound gauge theory based on this easiest noncommutative structure . general aspects of this noncommutative theory will then probably be in common with more refined choices of @xmath1 . in particular the choice @xmath9 constant breakes the lorentz group in a spontaneous way ; in a bigger theory we would like to consider @xmath10 ( or the related @xmath11 field ) dynamical and not frozen to a constant value , thus recovering lorentz covariance . one can also consider gauge theories with @xmath1 nondynamical but frozen to a particular nonconstant value , linear in the coordinates , such that one has a ( kappa ) deformed poincar symmetry , see @xcite . using seiberg - witten map @xcite , that relates commutative gauge fields to noncommutative ones in such a way that commutative gauge transformations are mapped in nc gauge transformations , one can construct nc gauge theories with arbirary gauge groups @xcite . these theories are invariant under both commutative and noncommutative gauge transformations . along these lines noncommutative generalizations of the standard model and gut theories have been studied @xcite . the sw map and the @xmath12 product allow us to expand these noncommutative actions order by order in @xmath1 and to express them in terms of ordinary commutative fields so that one can then study the physics properties of these @xmath1-expanded commutative actions , see for ex . it turns out that given a commutative ym theory , sw map and commutative / noncommutative gauge invariance are in general not enough in order to single out a unique noncommutative generalization of the original ym theory . one can follow different criteria in order to select a specific noncommutative generalization . we here focus on a classical analysis , in particular imposing the constraint that the noncommutative generalization of the standard model should be compatible with noncommutative gut theories . another issue would be to single out a noncommutative sm or gut that is well behaved at the quantum level . we refer to the problems relative to renormalization , see for ex . @xcite . on the other hand chiral gauge anomalies are absent in these models @xcite . in this talk , following @xcite , we present a general study of the ambiguities that appear when constructing ncym theories . we then see that at first order in @xmath1 there is no ambiguity in @xmath0 ncym theory . in particular no triple gauge bosons coupling of the kind @xmath13 is present . we further study the noncommutative sm compatible with @xmath0 . we next study the reality , hermiticity , charge conjugation , parity and time reversal properties of the sw map and of @xmath1-expanded ncym theories . this constraints the possible freedom in the choice of a `` good '' sw map . in @xcite the @xmath3 properties of ncqed were studied assuming the usual @xmath14 and @xmath15 transformations also for noncommutative fields . we here show that the usual @xmath3 transformation on commutative spinors and nonabelian gauge potentials imply , via sw map , the same @xmath3 transformations for the noncommutative spinors and gauge potentials . we also see that @xmath16 is always a symmetry of noncommutative actions . in @xcite @xmath16 is studied more axiomatically . the reality property of the sw map is then used to analyze the difference between the sm in @xcite and the gut inspired sm proposed here . it is a basic one , and can be studied also in a qed model . while in @xcite , and in general in the literature , left and right handed components of a noncommutative spinor field are built with the same sw map , we here use and advocate a different choice : if noncommutative left handed fermions are built with the @xmath17 sw map then their right handed companions should be built with the @xmath18 sw map ; this implies that both noncommutative @xmath19 and @xmath20 are built with the @xmath17 sw map . in other words , with this choice , noncommutativity does not distinguish between a left handed fermion and a left handed antifermion , but does distinguish between fermions with different chirality . this appears to be the only choice compatible with gut theories .

noncommutative generalizations of yang - mills theories using seiberg - witten map are in general not unique . we then present the noncommutative standard model compatible with @xmath0 gut . we next study the reality , hermiticity and @xmath3 properties of the seiberg - witten map and of these noncommutative actions at all orders in @xmath4 .

noncommutative generalizations of yang - mills theories using seiberg - witten map are in general not unique . we study these ambiguities and see that @xmath0 gut , at first order in the noncommutativity parameter @xmath1 , is unique and therefore is a truly unified theory , while @xmath2 is not . we then present the noncommutative standard model compatible with @xmath0 gut . we next study the reality , hermiticity and @xmath3 properties of the seiberg - witten map and of these noncommutative actions at all orders in @xmath4 . this allows to compare the standard model discussed in @xcite with the present gut inspired one .

astro-ph0501093

i

sequences of images made with the _ transition region and coronal explorer _ ( _ trace _ ) show that a small subset of large - scale loops appear to respond to nearby flares by exhibiting damped transverse oscillations ( e.g. , * ? ? ? * ; * ? ? ? damped doppler shift oscillations have also been detected over active regions with the solar ultraviolet measurements of emitted radiation ( sumer ) experiment on the _ solar and heliospheric observatory _ ( _ soho _ ) ( e.g. , * ? ? ? * ; * ? ? ? these doppler shifts are primarily observed in emission lines from ions formed at temperatures greater than 6 mk , and thus are probably associated with flare - like events . the study of these oscillations is fast developing into a new technology for diagnosing the the physical conditions in the loops and , hence , placing further constraints on possible coronal heating mechanisms ( e.g. , * ? ? ? * ; * ? ? ? detection of doppler shifts in high - temperature emission lines with sumer suggests that they might also be detectable with instruments capable of measuring doppler shifts in soft x - ray lines , such as the bragg crystal spectrometer ( bcs ) on the _ yohkoh _ spacecraft . @xcite have in fact detected some evidence for oscillations with a period of about 10 minutes in the position of the resonance line during the decay of a limb flare observed on 1980 november 13 with the solflex crystal spectrometer on the _ p78 - 1 _ satellite . in this letter i show that damped doppler shift oscillations are present in some of the flares observed with the bcs .

oscillations in solar coronal loops appear to be a common phenomenon . transverse and longitudinal oscillations have been observed with both the _ transition region and coronal explorer _ and extreme ultraviolet imaging telescope imaging experiments . damped doppler shift oscillations have been observed in emission lines from ions formed at flare temperatures with the solar ultraviolet measurements of emitted radiation spectrometer . these observations provide valuable diagnostic information on coronal conditions and may help refine our understanding of coronal heating mechanisms . the observations appear to be consistent with transverse oscillations .

oscillations in solar coronal loops appear to be a common phenomenon . transverse and longitudinal oscillations have been observed with both the _ transition region and coronal explorer _ and extreme ultraviolet imaging telescope imaging experiments . damped doppler shift oscillations have been observed in emission lines from ions formed at flare temperatures with the solar ultraviolet measurements of emitted radiation spectrometer . these observations provide valuable diagnostic information on coronal conditions and may help refine our understanding of coronal heating mechanisms . i have initiated a study of the time dependence of doppler shifts measured during flares with the bragg crystal spectrometer ( bcs ) on _ yohkoh_. this letter reports the detection of oscillatory behavior in doppler shifts measured as a function of time in the emission lines of and . for some flares , both lines exhibit damped doppler shift oscillations with amplitudes of a few km s@xmath0 and periods and decay times of a few minutes . the observations appear to be consistent with transverse oscillations . because the bcs observed continuously for almost an entire solar cycle , it provides numerous flare data sets , which should permit an excellent characterization of the average properties of the oscillations .

astro-ph0501093

r

figure [ fig : bcs_data ] shows the temporal behavior of the count rates and the physical parameters resulting from fits to the individual spectra for the and wavelength channels in one flare that exhibits damped oscillatory behavior . this c2.5 flare took place at s16w88 on 1992 october 2 , and is one of the nonocculted limb flares in the survey of occulted and nonocculted limb flares performed by @xcite . nonocculted flares in that study refers to events for which images obtained with the _ yohkoh _ soft x - ray telescope ( sxt ) showed that the footpoints of the flaring loops were not occulted by the solar limb . at the peak of the flare , the region of strong emission in the sxt images occupies only a few pixels above the solar limb , suggesting that the hot plasma detected with the bcs is confined to a relatively small volume . while the total count rate , temperature , emission measure , and nonthermal velocity show generally smooth behavior as a function of time , the doppler shift shows evidence of oscillatory behavior in both channels . in particular , the doppler shift in the channel appears to show evidence for a damped oscillation . to determine the characteristics of the oscillations observed in figure [ fig : bcs_data ] , i follow the example of earlier work on _ trace _ oscillations ( e.g. , * ? ? ? * ) and fit the observations with a combination of a damped sine wave and a polynomial background . for each channel i define a function of the form @xmath2 where @xmath3 is the trend in the background data . starting from an initial guess for the fit parameters , the data in each channel were fit to equation ( [ eq : sine_wave ] ) using levenberg - marquardt least - squares minimization ( e.g. , * ? ? ? for all the flares studied the number of terms needed for the background expression was generally one or two , although occasionally three terms produced a better fit . the doppler shift data shown in figure [ fig : bcs_data ] are sufficiently noisy that it is difficult to fit them with equation ( [ eq : sine_wave ] ) . since it is clear from the figure that the period of the sine wave is on the order of a few minutes , i have accumulated the bcs data for longer intervals by requiring that the minimum number of counts in a channel exceed 10,000 and that the accumulation time be at least 20 s. the top panels in figure [ fig : bcs_fits ] show the doppler shift data for the two channels accumulated in this manner . also plotted on the top panels is the best fit background trend . for the spectra , a two - term expression provided the best fit , while for , one term was sufficient . the bottom two panels of figure [ fig : bcs_fits ] show the background - subtracted data along with the best - fit damped sine wave . for both channels , only the regions between the vertical dashed lines were used in the fitting process . even with the longer accumulation time the data are still noisy , especially those from the channel . the fits to the data , however , do appear to be reasonable . reduced @xmath1 values are 5.8 and 1.2 for the and channels , respectively . table [ tab : results ] summarizes the fitting results . while the origin of time for the two channels was tied to the first fitted spectrum , the values in the table for have been adjusted to correspond to the same initial time used for the fits . the errors listed in the table correspond to the diagonal elements in the covariance matrix for the fits . examination of the results in the table shows that both bcs channels show evidence for the same oscillatory behavior in the doppler shift . this was generally the case with the other flares that showed damped oscillatory behavior .

i have initiated a study of the time dependence of doppler shifts measured during flares with the bragg crystal spectrometer ( bcs ) on _ yohkoh_. this letter reports the detection of oscillatory behavior in doppler shifts measured as a function of time in the emission lines of and . for some flares , both lines exhibit damped doppler shift oscillations with amplitudes of a few km s@xmath0 and periods and decay times of a few minutes .

oscillations in solar coronal loops appear to be a common phenomenon . transverse and longitudinal oscillations have been observed with both the _ transition region and coronal explorer _ and extreme ultraviolet imaging telescope imaging experiments . damped doppler shift oscillations have been observed in emission lines from ions formed at flare temperatures with the solar ultraviolet measurements of emitted radiation spectrometer . these observations provide valuable diagnostic information on coronal conditions and may help refine our understanding of coronal heating mechanisms . i have initiated a study of the time dependence of doppler shifts measured during flares with the bragg crystal spectrometer ( bcs ) on _ yohkoh_. this letter reports the detection of oscillatory behavior in doppler shifts measured as a function of time in the emission lines of and . for some flares , both lines exhibit damped doppler shift oscillations with amplitudes of a few km s@xmath0 and periods and decay times of a few minutes . the observations appear to be consistent with transverse oscillations . because the bcs observed continuously for almost an entire solar cycle , it provides numerous flare data sets , which should permit an excellent characterization of the average properties of the oscillations .

nucl-th0305030

i

quantum chromodynamics ( qcd ) is the fundamental theory of the strong interaction . qcd is an asymptotically free theory @xcite , i.e. , interactions between quarks and gluons become weaker as the mutual distance decreases or as the exchanged momentum increases . consequently , at very large temperatures and/or densities , the interactions which confine quarks and gluons inside hadrons should become sufficiently weak to release them @xcite . the phase where quarks and gluons are deconfined is termed the _ quark - gluon plasma _ ( qgp ) . lattice qcd calculations have established the existence of such a phase of strongly interacting matter at temperatures larger than @xmath0 mev and zero net - baryon density . depending on the number of quark flavors and the masses of the quarks , the transition between ordinary hadronic matter and the qgp could be a thermodynamic phase transition of first order , of second order , or simply a crossover transition . the qgp was certainly present in the evolution of the early universe . the early universe was very hot , but close to net - baryon free . in the opposite limit of small temperature and large baryon density , the qgp may exist even nowadays in the interior of compact stellar objects such as neutron stars . the main effort in present - day nuclear physics is to create the qgp under controlled conditions in the laboratory via collisions of heavy nuclei at ultrarelativistic energies @xcite . the temperatures and net - baryon densities reached in nuclear collisions depend on the bombarding energy . they interpolate between the extreme conditions of the early universe on one side and compact stellar objects on the other . if at all , the qgp is only transiently created in a nuclear collision ; free quarks and gluons will not be released . therefore , deciding whether a qgp was formed or not is not easy . detectors in the laboratory can only measure hadrons , leptons , or photons . the bulk of the particles emerging from a nuclear collision are hadrons with transverse momenta of order @xmath1 gev . they carry information about the final stage of the collision after hadronization of the qgp . the formation of the latter can only indirectly influence this final stage , for instance by modifying the collective dynamics of the system through a softening of the equation of state in the hadronization transition @xcite . very few hadrons are emitted with transverse momenta of the order of several gev . they arise from the fragmentation of jets and may carry information also about the earlier stages of the collision . of particular interest is the situation where the jet has to traverse hot and dense matter possibly formed in the collision and is quenched by multiple rescattering in the medium @xcite . from this `` jet - quenching '' process one may indirectly learn about the properties of the hot and dense environment . finally , leptons and photons only interact electromagnetically . once formed in the early stage of the collision , they leave the system unimpededly and carry information about this stage to the detector @xcite . the difficulty is to disentangle the thermal radiation from a hot , equilibrated qgp @xcite from the initial production of leptons and photons in the very first , highly energetic partonic collisions and from the thermal radiation of hot hadronic matter @xcite . in order to decide whether a qgp was formed , one has to have detailed knowledge about its properties . otherwise it is impossible to find an unambiguous signature for qgp formation in nuclear collisions . in this review , i present an overview of the _ thermodynamical properties _ of the qgp . section [ secphasediag ] contains a detailed discussion of the phase diagram of strongly interacting matter . the present status of knowledge is shown schematically in fig . [ phasediagramnm ] . depending on the temperature , @xmath2 , and the quark chemical potential , @xmath3 , strongly interacting matter may occur in three distinct phases : the hadronic phase , the qgp , and color - superconducting quark matter . the ground state of ( infinite ) nuclear matter is at @xmath4 mev . there is a line of first - order phase transitions emerging from this point and terminating in a critical endpoint at a temperature of order @xmath5 mev . at this point , the transition is of second order . this phase transition is the nuclear liquid - gas transition @xcite . to the left of the line nuclear matter is in the gaseous phase , and to the right in the liquid phase . above the critical endpoint , there is no distinction between these two phases . for temperatures below @xmath6 mev and quark chemical potentials below @xmath7 mev ( corresponding to net - baryon densities which are a few times the ground state density of nuclear matter ) , strongly interacting matter is in the hadronic phase . quite similar to the liquid - gas transition , there is a line of first - order phase transitions which separates the hadronic phase from the qgp and terminates in a critical endpoint where the transition is of second order . this endpoint is approximately at @xmath8 mev , cf . [ nonzeromu ] . for smaller quark chemical potentials ( smaller net - baryon densities ) , the transition becomes crossover , and there is no real distinction between hadronic matter and the qgp . as will be discussed in detail in sec . [ secphasediag ] , the position of the critical endpoint depends on the value of the quark masses . finally , at large quark chemical potential ( large baryon density ) and small temperature , quark matter becomes a color superconductor . there can be multitude of color - superconducting phases , depending on the symmetries of the order parameter for condensation of quark cooper pairs . the discussion in sec . [ secphasediag ] is qualitative and is meant to give an overview of the phase structure of strongly interacting matter at nonzero temperature and quark chemical potential . the discussion in the following sections is both more quantitative as well as technical and focusses on the properties of the qgp and color - superconducting quark matter . the early universe evolved close to the temperature axis in the phase diagram of strongly interacting matter . matter in the core of compact stellar objects , like neutron stars , is close to the quark chemical potential axis , at values of @xmath3 around 400 500 mev . nuclear collisions at bombarding energies around @xmath9 agev explore a region of temperatures and quark chemical potentials around @xmath10 mev . collisions at current rhic energies of @xmath11 agev are expected to excite matter in a region around and above @xmath12 mev . collision energies in between these two extremes cover the intermediate region and , in particular , may probe the critical endpoint . section [ lattqcd ] presents a review of lattice qcd . after a brief introduction to the basic principles , results on the order of the qcd phase transition , the equation of state of strongly interacting matter , the heavy quark free energy , and mesonic spectral functions are collected . for technical reasons , most lattice qcd calculations have been done at zero quark chemical potential . an extension to nonzero values of @xmath3 is difficult and has been started only fairly recently . first results will also be discussed . lattice qcd is in principle an exact method to solve qcd . if one had sufficiently large computer power , one could not only decrease the lattice spacing and increase the size of the system to come sufficiently close to the continuum and thermodynamic limit , one could also sample over a sufficiently large number of configurations to make the statistical errors arbitrarily small . however , one still has to interpret the results in physical terms . in this respect , analytic approaches to solve qcd have a certain advantage over lattice qcd . in an analytic approach , one has complete control over the physical assumptions entering the calculation . section [ seciii ] gives an overview of what is known about the qgp from analytic calculations . the most simple approach from a conceptual ( albeit not technical ) point of view is to determine the thermodynamical properties of the qgp by a perturbative computation of the qcd partition function in terms of a power series in the strong coupling constant , @xmath13 . this can be done up to terms of order @xmath14 . at order @xmath15 , the perturbative series breaks down @xcite , and the remaining nonperturbative contribution has to be determined , for instance , from a lattice qcd calculation . those terms of the perturbative series , which are analytically computable , are rapidly decreasing in magnitude at high temperatures where the strong coupling constant is small , @xmath16 . this gives rise to the hope that only the first few terms of the perturbative series are actually necessary to obtain physically reasonable values for the qcd partition function . for temperatures of order @xmath0 mev , however , @xmath17 and the perturbative series is obviously not convergent . therefore , one has tried other ways to compute the partition function , either by expanding around a nonperturbative ground state or by resumming certain classes of diagrams to improve the convergence properties of the perturbative series . in both approaches , quarks and gluons are considered as quasiparticles with a dispersion relation which is modified as compared to the one in the vacuum . still another approach is to construct an effective theory for qcd which can be solved exactly or at least within a many - body approximation scheme . all these approaches will be reviewed in sec . [ seciii ] . section [ csc ] contains an introduction to color superconductivity at large quark chemical potentials . in this case , analytic calculations are well under control , because corrections can be systematically computed in terms of powers of @xmath13 . after a derivation of the gap equation for the color - superconducting gap function , the excitation spectrum in a color superconductor is presented . the solution of the gap equation is discussed and the magnitude of the gap parameter is determined . as in ordinary superconductors , quark cooper pairs break up , if the thermal motion becomes too large . the critical temperature for the transition between the normal- and the superconducting phase is computed . finally , the properties of gluons and photons in color superconductors are discussed . section [ concloutl ] concludes this review with a brief summary of the material and an outlook towards future directions of research in this area . a lot of the material in this review can also be found in other places . the standard review for properties of hot and dense , strongly interacting matter is the seminal work of gross , pisarski , and yaffe @xcite . the contents as well as more recent developments have found their way into textbooks @xcite . for early reviews focussing on the properties of the qgp , see ref . an introduction to lattice qcd and recent results can be found in ref . @xcite . the present status of lattice qcd is also reviewed in ref . resummation techniques which attempt to compute the qcd partition function analytically are discussed in great detail in ref . @xcite . the present review tries to give a balanced overview of all subfields concerned with the equilibrium properties of the qgp . therefore , the presentation is not as detailed as in a more specialized review . on the other hand , i tried to explain the basics in somewhat greater detail than usually found in the literature . my hope is that in this way , this review will become useful for early - stage researchers working in both theory as well as experiment , and for all researchers who would like to get an overview of the theoretical activity related to equilibrium properties of the qgp . the only somewhat more specialized and thus more technical part is the section on color superconductivity . this field has seen a lot of activity only fairly recently , but there are already a couple of excellent reviews @xcite . these , however , focus mainly on the basics of the phenomenon of color superconductivity and its phenomenological implications . in contrast , sec . [ csc ] contains a very detailed discussion of how to compute properties of the quasiparticle excitations in a color superconductor in the weak - coupling limit . by clarifying some of the technical details , i hope to remove the obstacles that may prevent other researchers to enter this rapidly evolving and rather exciting new field of strongly interacting matter physics . due to space restrictions this review is forced to omit many things that could ( and possibly , should ) also have been said about strongly interacting matter at high temperature and/or density . fortunately , most of these have already been covered in review articles . these are , for instance , non - equilibrium properties of the qgp @xcite or the physics of instantons in non - abelian gauge theories @xcite . another important topic which is not mentioned in this work , but for which excellent reviews exist @xcite , are the experimental signatures for the qgp . recent developments in the field of color superconductivity are mainly focussed on deriving effective theories for quarks around the fermi surface . these greatly simplify calculations and allow to systematically study effects of nonzero quark masses , for details , see ref . @xcite . finally , the list of references is , necessarily , far from complete . i would like to apologize to all authors whose work should have been ( but was not ) mentioned . the units are @xmath18 . i work in euclidean space - time at nonzero temperature @xmath2 , i.e. , space - time integrals are @xmath19 , where @xmath20 is the 3-volume of the system . energy - momentum integrals are @xmath21 ; @xmath22 labels the matsubara frequencies @xmath23 for bosons and @xmath24 for fermions , @xmath25 . i denote 4-vectors with capital letters , but unless mentioned otherwise , retain a notation familiar from minkowski space : @xmath26 , where @xmath27 , and @xmath28 , where @xmath29 , with the metric tensor @xmath30 . 3-vectors @xmath31 have length @xmath32 and direction @xmath33 .

the phase diagram of strongly interacting matter is discussed , with emphasis on the quark - hadron phase transition and the color - superconducting phases of quark matter . lattice qcd results on the order of the phase transition , the thermodynamical functions , the heavy quark free energy , mesonic spectral functions , and recent results for nonzero quark chemical potential are presented . analytic attempts to compute the thermodynamical properties of strongly interacting matter , such as perturbation theory , quasiparticle models , finally , color - superconducting quark matter is considered in the limit of weak coupling . the gap equation and the excitation spectrum are derived . the solution of the gap equation , gap parameters in various color - superconducting phases , and critical temperatures for the transition to normal - conducting quark matter are presented . a summary of gluon and photon properties in color superconductors is given .

our current knowledge of the quark - gluon plasma in thermodynamical equilibrium is reviewed . the phase diagram of strongly interacting matter is discussed , with emphasis on the quark - hadron phase transition and the color - superconducting phases of quark matter . lattice qcd results on the order of the phase transition , the thermodynamical functions , the heavy quark free energy , mesonic spectral functions , and recent results for nonzero quark chemical potential are presented . analytic attempts to compute the thermodynamical properties of strongly interacting matter , such as perturbation theory , quasiparticle models , `` hard - thermal - loop '' ( htl)-resummed perturbation theory , the polyakov - loop model , as well as linear sigma models are discussed . finally , color - superconducting quark matter is considered in the limit of weak coupling . the gap equation and the excitation spectrum are derived . the solution of the gap equation , gap parameters in various color - superconducting phases , and critical temperatures for the transition to normal - conducting quark matter are presented . a summary of gluon and photon properties in color superconductors is given .

1601.06436

i

on the 25-th of november in 1915 , einstein presented his field equations , the basic equations of general relativity , to the prussian academy of sciences in berlin . this equation had a tremendous impact on physics , in particular on cosmology . the essence of the theory was expressed by wheeler by the words : _ spacetime tells matter how to move ; matter tells spacetime how to curve_. einsteins theory remained unchanged for about 40 years . then one started to investigate theories fulfilling mach s principle leading to a variable gravitational constant . brans - dicke theory was the first realization of an extended einstein theory with variable gravitational constant ( jordans proposal was not widely known ) . all experiments are , however , in good agreement with einstein s theory and currently there is no demand to change it . general relativity ( gr ) has changed our understanding of space - time . in parallel , the appearance of quantum field theory ( qft ) has modified our view of particles , fields and the measurement process . the usual approach for the unification of qft and gr to a quantum gravity , starts with a proposal to quantize gr and its underlying structure , space - time . there is a unique opinion in the community about the relation between geometry and quantum theory : the geometry as used in gr is classical and should emerge from a quantum gravity in the limit ( planck s constant tends to zero ) . most theories went a step further and try to get a space - time from quantum theory . then , the model of a smooth manifold is not suitable to describe quantum gravity , but there is no sign for a discrete space - time structure or higher dimensions in current experiments @xcite . therefore , we conjecture that the model of spacetime as a smooth 4-manifold can be used also in a quantum gravity regime , but then one has the problem to represent qft by geometric methods ( submanifolds for particles or fields etc . ) as well to quantize gr . in particular , one must give meaning to the quantum state by geometric methods . then one is able to construct the quantum theory without quantization . here we implicitly assumed that the quantum state is real , i.e. the quantum state or the wave function has a real counterpart and is not a collection of future possibilities representing some observables . experiments @xcite supported this view . then the wave function is not merely representing our limited knowledge of a system but it is in direct correspondence to reality ! then one has to go the reverse way : one has to show that the quantum state is produced by the quantization of a classical state . it is , however , not enough to have a geometric approach to quantum gravity ( or the quantum field theory in general ) . what are the quantum fluctuations ? what is the measurement process ? what is decoherence and entanglement ? in principle , all these questions have to be addressed too . here , the exotic smoothness structure of 4-manifolds can help finding a way . a lot of work was done in the last decades to fulfill this goal . it starts with the work of brans and randall @xcite and of brans alone @xcite where the special situation in exotic 4-manifolds ( in particular the exotic @xmath0 ) was explained . one main result of this time was the _ brans conjecture _ : exotic smoothness can serve as an additional source of gravity . i will not present the whole history where i refer to carl s article . here i will list only some key results which will be used in the following * exotic smoothness is an extra source of gravity ( brans conjecture is true ) , see asselmeyer @xcite for compact manifolds and sadkowski @xcite for the exotic @xmath0 . therefore an exotic @xmath0 is always curved and can not be flat ! * the exotic @xmath0 can not be a globally hyperbolic space ( see @xcite for instance ) , i.e. represented by @xmath2 for some 3-manifold . instead it admits complicated foliations @xcite . using non - commutative geometry , we are able to study these foliations ( the leaf space ) and get relations to qft . for instance , the von neumann algebra of a codimension - one foliation of an exotic @xmath0 must contain a factor of type @xmath3 used in local algebraic qft to describe the vacuum @xcite . * the end of @xmath0 ( the part extending to infinity ) is @xmath4 . if @xmath0 is exotic then @xmath4 admits also an exotic smoothness structure . clearly , there is always a topologically embedded 3-sphere but there is no smoothly embedded one . let us assume the well - known hyperbolic metric of the spacetime @xmath4 using the trivial foliation into leafs @xmath5 for all @xmath6 . now we demand that @xmath4 carries an exotic smoothness structure at the same time . then we will get only topologically embedded 3-spheres , the leafs @xmath5 . these topologically embedded 3-spheres are also known as wild 3-spheres . in @xcite , we presented a relation to quantum d - branes . finally we proved in @xcite that the deformation quantization of a tame embedding ( the usual embedding ) is a wild embedding so that the image @xmath7 is an infinite polyhedron or the triangulation needs always infinitely many simplices . ] . furthermore we obtained a geometric interpretation of quantum states : wild embedded submanifolds are quantum states . importantly , this construction depends essentially on the continuum , because wild embedded submanifolds admit always infinite triangulations . * for a special class of compact 4-manifolds we showed in @xcite that exotic smoothness can generate fermions and gauge fields using the so - called knot surgery of fintushel and stern @xcite . in the paper @xcite we presented an approach using the exotic @xmath0 where the matter can be generated ( like in qft ) . * the path integral in quantum gravity is dominated by the exotic smoothness contribution ( see @xcite or by using string theory @xcite ) . the paper is organized as follows . in the following three sections we will explain exotic 4-manifolds and motivate the whole approach by using the path integral for the einstein - hilbert action . here we will also present how to couple the matter and gauge fields to this theory . for a 4-manifold , there are two main invariants the euler and pontrjagin class which determine the main topological invariant of a 4-manifold , the intersection form . in section [ sec : action - induced - by - top ] , we will obtain the einstein - hilbert and holst action by using these two classes . at the first view , this section is a little bit isolated from the previous and subsequent sections but we will use this result later during the study of the scaling . in the main section [ sec : wild - embeddings ] , we will construct the foliation of an exotic @xmath0 of codimension ( equivalent to a lorentz structure ) . following connes , @xcite the leaf space is an operator algebra constructed from the geometrical information of the foliation ( holonomy groupoid ) . this operator algebra is a factor @xmath8 von neumann algebra and we will use the tomita - takesaki modular theory to uncover the structure of the foliation . it is not the first time that this factor was used for quantum gravity and we refer to the paper @xcite for a nice application . states in this operator algebra are represented by equivalence classes of knotted curves ( element of the kauffman bracket skein module ) . the reconstruction of the spatial space from the states gives a wild embedded 3-sphere as geometrical representation of the state . surprisingly , it fits with the properties of the exotic @xmath0 . if one introduces a global foliation of the exotic @xmath0 by a global time then one obtains a foliation into wild embedded 3-spheres . in contrast , if one uses a local but complicate foliation then this wild object can be omitted and one obtains a state given by a finite collection of knotted curves . interestingly , the operator algebra can be understood as observable algebra given by a deformation quantization ( turaev - drinfeld quantization @xcite ) of the classical observable algebra ( poisson algebra of holonomies a la goldman @xcite ) . in section [ sec : action - at - the - quantum - level ] , we will use the splitting of the operator algebra ( [ eq : crossed - product - factor - iii ] ) given by tomita - takesaki modular theory to introduce the dynamics ( see connes and rovelli @xcite with similar ideas ) . finally we will obtain a quantum action ( [ eq : quantum - action ] ) in the quantized calculus of connes @xcite . then the scaling behavior is studied in the next section . for large scales , the action can be interpreted as a non - linear sigma model . the renormalization group ( rg ) flow analysis @xcite gives the einstein equations for large scales . the short - scale analysis is much more involved , yielding for small fluctuations the einstein - hilbert action and a non - minimally coupled scalar field . in particular , we will obtain a @xmath9dimensional fractal structure . in section [ sec : some - properties ] we will present some direct consequences of this approach : the nonlinear graviton @xcite , a relation to lattice gauge field theory with a discussion of discreteness and the appearance of dimensional reduction from 4d to 2d . in section [ sec : where - does - fluctuation ] we will discuss the answer to a fundamental question : where does the quantum fluctuations come from ? the main result of this section can be written as : _ the set of canonical pairs ( as measurable variables in the theory ) forms a fractal subset of the space of all holonomies . then we can only determine the initial condition up to discrete value ( given by the canonical pair ) and the chaotic behavior of the foliation ( i.e. the anosov flow ) makes the limit not predictable . _ this interesting result is followed by a section where we will discuss the collapse of the wavefunction by the gravitational interaction by calculating the minimal decoherence time . furthermore we will discuss entanglement and the measurement process . in section [ sec : some - implications - for.cosmology ] we will list our work in cosmology which uses partly the results of this paper . in the last section [ sec : conclusion - and - open - questions ] , we will discuss some consequences and open questions . some mathematical prerequisites are presented in three appendices . this article is dedicated to my only teacher , carl h. brans for 20 years of collaboration and friendship . he is the founder of this research area . we had and will have many interesting discussions . carl always asked the right question and put the finger on many open points . during the 7 years of writing our book , we had a very fruitful collaboration and i learned so much to complete even this work . carl , i hope for many discussions with you in the future . i m very glad to count on your advice . happy birthday !

over the last two decades , many unexpected relations between exotic smoothness , e.g. exotic @xmath0 , and quantum field theory were found . some of these relations are rooted in a relation to superstring theory and quantum gravity . therefore one would expect that exotic smoothness is directly related to the quantization of general relativity . in this article we will support this conjecture and develop a new approach to quantum gravity called _ smooth quantum gravity _ by using smooth 4-manifolds with an exotic smoothness structure . in particular we discuss the appearance of a wildly embedded 3-manifold which we identify with a quantum state . this operator algebra can be understood as a deformation quantization of the classical poisson algebra of observables given by holonomies . this approach has some obvious properties : there are non - linear gravitons , a connection to lattice gauge field theory and a dimensional reduction from 4d to 2d . some cosmological consequences like the appearance of an inflationary phase are also discussed . at the end we will get the simple picture that the change from the standard @xmath0 to the exotic @xmath1 is a quantization of geometry .

over the last two decades , many unexpected relations between exotic smoothness , e.g. exotic @xmath0 , and quantum field theory were found . some of these relations are rooted in a relation to superstring theory and quantum gravity . therefore one would expect that exotic smoothness is directly related to the quantization of general relativity . in this article we will support this conjecture and develop a new approach to quantum gravity called _ smooth quantum gravity _ by using smooth 4-manifolds with an exotic smoothness structure . in particular we discuss the appearance of a wildly embedded 3-manifold which we identify with a quantum state . furthermore , we analyze this quantum state by using foliation theory and relate it to an element in an operator algebra . then we describe a set of geometric , non - commutative operators , the skein algebra , which can be used to determine the geometry of a 3-manifold . this operator algebra can be understood as a deformation quantization of the classical poisson algebra of observables given by holonomies . the structure of this operator algebra induces an action by using the quantized calculus of connes . the scaling behavior of this action is analyzed to obtain the classical theory of general relativity ( grt ) for large scales . this approach has some obvious properties : there are non - linear gravitons , a connection to lattice gauge field theory and a dimensional reduction from 4d to 2d . some cosmological consequences like the appearance of an inflationary phase are also discussed . at the end we will get the simple picture that the change from the standard @xmath0 to the exotic @xmath1 is a quantization of geometry . _ on the occasion of the 80-th birthday of carl h. brans _

1404.6693

m

the simulation calculations below treated a single ch@xmath0(ch@xmath1-o - ch@xmath1)@xmath2ch@xmath0 molecule in water by molecular dynamics , using parallel tempering@xcite to achieve enhanced sampling of chain conformations . we evaluated system sizes of @xmath20 = 1000 ( @xmath21 = 11 ) , and @xmath20 = 2000 ( @xmath21 = 21 , 31 ) . the chain molecules were represented by optimized potentials for liquid simulations ( opls - aa),@xcite and the spc / e model was adopted for water@xcite implemented with the gromacs 4.5.3 molecular dynamics simulation package.@xcite long - range electrostatic interactions were treated in standard periodic boundary conditions using particle mesh ewald with a cutoff of 0.9 nm . the nos - hoover thermostat maintained the temperature and hydrogen atom bond - lengths were constrained by the lincs algorithm . after energy minimization , density equilibration with @xmath22 md calculations established the constant volumes for each parallel tempering simulation . the parallel tempering spanned the 256 - 550k temperature range with 32 replicas ( for @xmath21 = 11 , and 21 cases ) and 40 replicas ( for @xmath21 = 31 ) . parallel tempering swaps were attempted at a rate of 100/ns , and the temperature grid resulted in a success rates of 15 - 25% . production calculations for each replica set were extended to 10 ns . limit ( eq . , dashed curves ) . the direct numerical simulation results are the solid curves . for the model eq . , the number of gaussian links , @xmath19 , was adjusted for agreement throughout a low-@xmath4 regime . in all cases here @xmath19 was about a third of the number of heavy atoms of ch@xmath0(ch@xmath1-o - ch@xmath1)@xmath2ch@xmath0 , _ i.e. , _ in coarse - grained models of these oligomers , coarsened monomers can represent about three effective - atoms for this characteristic . the local maxima for @xmath23 here correspond to @xmath24 . [ fig : fig5],width=307 ]

parallel - tempering md results for a ch@xmath0(ch@xmath1-o - ch@xmath1)@xmath2ch@xmath0 chain in water are exploited as a data - base for analysis of collective structural characteristics of the peo globule with a goal of defining models permitting statistical thermodynamic analysis of dispersants of corexit type . the chain structure factor , relevant to neutron scattering from a deuterated chain in neutral water ,

parallel - tempering md results for a ch@xmath0(ch@xmath1-o - ch@xmath1)@xmath2ch@xmath0 chain in water are exploited as a data - base for analysis of collective structural characteristics of the peo globule with a goal of defining models permitting statistical thermodynamic analysis of dispersants of corexit type . the chain structure factor , relevant to neutron scattering from a deuterated chain in neutral water , is considered specifically . the traditional continuum - gaussian structure factor is inconsistent with the simple @xmath3 behavior , but we consider a discrete - gaussian model that does achieve that consistency . shifting - and - scaling the discrete - gaussian model helps to identify the low-@xmath4 to high-@xmath4 transition near @xmath5 when an empirically matched number of gaussian links is about one - third of the total number of effective - atom sites . this short distance - scale boundary of 0.6 nm is directly verified with the @xmath6-space distributions , and this distance is thus identified with a natural size for coarsened monomers . the probability distribution of @xmath7 is compared with the classic predictions for both gaussian model and freely - jointed chains . @xmath8 , the contribution of the @xmath9-th chain segment to @xmath10 , depends on contour index about as expected for gaussian chains despite significant quantitative discrepancies which express the swelling of these chains in water . monomers central to the chain contour occupy the center of the chain globule . the density profiles of chain segments relative to their center of mass can show distinctive density structuring for smaller chains due close proximity of central elements to the globule center . but that density structuring washes - out for longer chains where many chain elements additively contribute to the density profiles . gaussian chain models thus become more satisfactory for the density profiles for longer chains .

1404.6693

c

chain structure factors , relevant to neutron scattering from a chain in neutral water , are compared in detail to a traditional continuum - gaussian model result . the most serious limitation of the traditional continuum - gaussian structure factor is the failure to match the trivially known @xmath3 limiting value . a discrete - gaussian model that is consistent with the correct @xmath3 value is considered . shifting - and - scaling the discrete - gaussian model helps to identify the low-@xmath4 to high-@xmath4 transition near @xmath5 when an empirically matched number of gaussian links is about one - third of the total number of effective - atom sites . the shifted - and - scaled discrete - gaussian model better identifies the transition from low-@xmath4 to high-@xmath4 behavior near @xmath49 , which thus provides a natural spatial size for the coarsened monomers . this short distance - scale boundary of 0.6 nm is directly verified with the @xmath6-space distributions . further testing of gaussian chain models for these systems shows that @xmath8 , the contribution of the @xmath9-th chain segment to @xmath10 , depends on contour index about as expected for gaussian chains despite quantitative discrepancies . the quantitative comparison expresses the swelling of these chains in water . monomers central to the chain contour are usually central to the chain globule . the density profiles of chain molecule segments relative to their center of mass can show distinctive density structuring for smaller chains due close proximity of central elements to the globule center . that density structuring washes - out for longer chains , and due to the coarsened length - scale @xmath50 , many chain elements then contributing additively to the density profiles . gaussian chain models thus become more satisfactory for the density profiles for longer chains .

the traditional continuum - gaussian structure factor is inconsistent with the simple @xmath3 behavior , but we consider a discrete - gaussian model that does achieve that consistency . shifting - and - scaling the discrete - gaussian model helps to identify the low-@xmath4 to high-@xmath4 transition near @xmath5 when an empirically matched number of gaussian links is about one - third of the total number of effective - atom sites . this short distance - scale boundary of 0.6 nm is directly verified with the @xmath6-space distributions , and this distance is thus identified with a natural size for coarsened monomers . the probability distribution of @xmath7 is compared with the classic predictions for both gaussian model and freely - jointed chains . @xmath8 , the contribution of the @xmath9-th chain segment to @xmath10 , depends on contour index about as expected for gaussian chains despite significant quantitative discrepancies which express the swelling of these chains in water . monomers central to the chain contour occupy the center of the chain globule . the density profiles of chain segments relative to their center of mass can show distinctive density structuring for smaller chains due close proximity of central elements to the globule center . but that density structuring washes - out for longer chains where many chain elements additively contribute to the density profiles . gaussian chain models thus become more satisfactory for the density profiles for longer chains .

parallel - tempering md results for a ch@xmath0(ch@xmath1-o - ch@xmath1)@xmath2ch@xmath0 chain in water are exploited as a data - base for analysis of collective structural characteristics of the peo globule with a goal of defining models permitting statistical thermodynamic analysis of dispersants of corexit type . the chain structure factor , relevant to neutron scattering from a deuterated chain in neutral water , is considered specifically . the traditional continuum - gaussian structure factor is inconsistent with the simple @xmath3 behavior , but we consider a discrete - gaussian model that does achieve that consistency . shifting - and - scaling the discrete - gaussian model helps to identify the low-@xmath4 to high-@xmath4 transition near @xmath5 when an empirically matched number of gaussian links is about one - third of the total number of effective - atom sites . this short distance - scale boundary of 0.6 nm is directly verified with the @xmath6-space distributions , and this distance is thus identified with a natural size for coarsened monomers . the probability distribution of @xmath7 is compared with the classic predictions for both gaussian model and freely - jointed chains . @xmath8 , the contribution of the @xmath9-th chain segment to @xmath10 , depends on contour index about as expected for gaussian chains despite significant quantitative discrepancies which express the swelling of these chains in water . monomers central to the chain contour occupy the center of the chain globule . the density profiles of chain segments relative to their center of mass can show distinctive density structuring for smaller chains due close proximity of central elements to the globule center . but that density structuring washes - out for longer chains where many chain elements additively contribute to the density profiles . gaussian chain models thus become more satisfactory for the density profiles for longer chains .

1506.02818

i

it was recently reported that over one year in a small los angeles business district , cars cruising for parking burned 47,000 gallons of gasoline and produced 730 tons of carbon dioxide @xcite . meanwhile , the consulting firm mckinsey recently claimed that the average car owner in paris spends four years of his or her life searching for a parking space @xcite . the parking assignment problem associated with electric vehicles becomes even more acute . due to the limited range of these vehicles , the marginal cost of expending energy to search for spaces may , in some cities , be prohibitively high . thus , there is a real and compelling societal and economic need to revisit parking . increases in car ownership , inadequate public and private parking facilities , and synchronised demand , have led to serious temporal mismatches in parking space supply and demand . finding a parking space at certain times of the day is a non - trivial challenge . furthermore , finding spaces is not only costly in terms of wasted time for the driver , but it also creates congestion and pollution affecting everyone . thus , improving parking improves both economic efficiency and environmental quality . indeed , already major companies and cities are responding to these challenges . for example , many city authorities , in order to safeguard resident on - street parking from people commuting to a city through the day , have initiated schemes such as resident permit parking , and a number of commercial initiatives have emerged in the parking area . sfpark and justpark provide examples of city authorities and companies investing heavily in parking research and products within a smart cities context . in this work , our objective is not to revisit prior work on the topic . rather , we propose a new solution that is widely applicable in cities . we consider two nearby entities that have complementary supply and demand , i.e. , there is a shortfall of parking space at one and a surplus at the other . _ we call the entity with a shortfall of parking a _ mini - city_. many examples come to mind : university campuses , technology parks , shopping centers , and government facilities located in the suburbs . in our work , we use the university campus as an example . the second entity is the area surrounding the mini - city . during business hours , while parking spaces are limited in the mini - city , many nearby residents leave home for work . thus , there is an opportunity for the mini - city to use these vacated parking spaces , as well as from schools , hotels , apartment complexes and so on . consequently , the mini - city has access to two classes of parking spaces : _ premium _ spaces , e.g. , those located on the university campus ; and _ secondary _ spaces located nearby and perhaps serviced by a shuttle . note that the secondary spaces are not owned by the mini - city but rather are rented from secondary parties or _ landlords_. given this basic scheme , we consider two specific design issues . first , we wish to guarantee a quality of service for the landlords by setting aside reserve spaces in the mini - city as contingency for events where secondary spaces are suddenly unavailable . second , we wish to ensure that the premium spaces are allocated optimally among _ users _ ( drivers ) while preserving each user s privacy .

first , given a quality of service requirement , how many spaces should be set aside as contingency during day - time for night - time users ? next , how can we replace the first - come - first - served access method by one that aims at optimal efficiency while keeping user preferences private ?

parking spaces are resources that can be pooled together and shared , especially when there are complementary day - time and night - time users . we answer two design questions . first , given a quality of service requirement , how many spaces should be set aside as contingency during day - time for night - time users ? next , how can we replace the first - come - first - served access method by one that aims at optimal efficiency while keeping user preferences private ?

1304.1918

r

invariant - mass distributions of the pion pairs for incident photon energies between 400 mev - 460 mev are summarized in fig . [ fig : invdiff ] . the distributions measured for pion pairs produced off quasi - free nucleons from the deuteron differ in shape and magnitude from those measured off free protons ( fig . [ fig : invdiff ] , top row ) . this may be partly attributed to fermi - smearing , but includes also differences in the elementary cross sections for protons and neutrons . this is important for comparisons of the nuclear data to model results , which have to rely on experimental input for the elementary cross sections . the data for carbon and lead from messchendorp et al . @xcite are in reasonable agreement with the present results for the neutral pairs ; but not for the mixed - charge channel . agreement between the @xmath19 data for calcium from bloch et al . @xcite and the present results is much better ( see fig . [ fig : invdiff2 ] ) . it had already been noticed that the @xmath19 data from references @xcite are probably in conflict because the mass dependence for the chain carbon - calcium - lead would have been very unnatural ( the magnitude of the calcium cross section normalized by mass number had been larger than both the carbon and lead data , but one would have expected it in between of them ) . the present measurement favors the previous results from bloch et al . @xcite with which they agree within systematic uncertainties . comparison of the invariant - mass distributions in fig . [ fig : invdiff ] shows , that for the @xmath18 and the @xmath19 pairs , strength shifts to small invariant masses for increasing mass of the nucleus . this general trend is certainly not related to properties of the @xmath9 meson , which does not couple to the mixed - charge channel . the effect can be studied in more detail with the help of the composite ratios defined by @xmath57 where @xmath58 are the invariant mass distributions and @xmath59 the total production cross sections for two nuclei with mass numbers @xmath60 and @xmath61 . results for incident - photon energies from 400 mev - 460 mev are summarized in fig . [ fig : ratio ] . they demonstrate that , at least in this energy range , the behavior of the invariant - mass distributions is almost identical for both isospin states , so that the dominant effect is most likely due to fsi of the pions with the nucleus . previous results @xcite for the composite ratio of carbon and lead indicated a stronger enhancement at low invariant masses for neutral pion pairs than for the mixed - charge pairs . however , comparison to the present invariant - mass distributions ( see fig . [ fig : invdiff ] ) suggests that this was due to statistical fluctuations , in particular in the lead data . using the lighter nuclei ( deuteron and @xmath26li ) as reference , the low - mass enhancement becomes larger , but in the same way for neutral and mixed - charge pairs . an estimate of how important fsi effects are for the pions can be deduced from the scaling of the cross sections with nuclear mass number @xmath62 . total cross sections as a function of incident photon energy , scaled by the mass number @xmath62 , are shown for both isospin states in the inserts of fig . [ fig : alpha ] . the scaling changes from threshold to higher incident photon energies . this behavior can be parameterized with the scaling coefficient @xmath63 from @xmath64 which is shown in fig . [ fig : alpha ] . their interpretation is straightforward . at incident photon energies close to the production threshold @xmath63 is close to unity , which means that the cross sections scale with the number of nucleons ( or the nuclear volume ) , indicating negligible losses due to pion absorption . the coefficient then drops as a function of @xmath65 and approaches 2/3 for beam energies between 500 mev and 600 mev , indicating a scaling proportional to the surface of the nuclei , which means strong absorption . this is expected from the absorption properties of nuclear matter for pions @xcite . nuclei are transparent for pions with kinetic energies below @xmath14 40 mev and ` black ' for pions with energies above @xmath14 100 mev , which may excite the @xmath66-resonance . in quasi - free kinematics , pions from pion pairs produced with incident photon energies around 500 mev ( 600 mev ) have kinetic energies around 50 mev ( 75 mev ) when the energy is symmetrically shared by the two pions ( up to 138 ( 150 ) mev for pions from extremely asymmetric energy distribution ) . the scaling behavior is similar for both isospin channels , so that comparable fsi effects are to be expected . the shapes of pion - pion invariant - mass distributions for different ranges of incident photon energies are compared in fig . [ fig : compinv ] . for both isospin channels , at the lowest incident photon energies , the distributions are similar for all nuclei . they basically agree with a fermi - smeared version of the elementary cross section average of proton and neutron cross sections , represented by the deuteron data . at higher incident photon energies they start to differ , and for fixed photon energy , the heaviest nuclei have the softest distributions . this general trend can be related to the increase of fsi with rising beam energy and rising mass . it can be easily understood that fsi tends to soften the distributions . two effects are important . inelastic scattering tends to decrease the kinetic energy of the pions and their mean - free path increases with decreasing energy . any effects due to in - medium modification of the @xmath9-meson can only be studied on top of the fsi effects , which requires detailed model descriptions of fsi . an efficient way to treat these ` trivial ' nuclear effects are transport - theoretical approaches @xcite . we compare typical invariant - mass distributions to the results of the giessen boltzmann - uehling - uhlenbeck ( gibuu ) model @xcite in figs . [ fig : invdiff ] and [ fig : invdiff2 ] . on an absolute scale , the production cross section for the neutral pairs is underestimated by the model at very low incident photon energies and agrees better at higher energies , while for the mixed - charge pairs agreement is good at low energies and becomes worse for the highest energies . these discrepancies are at least partly related to the uncertainty in the elementary input to the model ( the production cross sections off neutrons are not well known for most isospin channels ) . in order to facilitate the comparison of the shapes , rescaled versions of the model results are shown . the shapes of the invariant - mass distributions of the mixed - charge pairs agree for all discussed ranges of incident photon energy almost perfectly with the data . this demonstrates that for @xmath19 the observed evolution of the distributions with photon energy and atomic mass can be indeed explained by fsi . agreement is not as good for the neutral pairs where , at least for low incident photon energies , the measured distributions tend to be softer than the predicted ones , exhibiting additional strength at low invariant masses . however , this effect is not large and part of it is probably also related to the model input . the shape of the distribution measured for the deuteron target is softer than for the proton ( see fig . [ fig : invdiff ] ) and this effect is not included in the model .

results from a transport model calculation reproduce the shape of the invariant - mass distributions for the mixed - charge pairs better than for the neutral pairs , but also for the latter differences between model results and experiment are not large , leaving not much room for @xmath9-in - medium modification . , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,

photoproduction of @xmath0 and @xmath1 pairs from nuclei has been measured over a wide mass range ( @xmath2h , @xmath3li , @xmath4c , @xmath5ca , and @xmath6pb ) for photon energies from threshold to 600 mev . the experiments were performed at the mami accelerator in mainz , using the glasgow photon tagging spectrometer and a 4@xmath7 electromagnetic calorimeter consisting of the crystal ball and taps detectors . a shift of the pion - pion invariant mass spectra for heavy nuclei to small invariant masses has been observed for @xmath8 pairs but also for the mixed - charge pairs . the precise results allow for the first time a model - independent analysis of the influence of pion final - state interactions . the corresponding effects are found to be large and must be carefully considered in the search for possible in - medium modifications of the @xmath9-meson . results from a transport model calculation reproduce the shape of the invariant - mass distributions for the mixed - charge pairs better than for the neutral pairs , but also for the latter differences between model results and experiment are not large , leaving not much room for @xmath9-in - medium modification . , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,

1402.5922

i

consider modal logic as given by atomic propositions , boolean operations , and a unary box , together with its usual axiomatisation stating that box preserves finite meets . in @xcite , dunn answered the question of an axiomatisation of the positive fragment of this logic , where the positive fragment is given by atomic propositions , lattice operations , and unary box and diamond ( but no negation ) . here we seek to generalize this result from kripke frames to coalgebras for a weak pullback preserving functor . whereas dunn had no need to justify that the positive fragment actually _ adds _ a modal operator ( the diamond ) , the general situation requires a conceptual clarification of this step . and , as it turns out , what looks innocent enough in the familiar case is at the heart of the general construction . in the general case , we start with a functor @xmath4 . from @xmath5 we can obtain by duality a functor @xmath6 on the category @xmath7 of boolean algebras , so that the free @xmath8-algebras are exactly the lindenbaum algebras of the modal logic . we are going to take the functor @xmath8 itself as the category theoretic counterpart of the corresponding modal logic . how should we construct the positive @xmath5-logic ? dunn gives us a hint in that he notes that in the same way as standard modal logic is given by algebras over @xmath7 , positive modal logic is given by algebras over the category @xmath9 of ( bounded ) distributive lattices . it follows that the positive fragment of ( the logic corresponding to ) @xmath8 should be a functor @xmath10 which , in turn , by duality , should arise from a functor @xmath11 on the category @xmath1 of posets and monotone maps . the centrepiece of our construction is now the observation that any functor @xmath4 has a universal extension to a functor @xmath11 . theorem [ mainthm ] then shows that this construction @xmath12 indeed gives the positive fragment of @xmath8 and so generalizes dunn s theorem . an important observation about the positive fragment is the following : given any boolean formula , we can rewrite it as a positive formula with negation appearing only on atomic propositions . in other words , the translation @xmath13 from positive logic to boolean logic given by @xmath14 induces a bijection ( on equivalence classes of formulas taken up to logical equivalence ) . more algebraically , we can formulate this as follows . given a boolean algebra @xmath15 , let @xmath16 be the free boolean algebra generated by the set @xmath17 modulo the axioms of modal logic . given a distributive lattice @xmath18 , let @xmath19 be the free distributive lattice generated by @xmath20 modulo the axioms of positive modal logic . further , let us denote by @xmath21 the forgetful functor . then the above observation that every modal formula can be written , up to logical equivalence , as a positive modal formula with negations pushed to atoms , can be condensed into the statement that the ( natural ) distributive lattice homomorphism @xmath22 induced by equations - is an isomorphism . our main results , presented in sections [ sec : poscoalglog ] and [ sec : monotone_predicate_liftings ] , are the following . if @xmath23 is an extension of @xmath5 and @xmath24 are the induced logics , then @xmath25 exists . if , moreover , @xmath23 is the induced extension ( posetification ) of @xmath5 and @xmath5 preserves weak pullbacks , then @xmath13 is an isomorphism ( theorem [ mainthm ] ) . furthermore , in the same way as the induced logic @xmath8 can be seen as the logic of all predicate liftings of @xmath5 , the induced logic @xmath26 is the logic of all _ monotone _ predicate liftings of @xmath5 ( theorem [ thm : mon - lift ] ) . these results depend crucially on the fact that the posetification @xmath23 of @xmath5 is defined as a completion with respect to @xmath1-enriched colimits . we devote section [ sec : pos - functors ] to establishing some results on posetifications used later . we show that posetifications always exists ( theorem [ thm : posetification ] ) . moreover , we characterize those functors @xmath3 that arise as posetifications as the functors that preserve coinserters of ` truncated nerves of posets ' and discrete posets ( theorem [ thm : pres - nerves ] ) . we also establish properties of posetifications needed in section [ sec : poscoalglog ] , for example , that a functor @xmath27 preserves weak pullbacks if and only if its posetification preserves exact squares ( theorem [ thm : wpb_exsq ] ) . on the algebraic side , the move to @xmath1-enriched colimits guarantees that the modal operations are monotone . in section [ ak ] , and recalling ( * ? ? ? * theorem 4.7 ) stating that a functor @xmath10 preserves ordinary sifted colimits if and only if it has a presentation by operations and equations , we show that @xmath10 preserves _ enriched _ sifted colimits if and only if it has a presentation by _ monotone _ operations and equations ( theorem [ thm : presentmonop ] ) . to see the relevance of a presentation result specific to monotone operations , observe that in the example of positive modal logic it is indeed the case that both @xmath28 and @xmath29 are monotone . from the point of view of category theory the results of sections [ sec : pos - functors ] and [ ak ] are of independent interest . in addition to what we already discussed , we introduce the concept of functors @xmath3 with presentations in discrete arities . they generalise posetifications and are functors that arise as left kan extensions of functors @xmath30 along the discrete functor @xmath31 . they are characterised as those functors preserving coinserters of ` truncated nerves of posets ' ( theorem [ thm : discretearities ] ) . an important property of @xmath1-functors with presentations in discrete arities is that like @xmath0-functors but unlike general @xmath1-functors they preserve surjections ( proposition [ prop : t-pres - monot - surj ] ) . * acknowledgments*. the authors would like to thank the referees for their valuable suggestions .

his completeness result consists of an axiomatization that derives all modal formulas that are valid on all kripke frames and are built only from atomic propositions , conjunction , disjunction , box and diamond . in this paper , we provide a coalgebraic analysis of this theorem , which not only gives a conceptual proof based on duality theory , but also generalizes dunn s result from kripke frames to coalgebras for weak - pullback preserving functors . functors arising in this way are said to have a _ presentation in discrete arities_. in the case that @xmath2 is actually @xmath0-valued , we call the corresponding left kan extension @xmath3 its _ posetification_. a set functor preserves weak pullbacks if and only if its posetification preserves exact squares . a @xmath1-functor with a presentation in discrete arities preserves surjections . a functor @xmath3 is a posetification if and only if it preserves coinserters of truncated nerves of posets and discrete posets .

positive modal logic was introduced in an influential 1995 paper of dunn as the positive fragment of standard modal logic . his completeness result consists of an axiomatization that derives all modal formulas that are valid on all kripke frames and are built only from atomic propositions , conjunction , disjunction , box and diamond . in this paper , we provide a coalgebraic analysis of this theorem , which not only gives a conceptual proof based on duality theory , but also generalizes dunn s result from kripke frames to coalgebras for weak - pullback preserving functors . to facilitate this analysis we prove a number of category theoretic results on functors on the categories @xmath0 of sets and @xmath1 of posets : every functor @xmath2 has a @xmath1-enriched left kan extension @xmath3 . functors arising in this way are said to have a _ presentation in discrete arities_. in the case that @xmath2 is actually @xmath0-valued , we call the corresponding left kan extension @xmath3 its _ posetification_. a set functor preserves weak pullbacks if and only if its posetification preserves exact squares . a @xmath1-functor with a presentation in discrete arities preserves surjections . the inclusion @xmath2 is dense . a functor @xmath3 has a presentation in discrete arities if and only if it preserves coinserters of ` truncated nerves of posets ' . a functor @xmath3 is a posetification if and only if it preserves coinserters of truncated nerves of posets and discrete posets . a locally monotone endofunctor of an ordered variety has a presentation by monotone operations and equations if and only if it preserves @xmath1-enriched sifted colimits .

1304.4789

i

negative thermal expansion ( nte ) is a rare and counter - intuitive phenomenon found primarily in low density materials with crystal structures that are networks of linked coordination polyhedra . the study of these materials is not only of fundamental scientific importance , but also has many technological applications such as aerospace technologies @xcite , optics @xcite , and electronics @xcite . while much effort has been put into finding new materials and investigating the origin of nte in them , much less attention has been paid to the change in nte behaviour subject to heating and stress , which holds great importance for the possible applications of the material . for example , due to stresses and heating , problems such as phase transitions of the nte filler and thermal expansion misfit between the nte filler and matrix are always encountered in designed composites with tailored thermal expansion @xcite . in this paper , we conduct a simulation study of zn(cn)@xmath0 focusing on the pressure and temperature effects on its negative thermal expansion . we chose this material for several reasons . firstly , zn(cn)@xmath0 is a well - known representative nte material @xcite . it has a framework structure consisting of tetrahedral groups of atoms linked by diatomic rods of c n and has exceptionally large isotropic nte of @xmath1 mk@xmath2 ( twice as large as that of zrw@xmath0o@xmath3 @xcite ) . secondly , the material shows a variety of exotic properties in experiments @xcite , including reduction of its nte on heating , pressure - enhanced thermal contraction , and pressure - induced softening , none of which are fully understood . thirdly , with previous dft calculations of zn(cn)@xmath0 @xcite explaining the origin of nte of the material in terms of grneisen theory , it would be useful to draw a clear link between the values of the grneisen parameters in energy space and the structural vibrations in real space with full anharmonicity ( which should be important in such an nte system ) based on theoretically reproducing the aforementioned exotic properties . here , we have built a zn(cn)@xmath0 potential model based on first - principles calculations . lattice - dynamic calculations and large - scale molecular dynamics ( md ) simulations were carried out for the material using this model which was justified by comparing against the available experimental data . the results in both energy and real space provide us fundamental clues to understand the nte as well as the related exotic behaviours of zn(cn)@xmath0 .

the advantage of this study allows us to reproduce the exotic behaviours of the material , including the negative thermal expansion ( nte ) , the reduction of nte with elevated temperature , the pressure enhancement of nte and the pressure - induced softening . results of the study provide us detailed data to link the properties in the energy space and the real space , giving us insights to understand the properties and the connections between them .

pressure and temperature dependence of the negative thermal expansion in zn(cn)@xmath0 is fully investigated using molecular dynamics simulations with a built potential model . the advantage of this study allows us to reproduce the exotic behaviours of the material , including the negative thermal expansion ( nte ) , the reduction of nte with elevated temperature , the pressure enhancement of nte and the pressure - induced softening . results of the study provide us detailed data to link the properties in the energy space and the real space , giving us insights to understand the properties and the connections between them .

q-bio0603011

i

the biological functions of proteins are as much a function of particular motifs of peptide sequence as they are of the overall protein structure . it is of interest to the biologist to search for examples of convergent motifs as they are likely to indicate a functional role . while many approaches exist for finding longer sequence motifs ( 50 amino acids or more ) , finding relationships between short fragments ( 318 amino acids long ) of full protein sequences also promises great rewards in understanding novel aspects of protein structure and function . these relationships might be evolutionary in origin or might arise by convergence , that is , by acquisition of the same biological function in evolutionarily distant species . finding short motifs presents significant challenges because many of the apparent relationships between short fragments could have arisen by chance and thus have no functional significance . furthermore , most widely available tools for sequence database search and motif finding were designed with longer motifs in mind . for example , watt and doyle @xcite recently observed that the ncbi blast @xcite family of programs , the best known set of tools for searching biological sequence datasets , is not suitable for identifying shorter sequences with particular constraints and proposed a pattern search tool to find dna or protein fragments that match a given sequence or a pattern exactly . this paper outlines the protein fragment motif finder ( pmfind ) , a new tool that uses database search to identify the conserved short peptide motifs of a query sequence and associates them with the available functional annotations .

protein fragment motif finder ( pfmfind ) is a system that enables efficient discovery of relationships between short fragments of protein sequences using similarity search . pfmfind is freely available ( under a gpl licence ) for download from the web site of the centre for biodiscovery , victoria university of wellington , http://www.vuw.ac.nz/biodiscovery/publications/centre/pfmfind.aspx astojmir@uottawa.ca * pfmfind : a system for discovery of peptide homology and function * aleksandar stojmirovi@xmath0 , peter andreae@xmath1 , mike boland@xmath2 , + thomas william jordan@xmath3 , vladimir g. pestov@xmath4 .2 in @xmath5 department of mathematics and statistics , + university of ottawa , + 585 king edward ave . , ottawa , on k1n 6n5 , canada .2 in @xmath6 school of mathematics , statistics and computer science , + victoria university of wellington , + po box 600 , wellington , new zealand .2 in @xmath7 fonterra research centre , + private bag 11029 , palmerston north , new zealand .2 in @xmath8 school of biological sciences , + victoria university of wellington , + po box 600 , wellington , new zealand

protein fragment motif finder ( pfmfind ) is a system that enables efficient discovery of relationships between short fragments of protein sequences using similarity search . it supports queries based on score matrices and pssms obtained through an iterative procedure similar to psi - blast . pssm construction is customisable through plugins written in python . pfmfind consists of a gui client , an algorithm using an index for fast similarity search and a relational database for storing search results and sequence annotations . it is written mostly in python . all components communicate between themselves using tcp / ip sockets and can be located on different physical machines . pfmfind is available for unix and windows platforms . pfmfind is freely available ( under a gpl licence ) for download from the web site of the centre for biodiscovery , victoria university of wellington , http://www.vuw.ac.nz/biodiscovery/publications/centre/pfmfind.aspx astojmir@uottawa.ca * pfmfind : a system for discovery of peptide homology and function * aleksandar stojmirovi@xmath0 , peter andreae@xmath1 , mike boland@xmath2 , + thomas william jordan@xmath3 , vladimir g. pestov@xmath4 .2 in @xmath5 department of mathematics and statistics , + university of ottawa , + 585 king edward ave . , ottawa , on k1n 6n5 , canada .2 in @xmath6 school of mathematics , statistics and computer science , + victoria university of wellington , + po box 600 , wellington , new zealand .2 in @xmath7 fonterra research centre , + private bag 11029 , palmerston north , new zealand .2 in @xmath8 school of biological sciences , + victoria university of wellington , + po box 600 , wellington , new zealand

1002.0200

i

the relationship between energy and information has been investigated extensively in the context of computation energy cost including a modern analysis of maxwell s demon @xcite-@xcite . in this letter , we show a new energy - information relation from a different point of view . recently , it has been reported that energy can be transported by local operations and classical communication while retaining local energy conservation and without breaking causality @xcite-@xcite . such protocols are called quantum energy teleportation ( qet ) and are based on ground - state entanglement of many - body quantum systems including spin chains @xcite , cold trapped ions @xcite and quantum fields @xcite . by performing a local measurement on a subsystem a of a many - body system in the ground state , information about the quantum fluctuation of a can be extracted . because the post - measurement state is not the ground state in general , some amount of energy is infused into a as qet energy input during this measurement , and the ground - state entanglement gets partially broken . next , the measurement result is announced to another subsystem b of the many - body system at a speed much faster than the diffusion velocity of the energy infused by the measurement . soon after the information arrives at b , energy can be extracted from b as qet energy output by performing a local operation on b dependent on the announced measurement data . the root of the protocols is a correlation between the measurement information of a and the quantum fluctuation of b via the ground - state entanglement . due to the correlation , we are able to estimate the quantum fluctuation of b based on the announced information from a and devise a strategy to control the fluctuation of b. by the above - mentioned selected local operation on b , the fluctuation of b can be more suppressed than that of the ground state , yielding negative energy density around b in the many - body system . the concept of negative energy density has been investigated in quantum field theory for a long time @xcite . quantum interference among total energy eigenstates can produce various states containing regions of negative energy density , although the total energy remains nonnegative . the regions of negative energy density can appear in general many - body quantum systems by fixing the origin of the energy density such that the expectational value vanishes for the ground state . in spite of the emergence of negative energy density , the total energy also remains nonnegative for the general cases . in the qet protocols , during the generation of negative energy density at b , surplus positive energy is transferred from b to external systems and can be harnessed as the qet output energy . here it should be emphasized that this output energy existed not at a but at b _ even _ _ before _ the start of the protocol and was hidden inside the zero - point fluctuation of b. of course , this zero - point energy is not available by usual local operations for b. however , by using a local operation dependent on a s information , it becomes possible to dig out b s zero - point energy by pair creation of the positive output energy from b and the negative energy of b. hence , we do not need to hire any physical carrier of energy from a to b like electric currents and photons , at least , during short - time qet processes . needless to say , after the completion of qet process , the positive energy of a compensates for the negative energy of b during late - time free evolution of the many - body system . the amount of output energy from b is upper bounded by the amount of input energy to a. using the usual protocols of quantum teleportation , quantum states can be transported from one party to another by the consumption of shared entanglement between the two parties @xcite . as is well known @xcite , transfer of a large number of quantum states requires a large amount of consumption of shared entanglement as a physical resource . taking into account the fact , it seems natural for the qet protocols to expect that a large amount of teleported energy also requests a large amount of consumption of the ground - state entanglement between a and b. if such a non - trivial relation exists between teleported energy and breaking of ground - state entanglement by measurement , the relation may shed new light on the interplay between quantum physics and quantum information theory . in this letter , the first example of the energy - entanglement relation for a minimal qet model is presented . the minimal qet model is the smallest physical system for which non - trivial qet can be implemented ; this model consists of two qubits with an interaction of the ising spin chain in the presence of a transverse magnetic field . we explicitly show that for the minimal model , the consumption of entanglement between a and b during the measurement of a is lower bounded by a positive value that is proportional to the maximum amount of energy teleported from a to b. in addition , we obtain another inequality in which the maximum amount of energy teleported from a to b is lower bounded by a different positive value that is proportional to the amount of entanglement breaking between a and b by the measurement of a. these energy - entanglement inequalities are of importance because they help in gaining a profound understanding of entanglement itself as a physical resource by relating entanglement to energy as an evident physical resource .

protocols of quantum energy teleportation ( qet ) , while retaining causality and local energy conservation , enable the transportation of energy from a subsystem of a many - body quantum system to a distant subsystem by local operations and classical communication through ground - state entanglement . we prove two energy - entanglement inequalities for a minimal qet model . these relations help us to gain a profound understanding of entanglement itself as a physical resource by relating entanglement to energy as an evident physical resource . + + + + + _ department of physics , faculty of science , tohoku university , + sendai 980 - 8578 , japan + hotta@tuhep.phys.tohoku.ac.jp_

protocols of quantum energy teleportation ( qet ) , while retaining causality and local energy conservation , enable the transportation of energy from a subsystem of a many - body quantum system to a distant subsystem by local operations and classical communication through ground - state entanglement . we prove two energy - entanglement inequalities for a minimal qet model . these relations help us to gain a profound understanding of entanglement itself as a physical resource by relating entanglement to energy as an evident physical resource . + + + + + _ department of physics , faculty of science , tohoku university , + sendai 980 - 8578 , japan + hotta@tuhep.phys.tohoku.ac.jp_

1304.1800

i

dynamics of the quantum dot hybrid qubit is obtained from the schrieffer - wolff transformed effective hamiltonian in terms of effective exchange coupling interaction between pairs of electrons . spin dynamics in quantum dot have attracted wide attention in the scientific community both from experimental@xcite and theoretical@xcite point of view because of their long coherence times and potential scaling @xcite . several architectures have been proposed based on single @xcite , double @xcite and triple @xcite quantum dot , later implemented in gaas @xcite , si @xcite and insb @xcite nanostructures . in view of creating an architecture capable to assure the best compromise among fabrication , tunability , fast gate operations of one and two qubits , manipulability and scalability , hybrid qubits have been recently proposed @xcite . they consist of a double quantum dot with three electrons distributed during the operations between the two quantum dots , with at least one electron in each . the interest raised by this architecture is due to the possibility to obtain gate operations entirely implemented with purely electrical manipulations . this property enables much faster gate operations than using ac magnetic fields , inhomogeneous dc magnetic fields or mechanisms based on spin - orbit coupling . the heisenberg interaction which is the dominant mechanism of interaction between adjacent spins suffice for all the one- and two - qubits operations , removing the need of an inhomogeneous field which is required for instance in single - triplet qubits @xcite . not so surprisingly , such an architecture grants the same symmetries in spin space as the triple dot qubit proposed in ref.@xcite , but it is simpler and more compact to fabricate , as it requires only two dots instead of three . starting from the hubbard - like model , we derive a general effective hamiltonian for the hybrid qubit in terms of the spin operators of the three electrons and of their interactions , by defining a suitable projection operator that follows the method of schrieffer and wolff @xcite . the method here adopted enables us to obtain analytically the coupling constants between pairs of electrons under lesser restrictive conditions than those obtained in ref.@xcite , preserving an explicit dependence of all the parameters involved . the system is irrespective to the host material , whose properties are absorbed in the coupling coefficients . next , dynamics generated by the interaction terms is expressed . the heisenberg interaction should permit very fast gate operation , however by itself does not provide a universal gate . it can not generate any arbitrary unitary transformation on a collection of spin-1/2 qubits as it allows only rotations among states with the same quantum numbers . however , defining opportunely coded qubit states the heisenberg interaction alone is universal . the paper is organized as follows . section ii is devoted to the derivation of the effective hamiltonian for a single hybrid qubit and its dynamical behaviour , once realistic initial conditions are provided and a realistic implementation in silicon is studied in stationary conditions . in section iii the pictorial representation of the eigenvectors in the bloch sphere analyzing two limiting cases of interest , corresponding to the situation in which two electrons are confined in the right or in the left dot , is presented .

quantum dot hybrid qubits formed from three electrons in double quantum dots represent a promising compromise between high speed and simple fabrication for solid state implementations of single qubit and two qubits quantum logic ports . we derive the schrieffer - wolff effective hamiltonian that describes in a simple and intuitive way the qubit by combining a hubbard - like model with a projector operator method . as a result , the hubbard - like hamiltonian is transformed in an equivalent expression in terms of the exchange coupling interactions between pairs of electrons .

quantum dot hybrid qubits formed from three electrons in double quantum dots represent a promising compromise between high speed and simple fabrication for solid state implementations of single qubit and two qubits quantum logic ports . we derive the schrieffer - wolff effective hamiltonian that describes in a simple and intuitive way the qubit by combining a hubbard - like model with a projector operator method . as a result , the hubbard - like hamiltonian is transformed in an equivalent expression in terms of the exchange coupling interactions between pairs of electrons . the effective hamiltonian is exploited to derive the dynamical behaviour of the system and its eigenstates on the bloch sphere to generate qubits operation for quantum logic ports . a realistic implementation in silicon and the coupling of the qubit with a detector are discussed .

quant-ph0703138

i

in quantum information theory entanglement between parts of a system has been identified as the key resource that can possibly make quantum information processing more powerful than classical information processing . entanglement can also be a resource for long - distance quantum communication or distributed quantum computation , and it is at the heart of some quantum communication protocols . but entanglement is fragile under the influence of environment induced decoherence . all engineering hence thrives to better control and manipulate the quantum information stored in the system while keeping the detrimental effects of decoherence low . in nature , on the other hand , we mostly find less controllable systems , especially if the system size becomes macroscopic as in gases , fluids , solids or even biological systems . since these systems are usually open , noisy systems at possibly high temperatures one expects that environment induced decoherence will erase all entanglement between system degrees of freedom . this reasoning is true except for three cases . first , the environment and its coupling to the system could be special in a way that it creates rather than destroys entanglement . however , it is unlikely to find such an environment in nature where usually thermalization dominates , and we will only briefly touch upon the subject of such environments in this paper . second , if the system has an entangled ground state , as many solid state systems do , its thermal state will be entangled in a certain temperature range above zero by a continuity argument . coupling to a heat bath drives a system into its thermal state . but there is a temperature threshold for the bath above which the thermal state will be unentangled . third , the system might have a built - in entropy drain , meaning that the correlations with the environment are , by one way or another , erased such that the system can re - build entanglement through its quantum mechanical interactions . this entropy drain may even be local to exclude the trivial cases where entanglement is simply pumped " into the system , e.g. , by injecting fresh , entangled bell pairs . in @xcite we proposed such a local entropy drain in form of a reset mechanism , where system particles are randomly replaced by particles in some standard , mixed state of sufficiently low entropy . note that such a mechanism can not create entanglement , on the contrary , it erases any entanglement that might still be present between the particle that is reset and the rest of the system . only the interplay with the system hamiltonian can lead to entanglement in a steady state that is possibly far from thermodynamic equilibrium . this reset mechanism was studied for a toy model with two qubits , where analytic solutions could be obtained . also a multipartite scenario for a ( simplified ) gas model was discussed , and further generalizations were suggested . by gas - type systems we mean systems in which the decoherence processes act locally on the system particles , by strongly coupled systems we mean those where the decoherence processes act globally . to be more precise , local decoherence processes are those , which induce transitions between the eigenstates of the local , free hamiltonian alone , while global decoherence processes induce transitions between eigenstates of the total hamiltonian . in this paper we review the key idea of a reset mechanism but provide more in - depth material than in @xcite . we elaborate on the generalizations suggested in @xcite , namely on the influence of local entropy drains on the dynamics of entanglement and on the steady - state entanglement in gas - type systems as well as in strongly coupled systems . we prove that the master equation describing the evolution of the system coupled to a heat bath and subject to a reset mechanism is of lindblad form and hence generates a completely positive , i.e. , physical map . we analytically solve the master equation for small systems of two spins with special interaction hamiltonians , which enables us to illustrate the main features of the reset mechanism . in particular we show the following . 1 . steady - state entanglement in systems with reset mechanism is different from the entanglement in thermal states . 2 . in strongly coupled systems with constant coupling steady - state entanglement with reset can exist for higher temperatures than the entanglement in the thermal state , which is the steady state without reset . 3 . in gas - type systems steady - state entanglement with reset can exist even for arbitrary temperatures . these features are not due to the specially chosen interaction hamiltonians and decoherence processes . we demonstrate that the above properties are almost independent of both . one can also relax the conditions on the reset states and take mixed states with sufficiently low entropy instead of pure states . finally , a generalization to larger system sizes , possibly even with fluctuating particle numbers , still leads to similar results . hence , the reset mechanism is at the same time simple and generic . we remark that in cavity qed an incoherent generation of entanglement has been proposed , which bears resemblance to our work @xcite . there , an atom couples to two leaky optical cavities and is driven by a white noise field . this incoherent driving can , when the atom is finally traced out , result in entanglement between the cavity modes . entanglement is generated for intermediate cavity damping rates and intensities of the noise field , an effect labeled `` stochastic resonance '' in @xcite . we believe that this effect is more correctly interpreted as an example for a reset mechanism . in a subsequent work @xcite strongly related to @xcite , one single cavity entangles two atoms , giving yet another example for a reset mechanism even closer to the setups of this paper . the reset mechanism is certainly not a preferred way to actively protect entanglement and mostly can not even be compared to such strategies , but , because of its simplicity and generality , there is hope that such a mechanism may ultimately be identified in natural processes leading to an increased understanding whether entanglement can play a role in systems at high temperatures . the paper is organized as follows . we first concentrate on simple models with only two particles ( qubits ) . in section [ gasmodel ] we motivate the description by a master equation , explain in which cases the model is valid , and study several specific hamiltonians and noise channels analytically and others numerically . we also compare entangled steady states resulting from a reset mechanism to entangled steady states resulting from special choices of interaction hamiltonian and decoherence process . we show in section [ stronglycoupledmodel ] that we can find the same features in strongly coupled systems , and we give the conditions to be met by the reset mechanism such that entangled steady states can exist . then , in section [ multipartite ] , we extend the model to include more qubits and discuss the meaning of different kinds of entanglement that we use . finally we give a summary of the results in section [ summary ] .

quantum mechanical entanglement can exist in noisy open quantum systems at high temperature . a simple mechanism , where system particles are randomly reset to some standard initial state , can counteract the deteriorating effect of decoherence , resulting in an entangled steady state far from thermodynamical equilibrium . we point out in which way the entanglement resulting from such a reset mechanism is different from the entanglement that one can find in thermal states . we find that in gas - type systems , the reset mechanism can produce an entangled steady state for an arbitrary temperature of the environment , while this is not true in strongly coupled systems . but even then , the temperature range where one can find entangled steady states is typically much higher with the reset mechanism .

quantum mechanical entanglement can exist in noisy open quantum systems at high temperature . a simple mechanism , where system particles are randomly reset to some standard initial state , can counteract the deteriorating effect of decoherence , resulting in an entangled steady state far from thermodynamical equilibrium . we present models for both gas - type systems and for strongly coupled systems . we point out in which way the entanglement resulting from such a reset mechanism is different from the entanglement that one can find in thermal states . we develop master equations to describe the system and its interaction with an environment , study toy models with two particles ( qubits ) , where the master equation can often be solved analytically , and finally examine larger systems with possibly fluctuating particle numbers . we find that in gas - type systems , the reset mechanism can produce an entangled steady state for an arbitrary temperature of the environment , while this is not true in strongly coupled systems . but even then , the temperature range where one can find entangled steady states is typically much higher with the reset mechanism .

hep-th0703083

i

it is believed that in spite of the recent potential importance of magnetic monopoles@xcite,@xcite,@xcite and dyons @xcite towards the quark confinement problem @xcite of quantum choromodynamics , possible magnetic condensation of vacuum @xcite , cp - violation @xcite , their role as catalyst in proton decay @xcite and the current grand unified theories @xcite , the formalism necessary to describe them has been clumsy and manifestly non - covariant . keeping in view the potential importance of monopoles and the results of witten @xcite that monopoles are necessarily dyons , we @xcite have also constructed a self - consistent co - variant theory of generalized electromagnetic fields associated with dyons each carrying the generalized charge as complex quantity with its real and imaginary part as electric and magnetic constituents . on the other hand quaternions were invented by hamilton @xcite to extend the theory of complex numbers to three dimensions . maxwell s equations of electromagnetism were rewritten in terms of quaternions @xcite . finklestein et al @xcite developed the quaternionic quantum mechanics and adler @xcite described the theory of the algebraic structure of quantum choromodynamics for strong interactions . various aspects of quaternions are discussed by morita @xcite towards the kinematical structure of poincare gauge theory and the left - right weinberg - salam theory of quantum choromodynamics . we have also studied @xcite the quaternionic formulation for generalized field equations of dyons in unique , simpler and compact notations . quaternion non - abelian gauge theory has also been consistently discussed @xcite to maintain the structural symmetry between the theory of linear gravity and electromagnetism . it is also shown that quaternion formalism characterises the abelian and non - abelian gauge structures @xcite of dyons in terms of real and imaginary constituents of quaternion basis elements . altenatively , kravchenko @xcite and his coworkers have consistently analysed the maxwell s equations for time - dependent electromagnetic fields in homogeneous ( isotropic ) and chiral medium . extending this , we @xcite have also derived the generalised maxwells - dirac equation in the homogenous ( isotropic ) medium . it has been shown that the field equations of dyons also remains invariant under the duality transformations in isotropic homogeneous medium and the equation of motion reproduces the rotationally symmetric gauge invariant angular momentum of dyons . in order to extend the theory of monopoles and dyons in isotropic medium and consequently the relevance of quaternion formalism of dyons , in the present paper we have undertaken the study of the quaternion analysis of time dependent maxwell s equations in presence of electric and magnetic charges and the solution for the classical problem of moving sources are obtained in unique , simpler and consistent manner . quaternion forms of potential current , field equation and equation of motion are developed in compact manner and it is imphasized that the quantum equations in terms of quaternions are invariant under quaternion , lorentz and duality transformations . it has also been discussed that the quaternion analyticity of dyons in isotropic medium reproduces the results of kravchenko @xcite in the absence of magnetic monopole and accordingly this theory can be described symmetrically for pure monopole in the absence of electric charge or vice versa .

quaternion analysis of time dependent maxwell s equations in presence of electric and magnetic charges has been developed and the solutions for the classical problem of moving charges ( electric and magnetic ) are obtained in unique , simple and consistent manner . @xmath0department of physics + govt . p. g. college + pithoragarh -(ua ) , india @xmath1department of physics + kumaun university + s. s. j. campus + almora-263601 ( ua ) , india email:-@xmath0jgaria@indiatimes.com + @xmath1ps_bisht123@rediffmail.com + @xmath1 ops_negi@yahoo.co.in .

quaternion analysis of time dependent maxwell s equations in presence of electric and magnetic charges has been developed and the solutions for the classical problem of moving charges ( electric and magnetic ) are obtained in unique , simple and consistent manner . @xmath0department of physics + govt . p. g. college + pithoragarh -(ua ) , india @xmath1department of physics + kumaun university + s. s. j. campus + almora-263601 ( ua ) , india email:-@xmath0jgaria@indiatimes.com + @xmath1ps_bisht123@rediffmail.com + @xmath1 ops_negi@yahoo.co.in .

astro-ph9706049

i

the optical emission from low mass x - ray binaries ( lmxbs ) is generally dominated by the reprocessing of x - rays in the accretion disk and/or the mass donor ( see van paradijs & mcclintock 1995 for a review ) . the time history of the optical emission is thus a convolution of the x - ray intensity history with a function representing the spatial distribution of matter in the system . the most spectacular examples of this phenomenon are the optical novae accompanying soft x - ray transients , which can cause the optical counterpart to brighten by many magnitudes . of greater interest are those systems whose x - ray intensity histories are more regularly or sharply modulated . many lmxbs show periodic optical variability due to orbitally - modulated viewing of the x - ray heated mass donor , providing constraints on the binary inclination and the distribution of reprocessing material in the system ( see van paradijs & mcclintock 1995 and references therein ) . quasi - periodic oscillations ( qpos ) at various frequencies have been observed in both the x - ray and optical emission from the candidate black hole binary gx 3394 ( motch , ilovaisky , & chevalier 1982 ; motch et al . 1983 ; imamura et al . 1990 ) . correlated x - ray and optical bursts have been observed from several systems , and the time delay and smearing of the optical burst profiles with respect to the x - ray bursts have been used to probe the location and distribution of matter near the neutron star ( lewin , van paradijs , & taam 1993 ) . coherent optical pulsations have been detected from the lmxb pulsars her x-1 ( davidsen et al . 1972 ; middleditch & nelson 1981 ) , 4u 162667 ( ilovaisky , motch , & chevalier 1978 ; middleditch et al . 1981 ) , and gx 1 + 4 ( jablonski et al . 1997 ) , and likewise provide an important probe of the binary parameters and the distribution of reprocessing material in the system . the lmxb 4u 162667/kz tra consists of a 7.66 s pulsar accreting from an extremely low - mass companion in an ultracompact binary with a separation of @xmath4 lt - sec ( middleditch et al . 1981 ; levine et al . 1988 ) . the 7.66 s x - ray pulsations arise due to anisotropic accretion of matter on the surface of a rotating , highly - magnetized neutron star whose spin and magnetic dipole axes are misaligned . the spin frequency of the pulsar evolves on short ( @xmath5 yr ) time scales due to accretion torques ( chakrabarty et al . the optical counterpart has a strong ultraviolet excess ( mcclintock et al . 1977 ) , and optical pulsations are detected with the same frequency as the x - ray pulsations ( ilovaisky et al . the optical emission is understood as primarily due to reprocessing of the incident x - ray flux by material in the accretion disk and/or the binary companion s surface ( chester 1979 ; mcclintock et al . the system shows strong , correlated x - ray / optical flares every @xmath6 s that are of undetermined origin ( joss , avni , & rappaport 1978 ; mcclintock et al . 1980 ; li et al . a @xmath7 hz qpo has been detected in the x - ray emission ( shinoda et al . 1990 ; angelini et al . 1995 ) , and probably arises through an interaction between the pulsar s magnetosphere and the inner edge of the accretion disk ( alpar & shaham 1985 ; lamb et al . 1985 ) . high - sensitivity timing of the optical pulsations detected an additional weak , persistent pulsation in a lower - frequency sideband of the `` direct '' ( x - ray ) pulse frequency ( middleditch et al . this sideband was attributed to x - ray reprocessing on the surface of the companion , so that the 0.4 mhz downshift is due to the different effective pulsar rotation rate observed in the companion frame due to the binary orbit . the observed frequency shift implies a 42-min prograde orbit . x - ray timing measurements have repeatedly failed to detect periodic pulse arrival time delays or pulse frequency shifts due to a binary orbit , yielding an upper limit of @xmath8 lt - ms for the projected radius of the neutron star orbit ( levine et al . 1988 ; shinoda et al . 1990 ) . for a 42-min orbit , the x - ray timing limits imply a mass function @xmath9 , one of the smallest known for any stellar binary . this paper describes a program to confirm the persistent orbital sideband reported by middleditch et al . ( 1981 ) and also provides the first detailed study of the optical wavelength dependence of x - ray reprocessing in this system . as part of this program , the first example of an optical qpo in an x - ray pulsar system was discovered . a preliminary account of this work has appeared previously ( chakrabarty 1996 ) .

the optical pulsations , which are at the same frequency as the x - ray pulsations caused by rotation of the highly - magnetized accreting neutron star primary , are understood as reprocessing of the pulsed x - ray emission in the accretion disk or on the surface of the secondary . this is the first measurement of an optical qpo in an x - ray binary pulsar .

rapid _ ubvri _ photometry of the ultracompact low - mass x - ray binary ( lmxb ) pulsar 4u 162667/kz tra has detected 130.4 mhz ( 7.67 s ) optical pulsations in all five bands . the optical pulsations , which are at the same frequency as the x - ray pulsations caused by rotation of the highly - magnetized accreting neutron star primary , are understood as reprocessing of the pulsed x - ray emission in the accretion disk or on the surface of the secondary . the optical pulsed fraction is roughly 6% , independent of wavelength , indicating that the optical emission is dominated by x - ray reprocessing . a weaker ( 1.5% ) sideband , downshifted 0.395(15 ) mhz from the main optical pulsation , is also present . this is consistent with a previously reported sideband which was downshifted 0.4011(21 ) mhz from the main pulsation , corroborating the 42-min binary period proposed by middleditch et al . ( 1981 , apj , 244 , 1001 ) . a 0.048 hz optical quasi - periodic oscillation ( qpo ) , corresponding to a previously reported x - ray feature , was also detected in some of the observations , with a fractional rms amplitude of 35% . this is the first measurement of an optical qpo in an x - ray binary pulsar . i discuss constraints on the nature of the mass donor and show that mass transfer via a radiatively - driven wind is inconsistent with the optical data . i also review the basic theory of x - ray - heated accretion disks and show that such models provide a good fit to the optical photometry . if the effective x - ray albedo of lmxb accretion disks is as high as recently reported ( @xmath0 ) , then the optical data imply a distance of @xmath18 kpc and an x - ray luminosity of @xmath2 erg s@xmath3 . submitted june 1 , 1997 to the astrophysical journal

astro-ph9706049

r

absolute photometry of 4u 162667 on may 26 yielded the following magnitude and colors : @xmath13 , @xmath14 , @xmath15 , and @xmath16 . the individual magnitudes are given in table 2 . the @xmath17-band sky background observation was too short to allow determination of a reliable source magnitude , but the presence of 7.66-s @xmath17-band pulsations , in phase with those in the bluer bands ( see below ) , confirms that the source was detected in the @xmath17-band as well . assuming that the @xmath17-band pulsed fraction is also 6% ( as in the other optical bands ; see below ) , the source has @xmath18 . within the uncertainties , interstellar reddening can be neglected for this high latitude source , since the total galactic reddening in the direction of 4u 162667 is @xmath19 ( burstein & heiles 1982 ) . the @xmath20 magnitudes reported here are virtually identical to those measured on 1977 june 12 by mcclintock et al . ( 1977 ) , and they agree within 2@xmath21 with those measured on 1977 august 17 by grindlay ( 1978 ) . however , the present @xmath22-band measurement is 1.8(4 ) magnitudes brighter than previously reported by grindlay ( 1978 ) . the observed time series were transformed to the solar system barycenter frame using the jet propulsion laboratory de-200 solar system ephemeris ( standish et al . power spectra of the individual observations in all five bands showed strong 7.66 s pulsations , with a mean barycentric pulse frequency of 130.4398(7 ) mhz . this is consistent with the x - ray pulsation frequency measured at the midpoint of the ctio observations by the batse all - sky monitor on the _ compton gamma ray observatory _ ( chakrabarty et al . 1997 ) . to facilitate a study of the pulse shape and phase relationship of the optical pulsations at different wavelengths , a precise pulse phase ephemeris was derived from a subset of the batse observations ( 1995 may 9 1995 june 11 ) contemporaneous with the ctio observations . based on these data , the barycentric x - ray pulse phase during the ctio observations is well fit by @xmath23 where @xmath24 , @xmath25 hz , @xmath26 hz s@xmath3 , @xmath27 1995 may 27.5 tdb , and pulse phase is defined relative to the intensity minimum of the fundamental harmonic of the 2060 kev batse pulse profile . the ctio timing observations for each of the five filters were folded according to the timing model in equation ( 1 ) . the resulting pulse profiles , along with the batse 2060 kev pulse profile , are shown in figure 1 relative to the batse pulse phase . the mean optical pulse and the batse hard x - ray pulse agree in phase to within 5% ( i.e. , a relative time delay of @xmath28 s ) , consistent with previous measurements ( mcclintock et al . both the batse hard x - ray pulse and the optical pulse shapes have a dominant sinusoidal component , although the optical pulses clearly have additional harmonic content as well . the optical pulse shapes do not resemble any of the x - ray pulse shapes in the 213 kev range , all of which have an unusual and distinctive close double - peak structure ( levine et al . instead , the optical pulse shapes resemble the low - energy ( 12 kev ) and high - energy ( 1560 kev ) pulse shapes . this is consistent with previous observations by mcclintock et al . ( 1980 ) , who concluded that the 12 kev x - rays were chiefly responsible for the reprocessed optical emission . the pulsed fraction , independent of wavelength , is approximately 6% ( see table 2 ) , suggesting that the optical emission is dominated by x - ray reprocessing . figure 2 shows the fourier power spectrum of a 2-hour @xmath29-band observation ( run 15u ) . the spectrum has been rebinned into uniform logarithmic frequency intervals , the mean noise level due to poisson counting statistics subtracted off , and the power level normalized relative to the double - sided mean source power ( e.g. , miyamoto et al . in addition to the 130 mhz pulsation , a 0.048 hz qpo was also detected . this feature was fit with a lorentzian profile ( e.g. , shibazaki & lamb 1987 ) , @xmath30 where @xmath31 is the centroid frequency of the qpo and @xmath32 is its full width at half - maximum ( fwhm ) . the fractional root - mean - squared ( rms ) amplitude of the qpo was computed by integrating equation ( [ eq - qpo ] ) over the fwhm of the feature and taking the square root , yielding 3.4% for this observation . the qpo is also detected in the @xmath33 and @xmath22-band observations . the best - fit parameters for the qpo features are included in table 2 . these measurements provide the first detection of an optical qpo from an x - ray pulsar . a similar feature is observed at x - ray wavelengths ( shinoda et al . 1990 ; angelini et al . 1995 ; chakrabarty et al . 1997 , in preparation ) . for comparison , the fourier power spectrum of the 26 kev data from a 71 ks observation of 4u 162667 with the proportional counter array on the _ rossi x - ray timing explorer ( rxte ) _ is shown in figure 3 . this observation was made on 1996 february 11 . the qpo is clearly visible in the x - ray data with an rms strength of 6% , along with several harmonics of the coherent 7.66 s pulsation . ( the higher harmonics are very strong due to the very sharp 26 kev x - ray pulse shape of 4u 162667 . ) the _ rxte _ data will be discussed in further detail elsewhere ( chakrabarty et al . 1997 , in preparation ) . to study the detailed structure of the optical timing properties close to the pulsation frequency , an overresolved power spectrum was constructed by computing the fourier power @xmath34 at fractional bin intervals according to @xmath35 with @xmath36 , where @xmath37 is just the original time series @xmath38 multiplied by complex phase factors @xmath39 . note that while the @xmath40 shifted power spectrum bins @xmath41 are statistically independent of each other , they are _ not _ independent of the original power spectrum @xmath42 ( although the covariances are easily computed ; see , e.g. , jenkins & watts 1968 ) . generalizing this process , one can construct an @xmath43-times overresolved power spectrum by interleaving the bins from the original power spectrum and @xmath44 frequency - shifted power spectra . operationally , this is equivalent to padding the original @xmath40-point zero - mean time series with @xmath45 zeros and computing the power spectrum of the new @xmath46-point padded time series . use of an oversampled power spectrum gives more uniform frequency sensitivity at the expense of independent frequency bins , recovering fourier phase information which is normally lost when constructing the power spectrum from the fourier amplitudes . figure 4 shows a 5-times overresolved power spectrum of 4u 162667 in the immediate vicinity of the main pulsation . the power spectrum has been normalized relative to the mean noise power . to improve the signal - to - noise ratio , the power spectrum shown is the average of power spectra from three separate 1.8-hr observations ( runs 15u , 17b , and 23r ) . in addition to the fundamental pulsation at 130.4398(37 ) mhz , several other features are present . in considering these features , it is important to recall that the peaks due to periodic signals in a finite - length power spectrum are always accompanied by sidelobes . this can be understood by considering a finite time series as the product of an infinite data stream and a rectangular ( boxcar ) observation window function ( equal to unity during the observation and zero elsewhere ) . by the fourier convolution theorem , the fourier transform of this product is equal to the convolution of the fourier transforms of the infinite data stream and the observation window function ( e.g. , press et al . thus the power at frequency @xmath47 due to a sinusoidal signal with frequency @xmath48 in an ungapped observation of length @xmath49 is @xmath50 ^ 2,\ ] ] where @xmath51 is the power at the signal frequency . the dotted curve in figure 4 shows the fit of this function to the data ( with the expected mean noise level of unity added ) , assuming that @xmath52 mhz corresponds to the main pulsation peak . the expected sidelobe structure almost exactly accounts for the two symmetric sidelobes on either side of the main peak . however , after accounting for the expected sidelobe structure of the main pulsation , a residual power excess is clearly evident at @xmath53 mhz , downshifted 0.395(15 ) mhz from the main pulsation peak . this is consistent with the 0.4011(21 ) mhz shift for the lower sideband reported by middleditch ( 1981 ) . the amplitude of the sideband relative to the main pulsation is 25% ( compared to 20% measured by middleditch et al . 1981 ) , corresponding to a sideband pulsed fraction of 1.5% . to evaluate the statistical significance of this excess power , note that the powers in an average of three background - dominated power spectra obey ( within a constant scaling factor ) a @xmath54-distribution with six degrees of freedom . for a power spectrum normalized such that the mean noise power is unity , the probability of a noise fluctuation in a single bin exceeding a threshold power @xmath55 is @xmath56 thus , the observed excess power of 5.9 has a probability of @xmath57 of being due to a random fluctuation , making it significant at the 4.6@xmath21 level . accounting for the fact that all bins in the range 0.1290.132 hz were searched reduces the statistical significance to 4.0@xmath21 . it is especially striking to note that the frequency _ shift _ of the sideband agrees with that reported by middleditch et al . ( 1981 ) despite the fact that the actual value of the main pulsation frequency ( corresponding to the pulsar s spin ) has changed from 130.26 mhz to 130.44 mhz in the 15 years between the two observations ( chakrabarty et al . 1997 ) . our sideband detection strongly corroborates the 42-min binary period reported by middleditch et al . unfortunately , the signal - to - noise ratio of this detection is insufficient to permit a more detailed investigation of the binary parameters .

the optical pulsed fraction is roughly 6% , independent of wavelength , indicating that the optical emission is dominated by x - ray reprocessing . this is consistent with a previously reported sideband which was downshifted 0.4011(21 ) mhz from the main pulsation , corroborating the 42-min binary period proposed by middleditch et al .

rapid _ ubvri _ photometry of the ultracompact low - mass x - ray binary ( lmxb ) pulsar 4u 162667/kz tra has detected 130.4 mhz ( 7.67 s ) optical pulsations in all five bands . the optical pulsations , which are at the same frequency as the x - ray pulsations caused by rotation of the highly - magnetized accreting neutron star primary , are understood as reprocessing of the pulsed x - ray emission in the accretion disk or on the surface of the secondary . the optical pulsed fraction is roughly 6% , independent of wavelength , indicating that the optical emission is dominated by x - ray reprocessing . a weaker ( 1.5% ) sideband , downshifted 0.395(15 ) mhz from the main optical pulsation , is also present . this is consistent with a previously reported sideband which was downshifted 0.4011(21 ) mhz from the main pulsation , corroborating the 42-min binary period proposed by middleditch et al . ( 1981 , apj , 244 , 1001 ) . a 0.048 hz optical quasi - periodic oscillation ( qpo ) , corresponding to a previously reported x - ray feature , was also detected in some of the observations , with a fractional rms amplitude of 35% . this is the first measurement of an optical qpo in an x - ray binary pulsar . i discuss constraints on the nature of the mass donor and show that mass transfer via a radiatively - driven wind is inconsistent with the optical data . i also review the basic theory of x - ray - heated accretion disks and show that such models provide a good fit to the optical photometry . if the effective x - ray albedo of lmxb accretion disks is as high as recently reported ( @xmath0 ) , then the optical data imply a distance of @xmath18 kpc and an x - ray luminosity of @xmath2 erg s@xmath3 . submitted june 1 , 1997 to the astrophysical journal

astro-ph9706049

c

qpos in accretion - powered pulsars are widely believed to arise from interactions between the pulsar magnetosphere and the inner edge of an accretion disk . in the beat frequency model ( alpar & shaham 1985 ; lamb et al . 1985 ) , the qpo arises when inhomogeneous `` clumps '' of material at the inner edge of the disk are captured by the magnetosphere and accreted by the pulsar , producing a broad power spectral feature at the beat frequency @xmath58 between the keplerian frequency at the inner disk edge and the pulsar s spin frequency . [ an alternative explanation , the keplerian frequency model of van der klis et al . ( 1987 ) , predicts @xmath59 . however , it can only explain qpos where @xmath60 , and thus is not applicable in 4u 162667 . ] thus , the 0.048 hz x - ray qpo in 4u 162667 bolsters the premise that this is a disk - fed binary . the discovery of an optical qpo at the same frequency shows that a significant fraction of the optical luminosity from the binary simply mirrors the x - ray emission , and must therefore result from x - ray reprocessing . as noted by middleditch et al . ( 1981 ) , the existence of two distinct , persistent , coherent optical pulsation frequencies suggests that the reprocessing occurs in two separate sites , most likely the surface of the mass donor and the accretion disk . simultaneous x - ray and optical timing of these pulsations and the qpo may therefore provide a powerful probe of the geometry of the binary and physics of the accretion disk ( e.g. , arons & king 1993 ) . unfortunately , the batse hard x - ray measurements acquired simultaneously with the optical observations require @xmath61 d to detect the x - ray pulsations , making them useless for a correlative study on short time scales . however , more sensitive x - ray timing missions ( e.g. _ rxte _ ) are well suited to such a task if the observations can be coordinated with ground - based optical observations . a comparison of figures 2 and 3 gives a flavor of the kind of data sets that can be directly intercompared if measured simultaneously . ultraviolet timing observations with the _ hubble space telescope _ may also provide an important probe , as the reprocessing in the disk should be more efficient at these wavelengths than in the optical ( arons & king 1993 ; anderson et al . more generally , time - resolved ultraviolet / optical / infrared photometry may provide an important test for candidate multiwavelength counterparts in time - variable lmxbs whose companions remain unidentified . while x - ray binaries and cataclysmic variables with a hydrogen - rich mass donor can not reach orbital periods @xmath62 min ( paczynski & sienkiewicz 1981 ) , those with a hydrogen - depleted mass donor can evolve to extraordinarily short ( @xmath6310 min ) orbital periods while maintaining high mass transfer rates ( nelson , rappaport , & joss 1986 ) . few such systems are known , including the six am cvn cataclysmic variables ( see warner 1995 ) and the x - ray bursters 4u 182030 ( @xmath64 min ) and 4u 191605 ( @xmath65 min ) . the recently reported 20.6-min ultraviolet modulation in the x - ray burster 4u 1850087 is probably due to the same phenomenon ( homer et al . 1996 ) . with a 42-min binary period , 4u 162667 is clearly a member of this class as well ( levine et al . 1988 ) . in addition to the inferred 42-min binary period , there are several other constraints on scenarios for the mass donor in 4u 162667 . the stringent x - ray timing limit ( @xmath66 lt - ms ; levine et al . 1988 ; shinoda et al . 1990 ) on the projected radius of the pulsar orbit implies @xmath67 where @xmath68 is the mass ratio , @xmath69 is the companion mass , @xmath70 is the neutron star mass @xmath71 in units of @xmath72 , and @xmath73 is the binary period in units of 42 min . the _ a priori _ probability of observing a system within the inclination limit @xmath74 is given by @xmath75 . a second constraint is the assumption that the mass transfer in an ultracompact binary is driven by angular momentum losses via gravitational radiation ( e.g. , levine et al . . the resulting mass transfer rate will be ( e.g. , verbunt & van den heuvel 1995 and references therein ) @xmath76 where @xmath43 is the power - law exponent in the companion s mass - radius relation ( @xmath77 ) , and conservative mass transfer via roche lobe overflow has been assumed . since the bolometric x - ray flux from 4u 162667 has been measured ( @xmath78 erg @xmath79 s@xmath3 in the 0.560 kev band ; pravdo et al . 1979 ) , this also constrains the source distance and x - ray luminosity @xmath80 , where @xmath81 km is the neutron star radius and @xmath82 is the distance to the source . another constraint is a lower limit on @xmath83 from the observed spin history of the pulsar ( chakrabarty et al . if the pulsar is spinning up , then the maximum possible accretion torque on the neutron star will occur when the magnetospheric radius @xmath84 ( where the magnetic energy density is comparable to the kinetic energy density of the accreting matter ) is close to the corotation radius @xmath85 ( where the magnetic field lines move with the local disk velocity ) . this limit may be written as @xmath86 , where @xmath87 for a keplerian disk . however , the torque on the neutron star can be rewritten as @xmath88 where @xmath89 is the pulsar s moment of inertia ( ravenhall & pethick 1994 ) and @xmath90 is the spin frequency derivative a directly measurable quantity . noting that @xmath91 hz s@xmath3 was measured during the spin - up of 4u 162667 , chakrabarty et al . ( 1997 ) thus inferred that @xmath92 yr@xmath3 . given the measured x - ray flux , the @xmath83 limit requires @xmath93 kpc . in view of the source s high galactic latitude ( @xmath94 ) , the resulting distance out of the plane is also a consideration when contemplating mass donors . however , this need nt be a strong consideration , since it is plausible for neutron star lmxbs to have high velocities due to a supernova `` kick '' , leading to a considerable distance from the plane over the long x - ray lifetime of the source . indeed , the high - latitude ( @xmath95 ) lmxb pulsar her x-1/hz her is @xmath96 kpc distant , over 4 kpc out of the plane ( reynolds et al . 1997 ) . the possible types of roche - lobe - filling mass donor for 4u 162667 have been discussed previously by levine et al . ( 1988 ) and verbunt , wijers , & burm ( 1990 ) . i review and update those discussions here . there are three possible types of roche - lobe - filling donors for a 42-min neutron star binary . the first possibility is a @xmath97 helium or carbon - oxygen white dwarf . from equation ( [ eq - incl ] ) , the binary inclination for this case must be @xmath98 , with an _ a priori _ observation probability of 16% . the mass - radius relation for such a star is @xmath99 ( shapiro & teukolsky 1983 ) , so the mass transfer rate from equation ( [ eq - mdot ] ) is @xmath100 yr@xmath3 . this corresponds to a distance of about 1 kpc . although the this case has the most favorable inclination constraint of the roche - lobe - filling options ( due to the extremely small @xmath69 ) , the mass transfer rate driven by gravitational radiation alone is an order of magnitude below the minimum mass accretion rate inferred by chakrabarty et al . ( 1997 ) . the second roche - lobe - filling possibility is a @xmath101 hydrogen - depleted star which is not fully degenerate , with @xmath102 and an _ a priori _ probability of 1% . assuming @xmath103 , equation ( [ eq - mdot ] ) gives @xmath104 yr@xmath3 , corresponding to a distance of 3 kpc . these are identical to the lower limits on @xmath83 and @xmath82 inferred from the pulsar spin - up measurements , and thus are just consistent with the observations . finally , a @xmath105 roche - lobe - filling helium - burning star is also a possible donor for a 42-min neutron star binary . however , the small allowed inclination range ( @xmath106 ) has an _ a priori _ observation probability of only 0.03% , and the expected mass transfer rate ( @xmath107 yr@xmath3 ; savonije , de kool , & van den heuvel 1986 ) would require an unphysically large distance ( 36 kpc ) to be consistent with the observed x - ray flux . angelini et al . ( 1995 ) have proposed an alternative to a roche - lobe - filling donor . these authors detected an unusually strong complex of neon emission lines in the x - ray spectrum of 4u 162667 . since neon is a product of helium burning , angelini et al . ( 1995 ) suggest that the mass donor is a helium - burning star which underfills its roche lobe , transferring matter to the neutron star via a radiatively - driven wind . this possibility is of particular interest given the suggestion that the current spin - down of the pulsar is due to accretion from a retrograde disk ( nelson et al . 1997 ) , since formation of such a disk is much more plausible for wind accretion than for roche lobe overflow . however , the wind from a low - mass helium - burning star would not provide a high enough mass transfer rate to be consistent with the x - ray data , as is now shown . a mass of @xmath108 is required for core helium burning ( kippenhahn & weigert 1990 ) . a @xmath109 helium - burning donor would fill about 25% of its roche lobe ( eggleton 1983 ) and would have @xmath110 and an effective temperature @xmath111 k ( savonije et al . 1986 ) , yielding a blackbody spectrum consistent with or fainter than the optical photometry for distances @xmath112 kpc . more generally , helium - burning donors with @xmath113 would underfill the roche lobe and be consistent with or fainter than the optical measurements for somewhat larger distances , with @xmath114 and @xmath115 k. assuming a radiatively - driven wind similar to that observed in other hot stars , the wind mass loss rate with these parameters would be @xmath116 yr@xmath3 ( abbott 1982 ) . especially in light of the poor accretion efficiency expected for a wind - fed system ( @xmath117 ; e.g. , frank , king , & raine 1992 ) , this is several orders of magnitude too small to be consistent with the minimum accretion rate , @xmath118 yr@xmath3 . similar considerations seem to rule out any plausible donor transferring matter via a conventional radiatively - driven wind . on the other hand , a self - excited wind arising from x - ray heating of the mass donor might be a significant contributor to the mass transfer rate , whether or not the donor fills its roche lobe ( see tavani & london 1993 and references therein ) . it is instructive to consider whether a stellar spectrum can explain the optical photometry . the data can in fact be well fit by a single - temperature ( stellar ) blackbody spectrum , @xmath119 where @xmath120 is the flux density from the star per unit frequency @xmath47 , @xmath121 is the stellar radius , @xmath82 is the source distance , @xmath122 erg s is planck s constant , @xmath123 is the velocity of light , @xmath124 erg k@xmath3 is boltzmann s constant , and @xmath125 is the effective temperature of the star . the best - fit parameters are @xmath126 k and @xmath127 , so that @xmath128 kpc . a hydrogen - burning star with the correct temperature ( a main sequence or supergiant b star ) is obviously excluded both by the absurd ( @xmath129 kpc ) distance required and the infinitesimal _ a priori _ probability for the necessary binary inclination . a @xmath130 he - ms star with @xmath131 kpc would have the correct temperature and flux . however , as noted above , it would severely underfill its roche lobe and so probably could not transfer sufficient mass to the pulsar to explain the observed x - ray flux . in addition , the implied binary inclination for a 42-min orbit has an a priori probability of @xmath132 0.1% . however , assuming a typical white dwarf mass - radius relation , @xmath133 ( shapiro & teukolsky 1983 ) , we find @xmath134 kpc for a @xmath97 white dwarf . as noted above , such a star would just fill its roche lobe , and the expected mass transfer rate would be consistent with the observed x - ray flux . for such a close binary , x - ray heating would certainly dominate the intrinsic luminosity of the degenerate dwarf . assuming isotropic x - ray emission , we have @xmath135^{1/4 } = \left[\frac{l_x(1-\eta_*)}{4\pi\sigma a^2}\right]^{1/4 } \nonumber \\ & = & 2.1\times 10 ^ 4\ p_{42}^{-1/3}d_{\rm kpc}^{1/2}(1+q)^{-1/6}(1-\eta_*)^{1/4 } { \rm\ \ k } , \end{aligned}\ ] ] where @xmath136 is the binary separation , @xmath137 is the x - ray albedo of the white dwarf , and @xmath78 erg cm@xmath3 s@xmath3 has been used for the x - ray flux ( pravdo et al . thus , x - ray heating of a low mass wd would naively seem to provide a plausible model for the observed optical emission . unfortunately , this is an unrealistic model . the 0.04 hz qpo detected in the x - ray and optical data underscores the presence of an accretion disk ( e.g. , van der klis 1995 ) which must contribute significant optical luminosity . the flux from a geometrically thin , optically thick disk can be written as @xmath139 - 1},\ ] ] where @xmath140 is the disk s surface temperature as a function of mid - plane radius @xmath141 . given the x - ray timing limits , it is clear that @xmath142 . the outer disk may be assumed to cut off sharply at the tidal radius of the neutron star ( @xmath143 ; frank et al . 1992 ) , corresponding @xmath144 cm for 4u 162667 . the inner accretion disk should be disrupted by the pulsar s magnetosphere at roughly the neutron star s corotation radius , @xmath145 cm for a keplerian disk . ( strictly speaking , @xmath85 is an upper limit on @xmath146 , but the calculation is not sensitive to this quantity since most of the disk s optical emission comes from its outer parts . ) for an x - ray heated disk , the disk may be considered as consisting of up to three distinct regions : an innermost region powered primarily by internal viscous dissipation , a middle region of `` shallow '' x - ray heating , and an outer region of `` deep '' x - ray heating ( e.g. , cunningham 1976 ; arons & king 1993 ) . let us consider each of these regions in turn . the standard temperature profile for an unirradiated thin accretion disk is set by internal viscous dissipation ( shakura & sunyaev 1973 ; frank et al . 1992 ) @xmath147 where @xmath148 erg @xmath79 k@xmath149 s@xmath3 is the stefan - boltzmann constant , @xmath70 is the neutron star mass in units of 1.4 @xmath150 , @xmath151 is the mass accretion rate in units of @xmath152 yr@xmath3 , and @xmath153 is the mid - plane radius in units of @xmath154 cm . at sufficiently small radii , this internal heating will dominate over x - ray heating in setting the disk temperature . beyond a critical radius , however , x - ray heating of the disk surface will modify the temperature profile according to @xmath155 assuming that the disk is irradiated by a central x - ray point source , then we can write @xmath156 as @xmath157^{1/4 } \approx \left[\frac{l_x(1-\eta_d ) } { 4\pi\sigma r^2 } \left(\frac{dh}{dr } - \frac{h}{r}\right)\right]^{1/4 } , \label{eq - tx}\ ] ] where @xmath158 is the x - ray albedo of the disk , @xmath159 is the angle between the normal to the disk surface and the vector from the neutron star , and @xmath160 is the disk s scale height . thus , we see that the temperature profile due to x - ray heating is sensitive to the functional form of @xmath161 through the approximation for @xmath162 ( which assumes @xmath163 ) . in the shallow x - ray heating region , the surface temperature profile is set by x - ray heating but the _ central _ temperature of the disk is still set by internal viscous dissipation . thus , the disk thickness has the usual value for a standard unirradiated thin disk ( shakura & sunyaev 1973 ; frank et al . 1992 ) , @xmath164 where @xmath165 is an order unity dimensionless parametrization of the kinematic viscosity @xmath166 , @xmath167 is the isothermal sound speed , and @xmath168 is the mean molecular weight in units of the hydrogen atomic mass . ( note that @xmath169 for neutral hydrogen , 1/2 for ionized hydrogen , 4 for neutral helium , 2 for singly - ionized helium , and 4/3 for doubly - ionized helium . ) we thus find @xmath170 shallow x - ray heating will dominate internal viscous heating in setting the disk surface temperature when @xmath171 , which occurs at radii exceeding roughly @xmath172 cm . if @xmath173 , then x - ray heating will also dominate internal heating in setting the _ central _ temperature of the disk ( lyutyi & sunyaev 1976 ; spruit 1995 ) . here , @xmath174 is the disk s optical depth , given by @xmath175 for a standard @xmath165-disk ( frank et al . 1992 ) . in this region of deep x - ray heating , the vertical structure of the disk will not obey the @xmath176 relationship in equation ( [ eq - h98 ] ) , but will instead follow a @xmath177 power law ( e.g. , cunningham 1976 ; vrtilek et al . 1990 ; arons & king 1993 ) . however , deep x - ray heating will dominate over shallow heating only for radii exceeding roughly @xmath178 cm . in a binary as compact as 4u 162667 , the disk will terminate before deep heating becomes dominant , so that a combination of internal viscous heating and shallow x - ray heating [ equation ( 12 ) along with equations ( 11 ) and ( 15 ) ] should be valid over the entire disk . accounting for the presence of an x - ray heated accretion disk , it is clear that an x - ray heated low - mass white dwarf at a distance of 1 kpc is untenable for 4u 162667 , since the expected optical emission from the disk would be considerably brighter than the measured fluxes . instead , it is more appropriate to consider the opposite case of the disk providing most of the optical luminosity by fitting equations ( 10 ) and ( 12 ) along with equations ( 11 ) and ( 15 ) to the measured optical photometry . the free parameters for the fit are @xmath82 ( or , equivalently , @xmath179 ) and @xmath158 . as is evident from figure 5 , the x - ray heated disk model can easily fit the data . however , as shown in figure 6 , the optical data do not provide a strong joint constraint on @xmath82 and @xmath158 . ultraviolet observations will eventually provide a much stronger constraint , since the uv spectrum from an x - ray heated disk is much more sensitive to the values of @xmath179 and @xmath158 . in the absence of ultraviolet observations , it should be noted that de jong , van paradijs , & augusteijn ( 1996 ) have concluded that lmxb accretion disks have a very high effective x - ray albedo ( @xmath180 ) , based on observations of 4u 125469 , 4u 175533 , and sco x-1 . if this is the case , then the optical data constrain the distance to @xmath181 kpc ( 95% confidence ) , corresponding to an x - ray luminosity of @xmath182 erg s@xmath3 . lcccccl 15u & 1995 may 26 & 0408 & 2.0 & @xmath29 & no & yes ( strong detection ) + 17b & 1995 may 26 & 0638 & 1.8 & @xmath33 & yes & yes ( strong detection ) + 21i & 1995 may 27 & 0018 & 1.7 & @xmath17 & no & no ( clouds ) + 23r & 1995 may 27 & 0308 & 1.9 & @xmath22 & no & yes ( strong detection ) + 25v2 & 1995 may 27 & 0604 & 0.6 & @xmath183 & yes & no ( clouds ) + 29u & 1995 may 28 & 0001 & 0.7 & @xmath29 & yes & no ( clouds ) + 30u & 1995 may 28 & 0046 & 1.0 & @xmath29 & yes & yes + 32v & 1995 may 28 & 0224 & 1.0 & @xmath183 & yes & yes + 35u & 1995 may 28 & 0709 & 1.0 & @xmath29 & yes & yes + 36i & 1995 may 28 & 0813 & 1.0 & @xmath17 & yes & yes ( weak detection ) + lccccc source count rate ( count s@xmath3 ) & 137(2 ) & 122(2 ) & 111(4 ) & 177(3 ) & pulsed count rate ( count s@xmath3 ) & 7.9(3 ) & 6.9(3 ) & 7.0(5 ) & 11.8(5 ) & 25(2 ) sky count rate ( count s@xmath3 ) & 168(2 ) & 182(2 ) & 317(4 ) & 785(3 ) & 5405(30 ) magnitude & 17.50(29 ) & 18.70(24 ) & 18.68(15 ) & 18.68(26 ) & pulsed fraction & 5.8(2)% & 5.7(3)% & 6.3(5)% & 6.7(3)% & qpo fractional rms strength & 3.4% & 2.7% & & 1.9% & qpo centroid frequency ( hz ) & 0.048 & 0.049 & & 0.049 & qpo fwhm ( hz ) & 0.013 & 0.012 & & 0.009 & figure 1 : optical pulse profiles as a function of wavelength for 4u 162667 . also shown is the 2060 kev x - ray pulse profile measured contemporaneously by batse . two pulses are shown in each panel , and the pulse phase is plotted relative to the intensity minimum of the x - ray pulse . for the @xmath17-band optical and batse x - ray measurements , the intensity of the unpulsed ( dc ) component of the source emission was not measured . figure 2 : fourier power density spectrum of a 2-hour @xmath29-band observation ( run 15u ) of 4u 162667 , normalized relative to the mean source power . the dotted line indicates the noise power level due to poisson counting statistics , which has been subtracted off . a 0.048 hz quasi - periodic oscillation with 4.9% fractional rms amplitude is clearly detected , as is the 7.66-s coherent pulsation due to the neutron star s rotation . an underlying @xmath184 spectrum is measured on time scales @xmath185 s. figure 3 : fourier power density spectrum of a 71 ks 26 kev _ rxte_/pca observation of 4u 162667 on 1996 feb 11 , normalized relative to the mean x - ray source power . the dotted line indicates the noise power level due to poisson counting statistics , which has been subtracted off . although this power spectrum can not be directly compared to the optical power spectrum in figure 2 ( since they were not acquired contemporaneously ) , the overall similarities are obvious and bolster the idea that the optical emission is dominated by rapid x - ray reprocessing . several higher harmonics of the 0.1304 hz coherent pulsation are observed due to the highly non - sinusoidal x - ray pulse shape in the 26 kev band . figure 4 : a 5@xmath186 over - resolved fourier power spectrum of 4u 162667 in the vicinity of the coherent 7.66-s pulsation , normalized relative to the local noise power . the solid line is the average of three separate power spectra of 1.8-hr observations . the dotted line is a model of the main pulsation s expected sidelobe due to the finite length of the power spectrum . this model is able to explain the symmetric sidelobes on either side of the main pulsation . a residual sideband downshifted 0.395(15 ) mhz from the main pulsation ( 25% relative amplitude ) is also present , with a statistical significance of 4@xmath21 . this frequency shift is consistent with a @xmath187 s prograde binary orbit . figure 5 : optical ( _ ubvri _ ) photometry of 4u 162667 on 1995 may 26 . the solid curve indicates a typical x - ray heated disk solution . the particular solution shown assumed @xmath188 , @xmath189 kpc , @xmath190 cm , and @xmath191 cm . however , a range of values for @xmath158 and @xmath82 provide a good fit to the data ( see figure 6 ) . figure 6 : distance to 4u 162667 as a function of effective x - ray albedo of the disk , assuming that all the optical flux is due to an x - ray heated accretion disk with @xmath190 cm , and @xmath192 cm . the shaded region is consistent with the optical photometric data at the 95%-confidence level . based on observations of other lmxbs , de jong et al . ( 1996 ) conclude that @xmath0 . if this is correct , then the solutions allowed by the data must lie in the shaded region to the right of the vertical dotted line .

rapid _ ubvri _ photometry of the ultracompact low - mass x - ray binary ( lmxb ) pulsar 4u 162667/kz tra has detected 130.4 mhz ( 7.67 s ) optical pulsations in all five bands . a weaker ( 1.5% ) sideband , downshifted 0.395(15 ) mhz from the main optical pulsation , is also present . ( 1981 , apj , 244 , 1001 ) . a 0.048 hz optical quasi - periodic oscillation ( qpo ) , corresponding to a previously reported x - ray feature , i discuss constraints on the nature of the mass donor and show that mass transfer via a radiatively - driven wind is inconsistent with the optical data . i also review the basic theory of x - ray - heated accretion disks and show that such models provide a good fit to the optical photometry . if the effective x - ray albedo of lmxb accretion disks is as high as recently reported ( @xmath0 ) , then the optical data imply a distance of @xmath18 kpc and an x - ray luminosity of @xmath2 erg s@xmath3 . submitted june 1 , 1997 to the astrophysical journal

rapid _ ubvri _ photometry of the ultracompact low - mass x - ray binary ( lmxb ) pulsar 4u 162667/kz tra has detected 130.4 mhz ( 7.67 s ) optical pulsations in all five bands . the optical pulsations , which are at the same frequency as the x - ray pulsations caused by rotation of the highly - magnetized accreting neutron star primary , are understood as reprocessing of the pulsed x - ray emission in the accretion disk or on the surface of the secondary . the optical pulsed fraction is roughly 6% , independent of wavelength , indicating that the optical emission is dominated by x - ray reprocessing . a weaker ( 1.5% ) sideband , downshifted 0.395(15 ) mhz from the main optical pulsation , is also present . this is consistent with a previously reported sideband which was downshifted 0.4011(21 ) mhz from the main pulsation , corroborating the 42-min binary period proposed by middleditch et al . ( 1981 , apj , 244 , 1001 ) . a 0.048 hz optical quasi - periodic oscillation ( qpo ) , corresponding to a previously reported x - ray feature , was also detected in some of the observations , with a fractional rms amplitude of 35% . this is the first measurement of an optical qpo in an x - ray binary pulsar . i discuss constraints on the nature of the mass donor and show that mass transfer via a radiatively - driven wind is inconsistent with the optical data . i also review the basic theory of x - ray - heated accretion disks and show that such models provide a good fit to the optical photometry . if the effective x - ray albedo of lmxb accretion disks is as high as recently reported ( @xmath0 ) , then the optical data imply a distance of @xmath18 kpc and an x - ray luminosity of @xmath2 erg s@xmath3 . submitted june 1 , 1997 to the astrophysical journal

astro-ph9701093

c

as the observational techniques improve our ability to detect extremely faint sources , and higher redshift objects can be searched for to continue unravelling the history of galaxy formation , supernovae should become the brightest observable sources . these supernovae created the heavy elements that were expelled to the igm , and their progenitor stars are the most likely sources of the photons that reionized the universe . the expected rates of these supernovae , calculating under the assumption of a high baryon density ( @xmath68 ) , and an average metal production of @xmath21 , is as high as 1 supernova per square arc minute per year . to detect the supernovae , the flux limits of the faintest sources detectable with our telescopes will probably need to be pushed by another @xmath69 magnitudes , although the first examples might be discovered at brighter fluxes behind clusters of galaxies , using the lensing magnification . any low - mass stars that were formed in the first small galaxies where these supernovae took place should be observable today . we have argued that , if the imf in these galaxies was similar to the present one in our galactic disk , the population iii stars are likely to account for a large fraction of the stars in our galactic halo , although most of them should be in an as yet undetected outer halo with a shallower density profile than the known , inner stellar halo . allen , c. w. 1973 , _ astrophysical quantities _ ( london : athlone press ) burles , s. , & tytler , s. 1996 , submitted to science ( astroph 9603069 ) cen , r. , miralda - escud , j. , ostriker , j. p. , & rauch , m. 1994 , apj , 437 , l9 couchman , h. m. p. , & rees , m. j. , 1986 , mnras , 221 , 53 cowie , l. l. , gardner , j. p. , hu , e. m. , songaila , a. , hodapp , k .- w . , & wainscoat , r. j. 1994 , apj , 434 , 114 dekel , a. , & silk , j. 1986 , apj , 303 , 39 flynn , c. , gould , a. , & bahcall , j. n. 1996 , apj , 466 , l55 haiman , z. , rees , m. j. , & loeb , a. 1996 , apj , submitted ( astroph-9608130 ) hawkins , m. s. 1983 , mnras , 206 , 433 hernquist , l. , katz , n. , weinberg , d. h. , & miralda - escud , j. 1996 , apj , 457 , l51 hu , e. m. , & mcmahon , r. g. 1996 , nature , 382 , 231 lacy , m. , et al . 1994 , mnras , 271 , 504 madau , p. , meiksin , a. , & rees , m. j. 1996 , apj , submitted ( astroph 9608010 ) madau , p. , & shull , j. m. 1996 , , 457 , 551 mather , j. , & stockman , h. 1996 , nasa report . miralda - escud , j. , & fort , b. 1993 , apj , 417 , 5 miralda - escud , j. , cen , r. , ostriker , j. p. , & rauch , m. 1996 , apj , 471 , 582 morrison , h. l. 1993 , aj , 106 , 578 norris , j. , & hawkins , m. s. 1991 , apj , 380 , 104 paczyski , b. 1996 , ara&a , 34 , xxx rawlings , s. , lacy , m. , blundell , k. m. , eales , s. a. , bunker , a. j. , & garrington , s. t. 1996 , nature , 383 , 502 sackett , p. d. , morrison , h. l. , harding , p. , & boroson , t. a. 1994 , nature , 370 , 441 schmidt , m. 1965 , apj , 141 , 1295 schneider , d. p. , schmidt , m. , & gunn , j. e. 1991 , aj , 101 , 2004 scott , d. , & rees , m. j. 1990 , mnras , 247 , 510 songaila , a. , & cowie , l. l. 1996 , aj , in press ( astro - ph 9605102 ) spergel , d. n. , & hernquist , l. 1992 , apj , 397 , l75 steidel , c. c. , giavalisco , m. , pettini , m. , dickinson , m. , & adelberger , k. l. 1996 , apj , 462 , l17 theuns , t. , & warren , s. j. 1996 , submitted to mnras ( astro - ph 9609076 ) tytler , d. , fan , x .- m . , burles , s. , cottrell , l. , davis , c. , kirkman , d. , & zuo , l. 1995 , in qso absorption lines , ed . g. meylan , p. 289 tytler , d. , fan , x .- m . , & burles , s. 1996 , nature , 381 , 207 williams , r. , et al . 1996 , science with the hubble space telescope ii , eds . p. benvenuti , f. d. macchetto , & e. j. schreier ( baltimore : stsci ) , in press woosley , s. e. , & weaver , t. a. 1995 , apjs , 101 , 181 woosley , s. e. , & weaver , t. a. 1986 , ara & a , 24 , 205

we calculate that the rate of these supernovae is such that about one of them should be observable at any time per square arc minute . we also show that , under the assumption of a standard initial mass function , a significant fraction of the stars in the galactic halo should have formed in the early galaxies that reionized and enriched the igm , and which later must have merged with our galaxy .

recent evidence on the metal content of the high - redshift ly@xmath0 forest seen in quasar spectra suggests that an early generation of galaxies enriched the intergalactic medium ( igm ) at @xmath1 . we calculate the number of supernovae that need to have taken place to produce the observed metallicity . the progenitor stars of the supernovae should have emitted @xmath2 ionizing photons for each baryon in the universe , i.e. , more than enough to ionize the igm . we calculate that the rate of these supernovae is such that about one of them should be observable at any time per square arc minute . their fluxes are , of course , extremely faint : at @xmath3 , the peak magnitude should be @xmath4 with a duration of @xmath5 1 year . however , these supernovae should still be the brightest objects in the universe beyond some redshift , because the earliest galaxies should form before quasars and they should have very low mass , so their luminosities should be much lower than that of a supernova . we also show that , under the assumption of a standard initial mass function , a significant fraction of the stars in the galactic halo should have formed in the early galaxies that reionized and enriched the igm , and which later must have merged with our galaxy . these stars should have a more extended radial distribution than the observed halo stars .

0710.2451

i

the observations of high - redshift qso s @xcite and large - scale cmb polarization @xcite indicate that the intergalactic medium has been completely ionized by redshift @xmath4 through an extended process . the most probable cause was the ionizing radiation of the first stars and qso s . currently these are the two main direct observational constraints on this epoch . this scarcity of observational data is set to change dramatically in the next few years , however . a number of large observational projects are currently under way , e.g. observations at the redshifted 21-cm line of hydrogen ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , detection of small - scale cmb anisotropies due to the kinetic sunyaev - zeldovich ( ksz ) effect ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and surveys of high - redshift ly-@xmath1 emitters and studies of the igm absorption ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? the planning and success of these experiments relies critically upon understanding the large - scale geometry of reionization , i.e. the size- and spatial distribution of the ionized and neutral patches . this is best derived by large - scale simulations , although a number of semi - analytical models exist as well ( e.g. * ? ? ? recently we presented the first large - scale , high - resolution radiative transfer simulations of cosmic reionization @xcite and applied those to derive a range of reionization observables @xcite . here we summarize recent results on the characteristic scales and topology of reionization and implications of our simulations for the observability of high - redshift ly-@xmath1 sources .

this allowed making the first realistic predictions for a variety of observational signatures . we discuss recent results from large - scale radiative transfer and structure formation simulations on the observability of high - redshift ly-@xmath1 sources . [ scales],title="fig:",width=316 ] mpc box simulations for high ( bottom panels ) and low source efficiencies ( top ) and with ( right panels ) and without ( left panels ) sub - grid clumping . [ scales],title="fig:",width=307 ] mpc box simulations for high ( bottom panels ) and low source efficiencies ( top ) and with ( right panels ) and without ( left panels ) sub - grid clumping . [ spectra2],width=316 ]

recently the numerical simulations of the process of reionization of the universe at @xmath0 have made a qualitative leap forward , reaching sufficient sizes and dynamic range to determine the characteristic scales of this process . this allowed making the first realistic predictions for a variety of observational signatures . we discuss recent results from large - scale radiative transfer and structure formation simulations on the observability of high - redshift ly-@xmath1 sources . we also briefly discuss the dependence of the characteristic scales and topology of the ionized and neutral patches on the reionization parameters . mpc box simulations for high ( bottom panels ) and low source efficiencies ( top ) and with ( right panels ) and without ( left panels ) sub - grid clumping . [ scales],title="fig:",width=316 ] mpc box simulations for high ( bottom panels ) and low source efficiencies ( top ) and with ( right panels ) and without ( left panels ) sub - grid clumping . [ scales],title="fig:",width=307 ] mpc box simulations for high ( bottom panels ) and low source efficiencies ( top ) and with ( right panels ) and without ( left panels ) sub - grid clumping . [ scales],width=316 ] sources at redshift @xmath2 : transmission factor along sample lines - of - sight vs. @xmath3comoving distance from the most massive galaxy in the computational volume . there is significant transmission in the proximity zone and transmission gaps in the mean igm away from the source . gas infall results in some absorption red - ward of the line center . [ spectra2],width=288 ] sources at redshift @xmath2 : transmission factor along sample lines - of - sight vs. @xmath3comoving distance from the most massive galaxy in the computational volume . there is significant transmission in the proximity zone and transmission gaps in the mean igm away from the source . gas infall results in some absorption red - ward of the line center . [ spectra2],width=316 ]

0812.3589

i

coronal mass ejections ( cmes ) are energetic expulsions of plasma from the solar corona that are driven by the release of magnetic energy typically in the range of @xmath0 ergs . the majority of cmes originate from the eruption of pre - existing large - scale helmet streamers @xcite . less common fast cmes typically come from smaller , more concentrated locations of magnetic flux referred to as active regions . in this case , the cmes often occur shortly after the flux has emerged at the photosphere , but can also happen even as the active region is decaying . while cmes occur in a wide range of circumstances , all cmes originate above photospheric magnetic polarity inversion lines ( neutral lines ) , which exhibit strong magnetic shear . shear implies that the magnetic field has a strong component parallel to the photospheric line that separates magnetic flux of opposite sign , and in this configuration , the field possesses significant free energy . in contrast , a potential field runs perpendicular to the inversion line and has no free energy . there is enormous evidence for the existence of highly sheared magnetic fields associated with cmes and large flares . at the photosphere , magnetic shear is measured directly with vector magnetographs ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? higher in the atmosphere , the magnetic field is difficult to measure directly , but its direction may be inferred from plasma structures formed within the field . seen in chromospheric h@xmath1 absorption , filaments form only over photospheric inversion lines @xcite along which the magnetic field is nearly parallel @xcite . fibrils and h@xmath1 loops that overlay photospheric bipolar active regions are also indicative of magnetic shear @xcite . comparisons between vector magnetograms and h@xmath1 images show that the direction of the sheared photospheric magnetic field coincides with the orientation of such fibril structures @xcite . higher in the corona , evidence of magnetic shear is found in loops visible in the extreme ultraviolet @xcite and x - ray sigmoids @xcite . these structures run nearly parallel to the photospheric magnetic inversion line prior to cmes , and are followed by the reformation of closed bright loops that are much more potential in structure . finally , observations by the transition region and coronal explorer ( trace ) show that 86 percent of two - ribbon flares show a strong - to - weak shear change of the ribbon footpoints that indicates the eruption of a sheared core of flux @xcite . sheared magnetic fields are at the epicenter of solar eruptive behavior . large flares are preferentially found to occur along the most highly sheared portions of magnetic inversion lines @xcite . more recent analysis by @xcite found that shear flows associated with flux emergence drove enhanced flaring . similarly , active region cme productivity is also strongly correlated with magnetic shear as shown by @xcite . it is not coincidental that large flares and cmes are strongly associated with filaments , which are known to form only along sheared magnetic inversion lines @xcite . the buildup of magnetic shear is essential for energetic eruptions , and for this reason , it is of fundamental importance to understanding solar activity . currently the majority of cme initiation models rely on the application of artificially imposed shear flows . examples of such models include @xcite . until recently , there was no theory to account for these large scale shear flows . in this paper , we discuss a series of simulations that illustrate a physical process by which these shear flows are self - organized in emerging magnetic fields . we will give a close comparison of these simulations in the context of new observations that make a more complete and compelling picture of a fundamental cause of eruptive solar magnetic activity .

shear flows have been prescribed in numerical models of coronal mass ejections and flares for decades as a way of energizing magnetic fields to erupt . while such shear flows have long been observed in the solar atmosphere , until recently , there was no compelling physical explanation for them . finally , shear flows driven by the lorentz force are shown to produce a loss of equilibrium and eruption in magnetic arcades and flux ropes offering a convincing explanation for cmes and flares .

shear flows have been prescribed in numerical models of coronal mass ejections and flares for decades as a way of energizing magnetic fields to erupt . while such shear flows have long been observed in the solar atmosphere , until recently , there was no compelling physical explanation for them . this paper will discuss the discovery that such shear flows are readily explained as a response to the lorentz force that naturally occurs as bipolar magnetic fields emerge and expand in a gravitationally stratified atmosphere . it will be shown that shearing motions transport axial flux , and magnetic energy from the submerged portion of the field to the expanding portion , strongly coupling the solar interior to the corona . this physical process explains active region shear flows and why the magnetic field is found to be nearly parallel to photospheric polarity inversion lines where prominences form . finally , shear flows driven by the lorentz force are shown to produce a loss of equilibrium and eruption in magnetic arcades and flux ropes offering a convincing explanation for cmes and flares .

1009.5441

i

physical processes that occur during reionization are numerous and complex . nevertheless , ionization of neutral gas ( hydrogen & helium ) and heating of the inter - galactic medium ( igm ) can be considered the two primary influences of radiating objects during reionization . currently , the most promising `` direct '' probe of reionization is the redshifted 21-cm radiation emanating from neutral hydrogen during the epoch of reionization ( eor ) , which are to be measured using upcoming telescopes like lofar , mwa , paper and 21cma . the intensity of the observed 21-cm radiation depends on the ratio between the number density of electrons in the hyperfine states in the ground state of a neutral hydrogen atom . this ratio is normally expressed in terms of the so - called 21-cm spin temperature , @xmath1 . at the onset of the formation of the first reionizing objects the spin temperature is equal to the cmb temperature since at these redshifts the ratio between excited and ground hyperfine state electrons is completely determined by the cmb . however , as the number of ionizing sources increases , @xmath1 starts departing from @xmath7 ; slowly at the beginning , then rapidly approaching values larger than @xmath7 . this evolution is typically ignored in most previous studies of reionization which assumes @xmath8 at all times @xcite . recently , @xcite have relaxed this assumption on @xmath1 at the dawn of reionization and explored its impact on the brightness temperature . they found a considerable considerable deviation from assuming @xmath9 at the beginning of reionization . towards the end of reionization though , this assumption holds ground . but , in order to track the evolution of @xmath1 accurately , like in @xcite , it is necessary to perform a detailed 3-d ly@xmath5 radiative transfer calculation . the ly@xmath5 photons undergo a large number ( @xmath10 ) of scatterings even in a marginally neutral medium before it is sufficiently off line - centre to `` free stream '' . the scattering angle after each encounter is completely random and therefore the radiative transfer is often done in a monte carlo sense @xcite to capture this random nature of ly@xmath5 scatterings . unfortunately these monte carlo radiative transfer schemes are computationally very expensive , especially if we need to simulate large fields of view necessary to generate mock data sets for next generation radio telescopes . in order to circumvent the need to perform such computer - intensive calculations to obtain @xmath1 , we develop an algorithm along the lines of bears @xcite as an approximation . in this paper we present an algorithm that follows the decoupling of @xmath1 from @xmath7 owing to ly@xmath5 photons , which couples the spin temperature to the colour / kinetic temperature via the wouthuysen - field effect @xcite . collisional excitation and heating caused by secondary electrons resulting from hard x - ray radiation are also included . the dominant source of ly@xmath5 flux is the background created by the redshifting of photons in the lyman band into ly@xmath5 . these photons are blueward of ly@xmath5 and is injected into ly@xmath5 at some distance away from the source . the amount of intrinsic ly@xmath5 , ionizing and `` heating '' photons is a function of the source spectral energy distribution ( sed ) . thus the evolution of the spin temperature critically depends on the source of reionization . different reionization sources manifest themselves by influencing the igm in markedly different ways . for example , deficiency of hard photons in the seds of `` first stars '' , limit the extent to which they heat the igm @xcite , while miniquasars ( or miniqsos , characterized by central black hole masses less than a million solar ) , abundant in x - ray photons , cause considerable heating @xcite . ionization profiles similarly have their characteristic source - dependent behavior . although the question on which sources did the bulk of the reionization is up for debate , it is conceivable from observations of the local universe up to redshifts around 6.5 , that sources of reionization could have been a mixture of both stellar and quasar kinds ( their respective roles again are uncertain ) . implementing radiative transfer that include both ionizing and hard x - ray photons has been difficult and as a result most 3-d radiative transfer schemes restrict themselves to ionization due to stars @xcite . in @xcite , a `` semi '' hybrid model of stars and miniqsos , like the one hinted above , has been used albeit in sequential order instead of a simultaneous implementation . that is , pre - ionization due to miniqsos was invoked between @xmath11 , after which , stars reionize the universe at redshift 7 . we in this paper would like to address the issue of simulating the propagation of both the uv and hard x - ray photons , exactly in 1-d and as approximation in 3-d . the focus of this paper is therefore to introduce the algorithm that is used to implement igm heating in bears along with the procedure to estimate the spin temperature of the igm . as an application of this technique we explore the effects of heating due to miniqsos , stars and , for the first time , a mixed `` hybrid population '' . subsequently , we provide quantitative and qualitative analysis of the differences in the 21-cm eor signal with and without the usual assumption of @xmath1 being always decoupled from @xmath7 . the paper is organized as follows ; [ sec : simulations ] describes briefly the n - body and 1-d radiative transfer codes used . in [ sec : bearheat ] we describe the adaptation of bears to include @xmath6 , followed by the calculation of the @xmath1 and @xmath3 within the simulation box . bears is then applied to three different scenarios of reionization in [ sec : applications ] , _ viz_. , ( 1 ) the primary source being stars , ( 2 ) miniqsos and ( 3 ) a hybrid population of stars and miniqsos . subsequently , observational cubes of @xmath12 are generated for each of these scenarios and its properties discussed . in [ sec : stats ] we provide statistics on the simulated boxes and interpret the finding mainly from the point of view of the differences in @xmath3 with and without the usual assumption that @xmath1 is decoupled from @xmath13 . we also compare our work to that of @xcite in the same section . conclusions and discussions of the results are presented in [ sec : conclusion ] , along with a mention of a few topics that can be addressed using the data set simulated in this paper .

simulations estimating the brightness temperature ( @xmath0 ) of the redshifted 21-cm from the epoch of reionization ( eor ) often assume that the spin temperature ( @xmath1 ) is decoupled from the background cmb temperature and is much larger than it , i.e. , @xmath2 . although a valid assumption towards the latter stages of the reionization process , it does not necessarily hold at the earlier epochs . we also perform a number of statistical tests to quantify the imprint of the self - consistent inclusion of the spin temperature decoupling from the cmb .

simulations estimating the brightness temperature ( @xmath0 ) of the redshifted 21-cm from the epoch of reionization ( eor ) often assume that the spin temperature ( @xmath1 ) is decoupled from the background cmb temperature and is much larger than it , i.e. , @xmath2 . although a valid assumption towards the latter stages of the reionization process , it does not necessarily hold at the earlier epochs . violation of this assumption will lead to fluctuations in @xmath3 that are neither driven by density fluctuations nor by @xmath4 regions . therefore , it is vital to calculate the spin temperature self - consistently by treating the ly@xmath5 and collisional coupling of @xmath1 to the kinetic temperature , @xmath6 . in this paper we develop an extension to the bears algorithm , originally developed to model reionization history , to include these coupling effects . here we simulate the effect in ionization and heating for three models in which the reionization is driven by stars , miniqsos or a mixture of both . we also perform a number of statistical tests to quantify the imprint of the self - consistent inclusion of the spin temperature decoupling from the cmb . we find that the evolution of the spin temperature has an impact on the measured signal specially at redshifts higher than 10 and such evolution should be taken into account when one attempts to interpret the observational data . [ firstpage ] physical data processes : radiative transfer cosmology : theory observation diffuse radiation radio lines : general .

1009.5441

c

the focus of this paper was three - fold . 1 ) to introduce an extension to bears in order to incorporate heating ( including x - ray heating ) and discuss its application to two cases of reionization and heating , i.e. , for blackbody ( stellar ) and power - law ( miniqso ) type sources , 2 ) to monitor the evolution of spin temperature ( @xmath1 ) self - consistently and contrast its influence against the usual assumption made in most reionization simulation that @xmath169 , and 3 ) use the extended bears code to study reionization due to a hybrid population of stars and miniqsos as reionizing sources . to incorporate heating into bears , we embeded spheres of `` kinetic temperature '' around the sources of radiation , much like in the algorithm used to obtain the ionized fraction @xcite . the bears algorithm implemented is extremely fast , in that it takes @xmath170 hours ( 2ghz , 16-core , 32 gb shared ram ) to perform the radiative transfer ( including heating ) on about 35 different boxes ( @xmath14 and 100 @xmath171 comoving mpc ) between redshifts 12 and 6 . these snapshots are interpolated between redshifts to produce a contiguous data cube spanning redshifts @xmath172 , i.e. , the observational range of the lofar - eor experiment . the efficiency of the code facilitates the simulation of many different scenarios of reionization and test their observational signatures . apart from predicting the nature of the underlying cosmological signal , these simulations can be used in conjunction with others probes of reionization to enhance the detectability and/or constrain parameters concerning reionization . in @xcite these simulations were cross - correlated with the simulations of the cmb anisotropy ( mainly the kinetic and thermal sz - effect ) to probe reionization . in the same paper jelic et al . , repeated the same exercise by using reionization simulations from @xcite and found similar results , further emphasizing the validity of the approximate manner in which we solve the evolution of the kinetic temperature in our simulations . the improved bears code was used to simulate three distinct reionization scenarios , i.e. , miniqsos , stellar and a mixture of both . these simulations further emphasized that miniqsos were not only very efficient in increasing @xmath6 of the igm but the secondary ly@xmath5 flux produced by these sources was enough to drive @xmath1 away from @xmath7 in an extended region around the source thereby rendering the igm around the source `` bright '' in @xmath3 . this implies , if a miniqso hosting a black hole in the mass range @xmath173 is within the observing window of lofar , the value of @xmath3 and its spatial extent would be conducive to a possible detection . the code was also applied to simulate reionization with a hybrid population of stars and miniqsos . every dark matter halo was embedded with both a quasar and a stellar component . the relation between the two was set according to the `` magorrian relation '' we observe today . the total mass in quasars were constrained following black hole mass density estimates by @xcite . the effect of the hybrid population on the igm was an interpolation between the scenarios of stars and miniqsos i.e. , although the heating ( and ionization ) was not as extended as in the case of miniqsos , it was definitely larger than that for stars . our ultimate goal is to simulate mock data sets for the lofar - eor experiment . towards this end , reionization simulations performed on 35 different snapshots between redshifts 6 and 12 were combined to form `` frequency cubes '' ( reionization histories , @xcite ) for all three scenarios i.e. , stars , miniqsos and the hybrid case . to fold - in the effect of the instrument we smoothed these frequency cubes according to the lofar beam - scale . notwithstanding the convolution by the lofar beam , stark differences between the scenarios clearly persists . the r.m.s @xmath3 cleary shows this difference between scenarios . all three scenarios of reionization discussed above was performed for two different cases , i ) assuming that @xmath1 is always coupled to @xmath6 and ii ) following the evolution of @xmath1 self - consistently in the simulation . figures [ fig : histcomp ] and [ fig : histcompinf ] reflect the differences between the two cases . to further quantify the influence of the self - consistent evolution of @xmath1 , especially at the beginning of reionization , a suite of statistical analyses was performed . flux and heating induced by miniqsos . ] firstly , the 3-d power spectra of @xmath12 ( fig . [ fig : powspec ] ) for the two cases was calculated at four redshifts ( 12 , 10 , 8 and 6 ) . we see that although there is a considerable difference at the onset ( z=12 ) of reionization the power spectra of the brightness temperature match - up by a redshift of 8 . this is attributed to the volume filling nature of the spin temperature coupling induced by miniqsos . the minimum , maximum and mean value of @xmath174 as a function of redshift reveal similar differences between the two cases . the maximum value of @xmath174 is the same in both cases because regions where the igm is considerably heated also corresponds to regions with a large supply of ly@xmath5 photons and they are also regions where colliosional coupling is effective . the minimum and average values reveal a difference since under the assumption that @xmath175 , regions much below @xmath7 are artificially coupled to @xmath1 . as a final statistic we compute the 3-d power spectra of @xmath6 and @xmath1 and compare them ( fig . [ fig : powspectemp ] . vast differences do exist between the two almost till the end of reionization , when they become identical . an interesting result of this comparison is that the large scales of the two spectra get matched before the small scales in the box . the interpretation of this behaviour is given in section [ sec : stats ] . we also compared our results to that of @xcite and found good match for the evolution of gas temperature and the volume filling factor of x - ray radiation . in the near future calibration errors expected from a lofar - eor observational run will be added to these simulations along with the effects of the ionosphere and expected radio frequency interference ( rfi ) . subsequently , galactic and extra - galactic foregrounds modeled as in @xcite will be merged with these simulations to create the final `` realistic '' data cube . these data cubes will be processed using the lofar signal extraction and calibration schemes being developed to retrieve the underlying cosmological signal in preparation for the actual lofar - eor experiment which has already begun .

therefore , it is vital to calculate the spin temperature self - consistently by treating the ly@xmath5 and collisional coupling of @xmath1 to the kinetic temperature , @xmath6 . in this paper we develop an extension to the bears algorithm , originally developed to model reionization history , to include these coupling effects . here we simulate the effect in ionization and heating for three models in which the reionization is driven by stars , miniqsos or a mixture of both .

simulations estimating the brightness temperature ( @xmath0 ) of the redshifted 21-cm from the epoch of reionization ( eor ) often assume that the spin temperature ( @xmath1 ) is decoupled from the background cmb temperature and is much larger than it , i.e. , @xmath2 . although a valid assumption towards the latter stages of the reionization process , it does not necessarily hold at the earlier epochs . violation of this assumption will lead to fluctuations in @xmath3 that are neither driven by density fluctuations nor by @xmath4 regions . therefore , it is vital to calculate the spin temperature self - consistently by treating the ly@xmath5 and collisional coupling of @xmath1 to the kinetic temperature , @xmath6 . in this paper we develop an extension to the bears algorithm , originally developed to model reionization history , to include these coupling effects . here we simulate the effect in ionization and heating for three models in which the reionization is driven by stars , miniqsos or a mixture of both . we also perform a number of statistical tests to quantify the imprint of the self - consistent inclusion of the spin temperature decoupling from the cmb . we find that the evolution of the spin temperature has an impact on the measured signal specially at redshifts higher than 10 and such evolution should be taken into account when one attempts to interpret the observational data . [ firstpage ] physical data processes : radiative transfer cosmology : theory observation diffuse radiation radio lines : general .

1603.05249

i

understanding the frequency and mass function of free - floating planets ( ffps ) is integral for a complete comprehension of the formation and evolution of planetary systems . using deep photometric imaging primarily in near - infrared bands and , in some cases , astrometric and/or spectroscopic follow - up data , jupiter - mass ffps and ffp candidates have been detected in the trapezium cluster @xcite , the @xmath10 orionis open cluster @xcite , the ab doradus moving group @xcite , the @xmath11 pictoris moving group @xcite , the upper scorpius association @xcite , and in the field @xcite . yet detections from photometric surveys require and depend sensitively on an independent constraint for the object s age while the dynamical association of objects in moving groups is intrinsically more uncertain . in a broader statistical sense , @xcite examined two years of microlensing survey data from the microlensing observations in astrophysics ( moa ) collaboration . they found an excess of short - timescale events ( @xmath122 days ) above expectations based on an extrapolation of the stellar mass function down to low - mass brown dwarfs . from this they inferred a population of ffp candidates that outnumber main sequence stars by a ratio of @xmath13 . however , mass measurements do not exist for any of the candidate objects upon which the inference rests . the formation mechanisms for ffps remain an open theoretical question . one possible avenue is that these objects were originally formed in protoplanetary disks and were subsequently ejected . simulations by @xcite of the formation and evolution of planetary systems without eccentricity or inclination damping eject planets at a rate that is @xmath350 times lower than is needed to explain the moa result . indeed , @xcite assert that planet - planet scattering itself is insufficient to reproduce the abundance of ffp candidates seen by moa . in the context of open clusters , n - body dynamical simulations find that roughly half of star - planet and planet - planet interactions occur within the first 30 myr @xcite and that 80@xmath14 of the resulting ffps are ejected from the cluster while the remaining @xmath620@xmath14 become concentrated in the central @xmath62 pc @xcite . a second option is that ffps form via direct collapse of molecular clouds . @xcite found that opacity - limited fragmentation of collapsing clouds could , in principle , produce a fragment with a minimum mass as low as @xmath60.01@xmath15 . additionally , turbulent shocks could cause protostellar cores with masses in the brown dwarf regime to become gravitationally unstable and hypothesized that turbulent density fluctuations smaller than a critical mass could induce collapse into objects with the mass of giant planets @xcite . gravitational microlensing does not rely on the flux output from the lensing object and so is well - positioned to explore ffp demographics across a wide range of planet masses . the mass of an ffp lens , @xmath16 , is given by : @xmath17 where @xmath0 is the angular einstein radius , @xmath18 , and @xmath2 is the microlens parallax : @xmath19 here @xmath20 is the lens - source relative parallax , defined as @xmath21 , where @xmath22 and @xmath23 are the distances from the observer to the lens and source , respectively , and @xmath24 is the physical size of @xmath0 projected onto the plane of the observer . the most salient observable for a light curve arising from a single lensing mass is the einstein timescale @xmath25 , which measures the time required for the lens - source angular separation to change by one angular einstein ring radius and is defined as : @xmath26 where @xmath27 is the lens - source relative proper motion . the timescale is routinely measured for single - lens events . however , several physical properties are encoded within @xmath25 , including @xmath22 , @xmath16 , and @xmath27 . thus , in order to determine that the lensing object giving rise to the short timescale is indeed planetary - mass , it is crucial to measure both @xmath0 and @xmath2 . the angular einstein radius is typically determined by combining a measurement of @xmath1 , the angular radius of the source star normalized to @xmath0 , with multiband photometry to determine the color and , ultimately , the angular size of the source @xcite . lastly , a short - timescale event definitively due to a planetary - mass lens must be proven to be free - floating , which requires high - resolution photometry to search for flux from a possible lens host star . @xcite studied bound planets that are widely separated from their host star . they found that if the projected separation between a planet and its parent star is @xmath320 au , the resulting light curve can mimic that of an ffp , as the alignment between the source trajectory and the binary lens axis can cause the primary microlensing event due to the star _ not _ to be observed , allowing a bound planet to masquerade as an ffp . they also investigated the ability to identify the bound nature of a planet in the case of isolated planetary - mass lensing events via the caustic induced by the shear of the planet s host star , which would introduce magnification structure to the light curve of the event . fully characterizing an ffp requires that all of these criteria are met . however , the intersection of all aforementioned constraints is far from guaranteed for a given space mission . the goal of this paper is to map the regions of parameter space for which a given satellite will be sensitive to ffps , particularly _ k2 _ s campaign 9 ( _ k2_c9 ; see [ sec : kepler ] ) and _ wfirst _ ( see [ sec : wfirst ] ) , and to identify the dominant limiting factors in each regime . throughout the paper we will assume that the source is located in the bulge at a distance of @xmath28 kpc @xcite and focus on @xmath22 as an independent variable . it is possible to explore the demographics of ffps statistically without requiring that the parameters @xmath2 , @xmath1 , and @xmath4 each be measured for all systems . that said , the primary focus of this paper is on the subset of ffps that can be fully characterized via measurements of all three . the expected yield of ffps for a given microlensing survey depends , intrinsically and sensitively , on their underlying event rate . understanding the relative rates for different ffp populations can influence the observational strategy . the microlensing rate as a function of the ffp physical parameters , derived from the generic rate formula @xmath29 , is given by @xcite : @xmath30 here @xmath31 is the local space density of ffps , @xmath32 is the lens - source relative proper motion probability distribution , and @xmath33 is the ffp mass function . while @xmath34 is proportion to @xmath35 and @xmath36 can be assumed to be similar to that for the general galactic stellar population , @xmath31 and @xmath33 are precisely what the experiment is trying to measure and are hitherto unconstrained . furthermore , the kinematics for ffps will depend on the fraction that are the result of dynamical ejections versus those that form in situ . thus , in this paper we can not and do not predict the relative rates for different ffp populations but instead study the feasibility of characterizing ffps with various physical parameters , assuming that an event has occurred . our methodology builds upon and extends previous studies of lens characterization for ffps and also bound planets . @xcite examined the ability of a joint ground- and space - based microlensing survey to constrain the mass of ffps . considering a generic satellite at the earth - sun l2 point paired with a ground - based survey , they found that microlensing events arising from planetary - mass lenses can be detected for planet masses down to that of the earth . @xcite subsequently explored how to distinguish between isolated lensing events due to widely separated , bound planets from ffp events using interferometry to search for the astrometric signature of a lens host star . he found that for bright sources , with @xmath37 , a centroid shift can be measured given an astrometric precision that is of - order one microarcsecond . more generally , @xcite investigated how to measure lens masses and distances solely from measurements of the microlens parallax @xmath2 and the lens flux @xmath4 , circumventing the need to measure @xmath0 . she considered spacecraft in earth - trailing solar orbits and at earth - sun l2 , similar to those of _ kepler _ , _ spitzer _ , and _ wfirst_. naturally , lens flux can not be used as a tool for characterizing ffps , necessitating an additional constraint . @xcite advocate for a simultaneous ground - based survey to accompany the _ wfirst _ microlensing observations in order to obtain two - dimensional vector microlens parallax measurements . these would provide complete solutions , and thus masses and distances , for a substantial fraction of ffp events . we present the first combined treatment of constraints from @xmath2 , @xmath1 , and @xmath4 to explore regimes of detectability and characterization for ffps across a range of lens distances , source star properties , and satellite characteristics . in [ sec : satellites ] we briefly describe the parameters and goals of six relevant space missions . measuring @xmath2 with a space telescope requires a delicate balance between @xmath24 and the projected separation @xmath38 of the earth and the satellite as seen from the lens - source line - of - sight . we investigate the interplay between @xmath38 and @xmath24 for these satellite missions in [ sec : dproj_reproj ] . in [ sec : rho ] we discuss the probability of measuring @xmath1 through the detection of finite - source effects . finally , in [ sec : fl ] we detail the constraints from measuring the lens flux . we summarize our findings and discuss their applications in the context of _ k2_c9 and _ wfirst _ in [ sec : discussion ] , wherein we identify the regimes of parameter space to which each will ultimately be able to robustly characterize ffp events .

simultaneous space- and ground - based microlensing surveys , such as those planned with _ k2 _ s campaign 9 ( _ k2_c9 ) and , potentially , _ wfirst _ , facilitate measuring the masses and distances of free - floating planet ( ffp ) candidates . ffps are initially identified as events arising from a single lensing mass with a short timescale , ranging from one day for a jupiter - mass planet to a few hours for an earth - mass planet . measuring the mass of the lensing object requires measuring the angular einstein radius @xmath0 , typically by first determining the finite size of the source star @xmath1 , as well as the microlens parallax @xmath2 . a planet that is gravitationally bound to , but widely separated from , a host star ( @xmath320 au ) can produce a light curve that is similar to that of an ffp . we investigate the accessible parameter space for each of these components @xmath2 , @xmath1 , and @xmath4 considering different satellite missions for a range of ffp masses , galactic distances , and source star properties . together these indicate that the ability to characterize ffps detected during _

simultaneous space- and ground - based microlensing surveys , such as those planned with _ k2 _ s campaign 9 ( _ k2_c9 ) and , potentially , _ wfirst _ , facilitate measuring the masses and distances of free - floating planet ( ffp ) candidates . ffps are initially identified as events arising from a single lensing mass with a short timescale , ranging from one day for a jupiter - mass planet to a few hours for an earth - mass planet . measuring the mass of the lensing object requires measuring the angular einstein radius @xmath0 , typically by first determining the finite size of the source star @xmath1 , as well as the microlens parallax @xmath2 . a planet that is gravitationally bound to , but widely separated from , a host star ( @xmath320 au ) can produce a light curve that is similar to that of an ffp . this tension can be resolved with high - resolution imaging of the microlensing target to search for the lens flux @xmath4 from a possible host star . here we investigate the accessible parameter space for each of these components @xmath2 , @xmath1 , and @xmath4 considering different satellite missions for a range of ffp masses , galactic distances , and source star properties . we find that at the beginning of _ k2_c9 , when its projected separation from the earth ( as viewed from the center of its survey field ) is @xmath50.2 au , it will be able to measure @xmath2 for jupiter - mass ffp candidates at distances larger than @xmath62 kpc and to earth - mass lenses at @xmath68 kpc . at the end of its campaign , when @xmath7 au , it is sensitive to planetary - mass lenses for distances @xmath33.5 kpc , and even then only to those with mass @xmath3m@xmath8 . from lens flux constraints we find that it will be possible to exclude _ all _ stellar - mass host stars ( down to the deuterium - burning limit ) for events within @xmath62 kpc , and for events at any distance it will be possible to exclude main sequence host stars more massive than @xmath60.25 m@xmath9 . together these indicate that the ability to characterize ffps detected during _ k2_c9 is optimized for events occurring toward the beginning of the campaign . _ wfirst _ , on the other hand , will be able to detect and characterize ffps with masses at least as low as super - earths throughout the galaxy during its entire microlensing survey .

1603.05249

c

here we present the implications our findings have for the characterization of ffp candidate events . it is eminently possible to explore the frequency , galactic distribution , and even mass function of ffps without robustly measuring @xmath2 and @xmath0 ( via @xmath1 ) , which together provide mass and distance measurements for individual events . nor is fully excluding stellar - mass hosts a requirement for gaining traction in understanding ffp demographics . in this section , however , we will focus on the full set of constraints as they can be measured using data taken during _ k2_c9 or by _ wfirst_. the projected separation @xmath38 of _ k2_c9 reaches its minimum value of 0.07 au one week into the campaign , on 14/april/2016 , after which it increases monotonically to 0.81 au on 1/july . this significantly affects its ability to measure @xmath2 for ffp lenses with different masses and distances throughout the campaign . figure [ fig : mffp_dl ] shows @xmath16 as a function of @xmath22 . by assuming a value of @xmath24 that is equal to @xmath38 it is possible to determine the masses and distances of ffps that will yield detectable events at a given time during _ k2_c9 . as discussed in [ sec : reproj ] , the probability that events with @xmath124 will be detectable by the pair of observer locations is @xmath660@xmath14 , and this probability declines steeply as @xmath59 increases . we thus use this as a benchmark for sensitivity to @xmath2 . immediately we see that toward the end of _ k2_c9 @xmath2 can only be measured for lenses with mass lower than the deuterium - burning limit for @xmath125 kpc . near the beginning of the campaign it will be possible to measure a parallactic shift for nearby jupiter - mass lenses , with its sensitivity extending down to earth - mass ffps as the lens distance increases to @xmath126 kpc . but @xmath2 is only one of two ingredients necessary for measuring @xmath16 and @xmath22 . the other is @xmath1 , which helps determine @xmath0 . by rearranging the right - hand side of equation ( [ eq : rho_prob ] ) we compute @xmath16 as a function of @xmath22 for different values of @xmath1 , given an assumed physical source radius @xmath80 ( and thus angular source radius @xmath77 , assuming @xmath127 kpc ) . to compute @xmath1 for _ k2_c9 ( left panel of figure [ fig : mffp_dl ] ) we assume @xmath128 . we select this as the benchmark value of @xmath80 because @xmath129 , corresponding to @xmath130 , is likely too faint for _ k2_c9 and @xmath116 allows for the otherwise strongest lens flux constraints . from the left - hand side of equation ( [ eq : rho_prob ] ) , the probability of detecting finite - source effects , and thus measuring @xmath1 and , ultimately , determining @xmath0 , scales approximately as @xmath1 itself . thus , the value of @xmath1 at a given ( @xmath22 , @xmath16 ) coordinate gives the probability of measuring @xmath1 for an ffp with those physical properties . rephrased , @xmath131 indicates , roughly , the number of events with that specific ( @xmath22 , @xmath16 ) combination that would need to be detected in order to measure @xmath1 for at least one of them . the constraints for measuring @xmath2 and @xmath1 work in opposing directions . for a fixed @xmath38 , the mass to which the satellite is sensitive decreases as @xmath22 increases . however , as @xmath22 increases , the probability of measuring @xmath1 _ increases _ , for a fixed ffp mass . finally , we incorporate the flux constraint for ruling out the presence of lens host stars . from the left panel of figure [ fig : mffp_dl ] , the largest @xmath22 at which stellar - mass lens host stars can be excluded for sources with @xmath116 is @xmath61.8 kpc from our fiducial simulation . when considering all three factors , @xmath2 , @xmath1 , and @xmath4 , the optimal regime for characterizing ffps occurs for the smallest @xmath38 , when the sensitivity extends to ffps with the lowest masses , for a fixed @xmath22 , and for when the probability of measuring @xmath1 is the highest , i.e. , larger values of @xmath1 . this drives the sensitivity of _ k2_c9 toward the first few weeks of the campaign , when @xmath132 au , as is furthermore supported by the goal of excluding stellar - mass host stars , which requires that @xmath133 kpc . in this regime , however , while stellar hosts can be excluded at the three - sigma level from @xmath4 constraints , the probability of measuring both @xmath2 and @xmath1 is only @xmath61.5@xmath14 . at the end of _ k2_c9 , when @xmath7 au , the lowest mass lens for which it will be possible to measure @xmath2 and also constrain the flux will be @xmath134 , above the brown dwarf mass limit . the current plan is for each of _ wfirst _ s 72-day observing seasons to be centered on an equinox . its projected separation would thus be restricted to @xmath135 . nevertheless , given the uncertain nature of the orbital parameters ( see [ sec : dproj ] ) and the exact timing of the observing seasons , we presume @xmath136 au and @xmath137 au to bracket the full range possible for _ wfirst_. these are shown in the right panel of figure [ fig : mffp_dl ] . from the detectability limit of @xmath124 discussed in [ sec : reproj ] , this indicates that _ wfirst _ will be able to measure @xmath2 for earth - mass planets for @xmath138 kpc and for lower - mass planets at larger distances . were the sun - angle restrictions relaxed such that _ wfirst _ could observe toward the bulge near the june solstice , when its projected separation could reach as small as 10@xmath139 au , it would be sensitive to planets @xmath62 orders - of - magnitude less massive ( i.e. , free - floating moons ) . the typical source stars for _ wfirst _ will have @xmath130 , meaning that the probability to measure @xmath1 is @xmath310@xmath14 for earth - mass ffps with @xmath140 kpc . the corresponding source magnitude of @xmath129 , combined with the optimal lens flux simulation ( which is appropriate for _ wfirst _ ) , suggests that it will be possible to exclude host stars for ffps detected by _ wfirst _ for @xmath141 kpc . this means that _ wfirst _ will be sensitive to ffps at least down to the mass of super - earths throughout the galaxy . one possible limiting factor , however , could be the capabilities of the accompanying ground - based facilities . a source with @xmath129 will have an optical magnitude of @xmath142 2224 . this is below the sensitivity of current microlensing surveys . additionally , the maximum magnification limitation from having a larger @xmath1 means that many of these events may not get sufficiently bright to be detected even at peak . however , if future surveys will be conducted by larger telescopes , such as that proposed for subaru , this limit is no longer relevant . secondly , the bulge is visible only for @xmath617 hours from ctio ( as a representative for the southern hemisphere ) during the currently planned _ wfirst _ campaigns ( as shown on the bottom panel of figure [ fig : dproj ] ) . for telescopes in the northern hemisphere , such as subaru on mauna kea , the bulge is visible for only 60@xmath14 of each _ wfirst _ observing season and even then only up to a maximum of @xmath63 hours per night . work by cbh and ys was supported by an appointment to the nasa postdoctoral program at the jet propulsion laboratory , administered by universities space research association through a contract with nasa . we thank david ciardi , chas beichman , and chris gelino for useful discussions regarding adaptive optics observations . finally , we thank scott gaudi , dan maoz , matt penny , and sebastiano calchi novati for a careful and fruitful reading of the manuscript .

k2_c9 is optimized for events occurring toward the beginning of the campaign . _ wfirst _ , on the other hand , will be able to detect and characterize ffps with masses at least as low as super - earths throughout the galaxy during its entire microlensing survey .

simultaneous space- and ground - based microlensing surveys , such as those planned with _ k2 _ s campaign 9 ( _ k2_c9 ) and , potentially , _ wfirst _ , facilitate measuring the masses and distances of free - floating planet ( ffp ) candidates . ffps are initially identified as events arising from a single lensing mass with a short timescale , ranging from one day for a jupiter - mass planet to a few hours for an earth - mass planet . measuring the mass of the lensing object requires measuring the angular einstein radius @xmath0 , typically by first determining the finite size of the source star @xmath1 , as well as the microlens parallax @xmath2 . a planet that is gravitationally bound to , but widely separated from , a host star ( @xmath320 au ) can produce a light curve that is similar to that of an ffp . this tension can be resolved with high - resolution imaging of the microlensing target to search for the lens flux @xmath4 from a possible host star . here we investigate the accessible parameter space for each of these components @xmath2 , @xmath1 , and @xmath4 considering different satellite missions for a range of ffp masses , galactic distances , and source star properties . we find that at the beginning of _ k2_c9 , when its projected separation from the earth ( as viewed from the center of its survey field ) is @xmath50.2 au , it will be able to measure @xmath2 for jupiter - mass ffp candidates at distances larger than @xmath62 kpc and to earth - mass lenses at @xmath68 kpc . at the end of its campaign , when @xmath7 au , it is sensitive to planetary - mass lenses for distances @xmath33.5 kpc , and even then only to those with mass @xmath3m@xmath8 . from lens flux constraints we find that it will be possible to exclude _ all _ stellar - mass host stars ( down to the deuterium - burning limit ) for events within @xmath62 kpc , and for events at any distance it will be possible to exclude main sequence host stars more massive than @xmath60.25 m@xmath9 . together these indicate that the ability to characterize ffps detected during _ k2_c9 is optimized for events occurring toward the beginning of the campaign . _ wfirst _ , on the other hand , will be able to detect and characterize ffps with masses at least as low as super - earths throughout the galaxy during its entire microlensing survey .

1412.0266

i

the study of quantum phase transitions ( qpt ) remains a very active topic in many fields of physics , spurred by experimental progress to create novel tunable interacting systems . qpt occur in quite different materials , including heavy fermion compounds , * ? ? ? * unconventional superconductors , * ? ? ? * mott insulators , * ? ? ? * coupled spin systems , * ? ? ? * and ultracold atoms . * ? ? ? * in particular , the common phenomenon of bose einstein condensation ( bec ) of strongly interacting bosons by tuning the interaction or the chemical potential can now be found in a range of different physical systems . ultracold atomic gases allow the tuning of interactions via feshbach resonances , * ? ? ? * but also cross - dimensional phase transitions @xcite and berezinsky - kosterlitz - thouless ( bkt ) behavior @xcite have been observed recently . phase transitions in coupled spin dimer systems are prime examples of bec of strongly interacting triplons,@xcite which allow easy tuning of the chemical potential via the magnetic field . although qpt s occur at zero temperature as a function of a non - thermal control parameter such as the interaction , effective mass , or the chemical potential , a characteristic critical scaling with temperature can be observed in a large range above the critical point.@xcite in general a detailed analysis is necessary in order to understand how the critical behavior is reflected in the experiments and if the finite - temperature phase transition is affected in the vicinity the qpt , where thermal fluctuations are comparable to quantum fluctuations . compared to bosonic gases of atoms and magnons the temperature control is relatively easy in triplon gases , which allows a systematic analysis of the critical scaling behavior near the qpt . in this paper we focus on the theoretical analysis of quantum critical points of antiferromagnetic spin dimer systems which are weakly coupled in two - dimensions . two qpt s can be observed : as the field is increased through the lower critical value @xmath0 the spin dimers start to be occupied by triplons and the magnetization increases with characteristic two - dimensional logarithmic behavior . the second qpt corresponds to the saturation field @xmath1 . the intermediate phase is characterized by long - range phase coherence of triplons at @xmath2 and bkt behavior@xcite at finite @xmath3 . similar phase transitions occur in two - dimensional hard - core boson systems@xcite and in distorted frustrated lattices.@xcite the schematic behavior is illustrated in fig . [ scheme ] . in this paper we show that the crossover from bkt behavior to critical scaling is rather well defined by the cooling rate and by characteristic maxima in the susceptibility . however , this crossover occurs at distinctly higher temperatures than the bkt transition which can be determined by a careful analysis of the spin - stiffness . there is no directly measurable signal for the bkt transition in experiments,@xcite but we find that magneto - caloric measurements are ideally suited to show the critical scaling and pinpoint the exact location of the qpt . close to the qpt the bkt transition retains the characteristic logarithmic behavior , albeit with strongly renormalized parameters . we find , however , that the low temperature behavior above the qpt s does not fully follow theoretical expectations .

spin dimer systems are a promising playground for the detailed study of quantum phase transitions . using the magnetic field as the tuning parameter it is in principle possible to observe a crossover from the characteristic scaling near critical points to the behavior of a finite temperature phase transition . in this work the magneto - caloric behavior of the magnetization with temperature can be used to determine the critical fields with high accuracy , but the critical scaling does not show the expected logarithmic corrections . the results give a unified picture of the full quantum and finite temperature phase diagram .

spin dimer systems are a promising playground for the detailed study of quantum phase transitions . using the magnetic field as the tuning parameter it is in principle possible to observe a crossover from the characteristic scaling near critical points to the behavior of a finite temperature phase transition . in this work we study two - dimensional coupled spin dimer systems by comparing numerical quantum monte carlo simulations with analytical calculations of the susceptibility , the magneto - caloric effect , and the helicity modulus . the magneto - caloric behavior of the magnetization with temperature can be used to determine the critical fields with high accuracy , but the critical scaling does not show the expected logarithmic corrections . the zeros of the cooling rate are an excellent indicator of the competition between quantum criticality and vortex physics , but they are not directly associated with the quantum phase transition or the finite temperature berezinsky - kosterlitz - thouless transition . the results give a unified picture of the full quantum and finite temperature phase diagram .

1404.3688

i

two dimensional spiral waves are observed in many different situations @xcite . in excitable biological tissue such as the cerebral cortex , the myocardium or the retina , spirals are usually precursors to serious pathological conditions @xcite . thus there is great interest in understanding the dynamics of spiral waves , and how these are affected by model parameters and interactions with medium imperfections . one of the most important theoretical breakthroughs in the study of spiral waves has been the adoption of techniques from group - equivariant dynamical systems @xcite . typically the physical systems in which spirals are observed are modeled using systems of reaction - diffusion partial differential equations @xmath0 where @xmath1 is a function @xmath2 which can represent a vector of concentrations , electrical potentials , _ et cetera _ depending on the system being modeled . the function @xmath3 models local reaction dynamics , @xmath4 is an @xmath5 matrix of diffusion coefficients , and @xmath6 are model parameters . equation ( [ rdpde1 ] ) is invariant under the full euclidean group of planar rotations and translations , @xmath7 ( in fact , they are also invariant under reflections in space , but for our purposes , this symmetry will not be useful ) . rigidly and uniformly rotating spiral waves are now well - understood to be _ rotating wave _ solutions of ( [ rdpde1 ] ) in the sense of equivariant dynamical systems @xcite ; that is , evolution in time is the same as a uniform spatial rotation of the initial condition about some point in space . this fact has led to a model - independent understanding of many of the observed dynamical states and bifurcations of spirals , e.g. transition to meandering , resonant linear drifting @xcite . for the purposes of applications , equation ( [ rdpde1 ] ) and the associated symmetry describes a highly idealized situation which is almost never achieved in reality : infinite planar domain which is both homogeneous and isotropic . in practice , media of propagation are finite in extent , so boundaries can play a significant role . also , especially in excitable biological tissue , there are many potential sources of anisotropy and inhomogeneities . many experiments ( both numerical and physical ) have shown that these imperfections have a significant impact on the dynamics of spiral waves @xcite using a model - independent dynamical systems formulation based on the idea of forced symmetry - breaking from @xmath7 to a proper subgroup of @xmath7 , many of these effects ( which result from inhomogeneities and/or anisotropy ) can be explained in terms of simple dynamics and bifurcations @xcite . in some cases , this approach has even led to some predictions which have been later confirmed experimentally @xcite . it is this forced symmetry - breaking approach that we wish to pursue in this paper . specifically , we will be interested in cases in which the euclidean symmetry of ( [ rdpde1 ] ) is broken by a small perturbation which preserves only the symmetry of a regular square lattice . at the cellular level , excitable biological tissues exhibit inhomogeneities in conduction via the gap junctions which separate the cells @xcite . in cases where the spatial scale of the spiral wave is comparable to the cellular scale , it is not unreasonable to assume that the conduction inhomogeneities caused by these gap junctions may have an impact on the dynamics of the spiral . moreover , if one wants to investigate these effects , a reasonable simplifying first order approximation is to assume that the cells are distributed in a regular lattice array . see also @xcite for further motivation . based on the results of @xcite , we expect that the lattice may have stabilising ( anchoring ) effects on the spirals and/or induce meandering . these expectations will indeed be consequences of our results in this paper . at some phenomenological level , it is also expected that our results may be a first step in understanding potential numerical effects induced by spatial - discretization of the domain for integrations of reaction - diffusion partial differential equations . of course in most situations , we expect that numerical discretization effects will be negligeable if the spatial grid is fine enough . however , coarse grids ( relative to the spatial scale of the spiral ) could have effects on the observed dynamics , and our work here could point to what these effects may be . in a specific instance , we argue that forced lattice symmetry - breaking gives results which are consistent with numerically - observed transition from rigidly rotating wave to linearly translating waves ( with retracted tip ) as the rotation frequency of the spiral wave tends to zero @xcite . this paper is organized as follows . in the next section , we establish the symmetry properties we wish to consider , and derive the main center - bundle equations which represent the dynamics on perturbed relative equilibria ( i.e. rotating or travelling waves ) in the context of lattice forced symmetry - breaking . in section 3 , we recall a classic result by hale on averaging and the existence of invariant manifolds for perturbed systems , in a form suitable for our purposes . section 4 deals with the effects of lattice symmetry - breaking perturbations on rotating spiral waves , and section 5 considers the effects of the perturbation on travelling waves . we illustrate some of our results with numerical simulations which are presented in section 6 . the proofs of our two main results are presented in appendices a and b.

it is now well - known that the symmetry properties of the medium of propagation drives many of the dynamics and bifurcations which are experimentally observed for these waves . also , symmetry - breaking induced by boundaries , inhomogeneities and anisotropy have all been shown to lead to different dynamical regimes as to that which is predicted for mathematical models which assume infinite homogeneous and isotropic planar geometry . recent mathematical analyses incorporating the concept of forced symmetry - breaking from the euclidean group of all planar translations and rotations have given model - independent descriptions of the effects of media imperfections on spiral wave dynamics . in this paper , we continue this program by considering rotating waves in dynamical systems which are small perturbations of a euclidean - equivariant dynamical system , but for which the perturbation preserves only the symmetry of a regular square lattice .

spiral waves in two - dimensional excitable media have been observed experimentally and studied extensively . it is now well - known that the symmetry properties of the medium of propagation drives many of the dynamics and bifurcations which are experimentally observed for these waves . also , symmetry - breaking induced by boundaries , inhomogeneities and anisotropy have all been shown to lead to different dynamical regimes as to that which is predicted for mathematical models which assume infinite homogeneous and isotropic planar geometry . recent mathematical analyses incorporating the concept of forced symmetry - breaking from the euclidean group of all planar translations and rotations have given model - independent descriptions of the effects of media imperfections on spiral wave dynamics . in this paper , we continue this program by considering rotating waves in dynamical systems which are small perturbations of a euclidean - equivariant dynamical system , but for which the perturbation preserves only the symmetry of a regular square lattice .

1209.3232

c

the elastic properties of a model of interacting 4f - electron quadrupolar densities on a compressible fcc lattice have been investigated as a function of temperature and pressure . on the basis of previous theoretical work @xcite this model , supported by recent nuclear spectroscopy experiments @xcite , is taken as representative for the @xmath1 isostructural " phase transition in ce . in particular , we have studied by analytical theory the pressure dependent anomalies of the elastic constant @xmath3 at the phase transition from the quadrupolar orientationally disoredered phase which we identify with the @xmath6-phase ( space group @xmath19 ) to the quadrupolar orientationally ordered phase which we identify with the @xmath7-phase ( space group @xmath2 ) . as a result we find that @xmath3 ( equivalently the longitudinal sound velocity ) decreases by approaching the phase transition from the disoredered phase with increasing pressure @xmath224 , at the first order phase transition @xmath3 exhibits a positive jump , in the ordered phase @xmath3 increases continuously with pressure @xmath326 . on the other hand we find that the elastic constant @xmath4 ( equivalently the shear sound velocity ) exhibits no precursor effects near the transition . these theoretical results are in full qualitative agreement with experiments [ 34,21,22,33 ] on elastic anomalies at the @xmath1 isostructural " phase transition in solid ce . we notice that the hamiltonian @xmath32 , eq . ( [ m17 ] ) , which is quadratic in the electronic quadrupolar order parameter variables and linear in the lattice displacements , accounts as well for the elastic anomalies as for the isostructural " lattice contraction . the hamiltonian is reminiscent from the compressible ising model @xcite which is quadratic in the spin variables and linear in the lattice displacements . however , in the present case symmetry properties are more subtle and account for the interplay between antiferroquadrupolar order in the electronic densities and isostructural " lattice contraction . here a remark on symmetry reduction at the phase transition is in order . the quadrupolar interaction has its origin in the repulsive coulomb interaction between 4f - electrons on neighboring atoms . the ordering of the electronic quadrupoles on four sc sublattices reduces the repulsion and acts as an effective attraction . in reciprocal space the quadrupolar interaction matrix @xmath74 , eq . ( [ m10 ] ) , has negative eigenvalues at the @xmath16-point of the brillouin zone of the fcc lattice . phonon dispersions of ce measured by synchrotron radiation show pressure dependent anomalies related to the @xmath1 transition at the @xmath16-point of the brillouin zone @xcite . the explanation of these experiments is an outstanding challenge for theoretical work . a further problem is the quantitative improvement of the theory which should lead to increase the magnitude of the coupling coefficient @xmath146 in eq . ( [ m19 ] ) for @xmath32 . at present we believe that the theory should be extended by including the intrasite coupling between 4f - electrons and conduction electrons ( say 5d ) and a possible influence of this coupling on the interatomic bonding . an indication of the relevance of such a mechanism is provided by recent work on the ce dimer @xcite . likely such an extension of the theory would also contribute to elucidate the concept of a mott transition @xcite versus a kondo scenario @xcite at the @xmath1 transition . the authors acknowledge useful discussions with k. parlinski , m. krisch , f. decremps , r.m . pick , g. roth , g. gntherodt , a.v . tsvyashchenko and e.v . . financial support has been provided by the research group theory of condensed matter , university of antwerp and by the institut fr kristallographie , rwth aachen . here we express @xmath295 as a function of the order parameter susceptibility @xmath191 . starting from eqs . ( [ m35 ] ) and ( [ m70n ] ) we first notice that @xmath327 where @xmath328 we rewrite eq . ( [ m35 ] ) as @xmath329 . \nonumber \\ \label{a3}\end{aligned}\ ] ] we then approximate the four - point function @xmath330 by the factorization scheme @xmath331 or equivalently @xmath332 substituting this result into eq . ( [ a3 ] ) and using eq . ( [ fe39n ] ) we obtain @xmath333 taking the limit @xmath334 leads to the result of eq . ( [ m36 ] ) . d.c . koskenmaki and k.a . gschneidner , jr . , _ handbook on the physics and chemistry of rare earths _ gschneidner , jr . , and l. eyring ( amsterdam : north - holland , 1978 ) , p. 337 . p. w. bridgman , proc . arts sci . * 76 * , 55 ( 1948 ) . macpherson , g.e . everett , d. wohlleben , m.b . maple , phys . * 26 * , 20 ( 1971 ) . l. d. landau and e. m. lifshitz . : _ statistical physics _ , ( pergamon , bristol , 1995 ) , vol . 5 . a. w. lawson , t .- y . tang , phys . rev . * 76 * , 301 ( 1949 ) . b. johansson , phil . mag . * 30 * , 469 ( 1974 ) . b. johansson , i.a . abrikosov , m. aldn , a.v . ruban , and h.l . skriver , phys . lett . * 74 * , 2335 ( 1995 ) . murani , s.j . levett , and j.w . taylor , phys . lett . * 95 * , 256403 ( 2005 ) . a. hjelm , j. trygg , o. eriksson , b. johansson , and j. wills , phys . b * 50 * , 4332 ( 1994 ) . x. cao and m. dolg , mol . * 101 * , 1967 ( 2003 ) . roos , r. lindh , p .- a . malmqvist , v. veryazov , and p .- o . widmark , j. phys . a * 112 * , 11431 ( 2008 ) . nikolaev , phys . rev . a * 84 * , 012512 ( 2011 ) . allen , r.m . martin , phys . * 49 * , 1106 ( 1982 ) ; j.w . allen and l.z . liu , phys . b * 46 * , 5047 ( 1992 ) . m. lavagna , c. lacroix , and m. cyrot , phys . a * 90 * , 210 ( 1982 ) . p. fulde , _ electron correlations in molecules and solids _ ( springer heidelberg , 1995 ) . liu , j.w . allen , o. gunnarsson , n.e . christensen , and o.k . andersen , phys . b * 45 * , 8934 ( 1991 ) . b. johansson , a. v. ruban , and i. a. abrikosov , phys . . lett . * 102 * , 189601 ( 2009 ) . b. amadon , s. biermann , a. georges , and f. aryasetiawan , phys . lett . * 96 * , 066402 ( 2006 ) . j .- rueff , j .- iti , m. taguchi , c.f . hague , j .- mariot , r. delaunay , j .- kappber , and n. jaonen , phys . lett . * 96 * , 237403 ( 2006 ) . g.eliashberg , h.capellmann , jetp lett . * 67 * , 125 ( 1998 ) . jeong , t.w . darling , m. j. graf , th . proffen , r. h. heffner , y. lee , t. vogt , j. d. jorgensen , phys . lett . * 92 * , 105702 ( 2004 ) . lipp , d. jackson , h. cynn , c. aracne , w. j. evans , and a. k. mcmahan , phys . * 101 * , 165703 ( 2008 ) . a.v . nikolaev and k.h . michel , eur . j. b * 9 * , 619 ( 1999 ) . a.v . nikolaev and k.h . michel , eur . j. b * 17 * , 15 ( 2000 ) . a.v . nikolaev and k.h . michel , phys . b * 66 * , 054103 ( 2002 ) . r. sachidanandam and a.b . harris , phys . 67 * , 1467 ( 1991 ) ; p.a . heiney , j.e . fischer , a.r . mcghie , w.j . romanow , a.m. denenstein , j.p . mccauly jr . , a.b . smith iii , and d.e . cox , ibid . * 67 * , 1468 ( 1991 ) . david , r.m . ibberson , j.c . matthewman , k. prassides , t.j.s . dennis , j.p . hare , h.w . kroto , d.r.m . walton , nature , * 353 * , 147 ( 1991 ) . david , r.m . ibberson , t.j.s . dennis , j.p . hare , k. prassides , europhys . lett . * 18 * , 219 ( 1992 ) . heiney , g.b.m . vanghan , j.e . fischer , n. coustel , d.e . cox , j.r.d . copley , d.a . neumann , w.a . kamitakahara , k.m . creegan , d.m . cox , j.p . mccauley , jr . , and smith iii , phys . b * 45 * , 4544 ( 1992 ) . f. decremps , l. belhadi , d.l . farber , k.t . moore , f. occelli , m. ganthier , a. polian , d. antonangeli , c. m. aracne - ruddle , and b. amadon , phys . lett . * 106 * , 065701 ( 2011 ) . tsvyashchenko , a.v . nikolaev , a.i . velichkov , a.v . salamatin , l.n . fomicheva , g.k . ryasny , a.a . sorokin , o.i . kochetov , m. budzynski , and k.h . michel , phys . b * 82 * , 092102 ( 2010 ) ; a.v . tsvyashchenko , a.v . nikolaev , a.i . velichkov , a.v . salamatin , l.n . fomicheva , g.k . ryasny , a.a . sorokin , o.i . kochetov and m. budzynski , jetp * 111 * , 627 ( 2010 ) . m. krisch , d.l . farber , r. xu , d. antonangeli , c. m. aracne , a. beraud , t .- c . chiang , j. zarestky , d. y. kim , e. i. isaev , r. ahuja , and b. johansson , pnas ( usa ) * 108 * , 9343 ( 2011 ) . f. decremps , d. antonangeli , b. amadon , and g. schmerber , phys . b * 80 * , 132103 ( 2009 ) . f.f.voronov , l.f.vereshchagin and v.a.goncharova , doklad . nauk sssr , * 135 * , 1104 ( 1960 ) , engl soviet phys . doklady , * 135 * , 1280 ( 1960 ) . c. stassis , t. gould , o.d . mcmasters , and k.a . gschneidner , jr . , and r.m . nicklow , phys . b * 19 * , 5746 ( 1979 ) . w. schranz , a. fuith , p. dolinar , h. warhanek , m. haluska , and h. kuzmany , phys . lett . * 71 * , 1561 ( 1993 ) . a. lundin and b. sundqvist , phys . b * 53 * , 8329 ( 1996 ) bradley and a.p . cracknell , _ the mathematical theory of symmetry in solids _ , ( clarendon , oxford , 1972 ) . p. zielinski and k. parlinski , j. phys . c : solid state phys . * 17 * , 3287 ( 1984 ) . michel , j.r.d . copley , d.a . neumann , phys . 68 * , 2929 ( 1992 ) . d. lamoen , k.h . michel , phys . b * 48 * , 807 ( 1993 ) . moore , l. belhadi , f. decremps , d.l . faber , j.a . bradley , f. occelli , m. gauthier , a. polian , and c.m . aracne - ruddle , acta materialia * 59 * , 6007 ( 2011 ) . samara , j.e . schirber , b. morosin , l.v . hansen , d. loy , and a.p . sylwester , phys . lett . * 67 * , 3136 ( 1991 ) . g. kriza , j .- c . ameline , d. jrome , a. dworkin , h. swarc , c. fabre , d. schtz , a. rassat , p. bbernier , and a. zahab , j. phys . i ( france ) * 1 * , 1361 ( 1991 ) . p.m. chaikin and t.c . lubensky , _ principles of condensed matter physics _ , cambridge university press , cambridge ( 1995 ) . w. gtze and k.h . michel , in _ dynamical properties of solids _ , horton and a.a . maradudin eds . , north - holland publ . comp . 1974 , ch . 9 , zubarev , soviet physics uspekhi * 3 * , 320 ( 1960 ) . , t. gowers , editor , princeton university press ( 2008 ) , p. 27 . h. wagner and j. swift , z. phys . * 239 * , 182 ( 1970 ) . d.j . bergman and b.i . halperin , phys . b * 13 * , 2145 ( 1976 ) . k. gofryk , e.k.h . salje , d.j . safarik , j.l . smith , x. ding , a.c . lawson , p.s . riseborough , b. mihaila , and j.c . lashley ( submitted ) .

starting from a model of 4f - electron generated quadrupolar densities on a compressible fcc lattice , the elastic anomalies at the @xmath0 phase transition are studied by means of analytical theory . the model is taken as representative for the @xmath1 phase transition in ce . the condensation of the quadrupolar densities into the orientationally ordered @xmath2 structure is studied as function of temperature and pressure . the theoretical results are in excellent qualitative agreement with pressure experiments on the elastic constants ( equivalently on sound velocities ) at the @xmath1 transition in ce .

starting from a model of 4f - electron generated quadrupolar densities on a compressible fcc lattice , the elastic anomalies at the @xmath0 phase transition are studied by means of analytical theory . the model is taken as representative for the @xmath1 phase transition in ce . the coupling of the ( linear ) lattice displacements to the square of the quadrupolar orientational density fluctuations renormalizes the elastic constants . the condensation of the quadrupolar densities into the orientationally ordered @xmath2 structure is studied as function of temperature and pressure . precursor effects of the transition lead to an anomalous softening of the elastic constant @xmath3 while @xmath4 exhibits no such softening . the theoretical results are in excellent qualitative agreement with pressure experiments on the elastic constants ( equivalently on sound velocities ) at the @xmath1 transition in ce . lattice dynamical analogies in theory and striking similarities in experimental results with the @xmath0 transition in c@xmath5 fullerite are discussed .

cond-mat9509072

i

upt@xmath7 is generally believed to be a reduced symmetry superconductor , i.e. , one that breaks rotational and/or time reversal symmetries of the normal state , in addition to the u(1 ) gauge symmetry@xcite . the strongest basis for this belief is the phase diagram which displays multiple superconducting phases@xcite , just as liquid @xmath8he has multiple superfluid phases . in this paper we shall study surface superconductivity in upt@xmath7 , and see if competing models make differing predictions which might be experimentally tested . we briefly review the existing models for the order parameter in upt@xmath7 . there are two main classes . the first class , which we shall refer to as ` @xmath2 ' models@xcite , entails a single two - component order parameter , which may belong to any of the two - dimensional representations ( @xmath9 , @xmath10 , @xmath11 , @xmath12 ) of @xmath13 , the point group of normal upt@xmath7@xcite . the second class of models posits two independent order parameters belonging to different representations@xcite . in one subclass @xcite , which can be analyzed in great detail , comprising what we shall call ` @xmath1 ' models , both order parameters have the same parity ; one transforms as an @xmath14 representation and the other as a @xmath15 representation of @xmath13 . thus , if the common parity is even@xcite , the pair of order parameters transforms in one of four possible ways : ( @xmath16 , @xmath17 ) , ( @xmath16 , @xmath18 ) , ( @xmath19 , @xmath17 ) , ( @xmath19 , @xmath18 ) . this division into two classes is useful because in the simplest form of ginzburg - landau ( gl ) theory in which only terms that are formally of order @xmath20 are kept , all @xmath2 models have the same formal gl free energy , and all @xmath1 models have the same gl free energy . this leads one to sometimes refer to them in the singular as the @xmath2 model or the @xmath1 model . the @xmath2 model invokes a symmetry breaking field ( sbf ) , usually taken to be a weak antiferromagnetism that sets in at 5 k@xcite , in order to split the superconducting transition in zero field into two transitions as observed . the @xmath1 model posits two nearby transition temperatures by fiat . the original version of the @xmath2 model was shown to be incompatible @xcite with experiments in that it fails to yield a tetracritical point in the @xmath21-@xmath6 plane for @xmath4 @xcite . ( whether there is or is not a _ true _ tetracritical point in the experimentally observed phase diagram is irrelevant . at the very least one has two phase boundaries @xmath22 and @xmath23 that approach within 10 - 15 mk of one another , and the outermost line @xmath22 has a sharp change in the sign of the curvature near this apparent tetracritical point . the theory can not explain this ` near collision ' either . ) this led us to propose the @xmath1 model which does not have this flaw . our proposal in turn led sauls to propose a refinement of the @xmath2 model@xcite , which has three ingredients : ( i ) a specific @xmath12 order parameter ( see below ) , ( ii ) a nearly cylindrically symmetric fermi surface , and ( iii ) coupling of the gradient terms in the gl free energy to the sbf . a cylindrical fermi surface causes the dangerous gradient coupling terms in the free energy @xcite to vanish within weak coupling bcs theory for an @xmath24 order parameter , and in conjunction with ingredient ( iii ) restores the tetracritical point for @xmath4 . in this paper we shall use gl theory to calculate @xmath3 for upt@xmath7 within the original @xmath2 model and the @xmath1 model . the gl free energy for the refined @xmath2 model is mathematically isomorphic to , and can be regarded as a special case of , the @xmath1 model free energy@xcite . since the key issue that determines @xmath3 is the boundary condition on the order parameter , however , the refined @xmath12 model of sauls will have the same @xmath25 curves as the unrefined @xmath12 model for @xmath26 . indeed , @xmath3 curves may be similar for these two models even when @xmath27 , except that one must beware of kinks in the refined model . we will limit ourselves to cases where the field @xmath28 and the surface normal @xmath29 lie in high crystal symmetry directions or planes . further , we only consider ideal , or specularly reflecting surfaces . the motivation for this study is that we expect qualitative differences in the behavior of @xmath3 between the various models for various geometries . firstly , the boundary conditions are different amongst the @xmath2 models , leading to differences in @xmath3 . secondly , in the @xmath1 model the eigenvalue equations for @xmath3 decouple into separate equations for two components , and whenever the surface supports both components , the @xmath3 curve is expected to mirror @xmath30 and show a kink . in the @xmath2 model , on the other hand , even for @xmath31 , the gradient terms can couple the two components . it is thus possible for the kink in @xmath3 to be smoothed out . we shall see that whether this happens or not is a question of dynamics , not symmetry . in fact , there turns out to be no smoothing with the gradient coupling values we use . a short quantitative estimate of this effect seems to be hard to get , however , so we present the full analysis which follows . since an experimental measurement of @xmath3 has now been reported @xcite for some of the geometries that we study , we can use our results to restrict the acceptable order parameters for upt@xmath7 . we also hope that our work will spur a more detailed experimental study of @xmath3 in other geometries as well , as this will sharpen our understanding of the order parameter even further . we note here that as this paper was being written , we learned of a recent paper by samokhin@xcite , also discussing @xmath3 in upt@xmath7 within @xmath2 models . samokhin gives a microscopic foundation to the boundary conditions on the order parameter@xcite , while we take a purely phenomenological approach . further , he focuses on the case where @xmath27 , and the surface normal is arbitrarily oriented in the @xmath32-@xmath33 plane . we have largely avoided detailed study of the @xmath34 geometry because of the problems it presents in comparing to the observed bulk upper critical field . thus samokhin s work is nicely complementary to ours . the rest of the paper is organized as follows . in sec . ii , we recapitulate the bare essentials of the theory of surface superconductivity for fully symmetric superconductors with a complex scalar order parameter , paying special attention to the boundary conditions . we then extend these ideas to the @xmath1 and @xmath2 models . the case of the @xmath2 model is rather rich . depending on the exact order parameter and field and surface orientation , the surface may or may not suppress superconductivity . we tabulate these cases and proceed to study them in secs . iii and iv . certain technical aspects of the calculations are given in the appendix . in sec . v , we compare our results with the experiments of keller _ et . @xcite , and see which order parameters are compatible . our results are summarized in table iii , and the reader who is not interested in the details of the analysis should skip to that directly . we conclude with suggestions for future work .

surface superconductivity is studied within ginzburg - landau theory for two classes of models for the order parameter of upt@xmath0 . the first class assumes two independent one - dimensional order parameters ( @xmath1 models ) , while the second assumes a single two - dimensional order parameter ( @xmath2 models ) . assuming specular reflection , it is found that except when @xmath4 , the ratio @xmath5 is either unity or equals its ` s - wave ' value 1.695 , although the precise @xmath3 vs. @xmath6 curve predicted by the @xmath1 and @xmath2 models differs for various geometries .

surface superconductivity is studied within ginzburg - landau theory for two classes of models for the order parameter of upt@xmath0 . the first class assumes two independent one - dimensional order parameters ( @xmath1 models ) , while the second assumes a single two - dimensional order parameter ( @xmath2 models ) . @xmath3 is calculated for all cases where the surface normal and magnetic field lie along high symmetry directions . assuming specular reflection , it is found that except when @xmath4 , the ratio @xmath5 is either unity or equals its ` s - wave ' value 1.695 , although the precise @xmath3 vs. @xmath6 curve predicted by the @xmath1 and @xmath2 models differs for various geometries . the results are compared with recent experiments , and predictions are made for future experiments .

1610.04763

i

in high intensity accelerators , the nonlinear space - charge effect from charged particle interactions inside the beam has significant impact on beam dynamics through the accelerator . it causes beam emittance growth , halo formation , and even particle losses along the accelerator . to study the space - charge effect , multi - particle tracking has been employed to dynamically follow those charged particles through the accelerator . in the accelerator community , most of those multi - particle tracking codes use particle - in - cell ( pic ) method to include the space - charge effect self - consistently in the simulation @xcite . the particle - in - cell method is an efficient method in handling the space - charge effect self - consistently . it uses a computational grid to obtain the charge density distribution from a finite number of macroparticles and solves the poisson equation on the grid at each time step . the computational cost is linearly proportional to the number of macroparticles , which makes the simulation fast for many applications . however , those grid based , momentum conserved , pic codes do not satisfy the symplectic condition of classic multi - particle dynamics . violating the symplectic condition in multi - particle tracking might not be an issue in a single pass system such as a linear accelerator . in a circular accelerator , violating the symplectic condition may result in undesired numerical errors in the long - term tracking simulation . this issue together with the numerical grid heating was brought up during the 2015 space - charge workshop at oxford @xcite . a gridless spectral based macroparticle model was suggested by the author at the workshop to mitigate the numerical grid heating and to satisfy the symplectic condition of particle tracking . multi - symplectic particle - in - cell model was proposed to study vlasov - maxwell system and electrostatic system in plasmas using a variational method @xcite . to study the space - charge effect in high intensity beams , a quasi - static model is normally employed . in the quasi - static model , a moving beam frame is used to contain all charged particles through the accelerator . the poisson equation is solved in the beam frame to obtain electric coulomb fields from the charged particles . these electric fields are transformed to the laboratory frame through the lorentz transformation . the space - charge forces acting on each individual particle include both the electric fields and the magnetic fields , which is different from the electrostatic model that includes only electric fields . to the best of our knowledge , at present , there is no symplectic self - consistent space - charge model available in the accelerator community . in this paper , following the idea suggested at the oxford workshop , we present a two - dimensional and a three - dimensional symplectic quasi - static multi - particle tracking model for space - charge simulations . the model presented here starts from the multi - particle hamiltonian directly and uses a gridless spectral method to calculate the space - charge forces . the organization of this paper is as follows : after the introduction , we present the symplectic multi - particle tracking model including the space - charge effect in section ii ; we present a symplectic space - charge transfer map for a 2d coasting beam in section iii and a symplectic space - charge map for a 3d bunched beam in section iv ; we discuss computational complexity of the proposed model in section v and draw conclusions in section vi .

symplectic tracking is important in accelerator beam dynamics simulation . so far , to the best of our knowledge , there is no self - consistent symplectic space - charge tracking model available in the accelerator community . in this paper , we present a two - dimensional and a three - dimensional symplectic multi - particle spectral model for space - charge tracking simulation .

symplectic tracking is important in accelerator beam dynamics simulation . so far , to the best of our knowledge , there is no self - consistent symplectic space - charge tracking model available in the accelerator community . in this paper , we present a two - dimensional and a three - dimensional symplectic multi - particle spectral model for space - charge tracking simulation . this model includes both the effect from external fields and the effect of self - consistent space - charge fields using a split - operator method . such a model preserves the phase space structure and shows much less numerical emittance growth than the particle - in - cell model in the illustrative examples .

1105.2277

i

pseudogap or partial gap in the electronic structure , affecting some regions of the fermi surface while leaving other unaffected , is one of the key signatures of the underdoped cuprates @xcite . it is revealed through anomalous behaviors of the temperature - dependent resistivity , magnetization , nmr knight shift and relaxation rate , as well as in spectroscopic data @xcite . pseudogap shows the same @xmath7-space distribution as the superconducting gap @xcite and is universally observed in hole- and electron- doped cuprates in the underdoped regime . features consistent with pseudogap are also clearly found in hole doped feas - based materials ( see @xcite for a review ) . because the parent compounds of iron pnictides are metals , the pseudogap here is believed to arise from nesting instability @xcite . in ba(fe@xmath1t@xmath2)@xmath3as@xmath3 ( bat122 in the following)substitution of the transition metals into fe position leads to electron doping . nmr studies suggest the existence of a pseudogap in baco122 over the broad doping range including full domain of superconductivity , from magnetically ordered parent compound to non - superconducting metal . existence of pseudogap leads to a temperature - dependent knight shift @xmath8 , well described by a formula @xmath9 , where the first term describes contribution of the metallic portion of the fermi surface and the second activated term allows determination of the @xmath10 as 560 k @xmath11150 k at optimal doping @xcite . at temperatures @xmath12 this leads to temperature independent knight shift and a crossover to metallic temperature dependence in the inter - plane resistivity @xcite . no discernible features are observed in the in - plane resistivity @xcite , which suggests that the areas of the fermi surface affected by pseudo - gap are rather small and belong to the most warped parts of the fermi surface , contributing mostly to inter - plane transport . in this article we report a systematic study of the evolution of the inter - plane resistivity with doping by other transition metals inducing superconductivity in ba122 , @xmath4= rh , ni , pd . we show that similar anomalies are observed in the temperature dependent inter - plane resistivity for all types of substitution , with the characteristic temperature of resistive crossover being suppressed with doping . the rate of @xmath5 suppression with @xmath13 is however notably higher in ni and pd doped compositions , even with correction for a difference in number of added electrons . the doping - dependence of the pseudogap feature suggests that it represents an independent energy scale in the problem , different from that of structural / magnetic transition and superconductivity .

temperature - dependent inter - plane resistivity , @xmath0 , was measured systematically as a function of transition metal substitution in the iron - arsenide superconductors ba(fe@xmath1t@xmath2)@xmath3as@xmath3 , @xmath4= ni , pd , rh . these features are consistent with the existence of a charge gap covering part of the fermi surface .

temperature - dependent inter - plane resistivity , @xmath0 , was measured systematically as a function of transition metal substitution in the iron - arsenide superconductors ba(fe@xmath1t@xmath2)@xmath3as@xmath3 , @xmath4= ni , pd , rh . the data are compared with the behavior found in ba(fe@xmath1co@xmath2)@xmath3as@xmath3 , revealing resistive signatures of pseudogap . in all compounds we find resistivity crossover at a characteristic pseudogap temperature @xmath5 from non - metallic to metallic temperature dependence on cooling . suppression of @xmath5 proceeds very similar in cases of ni and pd doping and much faster than in similar cases of co and rh doping . in cases of co and rh doping an additional minimum in the temperature - dependent @xmath6 emerges for high dopings , when superconductivity is completely suppressed . these features are consistent with the existence of a charge gap covering part of the fermi surface . the part of the fermi surface affected by this gap is notably larger for ni and pd doped compositions than in co and rh doped compounds .

1105.2277

r

in the top panel of fig . [ rh ] we plot inter - plane resistivity of ba(fe@xmath1rh@xmath2)@xmath3as@xmath3 , using normalized scale @xmath16 . to avoid overlapping , the curves are offset progressively upwards for higher dopings . the data for parent compound are reproduced from ref . . several features of the temperature dependence are essentially the same as observed in compositions with co doping @xcite . for low doping @xmath17=0.012 , @xmath18 shows resistivity increase on cooling for @xmath19 ( marked with an arrow ) , which is the pseudogap feature in all compositions studied . on reaching a temperature of structural / magnetic transition @xmath20 , resistivity dives down , and decreases monotonically all the way to base temperature , showing some signatures of filamentary superconductivity at about 20 k due to strain @xcite . this decrease of resistivity below @xmath20 is similarly observed in lightly co doped composition @xmath21= 0.012 @xcite . for higher dopings @xmath17=0.026 and @xmath17=0.39 resistivity shows increase below @xmath20 and drop to zero below superconducting @xmath22 , in complete accord to the behavior found in co - doped compositions . finally , for compositions in which structural / magnetic transition is completely suppressed , @xmath23 , position of the resistivity maximum shifts down in temperature and for an ultimate doping @xmath24= 0.171 , when superconductivity is completely suppressed , the resistivity shows shallow minimum , marked with cross arrow in fig . [ rh ] . the fact of the appearance of the minimum at high dopings and even the doping value at which it appears are very similar to those found in co - doped compounds . we summarize our observations in the temperature - doping , @xmath4-@xmath13 , phase diagram in bottom panel of fig . [ rh ] . , normalized by its value at room temperature @xmath25 , for samples of ba(fe@xmath1rh@xmath2)@xmath3as@xmath3 with @xmath26 ( slightly above the concentration boundary for the superconducting dome ) . lines are offset , from bottom to top , @xmath17= 0 , 0.012 , 0.026 , 0.039 , 0.076 , 0.096 , 0.131 and 0.171 ( top panel ) . arrows show a position of the resistivity maximum , @xmath5 , cross - arrow shows a position of the resistivity minimum @xmath27 . bottom panel shows the @xmath28 phase diagram , in which lines of structural @xmath20 , magnetic @xmath29 and superconducting @xmath22 states are determined from in - plane resistivity and magnetization measurements , see ref . . , title="fig:",width=151 ] , normalized by its value at room temperature @xmath25 , for samples of ba(fe@xmath1rh@xmath2)@xmath3as@xmath3 with @xmath26 ( slightly above the concentration boundary for the superconducting dome ) . lines are offset , from bottom to top , @xmath17= 0 , 0.012 , 0.026 , 0.039 , 0.076 , 0.096 , 0.131 and 0.171 ( top panel ) . arrows show a position of the resistivity maximum , @xmath5 , cross - arrow shows a position of the resistivity minimum @xmath27 . bottom panel shows the @xmath28 phase diagram , in which lines of structural @xmath20 , magnetic @xmath29 and superconducting @xmath22 states are determined from in - plane resistivity and magnetization measurements , see ref . . , title="fig:",width=151 ] in fig . [ rhco ] we compare explicitly the phase diagrams of the pseudogap features in @xmath14-axis resistivity of co and rh doped compounds . within rather big error bars due to crossover character of features , the diagrams are overlapping . this fact is remarkable , since despite electronic equivalence of co and rh doping , the @xmath14-axis lattice parameters are different in two materials @xcite , and thus it would be natural that this difference should affect characteristic energy scales of the electronic overlap in the interplane direction . , in @xmath4=rh ( solid symbols , this study ) and @xmath4=co ( open symbols , ref . ) doped ba(fe@xmath1t@xmath2)@xmath3as@xmath3 . pseudogap features for two types of doping overlap within error bars , similar to lines of structural @xmath20 , magnetic @xmath29 and superconducting @xmath22 transitions , ref . . vertical lines separate composition ranges in which fermi surface topology changes in @xmath4=co @xcite . , width=302 ] in fig . [ ni ] and fig . [ pd ] we show doping - evolution of the temperature - dependent interplane resistivity in samples doped with transition metals of group 10 of mendeleev periodic table , 3@xmath30 @xmath4=ni and 4@xmath30 @xmath4=pd . these atoms donate two electrons on substituting fe , and thus substitution level required to induce superconductivity is two times lower than in cases of co and rh doping . bottom panels of the fig . [ ni ] and fig . [ pd ] , show doping phase diagram of the pseudogap features in interplane resistivity . the suppression of characteristic temperature of the resistivity maximum , @xmath5 , is much more rapid for cases of ni and pd doping , and @xmath31 line in the phase diagram suggests critical concentration very close to the edge of the superconducting dome . moreover , for highest doping levels resistivity monotonically decreases with temperature and does not reveal a minimum at @xmath27 as in cases of co and rh doping . on the other hand , similar to the case of co and rh , the phase diagrams of ni and pd dopings coincide within error bars , see top panel of fig . [ nipdrh ] . , normalized by its value at room temperature @xmath25 , for samples of ba(fe@xmath1ni@xmath2)@xmath3as@xmath3 with @xmath32 ( slightly above the concentration boundary for the superconducting dome ) . lines are offset , from bottom to top , @xmath33= 0 , 0.0067 , 0.016 , 0.024 , 0.032 , 0.054 , and 0.072 ( top panel ) . arrows show a position of the resistivity maximum , @xmath5 , used to plot the phase diagram , see fig . [ nipdphased ] . , width=302 ] , normalized by its value at room temperature @xmath25 , for samples of ba(fe@xmath1pd@xmath2)@xmath3as@xmath3 with @xmath34 ( slightly above the concentration boundary for the superconducting dome ) . lines are offset , from bottom to top , @xmath35= 0 , 0.012 , 0.021 , 0.027 , 0.030 , 0.053 , and 0.077 ( top panel ) . arrows show a position of the resistivity maximum , @xmath5 , used to plot the phase diagram , see fig . [ nipdphased ] . , title="fig:",width=302 ] = ni ( solid symbols ) and @xmath4=pd ( open symbols ) doped ba(fe@xmath1t@xmath2)@xmath3as@xmath3 as determined from inter - plane resistivity measurements . lines of structural @xmath20 , magnetic @xmath29 and superconducting @xmath22 states are determined from in - plane resistivity and magnetization measurements , see ref . . all characteristic features for two types of doping overlap within error bars . , title="fig:",width=302 ]

the data are compared with the behavior found in ba(fe@xmath1co@xmath2)@xmath3as@xmath3 , revealing resistive signatures of pseudogap . in all compounds we find resistivity crossover at a characteristic pseudogap temperature @xmath5 from non - metallic to metallic temperature dependence on cooling . an additional minimum in the temperature - dependent @xmath6 emerges for high dopings , when superconductivity is completely suppressed .

temperature - dependent inter - plane resistivity , @xmath0 , was measured systematically as a function of transition metal substitution in the iron - arsenide superconductors ba(fe@xmath1t@xmath2)@xmath3as@xmath3 , @xmath4= ni , pd , rh . the data are compared with the behavior found in ba(fe@xmath1co@xmath2)@xmath3as@xmath3 , revealing resistive signatures of pseudogap . in all compounds we find resistivity crossover at a characteristic pseudogap temperature @xmath5 from non - metallic to metallic temperature dependence on cooling . suppression of @xmath5 proceeds very similar in cases of ni and pd doping and much faster than in similar cases of co and rh doping . in cases of co and rh doping an additional minimum in the temperature - dependent @xmath6 emerges for high dopings , when superconductivity is completely suppressed . these features are consistent with the existence of a charge gap covering part of the fermi surface . the part of the fermi surface affected by this gap is notably larger for ni and pd doped compositions than in co and rh doped compounds .

1105.2277

c

in systematic study of doping phase diagrams for a variety of transition metal dopants : co , rh , ni , pd , cu and cu+co , it was found that the superconducting transition temperature @xmath22 scales with the number of doped electrons , @xmath36 , while the structural / magnetic transition temperatures scale with number of dopant atoms @xmath37 . it is therefore interesting if pseudogap features follow either of these scaling relations . while the break - up of @xmath38 scaling is obvious from the comparison of fig . [ rhco ] and figs . [ ni ] , [ pd ] , in bottom panel of fig . [ nipdrh ] we compare the phase diagrams of rh and pd doped bafe@xmath3as@xmath3 vs the number of extra electrons @xmath39 . it is clear that the pseudogap temperature does not scale with @xmath39 , contrary to the supercoducting transition temperature . because of relatively big error bar in determination of the pseudogap features , in the bottom panel of fig . [ nipdrh ] we compare pseudogap features for all four compounds studied . the difference between the two columns is still clearly resolved , supporting the lack of the scaling of pseudogap features with @xmath39 . the difference in doping dependence of pseudogap features pushes us to recognize pseugogap as an independent characteristic scale in the phase diagram of ba122 materials . . bottom panel shows phase diagram of the pseudogap features for all studied transition metals . resistivity maximum , @xmath5 , for rh ( blue solid up - triangles ) , co ( black solid diamonds ) , pd ( open down - triangles ) and ni ( red solid squares ) and resistivity minimum , @xmath27 , for rh ( solid pink star ) and co ( open black circles ) . , title="fig:",width=151 ] . bottom panel shows phase diagram of the pseudogap features for all studied transition metals . resistivity maximum , @xmath5 , for rh ( blue solid up - triangles ) , co ( black solid diamonds ) , pd ( open down - triangles ) and ni ( red solid squares ) and resistivity minimum , @xmath27 , for rh ( solid pink star ) and co ( open black circles ) . , title="fig:",width=151 ] the evolution of the fermi surface topology in baco122 with doping was studied using arpes and thermopower measurements @xcite . a sequence of three lifshits transitions was found , with concentration boundaries at @xmath40=0.3 , @xmath41=0.11 and @xmath42=0.195 @xcite . these are shown with grey lines in fig . unexpectedly , doping evolution of the pseudogap temperature @xmath5 shows little correlation with characteristic features in the fermi surface evolution . in particular , hole pocket near @xmath43 point in the brillouin zone changes shape from cylindrical to ellipsoidal at @xmath41 , but merely any feature can be noticed in @xmath31 , see fig . considering low anisotropy of electrical resistivity of the compounds , it is not clear which cylinder of the fermi surface is responsible for carrier activation , however , pseudogap affects most strongly the most warped portions . comparison of the temperature - dependent inter - plane resistivities for heavily overdoped rh @xmath17=0.171 and pd @xmath35=0.077 shows an interesting difference . the resistivity monotonically decreases with heating for @xmath35=0.077 , top curve in fig . [ pd ] , decreasing from low temperatures to room temperature by a factor of 2 . very similar magnitude of decrease is observed in sample with @xmath33=0.072 , top curve fig . the magnitude of decrease in @xmath17=0.171 , top curve in fig . [ rh ] , is merely 10% , and the curve shows metallic resistivity increase on heating above @xmath44200 k. this difference suggests that the intact metallic part of the fermi surface , contributing to the interplane transport , is notably smaller for ni and pd doping , than in cases of co and rh doping . it is interesting if this difference can be found in nmr studies as well .

suppression of @xmath5 proceeds very similar in cases of ni and pd doping and much faster than in similar cases of co and rh doping . in cases of co and rh doping the part of the fermi surface affected by this gap is notably larger for ni and pd doped compositions than in co and rh doped compounds .

temperature - dependent inter - plane resistivity , @xmath0 , was measured systematically as a function of transition metal substitution in the iron - arsenide superconductors ba(fe@xmath1t@xmath2)@xmath3as@xmath3 , @xmath4= ni , pd , rh . the data are compared with the behavior found in ba(fe@xmath1co@xmath2)@xmath3as@xmath3 , revealing resistive signatures of pseudogap . in all compounds we find resistivity crossover at a characteristic pseudogap temperature @xmath5 from non - metallic to metallic temperature dependence on cooling . suppression of @xmath5 proceeds very similar in cases of ni and pd doping and much faster than in similar cases of co and rh doping . in cases of co and rh doping an additional minimum in the temperature - dependent @xmath6 emerges for high dopings , when superconductivity is completely suppressed . these features are consistent with the existence of a charge gap covering part of the fermi surface . the part of the fermi surface affected by this gap is notably larger for ni and pd doped compositions than in co and rh doped compounds .

astro-ph0504239

i

despite their humble appearances , the dwarf spheroidal ( dsph ) satellites of the milky way provide a source of persistent intrigue . mysteries concerning their origin , evolution , mass density , and dynamical state make it difficult to know where to place these common galaxies in the context of standard ( e.g. cold dark matter ) models of structure formation . are they primordial building blocks of bigger galaxies , or debris from galaxy interactions ? while dsph galaxies have stellar populations similar in number to those of globular clusters ( @xmath2 ) , their stars are spread over a much larger volume ( @xmath3-@xmath4 kpc compared to @xmath5-@xmath6 pc in globular clusters ) resulting in the lowest luminosity ( i.e. , baryonic ) densities known in any type of galaxy . in many cases it is unclear how these galaxies could have avoided tidal disruption by the milky way over their lifetimes without the addition of considerable unseen mass . this characteristic of dsph galaxies suggests that the dynamics of these systems are dominated either by significant amounts of unseen matter , or that these galaxies are all far from dynamical equilibrium . in general , the jeans equations ( equations ( 4 - 21 ) , ( 4 - 24 ) , and ( 4 - 27 ) of binney & tremaine 1987 @xcite , hereafter , bt87 ) provide a robust description of the mass distribution , @xmath0 , of a collisionless gravitational system such as a dsph galaxy in viral equilibrium , equation ( [ eq : em ] ) below . their general form permits any number of mass components ( stellar , gas , dark ) , as well as anisotropy in the velocity dispersion tensor and a non - spherical gravitational potential . when applied to spherical stellar systems and assuming at most only radial or tangential velocity anisotropy , these equations can be simplified to estimate the radial mass distribution ( equation 4 - 55 of bt87 ) : @xmath7 where @xmath8 is the spatial density distribution of stars , @xmath9 is the mean squared stellar radial velocity at radius @xmath1 . the dimensionless isotropy parameter , @xmath10 , compares the system s radial and tangential velocity components : @xmath11 apart from the constraints on the geometry and the functional form of the anisotropy , equation ( [ eq : mrjeans ] ) is model - independent , making it an appealing tool . it is relevant that equation ( [ eq : mrjeans ] ) and ( [ eq : jns1 ] ) below are applicable to any tracer population that in equilibrium and satisfies the collisionless boltzman equation . kinematic datasets for individual dsph galaxies have historically been far too small ( typically containing radial velocities for @xmath12 30 stars ; see mateo 1998 ) to allow for a precise determination of @xmath0 using relations similar to equation ( [ eq : mrjeans ] ) . instead , authors have been forced to adopt additional strong assumptions that reduce the jeans equation to even simpler forms and where the relevant distributions ( @xmath13 and @xmath14 in equation [ eq : mrjeans ] ) are represented by parametric models . specifically , if one assumes isotropy of the velocity dispersion tensor ( i.e. , @xmath15 ) , spherical symmetry , and that the starlight traces the mass distribution ( effectively a single - component king model ( irwin and hatzidimitriou 1995 ) ) , then one obtains for the m / l ratio ( richstone and tremaine 1986 ) : @xmath16 where @xmath17 is the one - dimensional central velocity dispersion , @xmath18 is the central surface brightness , and @xmath19 is the half - light radius . the parameter @xmath20 is nearly equal to unity for a wide range of realistic spherical dynamical models so long as the mass distribution is assumed to match that of the visible matter . with this approach the modern variant of the classical ` king fitting ' procedure ( king 1966 ) the measured central radial velocity dispersion and surface brightness yield estimates of such quantities as the global and central m / l ratios . in all eight of the mw s measured dsphs , large central velocity dispersions have conspired with their low surface brightnesses to produce large inferred m / l values . this line of reasoning has led to a general belief that dsph galaxies are almost completely dark - matter dominated , and their halos have assumed the role of the smallest non - baryonic mass concentrations identified so far in the present - day universe . this analysis fails for galaxies that are far from dynamical equilibrium , for example due to the effects of external tidal forces from the milky way ( fleck and kuhn 2003 ; klessen and kroupa , 1998 ) . numerical models aimed to investigate this ( oh et al . 1995 ; piatek and pryor 1995 ) generally found that tides have negligible effects on the central dynamics of dsph galaxies until the survival time of the galaxy as a bound system becomes comparable to the orbital time ( about 1 gyr for the closer dsph satellites of the milky way ) . observations agree with this broad conclusion by finding that remote dsph galaxies are no less likely to contain significant dark matter halos than systems located closer to their parent galaxy ( mateo et al . 1998 ; vogt et al . 1995 ) . however , so - called resonance models ( fleck and kuhn 2003 ; kuhn 1993 ; kuhn et al . 1996 ) have been proposed that imply the central velocity dispersions can be significantly altered due to the inclusion of stars streaming outward from the barycenter of a galaxy and projected near the galaxy core . recent versions of these models invariably imply a significant extension of the affected galaxies along the line - of - sight ( more precisely , along the line between the center of the dwarf and the milky way ; kroupa 1997 ; klessen and kroupa 1998 ) and a massive tidal stream along the satellite s orbit . observations do not reveal strong evidence of significant line - of - sight distortions in dsph galaxies ( hurley - keller et al 1999 ; klessen et al . 2003 ) , other than sagittarius ( e.g. ibata et al . 1995 ) ; thus , for the purposes of this paper , we will assume that dsph galaxies are generally close to a state of dynamical equilibrium . even with this enabling assumption , the classical analysis of dsph masses as we describe it above is far from ideal for a number of reasons . first , though recent work ( e.g. irwin and hatzidimitriou 1995 ) has helped to greatly improve estimates of dsph structural parameters ( @xmath21 and @xmath22 in equation [ eq : moverl ] ) , the errors in the velocity dispersions often dominated by poisson uncertainties due to the small number of kinematic tracers contribute the principle source of uncertainty in m / l estimates . second , there is little reason to suppose the assumption that mass follows light in dsphs is valid . in all other galaxies the bulk of the matter resides in a dark halo extending far beyond the luminous matter , a trend that becomes more exaggerated toward smaller scales ( kormendy and freeman 2004 ) . finally , velocity anisotropies , if they exist , may mimic the presence of dark matter , and so represent a tricky degeneracy in the model even if the assumption of isotropy is dropped . modern instrumentation is poised to deliver dramatically larger kinematic datasets to help minimize the first problem . for example , the michigan / magellan fiber system , now operational at the magellan 6.5-m telescopes , obtains spectra from which high - precision radial velocities can be measured of up to 256 objects simultaneously . as a result , it is now feasible to obtain thousands of individual stellar spectra in many dsph systems , enlarging sample sizes by more than an order of magnitude . this not only reduces the statistical uncertainty of the dispersion estimation , but can also provide information on the spatial variation of the dispersion across the face of a galaxy . these rich datasets therefore allow for fundamentally improved results even using fairly conventional analysis techniques . for example , by parameterizing the velocity anisotropy , wilkinson et al . ( 2002 ) and kleyna et al . ( 2002 ) show that samples of @xmath23 stars can begin to break the degeneracy between anisotropy and mass in spherical systems . but these large datasets also allow us to aim higher . in this paper , we introduce and develop the formalism for a qualitatively different sort of analysis designed to make the most efficient use of large kinematic datasets . rather than adopting a model that parameterizes the various distributions used in the jeans equation ( e.g. , @xmath0 , @xmath13 , @xmath24 , or @xmath10 ) , we operate on the star count and radial velocity data directly to estimate the mass distribution non - parametrically . we estimate the true three - dimensional mass distribution from the projected stellar distribution and the line - of - sight velocity distribution . in this first application of our technique , we still require the assumptions of viral equilibrium , spherical symmetry , and velocity isotropy ( @xmath15 ) . in section 2 , we introduce notation and definitions of the three - dimensional as well as projected stellar and phase - space densities and review the jeans equation . in sections 3 and 4 , we show how to use very general shape constraints on the mass distribution to estimate the detailed form of the velocity dispersion profile and the radial mass distribution . we illustrate the process on simulated data , demonstrating that , when furnished with large datasets , nonparametric analysis is a powerful and robust tool for estimating mass distributions in spherical or near - spherical systems ( section 5 ) . we illustrate the application of our approach to an existing but relatively small kinematic dataset for the fornax dsph galaxy at the end of section 5 . our emphasis in this paper is the application of our technique to dsph kinematics , but the method described in this paper is applicable to any dynamically hot system in which the radial velocity field is sampled discretely at the positions of a tracer population . thus , our methodology would work for , say , samples of globular clusters or planetary nebulae surrounding large elliptical galaxies , or for individual stars within a globular cluster . our approach follows earlier non - parametric analysis of globular cluster kinematics by gebhardt and fischer ( 1995 ) and merritt et al . ( 1997 ) , though the details of our method differ significantly .

thanks to instrumental advances , new , very large kinematic datasets for nearby dwarf spheroidal ( dsph ) galaxies are on the horizon . past analyses have generally relied on specific dynamical models or highly restrictive dynamical assumptions . we describe a new , non - parametric analysis of the kinematics of nearby dsph galaxies designed to take full advantage of the future large datasets . the method takes as input the projected positions and radial velocities of stars known to be members of the galaxies , but does not use any parametric dynamical model , nor the assumption that the mass distribution follows that of the visible matter . we show that the galaxy contains a significant , extended dark halo some ten times more massive than its baryonic component . though applied here to dsph kinematics , this approach can be used in the analysis of any kinematically hot stellar system in which the radial velocity field is discretely sampled .

thanks to instrumental advances , new , very large kinematic datasets for nearby dwarf spheroidal ( dsph ) galaxies are on the horizon . a key aim of these datasets is to help determine the distribution of dark matter in these galaxies . past analyses have generally relied on specific dynamical models or highly restrictive dynamical assumptions . we describe a new , non - parametric analysis of the kinematics of nearby dsph galaxies designed to take full advantage of the future large datasets . the method takes as input the projected positions and radial velocities of stars known to be members of the galaxies , but does not use any parametric dynamical model , nor the assumption that the mass distribution follows that of the visible matter . the problem of estimating the radial mass distribution , @xmath0 ( the mass interior to true radius @xmath1 ) , is converted into a problem of estimating a regression function non - parametrically . from the jeans equation we show that the unknown regression function is subject to fundamental shape restrictions which we exploit in our analysis using statistical techniques borrowed from isotonic estimation and spline smoothing . simulations indicate that @xmath0 can be estimated to within a factor of two or better with samples as small as 1000 stars over almost the entire radial range sampled by the kinematic data . the technique is applied to a sample of 181 stars in the fornax dsph galaxy . we show that the galaxy contains a significant , extended dark halo some ten times more massive than its baryonic component . though applied here to dsph kinematics , this approach can be used in the analysis of any kinematically hot stellar system in which the radial velocity field is discretely sampled .

1212.6185

c

in the paper spontaneous generation of chromomagnetic fields in the lattice su(3 ) gluodynamics is investigated in the deconfinement phase . an approach for the detection of homogeneous condensate fields by direct measurements of the cartesian components of the field tensor on a lattice is developed . the method is based on two steps . first , the homogeneous background field is found at each simulated configuration by averaging the components of the field tensor over the lattice . second , the presence of condensate fields affect the statistical distribution of the extracted homogeneous background over the mc run . the p.d.f . of the absolute value of the background field depends only on the absolute value of the condensate field being distributed in accordance with the maxwell distribution in case of no condensate fields . a non - maxwell shape of the distribution indicates spontaneous generation of the condensate fields and allows to fit the value of the generated condensate . probing different lattice geometries and various temperatures ( see table 1 and fig . 5 ) , we found the evident spontaneously generated magnetic components of the field tensor in the ` neutral ' su(3 ) directions ( both in the third and eight ones ) whereas other su(3 ) directions show the clear zero background . this serves as an additional argument that our approach reflects well motivated physics and can not be interpreted as some random artificial lattice effects . in the physical units , the strength of condensate chromomagnetic fields monotonically grows with temperature increasing . we successfully fit the collected mc data by the phenomenological law with ` anomalous dimension ' : @xmath121 this law incorporates the results obtained by analytic perturbative approach @xcite as a high - temperature asymptotics . both the neutral chromomagnetic fields @xmath86 and @xmath87 are simultaneously generated in the deconfinement phase in the whole temperature range investigated . these condensate fields have the same functional temperature dependence , the same order of magnitudes , so they evolve in a balanced manner . the direct analysis of the cartesian components of the condensed fields shows that the fields are spontaneously generated in the same spatial direction . the main results of the paper are obtained in physical units . it is checked that the condensate field strengths are independent of the spatial lattice size . in general , the homogeneous chromomagnetic field in the whole space breaks the gauge invariance . thus , the formation of domain structure at large scales is expected , which should restore the gauge invariance . so , the investigation of domain structure on huge lattices is also an interesting subject of further studies . the method developed in sect . 2 to determine the magnetized vacuum state is quite general . it can be applied for any su(@xmath5 ) lattice gauge theory . in this paper we restrict the investigation to the su(3 ) gluodynamics as an important example . in sect . 4 we show that both the chromomagnetic fields @xmath86 and @xmath87 are simultaneously generated in the deconfinement phase in the wide temperature interval from 200 mev to 200 gev . these condensate fields have the same functional temperature dependence , so they evolve in a balanced manner . moreover , both the fields appear to be spontaneously generated in the same spatial direction . it is derived in mc simulations that the spontaneous vacuum magnetization takes place only for @xmath0 and @xmath1 chromomagnetic fields ( @xmath122 , @xmath123 ) , whereas there is no condensation of other chromomagnetic fields ( @xmath124 ) . in @xcite it was shown in the ` one - loop plus daisy ' perturbative approach that the chromomagnetic field @xmath86 is generated in the standard model . the source of spontaneous magnetization effect is in the gauge sector of the model . the fermionic sector of the standard model slightly weakens the effect only . the spontaneous vacuum magnetization was also studied in the mssm @xcite , where the fermionic sector of the model is extended with the s - particles . it was obtain therein that doubled fermionic sector of the mssm does not eliminate the effect . as for our results , fermions should be accounted in further investigations .

the spontaneous generation of homogeneous chromomagnetic fields in the lattice su(3 ) gluodynamics is investigated in the deconfinement phase of the model . a new approach based on direct measurements of the field strength on a lattice is developed . the temperature dependence of the spontaneously generated fields in physical units is fitted in the temperature interval 200 mev 200 gev as the usual power law with the anomalous dimension .

the spontaneous generation of homogeneous chromomagnetic fields in the lattice su(3 ) gluodynamics is investigated in the deconfinement phase of the model . a new approach based on direct measurements of the field strength on a lattice is developed . vacuum magnetization is established by its influence on the probability density function of the simulated field strength . it is found that both the chromomagnetic fields corresponding to the diagonal su(3 ) generators are simultaneously condensated and appear to be spatially co - directed . no vacuum magnetization is detected for the other su(3 ) components . the temperature dependence of the spontaneously generated fields in physical units is fitted in the temperature interval 200 mev 200 gev as the usual power law with the anomalous dimension .

hep-th0409256

i

the study of tachyons and their condensation processes has been a longstanding challenge in string theory . during recent years , the interest in branes has added significantly to the relevance of this issue since open string tachyons occur in various configurations of stable branes , the most important being the brane - antibrane system . fortunately , unstable brane configurations turned out to be much more tractable than bulk backgrounds with instabilities such as e.g. the 26-dimensional bosonic string . in fact , various different approaches have been employed over the last five years , including string field theory ( see e.g. @xcite and @xcite for a review ) , effective field theory models ( see @xcite for some early work ) , and world - sheet conformal field theory ( see e.g. @xcite and references therein ) . in @xcite , sen initiated the study of _ exact time - dependent solutions_. one goal of his work was to find a world - sheet description of so - called s - branes @xcite , i.e. of branes that are localized in time . in this context he proposed to add a @xmath1-shaped boundary interaction to the usual world - sheet model of d - branes in a flat space - time , @xmath2 \ = \ \frac{1}{4\pi } \int_\sigma d^2 z \ , \eta_{\mu\nu } \partial x^\mu \bar \partial x^\nu + \int_{\partial \sigma } d u \ , \lambda \cosh x^0(u ) \ \ .\ ] ] here , @xmath3 denotes the time - coordinate and we have chosen units in which @xmath4 . with such an interaction term the open string tachyon becomes large at early and late times and hence , according to an earlier proposal of sen @xcite , is believed to dissolve the brane for @xmath5 . unfortunately , the world - sheet model ( [ senact ] ) appears to be ill - defined without an additional prescription to select the proper vacuum . to resolve this issue , sen argued that the appropriate choice for super - string computations would be determined by wick rotation from the corresponding euclidean theory . this suggestion relates the study of open string tachyon condensation to the so - called boundary sine - gordon model @xmath6 \ = \ \frac{1}{4\pi } \int_\sigma d^2 z\ , \partial x \bar \partial x + \int_{\partial \sigma } du \ , \lambda \cos x(u)\ ] ] in which @xmath7 is a field with space - like rather than time - like signature . all spatial coordinates @xmath8 have been suppressed here since their contribution to the model is not affected by the interaction . the boundary sine - gordon theory has been studied rather intensively , see e.g. @xcite . let us briefly review some of the most important results . to begin with , we point out that the boundary interaction is exactly marginal so that the theory is conformal for all values of @xmath9 . properties of the model , however , depend crucially on the strength @xmath9 of the boundary potential . in fact , it is well known that variations of @xmath9 allow to interpolate smoothly between neumann and dirichlet boundary conditions . the former appear for all integer values of @xmath9 ( in particular for @xmath10 , of course ) while the latter are reached when @xmath11 . at these points , the theory describes a one - dimensional infinite lattice of d0 branes . from the geometric pictures we can infer that the spectra of boundary excitations must also depend drastically on the parameter @xmath9 . in fact , at the points @xmath12 with neumann boundary conditions , the open string spectrum is continuous . if we now start tuning @xmath9 away from these special values , the spectrum develops band gaps which become wider and wider until we reach the dirichlet points @xmath13 at which the spectrum is discrete . the first computation of the spectrum for generic values of @xmath9 can be found in @xcite ( see also @xcite for a much more elegant derivation ) . despite of these significant insights into the structure of the boundary sine - gordon model , there are several important quantities that remain unknown . this applies in particular to the boundary 2- and 3-point functions and the bulk - boundary operator product expansions . in the string theoretic context , these missing data determine the time - dependence of open string couplings on a decaying brane and the back - reaction to the bulk geometry . our desire to understand such important quantities is one of the main motivations to study the following , closely related world - sheet theory @xcite , @xmath14 \ = \ \frac{1}{4\pi } \int_\sigma d^2 z \ , \eta_{\mu\nu } \partial x^\mu \bar \partial x^\nu + \int_{\partial \sigma } d u \ , \mu_b \exp x^0(u ) \ \ .\ ] ] this model has been named time - like boundary liouville theory . since the tachyon vanishes in the far past , the model seems to describe a half - brane , i.e. a brane that dissolves as time progresses . after wick rotation @xmath15 , the theory of the time coordinate becomes . this might be relevant for comparisons with previous results in models with exponential interactions . ] @xmath16 \ = \ \left ( \frac{1}{4\pi } \int_\sigma d^2 z\ , \partial x \bar \partial x + \mu \exp 2b x(z,{\bar{z } } ) + \int_{\partial \sigma } du \ , \mu_b \exp b x(u)\right)^{\mu=0}_{b = i } \ \ .\ ] ] we have written the interaction term for general parameters @xmath17 and also added a similar interaction in the bulk , mainly to emphasize the relation with boundary liouville theory . what makes this relation so valuable for us is the fact that boundary liouville theory has been solved over the last years @xcite . needless to stress that the solution includes explicit formulas for the bulk - boundary structure constants @xcite and the boundary 3-point couplings @xcite . there is one crucial difference between liouville theory and the model we are interested in : whereas the usual liouville model is defined for real @xmath17 , our application requires to set @xmath18 . a continuation of results in liouville theory from @xmath19 to @xmath0 ( i.e. @xmath18 ) might appear to be a rather daring project , even more so as a naive inspection of the world - sheet action would suggest the @xmath0 model could not possibly be unitary . nevertheless , we shall show below that the theory is entirely well - defined and unitary . for the pure bulk theory , a similar result was established in @xcite . it was shown there that the bulk 3-point couplings of liouville theory possess a @xmath18 limit which is well - defined for real momenta of the participating closed strings . the @xmath18 theory , however , is no longer analytic in the momenta . furthermore , the limit turned out to agree with the @xmath0 limit of unitary minimal models which was constructed by runkel and watts in @xcite . our analysis here extends these findings to the boundary theory . we shall see that the latter is considerably richer than the bulk model . some qualitative properties of the @xmath0 boundary model can be understood using no more than a few general observations . to begin with , let us reconsider the simpler bulk model . recall from ordinary liouville theory that it has a trivial dependence on the coupling constant @xmath20 . since any changes in the coupling can be absorbed in a shift of the zero mode , one can not vary the strength of the interaction . this feature of liouville theory persists when the parameter @xmath17 moves away from the real axis into the complex plane . as we reach the point @xmath18 , our model seems to change quite drastically : at this point , the ` liouville wall ' disappears and the potential becomes periodic . standard intuition therefore suggests that the spectrum of closed string modes develops gaps at @xmath18 . but since the strength of the interaction can not be tuned in the bulk theory , the band gaps must be point - like . though our argument here was based on properties of the classical action which we can not fully trust , the point - like band - gaps are indeed a characteristic property of the @xmath0 bulk theory @xcite . these band - gaps also explain why the couplings of liouville theory cease to be analytic when we reach @xmath0 . for the boundary theory , we can go through a similar argument , but the consequences are more pronounced . in the presence of a boundary , liouville theory contains a second coupling constant @xmath21 which controls the strength of an exponential interaction on the boundary of the world - sheet and is a real parameter of the model . in fact , the freedom of shifting the zero mode can only be used for one of the couplings @xmath20 or @xmath21 . once more , the boundary potential becomes periodic at @xmath18 and hence the open string spectrum should develop gaps , as in the case of the bulk model . but this time , the width of these gaps can be tuned by changes of the parameter @xmath21 . hence , we expect the boundary liouville theory to possess gaps of finite width at @xmath0 . our exact analysis will confirm this outcome of the discussion . after these more qualitative remarks on the model we are about to construct , we shall summarize our main results in more detail . in section 3 we shall provide the boundary states for a family of boundary conditions of the @xmath0 liouville theory that is parametrized by one parameter @xmath22 . formulas for these boundary states are trivially obtained from the corresponding expressions in @xmath23 liouville theory and , as we shall also explain , through particular limits of boundary theories in minimal models . we shall then use both approaches to establish the existence of finite band gaps in the boundary spectrum of the @xmath0 boundary theories . more precisely , we show that boundary fields @xmath24 in the boundary theory with parameter @xmath25 carry a momentum whose allowed values are taken from the following set @xmath26 when @xmath25 is a half - integer , the set @xmath27 fills the entire real line . as we vary @xmath25 away from such half - integer values , the allowed momenta are restricted to intervals of decreasing width until we reach integer values of @xmath25 where the spectrum of boundary fields becomes discrete . in this sense the parameter @xmath25 interpolates between neumann - type and dirichlet - type boundary conditions . let us note that the boundary conditions with @xmath28 are related to those constructed by runkel and watts in @xcite . all other boundary theories , however , are new . it is worthwhile pointing out how closely the @xmath0 limit of liouville theory mimics the behavior of the boundary sine - gordon model . in both theories we can interpolate smoothly between continuous and discrete boundary spectra . even the geometric interpretation of the dirichlet points is very similar : in the context of the @xmath0 liouville model they describe a semi - infinite array of point - like branes from which individual branes can be removed through shifts of the boundary parameter @xmath25 . let us point out that finite arrays of such point - like branes are described by the @xmath0 limit of zz branes . that parametrize the zz branes correspond to the transverse position and the length of the finite array . ] hence , the picture we suggest for the dirichlet points of the @xmath0 fzzt branes provides a nice geometric interpretation for the well - known relation of fzzt and zz branes in liouville theory @xcite . there are two important quantities that we shall construct for all these new boundary theories . these are the boundary 2-point function and the bulk - boundary 2-point function . for the former we obtain @xmath29 \\[3 mm ] \mbox { where } & & \r^{s_1s_2}_{c=1}(p ) \ = \ \r^{is_1\ is_2}_{c=25 } ( 1-p)^{-1}\ \ . \end{aligned}\ ] ] detailed formulas for @xmath30 ( see eq . ( [ 2ptfctres1 ] ) ) and for the so - called reflection amplitude @xmath31 are spelled out in section 4 . here , we have expressed the result in terms of the reflection amplitude for the theory at @xmath32 . it is quite remarkable that the reflection amplitudes of the two models are related in such a simple way . let us point out , though , that the boundary reflection amplitude for the @xmath0 theory is only defined within a subset @xmath33 of momenta @xmath34 . it is more difficult to write down the bulk - boundary coupling @xmath35 of the @xmath0 model , i.e. the coefficient in the 2-point function of a bulk field @xmath36 with one of the allowed boundary fields , @xmath37 we shall prove below that this coupling @xmath35 is given by @xmath38 & & \hspace*{-3.5cm}\nonumber \times \,\bigg ( \frac{e^{-2\pi ip_{\alpha } ( s+1)}}{1-e^{-4\pi ip_{\alpha } } } \frac{g(y_0)^2 e^{-\frac{ih ( y_{0})}{2\pi}}}{y_0^{2 } \ , h''(y_0)}\ , \exp \int_0^\infty \frac{dt}{t } \ \frac{\left(e^{-p_\b t } - e^{2p_\a t}\right ) \sinh^2\frac{p_{\b}t}{2}}{\sinh^2\frac{t}{2}}-\ ( p_{\alpha}\rightarrow -p_{\alpha } ) \bigg ) \end{aligned}\ ] ] where @xmath39 and the functions @xmath40 and @xmath41 are defined through @xmath42 h ( y)&= & { \text{li}_{2}}(a_{0})-{\text{li}_{2}}(a_{0}y)+{\text{li}_{2}}(b_{0})-{\text{li}_{2}}(b_{0}y)\nonumber \\ & & -{\text{li}_{2}}(c_{0})+{\text{li}_{2}}(c_{0}y)-{\text{li}_{2}}(1)+{\text{li}_{2}}(y)+ \log y \log z_{0 } \ \ .\end{aligned}\ ] ] here , @xmath43 denotes the dilogarithm and we have abbreviated @xmath44 and the parameter @xmath45 is one of the two solutions of the following quadratic equation @xmath46 for more details and explicit formulas , see section 5 . we also show that the coefficients in the bulk - boundary operator product expansion vanish whenever the open string momentum @xmath47 lies within the band gaps , i.e. when @xmath48 . this provides another non - trivial consistency check for the couplings we propose . let us add that correlators with boundary insertions in a similar model where also discussed recently in @xcite . the techniques used there , however , only allowed to determine such correlations functions for a discrete set of boundary momenta @xmath49 .

it was shown that the bulk theory can be identified with the interacting @xmath0 limit of unitary minimal models . here these models share many features with the boundary sine - gordon theory , in particular they possess an open string spectrum with band - gaps of finite width . we propose explicit formulas for the boundary 2-point function and for the bulk - boundary operator product expansion in the @xmath0 boundary liouville model . as a by - product of our analysis we also provide a nice geometric interpretation for zz branes and their relation with fzzt branes in the @xmath0 theory .

the @xmath0 liouville theory has received some attention recently as the euclidean version of an exact rolling tachyon background . in an earlier paper it was shown that the bulk theory can be identified with the interacting @xmath0 limit of unitary minimal models . here we extend the analysis of the @xmath0-limit to the boundary problem . most importantly , we show that the fzzt branes of liouville theory give rise to a new 1-parameter family of boundary theories at @xmath0 . these models share many features with the boundary sine - gordon theory , in particular they possess an open string spectrum with band - gaps of finite width . we propose explicit formulas for the boundary 2-point function and for the bulk - boundary operator product expansion in the @xmath0 boundary liouville model . as a by - product of our analysis we also provide a nice geometric interpretation for zz branes and their relation with fzzt branes in the @xmath0 theory .

0801.4952

r

the alpha magnetic spectrometer @xcite ( ams ) is a particle detector to be installed in the international space station ( iss ) for at least three years . the spectrometer will be able to measure the rigidity ( @xmath0 ) , the charge ( @xmath1 ) , the velocity ( @xmath2 ) and the energy ( @xmath3 ) of cosmic rays from some mev up to @xmath41tev within a geometrical acceptance of @xmath50.5m@xmath6.sr . shows a schematic view of the ams spectrometer . at both ends of the ams spectrometer exist the transition radiation detector ( trd ) ( top ) and the electromagnetic calorimeter ( ecal ) ( bottom ) . both will provide ams with capability to discriminate between leptons and hadrons . additionally the calorimeter will trigger and detect photons . the trd will be followed by the first of the four time - of - flight ( tof ) system scintillator planes . the tof is composed of four roughly circular planes of 12 cm wide scintillator paddles , one pair of planes above the magnet , the upper tof , and one pair bellow , the lower tof . there will be a total of 34 paddles . the tof will provide a fast trigger within 200ns , charge and velocity measurements for charged particles , as well as information on their direction of incidence . the tof operation at regions with very intense magnetic fields forces the use of shielded fine mesh phototubes and the optimization of the light guides geometry , with some of them twisted and bent . moreover the system guarantees redundancy , with two photomultipliers on each end of the paddles and double redundant electronics . a time resolution of 140ps for protons is . the tracking system will be surrounded by veto counters and embedded in a magnetic field of about 0.9tesla produced by a superconducting magnet . it will consist on a silicon , made of 8 layers of double sided silicon sensors with a total area of @xmath46.7m@xmath6 . there will be a total of @xmath42500 silicon sensors arranged on 192 ladders . the position of the charged particles crossing the tracker layers is measured with a precision of @xmath410@xmath7 m along the bending plane and @xmath430@xmath7 m on the transverse direction . with a bending power ( bl@xmath6 ) of around 0.9t.m@xmath6 , particles rigidity is measured with an accuracy better than 2% up to 20gv and the maximal detectable rigidity is around 1 - 2tv . electric charge is also measured from energy deposition up to z@xmath426 . the ring imaging erenkov detector ( rich ) @xcite will be located right after the last tof plane and before the electromagnetic calorimeter . it will be described in detail in next section . [ fig : ams ] the long stay of ams in space and its large acceptance will allow the accumulation of a large statistic of events increasing in several orders of magnitude the sensitivity of the proposed physical measurements . with an average collection rate of 1000 events per second , a total of @xmath8 protons per year and around @xmath9 antiprotons will be accumulated . the main goals of the ams-02 experiment are : * a precise measurement of the charged cosmic ray spectrum between and @xmath41tev , and the detection of photons up to a few hundred gev ; * a search for heavy antinuclei ( @xmath10 ) , which if discovered would signal the existence of primordial antimatter ; * search for non - baryonic dark matter through the detection of annihilation products appearing as anomalies of the cosmic - ray spectra ( e@xmath11 , @xmath12 , @xmath13 and @xmath14 ) ;

the alpha magnetic spectrometer ( ams ) to be installed on the international space station ( iss ) will measure charged cosmic ray spectra of elements up to iron , in the rigidity range from 1gv to 1tv , for at least three years . two possible methods for reconstructing the erenkov angle and the electric charge with the rich will be discussed . a rich prototype consisting of a detection matrix with 96 photomultipliers , a segment of a conical mirror and samples of the radiator materials was built and its performance was evaluated using ion beam data . in addition , the reflectivity of the mirror was evaluated .

the alpha magnetic spectrometer ( ams ) to be installed on the international space station ( iss ) will measure charged cosmic ray spectra of elements up to iron , in the rigidity range from 1gv to 1tv , for at least three years . ams is a large angular spectrometer composed of different subdetectors , including a proximity focusing ring imaging cherenkov ( rich ) detector . this will be equipped with a mixed radiator made of aerogel and sodium fluoride ( naf ) , a lateral conical mirror and a detection plane made of 680 photomultipliers coupled to light guides . the rich detector allows measurements of particle s electric charge up to iron , and particle s velocity . two possible methods for reconstructing the erenkov angle and the electric charge with the rich will be discussed . a rich prototype consisting of a detection matrix with 96 photomultipliers , a segment of a conical mirror and samples of the radiator materials was built and its performance was evaluated using ion beam data . results from the last test beam performed with ion fragments resulting from the collision of a 158gev / c / nucleon primary beam of indium ions ( cern sps ) on a lead target are reported . the large amount of collected data allowed to test and characterize different aerogel samples and the naf radiator . in addition , the reflectivity of the mirror was evaluated . the data analysis confirms the design goals .

0801.4952

c

ams-02 will be equipped with a proximity focusing rich detector based on a mixed radiator of aerogel and sodium fluoride , enabling velocity measurements with a resolution of about 0.1% and extending the charge measurements up to the iron element . velocity reconstruction is made with a likelihood method . charge reconstruction is made in an event - by - event basis . evaluation of both algorithms on real data taken with in - beam tests at cern , in october 2003 was done . the detector design was validated and a refractive index 1.05 aerogel was chosen for the radiator , fulfilling both the demand for a large light yield and a good velocity resolution . the rich detetector is being constructed and its assembling to the ams complete setup is foreseen for 2008 . c. lechanoine - leluc , _ proc . 29th icrc ( pune ) _ * 3 * , 381 - 384 ( 2005 ) . f. baro , l. arruda , _ et al . _ , _ proc . 29th icrc ( pune ) _ * 9 * , 299 - 302 ( 2005 ) . c. lechanoine - leluc , _ proc . 29th icrc ( pune ) _ * 9 * , 299 - 302 ( 2005 ) . d. casadei et al . , nuclear physics b ( proc . suppl . ) * 113*,133 ( 2002 ) . .

ams is a large angular spectrometer composed of different subdetectors , including a proximity focusing ring imaging cherenkov ( rich ) detector . this will be equipped with a mixed radiator made of aerogel and sodium fluoride ( naf ) , a lateral conical mirror and a detection plane made of 680 photomultipliers coupled to light guides .

the alpha magnetic spectrometer ( ams ) to be installed on the international space station ( iss ) will measure charged cosmic ray spectra of elements up to iron , in the rigidity range from 1gv to 1tv , for at least three years . ams is a large angular spectrometer composed of different subdetectors , including a proximity focusing ring imaging cherenkov ( rich ) detector . this will be equipped with a mixed radiator made of aerogel and sodium fluoride ( naf ) , a lateral conical mirror and a detection plane made of 680 photomultipliers coupled to light guides . the rich detector allows measurements of particle s electric charge up to iron , and particle s velocity . two possible methods for reconstructing the erenkov angle and the electric charge with the rich will be discussed . a rich prototype consisting of a detection matrix with 96 photomultipliers , a segment of a conical mirror and samples of the radiator materials was built and its performance was evaluated using ion beam data . results from the last test beam performed with ion fragments resulting from the collision of a 158gev / c / nucleon primary beam of indium ions ( cern sps ) on a lead target are reported . the large amount of collected data allowed to test and characterize different aerogel samples and the naf radiator . in addition , the reflectivity of the mirror was evaluated . the data analysis confirms the design goals .

1207.6572

i

the analytic hierarchy process ( ahp ) is a method for ranking alternatives in multi - criteria decision making problems . developed by saaty @xcite , it consists of a three layer hierarchical structure : the overall goal is at the top ; the criteria are in the next level ; and the alternatives are in the bottom level . the ahp has been used in many different areas including manufacturing systems , finance , politics , education , business and industry ; for more details on the method , see the monographs by saaty - vargas and vaidya - kumar @xcite . the essence of the ahp can be described as follows . given @xmath0 alternatives we construct a _ pairwise comparison matrix _ ( _ pc_-matrix ) , @xmath1 for each criterion , in which @xmath2 indicates the strength of alternative @xmath3 relative to alternative @xmath4 for that criterion . pc_-matrix with the property that @xmath5 for all @xmath6 and @xmath7 for all @xmath3 is called a _ symmetrically reciprocal _ matrix ( _ sr_-matrix ) @xcite . ( note that this abbreviation might clash with the strongly regular matrices of butkovi @xcite , but not in this paper . ) sr_-matrix @xmath8 is constructed , the next step in the ahp is to derive a vector @xmath9 of positive weights , which can be used to rank the alternatives , with @xmath10 quantifying the weight of alternative @xmath3 . as observed by elsner and van den driessche @xcite , the ideal situation is where @xmath11 , in which case the _ sr_-matrix is _ transitive_. in practice , this will rarely be the case and it is necessary to approximate @xmath8 with a transitive matrix @xmath12 , where @xmath13 for some positive weight vector @xmath14 . the problem is then how to construct @xmath12 given @xmath8 . several approaches have been proposed including saaty s suggestion to take @xmath15 to be the perron vector of @xmath8 , or the approach of farkas et al . @xcite , which chooses @xmath15 to minimise the euclidean error @xmath16 . elsner and van den driessche @xcite suggested selecting @xmath15 to be the max algebraic eigenvector of @xmath8 . this is similar in spirit to saaty s approach and also generates a transitive matrix that minimises the maximal relative error @xmath17 . as noted in @xcite , minimising this functional is equivalent to minimising @xmath18 the different approaches to approximating an _ sr_-matrix @xmath8 with a transitive matrix @xmath12 will in general produce different rankings of the alternatives . the question of how these rankings are affected by the choice of scheme is considered in the recent paper of ngoc @xcite . in the classical ahp involving multiple criteria , a set of _ sr_-matrices is constructed : one for each criterion . one additional _ sr_-matrix is constructed based on comparisons of the different criteria . once weight vectors are obtained for each individual criterion , these are then combined using the entries of the weight vector for the criteria - comparison matrix . as an illustration , we take the following numerical example from saaty @xcite and show how the perron vectors of the comparison matrices are used to construct a weight vector . [ ex : saaty ] the problem considered is deciding where to go for a one week vacation among the alternatives : 1 . short trips , 2 . quebec , 3 . denver , 4 . five criteria are considered : 1 . cost of the trip , 2 . sight - seeing opportunities , 3 . entertainment , 4 . means of travel and 5 . dining . pc_-matrix for the criteria and its perron vector are given by @xmath19\quad \text{and}\quad c=\left [ \begin{array}{c } 0.179 \\ 0.239 \\ 0.431 \\ 0.818 \\ 0.237 \\ \end{array } \right ] .\ ] ] the above matrix @xmath20 describes the pairwise comparisons between the different _ criteria_. for instance , as @xmath21 , criterion 2 is rated more important than criterion 1 ; @xmath22 indicates that criterion 3 is rated more important than criterion 2 and so on . the vector @xmath23 contains the weights of the criteria ; in this method , criterion 4 is given most weight , followed by criterion 3 and so on . the _ sr_-matrices , @xmath24 , for each of the 5 criteria , their perron vectors and corresponding ranking schemes are given below . for instance , for criterion 1 , the first alternative is preferred to the second as the @xmath25 entry of @xmath26 is @xmath27 . similarly , for criterion 3 , the 4th alternative is preferred to the 1st as the @xmath28 entry of @xmath29 is @xmath30 . for the cost of the trip : @xmath31 , \quad v^{(1)}=\left [ \begin{array}{c } 0.877 \\ 0.46 \\ 0.123 \\ 0.064 \\ \end{array } \right ] , \quad 1>2>3>4\ ] ] for the sight - seeing opportunities : @xmath32 , \quad v^{(2)}=\left [ \begin{array}{c } 0.091 \\ 0.748 \\ 0.628 \\ 0.196 \\ \end{array } \right ] , \quad 2>3>4>1\ ] ] for the entertainment : @xmath33 , \quad v^{(3)}=\left [ \begin{array}{c } 0.57 \\ 0.096 \\ 0.096 \\ 0.81 \\ \end{array } \right ] , \quad 4>1>2=3\ ] ] for the means of travel : @xmath34 , \quad v^{(4)}=\left [ \begin{array}{c } 0.396 \\ 0.355 \\ 0.768 \\ 0.357 \\ \end{array } \right ] , \quad 3>1>4>2\ ] ] for the dining : @xmath35 , \quad v^{(5)}=\left [ \begin{array}{c } 0.723 \\ 0.642 \\ 0.088 \\ 0.242 \\ \end{array } \right ] , \quad 1>2>4>3\ ] ] to obtain the overall weight vector , we compute the weighted sum @xmath36 . this gives @xmath37\ ] ] with the associated ranking : @xmath38 . our work here is inspired by the max - algebraic approach to the ahp introduced by elsner and van den driessche @xcite and extends it in the following manner . in @xcite , the max eigenvector is used as a weight vector for a _ single criterion _ and it is shown to be optimal in the sense of minimising the maximal relative error as discussed above . this work naturally raises the question of how to treat multiple criteria within the max - algebraic framework . we address this question here by considering the multi - criteria ahp as a multi - objective optimisation problem , in which we have an objective function of the form ( [ eq : errf ] ) for each criterion ( and associated _ sr_-matrix ) . rather than combining individual weight vectors as in example [ ex : saaty ] , we consider three approaches within the framework of multi - objective optimisation , and use the optimal solution as a weight vector in each case . the advantage of this approach is that the weight vector can be interpreted in terms of the maximal relative error functions ( [ eq : errf ] ) associated with the _ sr_-matrices given as data for the problem . the optimisation problems we consider are the following . first , we investigate the existence of a single _ transitive _ matrix with a minimum distance to all matrices in the set simultaneously . we remark that this amounts to finding a common subeigenvector of the given matrices . clearly , this will not in general be possible . the second problem we consider is to obtain a transitive matrix that minimises the maximal distance to any of the given _ sr_-matrices . the third problem concerns the existence of a transitive matrix that is pareto optimal for the given set of matrices . to illustrate our results , we revisit example [ ex : saaty ] towards the end of the paper

the analytic hierarchy process ( ahp ) is widely used for decision making involving multiple criteria . elsner and van den driessche + _ keywords : _ analytic hierarchy process ( ahp ) , _ + _ ams codes : _ 91b06 , 15a80 , 90c29

the analytic hierarchy process ( ahp ) is widely used for decision making involving multiple criteria . elsner and van den driessche @xcite introduced a max - algebraic approach to the single criterion ahp . we extend this to the multi - criteria ahp , by considering multi - objective generalisations of the single objective optimisation problem solved in these earlier papers . we relate the existence of globally optimal solutions to the commutativity properties of the associated matrices ; we relate min - max optimal solutions to the generalised spectral radius ; and we prove that pareto optimal solutions are guaranteed to exist . + _ keywords : _ analytic hierarchy process ( ahp ) , _ sr_-matrix , max algebra , subeigenvector , generalised spectral radius , multi - objective optimization . + _ ams codes : _ 91b06 , 15a80 , 90c29

1207.6572

c

building on the work of elsner and van den driessche @xcite , we have considered a max - algebraic approach to the multi - criteria ahp within the framework of multi - objective optimisation . papers @xcite characterise the max eigenvectors and subeigenvectors of a _ single _ _ sr_-matrix as solving an optimisation problem with a single objective . we have extended this work to the multi - criteria ahp by directly considering several natural extensions of this basic optimisation problem to the multiple objective case . specifically , we have presented results concerning the existence of : globally optimal solutions ; min - max optimal solutions ; pareto optimal solutions . the principal contribution of the paper is to draw attention to this max - algebraic perspective on the multi - criteria ahp , with the main results in this direction being : establishing the connection between the generalised spectral radius and min - max optimal solutions ( proposition [ pro : opt2 ] ) ; proving the existence of pareto optimal solutions and showing that it is possible to simultaneously solve the pareto and min - max optimisation problems ( proposition [ pro : existence ] and corollary [ cor : existence ] ) . we have also related the existence of globally optimal solutions to the existence of common subeigenvectors and highlighted connections between this question and commutativity ( theorem [ thm:3b3cond ] ) . buket benek gursoy and oliver mason acknowledge the support of irish higher educational authority ( hea ) prtli network mathematics grant ; serge sergeev is supported by epsrc grant rrah15735 , rfbr - cnrs grant 11 - 01 - 93106 and rfbr grant 12 - 01 - 00886 . b. heidergott , g. j. olsder , j. van der wounde , max plus at work : modeling and analysis of synchronized systems , a course on max - plus algebra and its applications , princeton university press , princeton , nj ( 2006 ) . d. hershkowitz , h. schneider , one - sided simultaneous inequalities and sandwich theorems for diagonal similarity and diagonal equivalence of nonnegative matrices , elec . j. of linear algebra 10 ( 2003 ) 81 - 101 . krivulin , evaluation of bounds on the mean rate of growth of the state vector of a linear dynamical stochastic system in idempotent algebra , vestnik st . petersburg university : mathematics 38 ( 2005 ) 45 - 54 .

@xcite introduced a max - algebraic approach to the single criterion ahp . we extend this to the multi - criteria ahp , by considering multi - objective generalisations of the single objective optimisation problem solved in these earlier papers . we relate the existence of globally optimal solutions to the commutativity properties of the associated matrices ; we relate min - max optimal solutions to the generalised spectral radius ; and we prove that pareto optimal solutions are guaranteed to exist . sr_-matrix , max algebra , subeigenvector , generalised spectral radius , multi - objective optimization .

the analytic hierarchy process ( ahp ) is widely used for decision making involving multiple criteria . elsner and van den driessche @xcite introduced a max - algebraic approach to the single criterion ahp . we extend this to the multi - criteria ahp , by considering multi - objective generalisations of the single objective optimisation problem solved in these earlier papers . we relate the existence of globally optimal solutions to the commutativity properties of the associated matrices ; we relate min - max optimal solutions to the generalised spectral radius ; and we prove that pareto optimal solutions are guaranteed to exist . + _ keywords : _ analytic hierarchy process ( ahp ) , _ sr_-matrix , max algebra , subeigenvector , generalised spectral radius , multi - objective optimization . + _ ams codes : _ 91b06 , 15a80 , 90c29

astro-ph0310130

c

the construction of the antares detector is underway . it is planned to be fully deployed and start to take data by the end of 2006 . calculations based on the data on environmental conditions at the experiment site and on studied properties of electronic components shows that predicted sensitivity of the detector to diffuse neutrino fluxes , point - like neutrino searches and wimp searches is better by several orders of magnitude compared to data published by other experimental groups . the deployment of the antares neutrino telescope can be considered as a step toward the deployment of a 1 km@xmath30 detector in the mediterranean sea . 99 amanda : p. desiati _ et al . _ , astro - ph/0306536 ; http://amanda.uci.edu/ antares : e. aslanides _ et al . _ , astro - ph/9907432 ; http://antares.in2p3.fr/ baikal : r. wischnewski _ et al . _ , astro - ph/0305302 ; http://nt200.da.ru/ icecube : a. goldschmidt _ et al . _ , nucl.phys.proc.suppl . * 110 * ( 2002 ) 516 ; http://icecube.wisc.edu/ nemo : g. riccobene _ et al . _ , 2nd workshop on methodical aspects of underwater / ice neutrino telescopes , hamburg , 2001 , p.61 ; http://nemoweb.lns.infn.it/ nestor : s. e. tzamarias _ et al . _ , nim * a502 * ( 2003 ) 150 ; http://www.nestor.org.gr/ p. amram _ et al . _ , astropart.phys . * 13 * ( 2000 ) 127 . p. amram _ et al . _ , astropart.phys . * 19 * ( 2003 ) 253 . p. amram _ et al . _ , nim * a484 * ( 2002 ) 369 . m. c. bouwhuis for the antares collaboration , submitted to 28th icrc . m. circella for the antares collaboration , submitted to 28th icrc . t. montaruli for the antares collaboration , astro - ph/0207531 and physics/0306057 ; j. j. hernndez - rey for the antares collaboration , nuclphys.proc.suppl . * 114 * ( 2003 ) 211 . e. waxmann , j. n. bahcall , phys.rev . * d59 * ( 1999 ) 023002 . c. distefano _ , astrophys.j . * 575 * ( 2002 ) 378 .

the antares project aims to build a deep underwater cherenkov neutrino telescope in the mediterranean sea . the final antares detector consisting in 12 strings each equipped with 75 photomultiplier tubes is planned to be fully deployed and taking data by the end of 2006 . _

the antares project aims to build a deep underwater cherenkov neutrino telescope in the mediterranean sea . currently the experiment is in the construction phase and has recently achieved two important milestones . the electro - optical cable to shore and the junction box that will distribute power to detector strings and allow data transmission have been deployed at the sea floor . a prototype string and a string for environmental parameter measurement have been deployed , connected to the cable using a manned submarine . data have been sent to shore . the final antares detector consisting in 12 strings each equipped with 75 photomultiplier tubes is planned to be fully deployed and taking data by the end of 2006 . _ talk given at 4th international conference on non - accelerator new physics , + dubna , russia , june 2328 , 2003 .

cond-mat9801231

i

the theory of polymers near surfaces is a very important subject for theoretical investigation . the main reason is the very broad and deep theoretical research possible for these types of systems . modern theories have been developed and brought to a very high standard @xcite . on the other hand there is a large demand on practical interest on studying polymers near surfaces . one of them is surface protection . the theory on polymer brushes @xcite is a typical example of these type of applications . polymers are attached to surfaces to protect the surface from further adsorption of , e.g. , biological active molecules such as proteins . these molecules need to be pretended to from all kind of surface interactions in order to save their biological function @xcite . the ( technical ) problem with polymer brushes is , that a large surface coverage is needed to protect the surface in a most effective way . polymers attached chemically or physically at one end at the surface form brushes , i.e. , the chains are extended and the brush height @xmath0 follows a scaling law @xmath1 ( in good solvent ) , where @xmath2 is the area per chain an is thus related to the grafting density . @xmath3 the degree of polymerization of the chains . the problem is to set up a small value of @xmath2 , or , correspondingly a large grafting density . for low values of the grafting density the chains behave as `` mushrooms '' and the surface protection is incomplete . in earlier papers it has been shown by one of us , that the use of branched chains in much more effective @xcite . chains , polymers and polymeric fractals with a larger connectivity seem to be more appropriate to protect surfaces more effectively . indeed due to their connectivity their occupied area is larger and it turns out that these systems behave more like single chain fractals . typical many body effects , such as occur in conventional polymer brushes do not play a significant role . in the present paper we suggest a different route of surface protection by using microgels and branched structure . microgels had become an important tool in designing polymeric nano structures . these systems can be synthesized @xcite with different structures . indeed the structure of these microgels can range from a fractal state , i.e. , a branched self - similar polymer with a large connectivity , up to almost hard and highly crosslinked spheres . such systems are well designed to study the transition form polymer to colloid behavior by variation of the structure and the crosslinking state . we have shown earlier @xcite , that fractal polymers and gels can interpenetrates each other and screen excluded volume forces , wherever their connectivity is low . in terms of the spectral dimension this is the case , when it is lower than a critical value , i.e. @xmath4 . thus fractals with lower spectral dimensions screen their excluded volume , whereas polymeric fractals with larger spectral dimension saturate . then they form soft balls , which can not interpenetrate each other and are well separated from each other @xcite . this state has an analogon in the case of linear polymers . polymer melts in two dimensions correspond to a saturated state . the individual chains are separated from each other and form on average disks on a hexagonal lattice @xcite . for surface protection in three dimensions it would thus be more effective to use fractal microgels with a large connectivity . then the surface coverage is ruled by the single gel behavior . alternatively crosslinked gels can be used to have the same effect . sufficiently crosslinked gels can not interpenetrate each other . the adsorption behavior can be studied then by the single gel adsorption . the significant parameters are either the connectivity ( spectral dimension @xmath5 ) or the crosslink number @xmath6 . in the following we emphasize mainly on the crosslinked gels rather on the self similar connected polymeric fractals . nevertheless we will consider both cases below . the paper is organized as follows . in section [ 2 ] we introduce the model of self crosslinked polymer chains , which form the microgels . in section [ 3 ] we repeat briefly the scaling behavior of ideal microgels before we consider in section [ 4 ] the effects of excluded volume in the bulk . sections [ 5 ] and [ 6 ] treat the adsorption behavior of the gels close to attracting walls using simple scaling arguments . in section [ 5 ] we will also make some remarks on fractal type gels .

two different types of microgels can be studied , i.e. , fractal type microgels and randomly crosslinked polymer chains . in the first case fractal gels with low connectivity adsorb easier than gels with a large connectivity dimension . we discuss also consequences on surface protection by microgels .

the behavior of microgels near surfaces and their adsorption is studied by simple scaling theory . two different types of microgels can be studied , i.e. , fractal type microgels and randomly crosslinked polymer chains . in the first case the gel can be described mainly by introducing a spectral dimension . the second type requires more attention and uses the number of crosslinks as parameter . the main result is that soft gels with weakly coupled crosslinks and a low number of crosslinks adsorb much better than hard gels , with many crosslinks . similar results for fractal gels and branched polymer are presented . fractal gels with low connectivity adsorb easier than gels with a large connectivity dimension . we discuss also consequences on surface protection by microgels .

1505.00074

i

we consider the standard problem of denoising grayscale images that are corrupted with additive white gaussian noise @xcite . in this setup , we are given the _ corrupted _ ( or _ noisy _ ) image @xmath0 where @xmath1 is some finite rectangular domain of @xmath2 , @xmath3 is the unknown _ clean _ image , @xmath4 are independent and distributed as @xmath5 , and @xmath6 is the noise level . the goal is find a _ denoised _ estimate @xmath7 of the clean image from the corrupted samples . the denoised image should visually resemble the clean image . one way to quantify the resemblance is using the mean - squared - error ( mse ) which is defined to be @xmath8 later in the paper , we will use the peak signal - to - noise ratio ( psnr ) which is given by @xmath9 . the image denoising problem has been extensively studied and a survey of even a fraction of this literature is beyond the scope of this paper . we instead refer the interested reader to @xcite - @xcite and the references therein . our present interest is in the image denoising applications of the edge - preserving bilateral filter @xcite . the denoised image in this case is set to be @xmath10 where @xmath11 the gaussian kernels in are respectively referred to as the _ spatial _ and _ range _ kernels . in practice , the domain @xmath12 is restricted to some neighbourhood of the origin . typically , @xmath12 is a square neighbourhood , @xmath13 \times [ -w , w]$ ] , where @xmath14 @xcite . we refer the reader to @xcite for a detailed exposition on the working and in particular the edge - preserving property of the filter . the bilateral filter has received renewed attention in the image processing community in the context of image denoising @xcite . it is well - known that , while the filter is quite effective in removing modest levels of additive noise , its denoising performance drops at large noise levels @xcite . it was demonstrated in @xcite that a patch - based extension of the filter can be used to bring the denoising performance of the filter at par with state - of - the - art methods . these , and other advanced patch - based methods @xcite , are however much more computation - intensive than the bilateral filter . in this work , we present a couple of ideas for improving the denoising performance of the classical bilateral filter , and give fast algorithms for the same . the contributions ( and the organization ) of the paper are as follows : @xmath15 in section [ sec : rbf ] , we demonstrate how the denoising performance of the bilateral filter can be improved at large noise levels ( at almost no additional cost ) by incorporating a simple pre - processing step into the framework . @xmath15 the modified filter is designed to be robust at large noise levels , and tends to perform poorly below a certain noise threshold . to get the best of the either filters at all noise levels , we propose to optimally combine them in a weighted fashion in section [ sec : owf ] . the optimality is in terms of a certain surrogate of the mean - squared - error ( mse ) known as stein s unbiased risk estimate ( sure ) @xcite . this mse - estimate is known to be quite accurate in practice @xcite and , as a result , the combined filter is almost always guaranteed to provide a lower mse than the original filter . @xmath15 following @xcite , we present an approximation for the proposed filtering in section [ sec : fastsure ] that has a fast implementation . we derive the sure estimator for this approximation , and demonstrate how it can be efficiently computed in the process of approximating the bilateral filter . the overall cost of computing the estimator and the optimally - weighted filters is about twice the cost of computing a single bilateral filtering using the fast algorithm in @xcite . we provide both visual and quantitative denoising results on standard test images in section [ sec : experiments ] which demonstrate that the improvement over the original filter is significant both visually and in terms of psnr .

the bilateral filter is known to be quite effective in denoising images corrupted with small dosages of additive gaussian noise . the modified filter is designed to be robust at large noise levels , and often tends to perform poorly below a certain noise threshold . to get the best of the original and the modified filter , we propose to combine them in a weighted fashion , where the weights are chosen to minimize ( a surrogate of ) the oracle mean - squared - error ( mse ) . we also provide a fast algorithm for the weighted filtering . visual and quantitative denoising results on standard test images are reported which demonstrate that the improvement over the original filter is significant both visually and in terms of psnr . image denoising , bilateral filter , unbiased risk estimator , fast algorithm .

the bilateral filter is known to be quite effective in denoising images corrupted with small dosages of additive gaussian noise . the denoising performance of the filter , however , is known to degrade quickly with the increase in noise level . several adaptations of the filter have been proposed in the literature to address this shortcoming , but often at a substantial computational overhead . in this paper , we report a simple pre - processing step that can substantially improve the denoising performance of the bilateral filter , at almost no additional cost . the modified filter is designed to be robust at large noise levels , and often tends to perform poorly below a certain noise threshold . to get the best of the original and the modified filter , we propose to combine them in a weighted fashion , where the weights are chosen to minimize ( a surrogate of ) the oracle mean - squared - error ( mse ) . the optimally - weighted filter is thus guaranteed to perform better than either of the component filters in terms of the mse , at all noise levels . we also provide a fast algorithm for the weighted filtering . visual and quantitative denoising results on standard test images are reported which demonstrate that the improvement over the original filter is significant both visually and in terms of psnr . moreover , the denoising performance of the optimally - weighted bilateral filter is competitive with the computation - intensive non - local means filter . image denoising , bilateral filter , unbiased risk estimator , fast algorithm .

1505.00074

c

we demonstrated how a simple pre - processing step can substantially improve the denoising performance of the bilateral filter . to consistently get the best of the standard and the pre - processed filter at all noise levels , we proposed to optimally weight them using stein s unbiased estimate of the mse . the optimal weights were found by solving a small linear system . a fast algorithm for implementing the optimally - weighted filters was also described . we reported visual and psnr results on test images which confirmed the improvement over the original bilateral filter . an interesting finding was that the weighted bilateral filter is competitive with the non - local means filter . j. portilla , v. strela , m. j. wainwright , and e. p. simoncelli , `` image denoising using scale mixtures of gaussians in the wavelet domain , '' _ ieee transactions on image processing _ 1338 - 1351 , 2003 . s. p. awate and r. t. whitaker , `` unsupervised , information - theoretic , adaptive image filtering for image restoration , '' _ ieee transactions on pattern analysis and machine intelligence _ , vol . 3 , pp . 364 - 376 , 2006 .

the denoising performance of the filter , however , is known to degrade quickly with the increase in noise level . several adaptations of the filter have been proposed in the literature to address this shortcoming , but often at a substantial computational overhead . in this paper , we report a simple pre - processing step that can substantially improve the denoising performance of the bilateral filter , at almost no additional cost .

the bilateral filter is known to be quite effective in denoising images corrupted with small dosages of additive gaussian noise . the denoising performance of the filter , however , is known to degrade quickly with the increase in noise level . several adaptations of the filter have been proposed in the literature to address this shortcoming , but often at a substantial computational overhead . in this paper , we report a simple pre - processing step that can substantially improve the denoising performance of the bilateral filter , at almost no additional cost . the modified filter is designed to be robust at large noise levels , and often tends to perform poorly below a certain noise threshold . to get the best of the original and the modified filter , we propose to combine them in a weighted fashion , where the weights are chosen to minimize ( a surrogate of ) the oracle mean - squared - error ( mse ) . the optimally - weighted filter is thus guaranteed to perform better than either of the component filters in terms of the mse , at all noise levels . we also provide a fast algorithm for the weighted filtering . visual and quantitative denoising results on standard test images are reported which demonstrate that the improvement over the original filter is significant both visually and in terms of psnr . moreover , the denoising performance of the optimally - weighted bilateral filter is competitive with the computation - intensive non - local means filter . image denoising , bilateral filter , unbiased risk estimator , fast algorithm .

nlin0702018

i

the fermi accelerator is a dynamical system , proposed by enrico fermi @xcite to describe cosmic ray acceleration , in which a charged particle collides with a time dependent magnetic field . with base in different applications , the original model was later modified and studied by other authors . one of them is the well known fermi - ulam model ( fum ) @xcite , in which a ball is confined between a rigid fixed wall and an oscillatory moving one . in this model the ball collides elastically with the walls and the system is described by an area preserving map . in high energies regime the phase space presents kolmogorov - arnold - moser ( kam ) islands surrounded by locally chaotic regions , which are limited by spanning curves . below the invariant spanning curve of lower energy a globally chaotic sea involves kam islands . the presence of invariant spanning curves limits the orbits in phase space impeding unlimited energy growth ( fermi acceleration ) @xcite . another model , very similar to fum , in which the ball is in a gravitational field , so - called bouncer @xcite , presents , differently from fum , the property of fermi acceleration depending on values of control parameter and initial conditions . this difference between the two models was later explained by lichtenberg et al @xcite . hybrid versions @xcite involving both fum and bouncer and versions of fum with energy dissipation @xcite were also explored . quantum models based on fum and bouncer have also been studied @xcite . the study of such systems is interesting because it allows to compare theoretical predictions with experimental results @xcite ; moreover the knowledge about how time - dependent perturbations affect the dynamics of hamiltonian systems is something that needs to be more explored . therefore it is useful to study such perturbations in simple models because they furnish insights about more complex systems ; even more , the formalism used in its characterization can be extended to the billiard class of problems @xcite . the simplified fermi - ulam model ( sfum ) @xcite is an approximation in which the position of the _ moving wall _ is considered as _ fixed _ , but it transfers momentum and energy to the particle . this geometrical change of the complete model can be neglected when the amplitude of oscillation is much smaller than the distance between the two walls and the velocity of the particle is larger than the wall maximal velocity . it is clear that the simplified versions can speed up the simulations . however the main interest in these simplified models is that they can be studied by analytical methods whose results are often compared with the numerical results of the simplified model . moreover , these analytical results are , sometimes , also useful in study of the full models . the moving wall in the fermi - ulam model represents an external force that acts as a perturbation in the system . if the oscillation amplitude of the moving wall is zero the system is integrable but as soon as this amplitude is different from zero the fermi - ulam model behaves chaotically @xcite . near the integrable to non - integrable transition , average quantities can be described by scaling functions . this kind of analysis was originally proposed in a study of the sfum , where the collision number with the moving wall is employed as independent variable @xcite . in a recent work @xcite , also based on the sfum , we proposed a similar analysis in which time is considered as independent variable and we showed that the average energy can also be described by scaling functions but with a different exponents set . moreover , we showed that the average energy _ decays _ at long times . in the present work we investigate the chaotic sea below the spanning curve of lowest energy for the full fermi - ulam model , where scaling properties of average energies are studied on variables _ time _ and _ iteration _ ( or _ collision _ ) _ number_. we show that if the time is employed as independent variable , then the exponents related to the scaling properties of fum are not the same that the ones of sfum . however , if the iteration number is employed as independent variable , then both fum and sfum present the same set of exponents . we show that the energy decay found for long time in the sfum @xcite does not exist for the fum and we justify physically the origins of the similarities and differences between the fum and sfum . we provide also some analytical results for the scaling exponents and , moreover , we show that although the exponents related to the variables _ time _ and _ collision number _ are not the same a relation between them can be established . this paper is organized as follows : in the next section the fermi - ulam model and the average quantities of interest are defined . we present also the procedures to obtain these averages when time is the independent variable . in section iii we present the results of the numerical simulations , the scaling properties of average energies as function of both time and collision number , and we determine the exponents related to these averages . in section iv analytical arguments to determine some exponents and to derive a relation between the exponents of time and collision number analyses are discussed . finally , we draw the conclusions in section v , where we also present a summary of this present work .

the chaotic sea below the lowest energy spanning curve of the complete fermi - ulam model ( fum ) is numerically investigated when the amplitude of oscillation @xmath0 of the moving wall is small . we use scaling analysis near the integrable to non - integrable transition to describe the average energy as function of time @xmath1 and as function of iteration ( or collision ) number @xmath2 . if @xmath1 is employed as independent variable , the exponents related to the energy scaling properties of the fum are different from the ones of a well known simplification of this model ( sfum ) . however , if @xmath2 is employed as independent variable , the exponents are the same for both fum and sfum . in the collision number analysis , we present analytical arguments supporting that the exponents @xmath3 and @xmath4 related to the initial velocity and to @xmath0 are given by @xmath5 and @xmath6 . we derive also a relation connecting the scaling exponents related to the variables time and collision number . moreover , we show that , differently from the sfum , the average energy in the fum _ saturates _ for long times and we justify the physical origins for some differences and similarities observed between the fum and its simplification .

the chaotic sea below the lowest energy spanning curve of the complete fermi - ulam model ( fum ) is numerically investigated when the amplitude of oscillation @xmath0 of the moving wall is small . we use scaling analysis near the integrable to non - integrable transition to describe the average energy as function of time @xmath1 and as function of iteration ( or collision ) number @xmath2 . if @xmath1 is employed as independent variable , the exponents related to the energy scaling properties of the fum are different from the ones of a well known simplification of this model ( sfum ) . however , if @xmath2 is employed as independent variable , the exponents are the same for both fum and sfum . in the collision number analysis , we present analytical arguments supporting that the exponents @xmath3 and @xmath4 related to the initial velocity and to @xmath0 are given by @xmath5 and @xmath6 . we derive also a relation connecting the scaling exponents related to the variables time and collision number . moreover , we show that , differently from the sfum , the average energy in the fum _ saturates _ for long times and we justify the physical origins for some differences and similarities observed between the fum and its simplification .

1001.0090

i

the meissner effect in a mesoscopic cylindrical structure consisting of a superconductor coated with a pure normal - metal layer has interesting features due to the coherent quantum effects in the normal metal . they are observable when there is a good contact between s and n constituents . this problem within the quasiclassical eilenberger formalism was first investigated theoretically by zaikin @xcite . recent advanced technologies of preparation of pure samples have enabled to investigate the coherence properties of mesoscopic samples taking a proper account of the proximity effect @xcite . the samples were superconducting nb wires with a radius @xmath0 of tens of microns coated with a thin layer @xmath1 of high - purity cu , ag or au . mota and co - workers @xcite detected surprising behavior of the magnetic susceptibility @xmath2 of a cylindrical ns structure ( n and s are for the normal metal and the superconductor , respectively ) at very low temperatures ( @xmath3 @xmath4 mk ) in an external magnetic field parallel to the ns boundary . most intriguingly , a decrease in the sample temperature below a certain point @xmath5 ( at a fixed field ) produced a paramagnetic reentrant effect : the decrease of magnetic susceptibility of the structure is changed to an unexpected grow . a similar behavior was observed in the isothermal reentrant effect in a field decreasing to a certain value @xmath6 below which the susceptibility started to grow sharply . it is emphasized in ref . @xcite that the detected magnetic response of the ns structure is similar to the properties of the persistent currents in mesoscopic normal rings . there have been numerous attempts to explain the paramagnetic reentrant effect theoretically @xcite . however , the predicted amplitudes of the effect were too small ( except for @xcite ) to account for the experimental facts . fauchere , belzig and blatter @xcite explain the large paramagnetic effect assuming strong repulsive electron - electron interaction in noble metals . the proximity effect in the n metal induces an order parameter will be shifted by @xmath7 from the order parameter @xmath8 of the bulk superconductor . this generates the paramagnetic instability of the andreev states , and the density of states of the ns structure exhibits a * _ single _ * peak near zero energy . the theory developed in ref . @xcite essentially relies on the assumption of the repulsive electron interaction in the normal region . maki and haas @xcite made the assumption that * * * * in noble metals ( ag , au ) p - wave superconductors may occur with a transition temperature of order @xmath9 mk . below @xmath10 p -wave triplet superconductivity emerges around the periphery of the cylinder . the diamagnetic current flowing in the periphery is compensated by a quantized paramagnetic current in the opposite direction thus providing a simple explanation for the reentrant effect . as in @xcite , the authors of @xcite also allow for paramagnetic current in the system , which flows in the opposite direction to the diamagnetic current . its amplitude is sufficient to explain the reentrant effect , but this theory says nothing about the temperature and field dependences of magnetic susceptibility at ultra - low temperatures and in low magnetic fields . a theoretical basis for understanding the paramagnetic reentrant effect has been proposed in @xcite . the theory is essentially based on the properties of the quantized levels of the ns structure . the meissner effect is rather special in a superconducting cylinder coated with a pure normal - metal layer . the applied magnetic field generates superconducting current in the surface layer whose thickness is equal to the field penetration depth @xmath11 . simultaneously , the aharonov - bohm effect generates persistent current ( through the mechanism of the andreev scattering of quasiparticles ) in the normal layer near the ns boundary . if n and s metals are separated by a dielectric layer destroying the andreev scattering , the additional current disappears , and the meissner effect returns to its usual form . the levels with energies no more than @xmath8 ( 2@xmath8 is the gap of the superconductor ) appear inside the normal metal bounded by the dielectric ( vacuum ) on one side and the superconductor on the other side . because of the aharonov - bohm effect @xcite , the spectrum of the ns structure in a weak field is a function of the magnetic flux . the specific feature of the andreev quantum levels of the structure is that by varying field @xmath12 ( or temperature @xmath13 ) each level in the well periodically comes into coincidence with the chemical potential of the metal . as a result , the state of the system suffer strong degeneracy , and the density of states on the energy of the ns sample experiences resonance spikes @xcite . this contributes significantly to the magnetic moment and causes a reentrant effect . note that in @xcite the calculation was performed for orbital susceptibility . in @xcite the explanation involves the spin ( pauli ) susceptibility of the system . in this study we calculated the free energy of the ns structure and its magnetic moment ( current of magnetization ) in the magnetic field . an approximate analytical calculation was supplemented with a numerical one based on the exact spectrum of andreev levels @xcite in the ns contact . our approach is not based on application of the eilenberger equation . we calculate the thermodynamic potential to obtain the magnetic moment .

the coherent phenomena in mesoscopic cylindrical normal metal ( n ) - superconductor ( s ) structures have been investigated theoretically . the magnetic moment ( persistent current ) of such a structure has been calculated numerically and ( approximately ) analytically . this occurs when the persistent current is unable to screen the external field . rev . lett . * 65 * , 1514 ( 1990 ) .

the coherent phenomena in mesoscopic cylindrical normal metal ( n ) - superconductor ( s ) structures have been investigated theoretically . the magnetic moment ( persistent current ) of such a structure has been calculated numerically and ( approximately ) analytically . it is shown that the current in the n - layer corresponding to the free energy minimum is always diamagnetic . as the field increases , the magnetic moment ( current ) exhibits jumps at certain values of the trapped magnetic flux and the ns structure changes to a state with smaller absolute value of the diamagnetic moment . this occurs when the persistent current is unable to screen the external field . the magnetic moment increase stepwise and the system changes into a new stable state . the magnetic field penetrates into a larger volume of the n - layer . the new state has smaller absolute value of the diamagnetic moment . experimentally , this is interpreted as the presence of a paramagnetic addition in the system ( paramagnetic reentrant effect ) . the results obtained are in qualitative agreement with the experiments conducted by p. visani , a. c.mota , and a. pollini , phys . rev . lett . * 65 * , 1514 ( 1990 ) .

1001.0090

c

the goal of our study was to interpret the experiments performed by a. c. mota et al . , @xcite , who detected an anomalous behavior of the magnetic susceptibility of the ns structure in a weak magnetic field at millikelvin temperatures . on the magnetic field @xmath190 . b ) the relative free energy @xmath191 ( @xmath192 ) as a function of the magnetic field @xmath190.,width=384 ] previously @xcite , the anomalous behavior of the ns structure was attributed to the properties of the quantized andreev levels depending on the magnetic flux that varies with the temperature and magnetic field . we used the `` thermodynamic '' approach for the calculation of the magnetic moment of normal region of ns structure . within the framework of the self - consistent equation ( [ e5 ] ) , we have managed to trace the role of the parameter @xmath35 in thermodynamics of ns of structures ( * fig . 4 * and * fig . 5 failure connected with the use of the quasi - classical green - function technique @xcite for the explanation of the experimental data ( mota et al ) is a consequence of account for states which are non - andreev ones ( @xmath44 ) for the cylindrical ns structures . geometrically , this can be seen from figure * fig . 1*. the quasiparticle trajectories ( @xmath44 ) hitting the dielectric boundary only are responsible for the paramagnetic current of a small amplitude ( @xmath193 ) ( we neglected this current ) . the proximity effect is crucial for the reentrant effect . the amplitude of the resonance spikes in the density of states strongly depends on the probability of the andreev reflection at the ns boundary . it is therefore assumed that the normal metal and the superconductor are in a good electric contact . the spectrum eq . ( [ e4 ] ) was obtained by the method of multidimensional quasi - classical approach @xcite . . b ) isothermal dc - magnetization curve at @xmath194 mk for the sample 41aunb @xcite . used by courtesy of a. c. mota.,width=384 ] in doing so , we assumed ( i ) the condition of smallness of n - layer thickness in comparison with the radius of the cylindrical superconductor , ( ii ) the validity of the model of a stepwise - varing order parameter of the structure , ( iii ) the independence of @xmath8 on the magnetic field . this permitted us to pass over from the curved ns boundary to a flat one . the information about the cylindrical geometry of the sample was retained because the critical angle at which a quasiparticle hits the dielectric boundary @xmath195 is smaller than @xmath35 . the problem was further simplified by assuming that the reflected quasiparticle performed a reciprocating motion , i.e. , a `` particle '' and a `` hole '' pass along the same trajectory but in opposite direction . actually , here there exists a lot of quasi reciprocating trajectories with the energies near @xmath196 . these trajectories lead to the spikes in the density of states and were taken into account for numerical computation . the numerical calculation shows that the nonlinearity of flux @xmath197 field dependence ( @xmath198 constant ) ( * fig.6a * ) gives rise to quite interesting features of @xmath111 . the magnetic moment in the n layer appears to be always diamagnetic . the paramagnetic contribution to current ( the paramagnetic reentrant effect ) was not detected . however , we have obtained the stepwise change in absolute value of the magnetic moment with increasing magnetic field ( * fig.7a * ) . this behavior can be interpreted as an appearance in the magnetic moment the paramagnetic additives . a behaviour of the ns structure changes from one stable state to another and the magnetic field penetrates further into a bulk of the n layer . the new state has smaller absolute value of the diamagnetic moment , which is interpreted experimentally as an evidence of a paramagnetic addition in the system ( * fig.7b * ) . when the field grows further , @xmath199 increases again until its new value makes the system to jump to a next stable state with a smaller absolute value of the diamagnetic moment , and the magnetic field penetrates deeper inside the normal metal ( * fig.7a * ) . the number of the moment jumps depends on the number of andreev levels in the ns structure . under the isothermal condition , the values of the magnetic field at which jumps occur , do not coincide when the magnetic field changes from small to larger values and in the opposite direction because of a special dependence of the gibbs free energy on the field . this sort of hysteresis was observed experimentally in @xcite ( * fig.7b * ) . numerical comparison between data presented at * fig.7b * and * fig.7a * shows that @xmath111 ( * fig . 7a * ) gives the qualitative description of the experimental data which obey the scaling rule : @xmath200 . for the quantitative description of the temperature and magnetic field dependence of the magnetic moment ns of structures , it will be important to take into account the exact spectrum of andreev levels , the latter is supposedly possible within the framework of the bogoliubov de gennes equations only . note that our consideration was entirely based on the model of free electrons without account of strong electron - electron repulsion .

as the field increases , the magnetic moment ( current ) exhibits jumps at certain values of the trapped magnetic flux and the ns structure changes to a state with smaller absolute value of the diamagnetic moment . the magnetic moment increase stepwise and the system changes into a new stable state . the magnetic field penetrates into a larger volume of the n - layer . the new state has smaller absolute value of the diamagnetic moment . experimentally , this is interpreted as the presence of a paramagnetic addition in the system ( paramagnetic reentrant effect ) . the results obtained are in qualitative agreement with the experiments conducted by p. visani , a. c.mota , and a. pollini , phys .

the coherent phenomena in mesoscopic cylindrical normal metal ( n ) - superconductor ( s ) structures have been investigated theoretically . the magnetic moment ( persistent current ) of such a structure has been calculated numerically and ( approximately ) analytically . it is shown that the current in the n - layer corresponding to the free energy minimum is always diamagnetic . as the field increases , the magnetic moment ( current ) exhibits jumps at certain values of the trapped magnetic flux and the ns structure changes to a state with smaller absolute value of the diamagnetic moment . this occurs when the persistent current is unable to screen the external field . the magnetic moment increase stepwise and the system changes into a new stable state . the magnetic field penetrates into a larger volume of the n - layer . the new state has smaller absolute value of the diamagnetic moment . experimentally , this is interpreted as the presence of a paramagnetic addition in the system ( paramagnetic reentrant effect ) . the results obtained are in qualitative agreement with the experiments conducted by p. visani , a. c.mota , and a. pollini , phys . rev . lett . * 65 * , 1514 ( 1990 ) .

cond-mat0410027

i

recently,@xcite the low - temperature internal friction , thermal conductivity , specific heat , and heat release of plastically deformed , high - purity superconducting crystalline samples of al , nb , and ta have been experimentally studied and compared with measurements on amorphous sio@xmath0 specimen.@xcite in particular , it was established that plastic deformation has a pronounced effect on the internal friction and the thermal conductivity . namely , the value of the internal friction can be increased by two orders of magnitude over that observed on annealed samples and it becomes comparable to that of amorphous sio@xmath0 . likewise , the thermal conductivity was found to have the similar value as that of amorphous sio@xmath0.@xcite at the same time , neither long - time heat release nor additional contribution to the heat capacity expected for amorphous systems was observed . this finding indicates that the phonon scattering by dislocations appearing in crystals under plastic deformations could be of importance . as is well known , there are two principal mechanisms of phonon scattering by dislocations : the static strain - field scattering and the reradiation scattering.@xcite the first one is due to the anharmonicity of the dislocation strain field while the second one results from a possibility of the sound wave to induce a dislocation vibration . in this case , the incident energy will be dissipated as long as the dislocation radiates elastic waves . this is so - called _ fluttering _ mechanism which is dynamical in its origin . it is a difficult problem to experimentally clarify what kind of scattering actually dominates and especially to obtain a quantitative agreement between the observed effect and theoretical calculations based on either static or dynamic models . moreover , it was shown that both mechanisms of phonon scattering by an array of single dislocations are failed in the description of various experiments.@xcite for example , the estimated contribution to the thermal conductivity due to the resonant interaction was found to have a reasonable agreement with the experimental data only at very short lengths of dislocation lines ( otherwise the resonant frequency becomes too low ) . notice that a similar problem has already emerged in experiments with plastically deformed lif.@xcite namely , the measurements of the thermal conductivity and the ballistic phonon propagation in deformed lif at low temperatures show that the obtained phonon scattering is too strong to be explained by static mechanisms of phonon - dislocation interaction , but is in rough agreement with calculations based on a resonant or dynamic interaction with dislocations which can flutter in the stress field of passing phonons . the crucial role in explanation of the experimental data plays an assumption given in ref . that a reasonable density of optically vibrating dislocation dipoles is present in lif . in this case , the resonant frequency becomes markedly higher . it should be mentioned that dislocation dipoles with a rather high density were actually observed in lif @xcite as well as in some other materials . for example , estimates from experiments of the ratio of the dislocation dipole density to a density of single dislocations range from @xmath1 ( in strain - hardening measurements @xcite ) to @xmath2 ( by deformation - induced bulk - density changes @xcite ) and less ( by electron microscopy @xcite ) . the purpose of this paper is to show that the concept of dynamical scattering of phonons by dislocation dipoles @xcite previously used for the explanation of the experiments in lif @xcite could also be suitable for al , nb , and ta . as was observed in refs . , these metals show a complex dislocation structure under plastic deformation . we assume that , by analogy with lif , dislocation dipoles are also present in plastically deformed al , nb , and ta . it should be noted that the dipole is a stable dislocation structure arising under plastic deformation in metals ( see , e.g. , ref . ) . recently,@xcite the substructure of the dislocation ensemble in al and cu was experimentally studied under cyclic deformation . in particular , it was found in ref . that for al deformed at 77 k the microstructure is composed exclusively of vein dipole bundles and channels without persistent slip bands . the dislocation density in the veins is about @xmath3 m@xmath4 , and the density in the channels is about @xmath5 m@xmath4 with the dipole separation in a range from 3 nm to 30 nm . it is important to note that all of the channel defects were found to be edge dipoles . in addition , the computer modelling performed in ref . shows that there is a critical size of the dipole separation ( 1.6 nm for al and 0.42 nm for cu ) above which edge - dislocation dipoles in al and cu become stable with respect to the athermal annihilation . notice that we consider in our paper dislocation dipoles in al with a separation close to 20 nm , that is much larger the critical size found in ref .. thus , as for lif the gain in resonant frequency can be achieved due to optically vibrating dipoles having a reasonable dipole separation and dislocation length . this allows us to obtain a quantitative agreement with the experimental data for all three metals . evidently , the presence of the fluttering dislocation dipoles will affect not only the thermal conductivity but also other physical characteristics , in particular , the internal friction . we study the contribution to the internal friction due to vibrating dislocation dipoles in the framework of the modified granato - lcke string theory . as is known , the granato - lcke vibrating string model is based on an analogy between the vibration of a pinned dislocation line segment and the forced damped vibration of a string.@xcite our study shows that a good agreement with the internal friction experiments in al , nb , and ta @xcite can be obtained only in the presence of some random component of the stresses . this idea has been recently proposed and studied in refs . and . in particular , it was found that the action of random forces on the dislocation gives a substantial contribution to the decrement . as was observed experimentally,@xcite the decrement has an unexpectedly large value and practically does not depend on the amplitude and the frequency of external stresses . this means that the noise parameters should be governed by the characteristics of an external signal because this is the only way to provide the constant contribution to the decrement . therefore , we suggest that the external force introduces also a specific time scale for correlations of stress fluctuations in dislocation ensemble which always has its own stochastic dynamics.@xcite this time scale determines the time of an additional relaxation of internal stresses due to random stresses . it seems reasonable to assume that this time is related to the frequency of the external force . as the simplest approximation , we use the correlation function exponentially decreasing with time . what is important , the introduction of a time scale means that dislocations experience the influence of the _ colored _ noise . finally , we adapt the theory proposed in refs . and to the case of dislocation dipoles and introduce the additional noise component with the above - mentioned correlation function in the equations of motion .

the contribution to the low frequency internal friction and the thermal conductivity due to optically vibrating edge dislocation dipoles is calculated within the modified granato - lcke string model . we found that the problem can be solved by assuming random forces acting on the dislocation dipoles . this gives an additional contribution to the internal friction which describes well the experimental data at low temperatures while their contribution to the thermal conductivity is found to be negligible .

the contribution to the low frequency internal friction and the thermal conductivity due to optically vibrating edge dislocation dipoles is calculated within the modified granato - lcke string model . the results are compared with the recent experiments on plastically deformed samples of al , ta and nb at low temperatures . it is shown that the presence of a reasonable density of optically vibrating dislocation dipoles provides a good fit to the thermal conductivity in superconducting samples . at the same time , the internal friction experiments can not be described within the standard fluttering string mechanism . we found that the problem can be solved by assuming random forces acting on the dislocation dipoles . this gives an additional contribution to the internal friction which describes well the experimental data at low temperatures while their contribution to the thermal conductivity is found to be negligible . 0.2 cm 0.5 cm

astro-ph0511054

c

the cross - correlation between cosmic microwave background ( cmb ) temperature anisotropies and the large scale structure ( lss ) traced by the galaxy distribution , or sources at different wavelengths , is now well known . this correlation results from the integrated sachs - wolfe ( isw ) effect in cmb anisotropies and provides a measure of dark energy and its physical properties . in a reionized universe , electron scattering at low redshifts leads to a large - scale polarization contribution . in addition to the primordial quadrupole , involving anisotropies at the last scattering surface , the isw quadrupole rescatters and contributes to large - scale polarization signal . thus , in principle , the large - scale polarization bump in the e - mode should also be correlated with the galaxy distribution . unlike cmb - lss correlation that peaks for tracers at low redshifts , due to the decreasing visibility function at low redshifts and the decreasing isw contribution at high redshifts , the correlation peaks mostly at redshifts between 1 and 3 . under certain conditions , mostly involving a low optical depth to reionization , the polarization signal should be detectable , though signal - to - noise ratios involving an all - sky map of the galaxy distribution is not expected to be high and is likely to be at the level of two to three if the universe reionized at a redshift around 6 . if the universe reionized at a redshift higher than 8 , it is unlikely that this correlation will be detectable . unknown physics related to the dark energy as well as still uncertain issues related to the large angular scale cmb and polarization anisotropies , however , may compel attempts to measure this correlation using upcoming cmb polarization e - mode maps .

the cross - correlation between cosmic microwave background ( cmb ) temperature anisotropies and the large scale structure ( lss ) traced by the galaxy distribution , or sources at different wavelengths , is now well known . this correlation results from the integrated sachs - wolfe ( isw ) effect in cmb anisotropies generated at late times due to the dark energy component of the universe . in a reionized universe , electron scattering at low redshifts leads to a large - scale polarization contribution . in addition to the primordial quadrupole , involving anisotropies at the last scattering surface , the isw quadrupole rescatters and contributes to the large angular scale polarization signal . thus , in principle , the low multipole polarization bump in the e - mode should be correlated with the galaxy distribution . unlike cmb temperature lss correlation that peaks for tracers at low redshifts , due to the increasing visibility function , while the fractional isw quadrupole is decreasing , with increasing redshift , the polarization galaxy correlation peaks mostly at redshifts between 1 and 3 . under certain conditions , mostly involving a low optical depth to reionization if the universe reionized at a redshift around 6 , the cross polarization if the universe reionized at a redshift higher than 10 , it is unlikely that this correlation will be detectable even with no instrumental noise all - sky maps . while our estimates do not guarantee a detection , unknown physics related to the dark energy uncertain issues related to the large angular scale cmb and polarization anisotropies , and uncertainties related to the reionization history of the universe may motivate attempts to measure this correlation using upcoming cmb polarization e - mode maps and large - scale structure maps of the high - redshift universe with large synoptic survey telescope and quasar catalogs , among others

the cross - correlation between cosmic microwave background ( cmb ) temperature anisotropies and the large scale structure ( lss ) traced by the galaxy distribution , or sources at different wavelengths , is now well known . this correlation results from the integrated sachs - wolfe ( isw ) effect in cmb anisotropies generated at late times due to the dark energy component of the universe . in a reionized universe , electron scattering at low redshifts leads to a large - scale polarization contribution . in addition to the primordial quadrupole , involving anisotropies at the last scattering surface , the isw quadrupole rescatters and contributes to the large angular scale polarization signal . thus , in principle , the low multipole polarization bump in the e - mode should be correlated with the galaxy distribution . unlike cmb temperature lss correlation that peaks for tracers at low redshifts , due to the increasing visibility function , while the fractional isw quadrupole is decreasing , with increasing redshift , the polarization galaxy correlation peaks mostly at redshifts between 1 and 3 . under certain conditions , mostly involving a low optical depth to reionization if the universe reionized at a redshift around 6 , the cross polarization source signal is marginally detectable if all - sky maps of the large scale structure at redshifts between 1 and 3 is available . if the universe reionized at a redshift higher than 10 , it is unlikely that this correlation will be detectable even with no instrumental noise all - sky maps . while our estimates do not guarantee a detection , unknown physics related to the dark energy uncertain issues related to the large angular scale cmb and polarization anisotropies , and uncertainties related to the reionization history of the universe may motivate attempts to measure this correlation using upcoming cmb polarization e - mode maps and large - scale structure maps of the high - redshift universe with large synoptic survey telescope and quasar catalogs , among others

1012.3101

i

electromagnetic processes have always provided invaluable probes of the strong interactions , the most prominent example being the deep inelastic scattering experiments in the early 1970s which eventually established qcd as the fundamental theory of the strong interactions . among the current challenges of qcd is the description of the plethora of charmoniumlike states discovered during the past years , the so - called xyz " ( for reviews see , e.g. , refs . @xcite ) , that lie above the @xmath1 threshold , and do not fit potential model expectations . it is widely accepted that the effects of the coupling of a core charmonium , namely , a mainly @xmath8 bound state , to a @xmath1 meson pair , the so - called coupled - channel effects , are an important ingredient to understand those states . we shall call the latter continuum states and the former valence states . we will argue below that two - photon transitions between heavy quarkonium states may provide important experimental information on the continuum - valence coupling . historically , it has been recognized for a long time that the continuum states may shift the mass spectrum of a pure @xmath9 state considerably @xcite . recently , exploratory investigations on the mixing between discrete and continuum states in charmonium have been carried out in lattice qcd @xcite . lattice qcd has also provided a detailed study of the so - called string breaking " in the static approximation @xcite , which may be used to extract information on the continuum - valence coupling @xcite . if the heavy quark mass @xmath10 is much larger than the remaining scales in the system , then the heavy quarks move slowly in their center - of - mass frame , say with a typical velocity @xmath11 , that is , with typical three momentum @xmath12 and hence with typical binding energy @xmath13 . nonrelativistic qcd ( nrqcd ) @xcite can be used to factorize the contributions from energies larger or of the order of @xmath10 , and provides a good starting point . recall that the heavy - light meson pair threshold lies at a typical nonrelativistic energy @xmath14 , according to heavy quark effective theory ( hqet ) counting rules @xcite . then , if the binding energy of a heavy quarkonium state lies much below open flavor threshold , namely , @xmath15 one can integrate out energies of order @xmath14 . this leads to potential nrqcd ( pnrqcd ) in the strong coupling regime @xcite . the dynamics of this effective theory reduces to a heavy quark and a heavy antiquark interacting through a potential@xcite ( see @xcite for a review ) . hence , in order to understand the properties of these states , there is no need to introduce explicitly the continuum states if the potential is chosen appropriately . however , for states close to or above the open flavor threshold , the coupling of continuum to valence states needs to be addressed , and so far it is not known how to proceed in a model independent way . , which includes coupled channel effects @xcite . see also @xcite for an even more recent proposal . ] hence , most of the analysis has been done by using different models . recently , some general features of the coupled - channel effects have been obtained in the quark model @xcite under the assumptions that valence - continuum coupling is described by the @xmath16 model @xcite and the interaction between two mesons is negligible . these results suggest that for the low - lying states the effect of continuum channels is hidden in the parameters in the potential model . in ref . @xcite , it is mentioned that the radiative transition process may be sensitive to the continuum components . however , previous works , based on cornell coupled - channel formalism , indicate that the relativistic corrections @xcite may be more important than the continuum contributions @xcite . therefore , it is not straightforward to disentangle the continuum contributions in the one - photon transition process . here , we propose a new process , namely , @xmath17 which can provide an additional opportunity to pin down the valence - continuum coupling . from the theoretical point of view , electromagnetic transitions allow a cleaner analysis than hadronic decay processes . at the amplitude level , the contribution to this two - photon transition can be divided into two parts . we refer to the first one as the discrete part , which involves charmonium states only . the discrete part is dominated by the following process : the @xmath18 state decays into a real or virtual @xmath2 state by radiating one photon , and then , the real or virtual @xmath2 state decays into @xmath7 plus another photon . this process not only includes the cascade decay process ( on - shell region ) , but also the off - shell region . we will study the whole phase space . the second part is referred to as the continuum part , in which at least one photon is emitted by an intermediate charmed meson . in the discrete part , the @xmath19 states can be on - shell , so the total contribution of the discrete subprocess should be much larger than that of the continuum part . however , when the invariant mass of @xmath7 and one of the photons is far away from the resonance regions of the @xmath19 states , the discrete part contribution will drop down very fast . thus , the contribution of the continuum part may be important and measurable in the off - shell region . let us mention that in ref . @xcite , a similar decay process of @xmath20 is suggested to determine the values of the strong couplings @xmath21 and @xmath22 . on the experimental side , such a two - photon transition process has already been studied in the 1970s and 1980s @xcite . in recent years , more precise measurements were carried out by the besiii @xcite and cleo @xcite collaborations . however , they focused on the investigation of the cascade decay @xmath23 followed by @xmath24 and on the study of the properties of the @xmath25 states . only in ref.@xcite , was a discussion made on the possible amplitude of the two - photon transition in treating the backgrounds of the @xmath25 states . hence , so far , no one has ever used it to study coupled - channel effects . recently , the besiii @xcite collaboration reported the significant data excess from the known cascade backgrounds , which was interpreted as the nonresonance decay of @xmath26 . we remark that this measurement is very sensitive to the line shapes of the @xmath25 states , especially in the data selection region . because of the above reason , the significance of an eventual experimental determination of the continuous process depends very much on our knowledge on the discrete states . as far as we know , the discrete contribution has not been fully studied yet , and only the individual contribution of each @xmath25 state is known by using the non relativistic breit - wigner formula together with the dynamical factors to describe the @xmath25 line shape in the cascade decay of @xmath23 and @xmath24 @xcite . so , in this paper we restrict ourselves to analyze the discrete contribution to this decay assuming that the coupling of @xmath27 and @xmath7 to @xmath28 is zero , and leave for a future work , the detailed evaluation of @xmath1 meson pair loops effects . in this work , we will use effective field theory methods to calculate the decay width , the photon spectrum , and the @xmath7 polarization in the discrete subprocess . a complete study of the whole contribution of the discrete @xmath29 states together with some higher radial excitations , @xmath4 states , where @xmath30 , are ignored . ] , will be carried out . the rest of this paper is organized as followings : in sec.ii , we will briefly introduce the effective lagrangian we use and determine the value of the effective couplings ; in sec.iii , we will calculate the discrete contribution to the @xmath0 process and show the results , and the discussion and summary will be given in the last section .

the decay mode @xmath0 is proposed in order to experimentally identify the effects of the coupling of charmonium states to the continuum @xmath1 states . to have a better understanding of such a two - photon decay process , in this work we also provide the photon spectrum and study the polarization of @xmath7 .

the decay mode @xmath0 is proposed in order to experimentally identify the effects of the coupling of charmonium states to the continuum @xmath1 states . to have a better understanding of such a two - photon decay process , in this work we restrict ourselves to investigate the contribution of the discrete part , in which the photons are mainly produced via the intermediate states @xmath2 . besides calculating the resonance contributions of @xmath3 , we also take into account the contributions of the higher excited states @xmath4 and the interference effect among the @xmath5 and @xmath6 states . we find that the contribution of the @xmath6 states and the interference terms to the total decay width is very tiny . however , for specific regions of the dalitz plot , off the resonance peaks , we find that these contributions are sizable and should also be accounted for . we also provide the photon spectrum and study the polarization of @xmath7 .

1504.07287

i

several texts provide an elementary derivation of the kinematics of special relativity , eventually based on the first part of einstein s fundamental paper of 1905 . @xcite starting from the two postulates of the total equivalence of inertial reference systems , and of the constancy of the speed of light in all such systems , it is in fact easy to obtain the expression of the lorentz transformation of space - time coordinates . a particularly simple and appealing derivation is obtained by exploiting bondi s so - called @xmath0-calculus , @xcite itself based on the doppler effect . nevertheless going from kinematics ( the lorentz transformation ) to dynamics , and in particular to the relativistic expressions of momentum and energy , is often achieved by resorting to more sophisticated concepts , like that of a four - vector , or by the use of quantum considerations . ( one example of this approach is the `` elementary derivation '' suggested by f. rohrlich , @xcite which exploits the expressions of the momentum and energy of a photon of frequency @xmath1 . ) einstein himself had originally derived the mass - energy equivalence via an explicit use of electrodynamics , @xcite and not just by the kind of kinematic considerations which he had developed in the first part of his 1905 paper , which are based on the constancy of the speed of light , but do not otherwise depend on maxwell s equations . einstein had remarked this problem , and he proposed in 1935 an elementary derivation of the mass - energy relation , independent of his 1905 argument , motivating it with the following words : @xcite _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ the special theory of relativity grew out of the maxwell electromagnetic equations . so it came about that even in the derivation of the mechanical concepts and their relations the consideration of those of the electromagnetic field has played an essential role . the question as to the independence of those relations is a natural one because the lorentz transformation , the real basis of the special relativity theory , in itself has nothing to do with the maxwell theory and because we do not know the extent to which the energy concepts of the maxwell theory can be maintained in the face of the data of molecular physics . in the following considerations , except for the lorentz transformation , we will depend only on the assumption of the conservation principles for impulse and energy . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ einstein s considerations exploit a conceptual experiment introduced by g.n . lewis and r.c . tolman @xcite and further discussed by p.s . epstein , @xcite where one considers collisions between pairs of particles in different inertial reference frames , and one looks for the expressions of momentum and energy by postulating their conservation . it is interesting to point out that lewis and tolman s paper , as well as epstein s one , only consider elastic collision and derive the relativistic expression of momentum , while they provide a doubtful argument for the mass - energy equivalence by the consideration of the change of the `` relativistic mass '' with speed . `` relativistic mass '' is in fact a rather problematic concept,@xcite and there is a growing consensus to avoid its introduction in the teaching of relativity . einstein derives instead the equivalence by simply extending the argument to inelastic collisions . the advantage of this approach for introducing the basic concepts of special relativity has been well remarked by r.f . feynman who , in his _ lectures _ ( ref . ) , derives the relativistic expressions of momentum and energy in a way that closely resembles einstein s one . ( feynman s derivation is however marred by his use of the `` relativistic mass '' . ) einstein s argument has been more recently discussed by f. flores , @xcite who identifies three closely related but different claims within the mass - energy equivalence concept , and compares einstein s 1935 argument with his original 1905 derivation @xcite and with m. friedman s 1983 derivation , @xcite which rests upon the consideration of newton s equations in special relativity . in this note , i present this line of thought in the hope that it may be found useful for the presentation of these fundamental concepts of special relativity in introductory courses for students of physics and mathematics . while the derivation of the relativistic expression of momentum in sec . [ sec : qdm ] is close to epstein s and feynman s arguments , the discussion of the expression of the kinetic energy and of the mass - energy equivalence is closer to einstein s one .

the derivation of the expressions of momentum and energy of a particle in special relativity is often less than satisfactory in elementary texts . in some , it is obtained by resorting to quantum or electrodynamic considerations , in others by introducing less - than - elementary concepts , like that of a four - vector , or even misleading ones , like `` relativistic mass '' . nevertheless it is possible , following ideas described by einstein in 1935 , to obtain a fully elementary derivation of these expressions based only on the lorentz transformations , on the conservation laws , and on the newtonian limit . the resulting argument allows for a clearer and logically consistent introduction to the basic concepts of relativistic dynamics .

the derivation of the expressions of momentum and energy of a particle in special relativity is often less than satisfactory in elementary texts . in some , it is obtained by resorting to quantum or electrodynamic considerations , in others by introducing less - than - elementary concepts , like that of a four - vector , or even misleading ones , like `` relativistic mass '' . nevertheless it is possible , following ideas described by einstein in 1935 , to obtain a fully elementary derivation of these expressions based only on the lorentz transformations , on the conservation laws , and on the newtonian limit . the resulting argument allows for a clearer and logically consistent introduction to the basic concepts of relativistic dynamics .

astro-ph0501138

i

the stellar imf at high redshift is of great importance for a wide range of astrophysical problems , such as the ionization and enrichment of the intergalactic medium , the extragalactic background light , the visibility of galaxies and the rate at which baryons are locked - up into stars and stellar remnants . there are two complementary approaches to the determination of the imf long ago and far away : one is to observe directly high redshift objects , and attempt inferences on the stellar imf from the integrated spectrum and photometry , while the second approach analyses the fossil record in old stars at low redshift . the characterization of the stellar imf in external galaxies , compared to that in the milky way , is a crucial step in deciphering the important physical processes that determine the distribution of stellar masses under a range of different physical conditions . the low mass stellar imf at the high redshifts at which these stars formed is directly accessible through star counts , plus a mass - luminosity relation . the high mass imf at these high redshifts is constrained by the chemical signatures in the low mass stars that were enriched by the supernovae from the high mass stars . i will discuss both ends of the imf at high redshift , in an external galaxy .

however , the environment in which its stars formed was clearly different from that in the globular clusters in the milky way galaxy what was the stellar imf in this external galaxy a long time ago ? the massive star imf at early times is constrained by elemental abundances in low - mass stars , and we discuss the available data . all data are consistent with an invariant imf , most probably of salpeter slope at the massive end , with a turnover at lower masses .

the dwarf spheroidal galaxy in ursa minor is apparently dark - matter dominated , and is of very low surface brightness , with total luminosity only equal to that of a globular cluster . indeed its dominant stellar population is old and metal - poor , very similar to that of a classical halo globular cluster in the milky way galaxy . however , the environment in which its stars formed was clearly different from that in the globular clusters in the milky way galaxy what was the stellar imf in this external galaxy a long time ago ? the fossil record of long - lived , low - mass stars contains the luminosity function , derivable from simple star counts . this is presented here . the mass function requires a robust mass - luminosity relation , and we describe the initial results to determine this , from our survey for eclipsing low - mass binaries in old open clusters . the massive star imf at early times is constrained by elemental abundances in low - mass stars , and we discuss the available data . all data are consistent with an invariant imf , most probably of salpeter slope at the massive end , with a turnover at lower masses . # 1#1@xmath0 # 1

1001.1240

i

the effect of quenched randomness on the equilibrium and dynamic properties of macroscopic systems is a subject of great theoretical and practical interest . it is well known that quenched bond randomness may produce drastic changes on phase transitions depending on the type of the transition @xcite . thus , symmetry - breaking first - order transitions are converted to second - order phase transitions by infinitesimal bond randomness for spatial dimensionality @xmath0 @xcite and by bond randomness beyond a threshold strength in @xmath1 @xcite , as indicated by general arguments @xcite and in some cases by rigorous mathematical work @xcite . in particular , this rounding effect of first - order transitions has now been rigorously established in a unified way in low dimensions ( @xmath2 ) including a large variety of types of randomness in classical and quantum spin systems @xcite . historically , the effects of disorder on phase transitions have been studied in two extreme cases , i.e. in the limits of weak and strong ( near the percolation point ) disorder . the first important conjecture , known today as the harris criterion @xcite , relates the value of the specific heat exponent @xmath3 in a continuous transition with the expected effects of uncorrelated weak disorder in ferromagnets . according to the harris criterion , for continuous phase transitions with a negative exponent @xmath3 , the introduction of weak randomness is expected to be an irrelevant field and the disordered system to remain in the same universality class . on the other hand , the weakly disordered system is expected to be in a different universality class in the case of a pure system having a positive exponent @xmath3 . pure systems with a zero specific heat exponent ( @xmath4 ) are marginal cases of harris criterion ( since the criterion does not give any information ) and their study , upon the introduction of disorder , has been of particular interest . the paradigmatic model of the marginal case is , of course , the general random 2d ising model ( random - site , random - bond , and bond - diluted ) and this model has been extensively investigated and debated @xcite . several recent studies , both analytical ( renormalization group and conformal field theories ) and numerical ( mainly monte carlo ( mc ) simulations ) devoted to this model , have provided very strong evidence in favor of the so - called logarithmic corrections s scenario . according to this , the effect of infinitesimal disorder gives rise to a marginal irrelevance of randomness and besides logarithmic corrections , the critical exponents maintain their 2d ising values . in particular , the specific heat is expected to slowly diverge with a double - logarithmic dependence @xcite . here , we should mention that there is not full agreement in the literature and a different scenario predicts a negative specific heat exponent @xmath3 leading to a saturating behavior @xcite , with a corresponding correlation length exponent @xmath5 @xcite . in general , a unitary and rigorous physical description of critical phenomena in disordered systems still lacks and certainly , lacking such a description , the study of further models for which there is a general agreement in the the behavior of the corresponding pure cases is very important . historically , such a suitable candidate for testing the above predictions , that has been also quite extensively studied , is the general 2d @xmath6-state potts model @xcite . this model includes the ising model ( @xmath7 ) , cases of a pure system having continuous transitions with a positive exponent @xmath3 ( @xmath8 ) and also the large @xmath6-cases ( @xmath9 ) for which one could observe and try to classify the above mentioned softening of first - order transitions in 2d models . another similarly interesting candidate , not yet as much studied in the random - bond version , is the 2d blume - capel ( bc ) model @xcite . we may note here that most of the existing literature on the bc model with randomness concerns randomness applied to the crystal field and/or spin glass exchange interactions @xcite . as it is well known , the pure version of the bc model undergoes an ising - like continuous phase transition to an ordered ferromagnetic phase as the temperature is lowered for crystal - field couplings less than a tricritical value and a first - order transition for larger values of the crystal - field coupling . therefore , this model provides also the opportunity to study two different and very interesting topics of the above described effects of disorder in critical phenomena , namely the double - logarithmic scenario for the specific heat in the regime where the 2d bc model is in the same universality class with the 2d random - bond ising model and also the softening of the transition in the first - order regime . recently the present authors @xcite have considered this model and provided strong numerical evidence clarifying two of the above mentioned effects induced in 2d systems by bond randomness . by implementing a two - stage wang - landau ( wl ) approach @xcite , we presented essentially exact information on the 2d bc model under quenched bond randomness . in this investigation , we found dramatically different critical behaviors of the second - order phase transitions emerging from the first- and second - order regimes of the pure bc model and since , these second - order transitions were found to have different critical exponents , our study indicated an interesting strong violation of universality @xcite . namely , different sets of critical exponents on two segments of the same critical line appeared to describe the two regimes : still - second - order and ex - first - order . in this paper , we extend our earlier work @xcite , by implementing essentially the same two - stage wl approach ( sec . [ sec:2 ] ) and try to give a more complete picture by concentrating in the weak ( still - second - order ) regime and simulate the model for several disorder strengths and many values of the crystal - field coupling . the above statement means that , effectively we will restrict our study to moderate values of the crystal field and moderate values of the disorder , intending to observe the frontier between the weak- and the strong - disorder universality classes from the disappearance of the expected 2d random ising universality class behavior . thus , in sec . [ sec:3 ] we will produce phase diagram points for the random - bond model but also for the pure model , reporting for the pure case a comparison with existing estimates in the literature . more generally , in carrying out this project we have also considered the pure 2d bc model for several values of the crystal - field , in the second - order regime , observing its finite - size scaling ( fss ) behavior . [ sec:4 ] presents such a comparative study between random and pure models concerning the behavior of all thermodynamic parameters used in the traditional fss analysis of mc data . this study enables us to observe some peculiarities of the pure model , due to the onset of tricriticality , and compare them with the corresponding behavior of the random model . furthermore , we try to focus , understand and shed light to the extent of universality of the random - bond 2d bc model with the corresponding random - bond ising model , for which the scenario of logarithmic corrections seems to be the strongest option in the current literature @xcite . the prediction of the range of such universality is far from trivial and the two regimes ( weak and strong ) have many dissimilarities which are also reflected in the ground - state structure , as further discussed below . the attempt to estimate the range of the above mentioned universality is accomplished by the novel idea which assumes the truth of the double logarithmic scenario for the specific heat in a suitable restricted range . this is presented in sec . [ sec:5 ] together with some further crucial observations concerning the behavior of the strong disorder regime , i.e. the regime where the ising class universality does not apply and the system has a rather complex and yet not understood behavior . our conclusions are summarized in sec . [ sec:6 ] .

several disorder strengths are considered . accepting , for the weak random version , the assumption of the double logarithmic scenario for the specific heat we attempt to estimate the range of universality between the pure and random - bond models . the behavior of the strong disorder regime is also discussed and a rather complex and yet not fully understood behavior is observed .

the effects of bond randomness on the phase diagram and critical behavior of the square lattice ferromagnetic blume - capel model are discussed . the system is studied in both the pure and disordered versions by the same efficient two - stage wang - landau method for many values of the crystal field , restricted here in the second - order phase transition regime of the pure model . for the random - bond version several disorder strengths are considered . we present phase diagram points of both pure and random versions and for a particular disorder strength we locate the emergence of the enhancement of ferromagnetic order observed in an earlier study in the ex - first - order regime . the critical properties of the pure model are contrasted and compared to those of the random model . accepting , for the weak random version , the assumption of the double logarithmic scenario for the specific heat we attempt to estimate the range of universality between the pure and random - bond models . the behavior of the strong disorder regime is also discussed and a rather complex and yet not fully understood behavior is observed . it is pointed out that this complexity is related to the ground - state structure of the random - bond version .

1210.5618

i

recently , slow anomalous diffusion , which is defined by the sublinear dependence of the mean square displacement ( msd ) on time , has been found in various phenomena including lipid granules diffusing in living fission yeast cells @xcite , colloidal particles diffusing on sticky surfaces @xcite and in networks of entangled actin filaments @xcite , mrna molecules diffusing in _ e. coli _ @xcite , chromosomal loci diffusing in bacteria @xcite , telomeres diffusing in nuclei of eukaryote cells @xcite , and proteins diffusing in dextran solutions @xcite . to understand these phenomena , two types of slow diffusion models have been extensively studied so far : ( 1 ) continuous - time random walks ( ctrws ) @xcite and ( 2 ) the generalized langevin equation ( gle ) and fractional brownian motions ( fbms ) @xcite . for the ctrw model , if the probability density function ( pdf ) of the waiting times between jumps of the particle is a power law @xmath0 with @xmath1 , the ensemble - averaged msd ( eamsd ) shows slow diffusion @xcite : @xmath2 '' to stand for an asymptotic relation , i.e. , @xmath3 means @xmath4 for some asymptotic limit such as @xmath5 . on the other hand , we use `` @xmath6 '' to stand for a stricter asymptotic relation : @xmath7 means @xmath8 for some asymptotic limit . furthermore , we use `` @xmath9 '' when @xmath10 is an approximation of @xmath11 , and `` @xmath12 '' when @xmath10 is proportional to @xmath11 , that is , they are not necessarily asymptotic relations . ] . typical origins of such power - law waiting times are complex energy landscapes @xcite and diffusion in inner degrees of freedom @xcite . similarly , eamsd of gle shows slow diffusion if the memory kernel @xmath13 decays algebraically @xmath14 with @xmath1 @xcite . a possible origin of this non - markovian memory effect is the viscoelasticity of the medium @xcite . a primary difference between these two stochastic processes ctrws and gle is in their ergodic properties . even if the memory kernel of a gle is given by a power function as stated above , the gle satisfies the ergodic property , that is , time - averaged quantities coincide with ensemble - averaged quantities @xcite . in contrast , this equivalence between the two averages does not hold in the ctrws with power - law waiting times . however , such ctrws exhibit an extended form of ergodicity time - averaged quantities become random variables following a distribution function @xcite . this distributional ergodicity is called weak ergodicity breaking @xcite or infinite ergodicity @xcite . in addition to the above mentioned examples , ctrws are frequently used in various fields of science @xcite . however , there are cases in which some finite - size effects should be considered in order to compare the model with experimental data . in particular , cutoffs at the tail of the power - law waiting time distribution @xcite and spatial confinement effects @xcite arise in many systems . the typical origins of waiting time cutoffs are physical limits with respect to energy and spatial extensions ( e.g. , @xcite ) . theoretical analysis of the ctrws with such cutoffs is difficult , because it is necessary to investigate the transient behavior . however , this difficulty is avoidable by using the tempered stable distribution ( tsd ) @xmath15 @xcite . the tsd has exponentially smooth cutoffs , and is a modified version of the truncated stable distribution , which has a sharp cutoff at the tail @xcite . furthermore , the tsd has the property called infinite divisibility @xcite , which allows a rigorous analysis even for transient behavior . the tsd is a special model for the cutoffs , but it shows typical behavior of cutoff distributions such as a slow convergence to the gaussian distribution @xcite . furthermore , the generalized fractional fokker - planck equation ( gffpe ) , which we will use in this paper to study eamsd , has been derived for ctrws with tempered stable waiting times @xcite . the ergodic properties of the system without confinement have also been clarified in @xcite , where the existence of a clear transition from weak ergodicity breaking ( an irreproducible regime ) to ordinary ergodicity ( a reproducible regime ) was shown analytically for the case of a non - equilibrium initial ensemble ( see sec . [ sec : tsd ] for a precise definition of the non - equilibrium and equilibrium ensembles ) . another important finite - size effect is spatial confinements . for example , to understand the transport phenomena in cells @xcite , confinements due to cell membranes should be considered . confinement effects in ctrws with power - law waiting times were studied numerically in @xcite and analytically in @xcite ; it was found that the time - averaged msd ( tamsd ) shows a crossover from normal diffusion at short timescales to anomalous slow diffusion at longer timescales . they also reported numerically the weak ergodicity breaking in tamsd . recently , the ctrw model with the two finite - size effects ( i.e. , waiting time cutoffs and spatial confinements ) has been used as a model for the transport of lipid granules in living fission yeast cells @xcite , in which confinement effects are caused by a hookean force exerted by optical tweezers . the model clearly explains the experimental results such as the crossover in tamsd and weak ergodicity breaking . these studies mainly used numerical simulations , but a detailed theoretical analysis has not yet been reported . also , they studied only non - equilibrium ensemble , and thus the dependences of the ergodic properties on initial ensembles are still unknown . in this paper , we present theoretical results for ctrws with two finite - size effects : the effects of cutoffs in the waiting time distribution and the confinement effects . in particular , we focus on tamsd as an observable , and study the crossover from normal to anomalous diffusion in the tamsd and ergodic properties in terms of the scatter of diffusion constant for the tamsd . the tamsd , which is often used in single - molecule tracking experiments @xcite , is defined as @xmath16 where @xmath17 is the position of the particle at time @xmath18 , @xmath19 is the total measurement time , and @xmath20 is the time interval . hereinafter we assume that @xmath21 . here we define a generalized diffusion constant @xmath22 as @xmath23 . in some experiments , it has been reported that @xmath22 behaves like a random variable depending on each time series @xcite . therefore , the scatter in tamsd or @xmath22 has been used to check the consistency of the model with experimental data @xcite . in this paper , we use the tsds @xcite as waiting time distributions of ctrws . for the tsd , it is possible to explicitly write the convoluted waiting distributions of any order [ eq . ( [ e.prob.na ] ) ] . moreover , we use the numerical method for the tsd presented in @xcite and appendix [ sec : num.method ] , and study the initial and boundary value problem of the gffpe to understand the confinement effect . the rest of this paper is organized as follows . in sec . [ sec : tsd ] , we introduce the tsds . then , in sec . [ sec : ea.tamsd ] , we show the crossover from normal to anomalous diffusion in tamsd by using the gffpe . in sec . [ sec : stat.tamsd ] , ergodic properties of tamsd are studied using renewal theoretic analysis . secs . [ sec : conclusion ] and [ sec : discussion ] are devoted to conclusion and discussion . in the appendices , we summarize some technical matters , including a derivation of gffpe from ctrws as well as the ergodic properties of general observables .

we also investigate dependences of ergodic properties on initial ensembles ( i.e. , distributions of the first waiting time ) . here , it is shown that the time - averaged mean square displacement ( tamsd ) exhibits a crossover from normal to anomalous diffusion due to the spacial confinement and this crossover does not vanish even in the long measurement time limit . moreover , for the non - equilibrium ensemble , we show that the probability density function of the diffusion constant of tamsd follows the transient mittag - leffler distribution , and that scatter in the tamsd shows a clear transition from weak ergodicity breaking ( an irreproducible regime ) to ordinary ergodic behavior ( a reproducible regime ) as the measurement time increases . this convergence to ordinary ergodicity requires a long measurement time compared to common distributions such as the exponential distribution ; in other words , the weak ergodicity breaking persists for a long time . in addition , it is shown that , besides the tamsd , a class of observables also exhibits this slow convergence to ergodicity .

the effects of spatial confinements and smooth cutoffs of the waiting time distribution in continuous - time random walks ( ctrws ) are studied analytically . we also investigate dependences of ergodic properties on initial ensembles ( i.e. , distributions of the first waiting time ) . here , we consider two ensembles : the equilibrium and a typical non - equilibrium ensembles . for both ensembles , it is shown that the time - averaged mean square displacement ( tamsd ) exhibits a crossover from normal to anomalous diffusion due to the spacial confinement and this crossover does not vanish even in the long measurement time limit . moreover , for the non - equilibrium ensemble , we show that the probability density function of the diffusion constant of tamsd follows the transient mittag - leffler distribution , and that scatter in the tamsd shows a clear transition from weak ergodicity breaking ( an irreproducible regime ) to ordinary ergodic behavior ( a reproducible regime ) as the measurement time increases . this convergence to ordinary ergodicity requires a long measurement time compared to common distributions such as the exponential distribution ; in other words , the weak ergodicity breaking persists for a long time . in addition , it is shown that , besides the tamsd , a class of observables also exhibits this slow convergence to ergodicity . we also point out that , even though the system with the equilibrium initial ensemble shows no aging , its behavior is quite similar to that for the non - equilibrium ensemble .

cond-mat0012500

i

the interaction of moving ions with solids has represented an active field of basic and applied physics@xcite . charged particles moving near metallic surfaces loose energy as a consequence of the creation of different kind of excitations in the metal , such as electron - hole pairs and both bulk and surface plasmons@xcite . also , the theoretical understanding of the electronic excitations is well known to be relevant in surface physics , as these modes are invariably involved in a variety of surface spectroscopies[5 - 9 ] . quantum - size effects ( qse ) were first investigated by schulte@xcite within a jellium model of the thin film and later by feibelman@xcite , showing that the various physical properties exhibit an oscillatory behaviour as a function of the thickness of thin metallic films . these effects , which decrease as the size of the thin film increases , can be observed experimentally@xcite . qse on the surface energy and the work function have been examined recently , within a stabilized jellium model of the electron system@xcite . in this paper we focus on the investigation of qse on the energy - loss spectra of charged particles moving parallel with metallic slabs . the energy loss is calculated , within linear response theory , from the knowledge of the density - response function of the inhomogeneous electron system , which we evaluate either in the random - phase approximation or with the use of an adiabatic and local exchange - correlation kernel . in section 2 we present general expressions for the energy loss of charged particles moving along a definite trajectory . the results of our self - consistent calculations are presented in section 3 , and in section 4 our main conclusions are summarized . atomic units are used throughout , i.e. , @xmath4 .

the electronic properties of thin films present quantum - size effects , which are a consequence of the finite size of the system . here we focus on the investigation of these effects on the electronic energy loss of charged particles moving parallel with thin metallic films . the energy loss is calculated , within linear - response theory , from the knowledge of the density - response function of the inhomogeneous electron system , which we evaluate either in the random - phase approximation or with the use of an adiabatic and local exchange - correlation kernel . * thin - film effects on the surface stopping power of a free electron gas * + a. garca - lekue@xmath0^{)}$ ] and j.m .

the electronic properties of thin films present quantum - size effects , which are a consequence of the finite size of the system . here we focus on the investigation of these effects on the electronic energy loss of charged particles moving parallel with thin metallic films . the energy loss is calculated , within linear - response theory , from the knowledge of the density - response function of the inhomogeneous electron system , which we evaluate either in the random - phase approximation or with the use of an adiabatic and local exchange - correlation kernel . * thin - film effects on the surface stopping power of a free electron gas * + a. garca - lekue@xmath0^{)}$ ] and j.m . pitarke@xmath1 + _ @xmath2 materia kondentsatuaren fisika saila , zientzi fakultatea , euskal herriko unibertsitatea , 644 posta kutxatila , + 48080 bilbo , basque country , spain _ + _ @xmath3 donostia international physics center ( dipc ) and centro mixto csic - upv / ehu , donostia , basque country , spain _ + : 71.45.gm , 79.20.rf , 34.50.bw : electronic energy loss ; quantum size effects

astro-ph9907071

i

the astrophysical rapid neutron - capture process ( r - process ) has been recognized for a long time as the scenario responsible for the synthesis of approximately half of the nuclear species in nature , which are more massive than fe @xcite . it requires environments with a high neutron density , where neutron captures are faster than @xmath0-decays , even for neutron - rich unstable nuclei up to 15 - 30 units from stability . only under such conditions it is possible that highly unstable nuclei are produced near the neutron drip - line via neutron captures , @xmath1-photodisintegrations , @xmath2-decays and @xmath0-delayed processes , leading also to the formation of the heaviest elements in nature like th , u , and pu . far from stability , magic neutron numbers are encountered for smaller mass numbers a than in the valley of stability , which shifts the r - process abundance peaks in comparison to the s - process peaks ( which occur at neutron shell closures at the stability line due to small neutron capture cross sections ) . besides this basic understanding , the history of r - process research has been quite diverse in suggested scenarios ( for reviews see @xcite ) . starting with a seed distribution somewhere around a=50 - 80 before massive neutron - capture sets in , the operation of an r - process requires 10 to 150 neutrons per seed nucleus to form all heavier r - nuclei . the question is which kind of environment can provide such a supply of neutrons to act before decaying with a 10 min half - life . the logical conclusion is that only explosive environments , producing or releasing these neutrons suddenly , can account for such conditions . without having discussed any stellar models yet , we want to mention some recent literature on these issues . the r - process site is not a settled one ; however , two astrophysical settings are suggested most frequently : ( i ) type ii supernovae ( snii ) with postulated high - entropy ejecta @xcite , where the delayed emergence of r - process matter in galactic evolution @xcite indicates that these can probably only be sn with small progenitor mass ; and ( ii ) neutron star mergers or other events with low - entropy ejecta @xcite . after this ad hoc introduction of sites , we want to return first to the conditions in high - temperature explosive plasmas in order to test what kind of nuclear - physics input is required , and also what type of thermodynamic environment properties can lead to the neutron to seed ratios mentioned above . the main aspect is that a whole variety of burning processes responsible for the abundances of intermediate and heavy nuclei , like e.g. explosive o and si - burning , are leading to partial ( quasi ) or full equilibria of reactions ( qse or nse ) . these are described by the chemical potentials of nuclei which form a boltzmann gas . the abundance ratios are ( besides thermodynamic environment properties ) determined by mass differences . therefore , mass uncertainties matter , while uncertainties in cross sections do not enter abundance determinations . non - equilbrium regions are identified by small reaction cross sections , either due to small q - values for reactions out of the magic numbers or due to small level or resonance densities for light nuclei . for sufficiently high temperatures all qse groups merge to a full nse . the chemical equilibrium for neutron or proton captures leads to abundance maxima at specific neutron or proton separation energies @xmath3^{3/2 } \bigl[{{2\pi \hbar^2}\over { m_ukt}}\bigr]^{3/2 } { \rm exp}(s_{p}(a_c)/kt ) \\ { s_{p}(a_c ) \over kt}&= & 24 \ln\bigl [ ( { a_ta_p \over { a_c}})^{3/2 } ( { g(a_t)g_p \over 2g(a_c)})^{3/2 } ( { t \over { 10 ^ 9{\rm k}}})^{3/2 } { n_a \over { n_{p}/{\rm cm}^3}}\bigr].\end{aligned}\ ] ] these equations are valid for neutron , proton and/or @xmath4 captures , as indicated by the subscript @xmath5 ( projectile ) ; subscript @xmath6 stands for target and @xmath7 for the compound nucleus . the @xmath8 s are abundances related to number densities @xmath9 via @xmath10 , where @xmath11 denotes the mass density and @xmath12 the avogadro number . at the maximum in an isotopic or isotonic line we have @xmath13 , if the partition functions g are neglected . this is slightly modified by logarithmic dependences on projectile ( neutron or proton ) density @xmath14 and temperature @xmath15 . in case an equilibrium with neutrons and protons exists , the abundance maximum is found in the nuclear chart at the intersection of the relevant neutron and proton separation energies . the free neutron and proton densities reflect the total neutron / proton ratio in matter , which is determined by slow ( not in equilibrium ) , weak interactions via changing the total proton / nucleon ratio @xmath16@xmath17@xmath18@xmath19 . the understanding that explosive burning stages are governed by qse or even nse is growing @xcite . this has been shown recently in calculations of snii nucleosynthesis @xcite with two different libraries of nuclear reaction rates . different types of qse - groups can emerge in explosive burning . the high temperature phase of the rp - process ( rapid proton capture ) in x - ray bursts , where no neutrons are available , witnesses isotonic lines in a ( @xmath20 equilibrium @xcite . another application is the r - process , the focus of the present paper . here the qse - groups are isotopic lines in an ( @xmath21 equilibrium . the connecting weak interactions for both processes are @xmath22- or @xmath2-decays . during the final freeze - out from equilibria , when temperatures decline below equilibrium conditions , reaction rates and capture cross sections can count again . in general , it should be pointed out that equilibria simplify the understanding of explosive nucleosynthesis processes and individual cross sections play a much less important role than reaction q - values . since the rp- and r - process explore exotic nuclei close to the proton or neutron drip - lines , we need to focus on nuclear masses and @xmath0-decay properties . an understanding of the underlying nuclear structure is essential for both types of nuclear parameters . such information usually comes from a close interplay between experiment and theory . this will be discussed in more detail in sections 3 and 4 . in order to underline why ( within an understanding of the - nuclear - functioning of the r - process ) the two scenarios mentioned in the beginning of this section seem to be the most promising ones , we want to present here two major results found recently by freiburghaus et al . they performed an analysis of neutron to seed ratios in different types of adiabatic expansions with a given entropy s , proton / nucleon ratio @xmath23 , and expansion time scale . in order to obtain the required 10 to 150 neutrons per r - process seed nucleus ( in the fe - peak or somewhat beyond ) permitting to produce nuclei with masses a@xmath19200 , this translates into a @xmath16@xmath17@xmath18@xmath19@xmath240.120.3 for a composition of fe - group nuclei and free neutrons . such a high neutron excess is only available for high densities in neutron stars under @xmath0-equilibrium ( @xmath25 , @xmath26 ) , based on the high electron fermi energies which are comparable to the neutron - proton mass difference @xcite . another option is a so - called extremely @xmath4-rich freeze - out in complete si - burning with moderate @xmath23@xmath190.40 . this corresponds to a freeze - out from qse with a weak connection between the light ( @xmath27 ) and heavy ( mg kr ) qse groups due to low densities . the links accross the particle - unstable a=5 and 8 gaps are only possible via the three - body reactions @xmath28 and @xmath29 to @xmath30c and @xmath31be , whose reaction rates show a quadratic density dependence . the entropy can be used as a measure of the ratio between the remaining he mass - fraction and heavy nuclei . similarly , the ratio of neutrons to heavy nuclei ( i.e. the neutron to seed ratio ) is a function of entropy and permits for high entropies , with large remaining he and neutron abundances compared to small heavy - seed abundances , neutron captures which proceed to form the heaviest r - process nuclei @xcite . after the freeze - out of charged - particle reactions in matter , which expands from high temperatures but relatively low densities , as much as 90% of all matter can be locked into @xmath32he with @xmath33=@xmath34 , which leaves even for moderate @xmath23 s a large neutron / seed ratio for the few existing heavier nuclei . the behaviour of these two environments , representing a normal ( low - entropy ) and an @xmath4-rich ( high - entropy ) freeze - out , is summarized in fig . 1 . the available number of neutrons per heavy nucleus @xmath35 after charged - particle freeze - out , when the large qse - groups break up into isotopic lines , is shown as a function of entropy and initial @xmath23 . at low entropies the transition to a normal freeze - out occurs , indicated by the negligible entropy dependence . this introduction centered ( in a cursory way ) on the questions : ( i ) how can one obtain - after an expansion and cooling to temperatures of @xmath36k , when the charged - particle freeze - out occurs - the neutron to seed ratios required for a successful r - process ; and ( ii ) what type of nuclear - physics input is of dominant importance . in the following section 2 , we will discuss in more detail the methods to follow abundance changes during the neutron - capture phase , and will show how in simplified r - process models the observed abundance features and nuclear properties far from stability are related . in section 3 , we present the nuclear - data input employed , and show the strong effects which the choice of nuclear data can have . section 4 summarizes the experimental information on r - process nuclei , to a large extent obtained at cern / isolde . finally , in section 5 we discuss how r - process calculations evolved over the past decade with continuously improved nuclear - structure knowledge from initially classical equilibrium calculations to recent results from specific astrophysical sites .

a correct understanding and modeling requires the knowledge of nuclear properties far from stability and a detailed prescription of the astrophysical environment . initial examinations paid attention to far unstable nuclei with magic neutron numbers related to r - process peaks , while present activities are centered on the evolution of shell effects with the distance from the valley of stability . we first show in site - independent applications the effect of both types of nuclear properties on r - process abundances .

the focus of the present review is the production of the heaviest elements in nature via the r - process . a correct understanding and modeling requires the knowledge of nuclear properties far from stability and a detailed prescription of the astrophysical environment . experiments at cern / isolde have played a pioneering role in exploring the characteristics of nuclear structure in terms of masses and @xmath0-decay properties . initial examinations paid attention to far unstable nuclei with magic neutron numbers related to r - process peaks , while present activities are centered on the evolution of shell effects with the distance from the valley of stability . we first show in site - independent applications the effect of both types of nuclear properties on r - process abundances . then , we explore the results of calculations related to two different ` realistic ' astrophysical sites , ( i ) the supernova neutrino wind and ( ii ) neutron star mergers . we close with a list of remaining theoretical and experimental challenges needed to overcome for a full understanding of the nature of the r - process , and the role cern / isolde can play in this process . nuclear astrophysics , r - process nucleosynthesis , isotope and isomer separation via hf splitting , laser ion source , nuclear structure , neutron - rich isotopes , ultra - metal - poor halo stars

astro-ph9907071

r

the experimental study of neutron - rich nuclides lying in and near the projected r - process path serves two purposes , provision of direct data for use in nucleosynthesis calculations , and testing the theories from which nuclear properties of far - unstable isotopes are derived when no data are available . as is infered from the nucleosynthesis snapshots shown in the previous section , the predictions of the presently existing global nuclear models quite obviously differ considerably when approaching the limits of particle binding . the reason may well be that the model parameters used so far , which were mainly determined to reproduce known properties near @xmath0-stability , need not always be proper to be used at the drip - lines . therefore , experiments very far from stability will be essential to verify possible nuclear - structure changes with isospin , and to motivate improvements in nuclear theories . as already mentioned in sect . 3 , only about a decade ago the area of experiments _ in the r - process path _ started with the identification of the first two classical , neutron - magic ` waiting - point ' isotopes : @xmath92zn@xmath93 ( situated 10 mass - units away from stability ) and @xmath90cd@xmath91 ( even 16 units beyond stable @xmath112cd ) @xcite . in the following , we will give some technical details on the identification of @xmath90cd , in order to convince also outsiders from our particular field that such , in principle quite simple experiments are not at all easy. neutron - rich cd isotopes were produced at that time at the old cern / isolde mass separator connected to the 600-mev proton synchro - cyclotron . in this experiment , a uc@xmath113 target in a graphite - cloth matrix was connected to a plasma - discharge ion source via a heated quartz tansfer line . this tube was assumed to serve as a kind of thermochromatography column allowing preferential extraction of volatile species , whereas non - volatile elements should be retained . in this way , some chemical selectivity was intruduced to the otherwise non - selective plasma ionization . nevertheless , at a=130 strong isobaric contaminations of @xmath90 in and @xmath90cs were observed which made @xmath114- and @xmath39-spectroscopy of the orders of magnitude weaker produced @xmath90cd impossible . moreover , even with the selective detection method of @xmath0-delayed neutron ( @xmath0dn ) counting , the occurrence of a priori unexpected [ @xmath115cabr]@xmath116 molecular ions , at a=130 containing the 1.9-s @xmath117br @xmath0dn - precursor , severely complicated the experimental conditions . to optimize the detection conditions for the searched @xmath90cd , data from about 36,000 growth ( 300 ms collections ) and decay ( 900 ms ) cycles were accumulated . a careful analysis of the resulting complex @xmath0dn - multiscaling curves @xcite yielded after subtraction of the @xmath117br @xmath0dn - component an estimate of the @xmath90cd half - life between maximum 230 ms ( presumably representing a t@xmath97 mixture of cd - mother and in - daughter decays ) and 160 ms ( derived from the growth curve during activity collection , where the cd signals should be enhanced compared to the in - daughter activity ) . after all these experimental difficulties , it was quite satisfying to see that our experimental half - life value of ( 195@xmath11835 ) ms turned out to be in reasonable agreement with the n@xmath94(z)@xmath109@xmath119@xmath101(z)@xmath120const . waiting - point expectation of ( 180@xmath11820 ) ms , derived independently at that time by hillebrandt ( see , kratz , thielemann , hillebrandt et al . the correlation found between the @xmath121 in and @xmath90cd half - lives and the observed solar abundances of their stable isobars , which was for the first time exclusively based on experimental numbers , immediately became very important to constrain the equilibrium conditions of an r - process . and this success strongly motivated further experimental and theoretical nuclear - structure investigations , as well as astrophysical r - process studies @xcite . for example , at isolde the second n=50 waiting - point isotope @xmath122cu could be identified again using a chemically non - selective plasma - ion source @xcite ; experimentally known strong p@xmath98 branches were shown to be the nuclear - structure origin of the odd - even staggering in the a@xmath6580 n@xmath94 peak @xcite ; and from the interpretation of the @xmath92zn decay scheme in terms of j@xmath123=1@xmath116 , two - quasi - particle ( 2qp ) configurations , evidence for a vanishing of the spherical n=50 shell closure far from stability was obtained @xcite . since the late 1980 s , considerable progress has been achieved in the study of neutron - rich medium- to heavy - mass nuclei at various laboraties , with isolde always playing a leading role in this field . however , due to the generally very low production yields , the occurrance of isobar , multi - charged ion and molecular - ion contaminations from chemically non - selective ionization modes , or because of the application of non - selective detection methods , _ direct _ information on isotopes lying in the r - process path(s ) could be obtained but in a few exceptional cases . from the majority of investigations , originally dedicated to study nuclear - structure developments as a function of isospin , only _ indirect _ but nevertheless also important information for r - process calculations can be deduced ( see , e.g. @xcite ) . in this context , we would like to remind the reader of the fascinating phenomenon of the _ sudden onset and saturation of ground - state deformation at n=60 _ ( see , e.g. @xcite ) , which had in fact led to the first astrophysical request of n=82 shell quenching @xcite . because of the severe experimental problems to identify r - process nuclei , recent progress has undoubtedly benefitted from the * selectivity * in their production and detection , by applying e.g. z - selective laser ion - source ( lis ) systems , isobar separation or multifold - coincidence techniques . today , there are mainly three mass regions , where nuclear - structure information is of particular astrophysical interest . the first is the seed region of the classical r - process which involves very neutron - rich fe - group isotopes up to the double - magic nucleus @xmath124ni . we will discuss recent studies in that mass - region in subsect . the second region of interest is that of far - unstable isotopes of refractory elements ( zr to pd ) around a@xmath65115 . here , most r - process calculations show a pronounced r - abundance _ trough _ , which is believed to be due to deficiencies at and beyond n=72 mid - shell ( see , e.g. @xcite . recent experimental information using chemical separation procedures , or ion - guide and projectile - fragmentation techniques combined with mass separation can , for example be found in @xcite . the third region of strong nuclear - structure and astrophysics interest is that around the double - magic nucleus @xmath125sn , which we will discussed in subsect . recent spectroscopic studies around the double ( semi- ) magic @xmath126ni ( z=28 , n=40 ) at lisol in louvain - la - neuve , at ganil / lise in caen and also at cern / isolde ( see , e.g. @xcite , and references therein ) , have revealed new structure features which are not easy to reconcile with established shell - model calculations in the neutron - rich region between @xmath127ca and @xmath124ni . most ( but not all ) of the models find that n=40 is a good closed subshell and predict near - zero deformation for neutron numbers in its vicinity . of course , these ideas are supported by existing data for @xmath128ni , @xmath129zn , @xmath130ge and @xmath131se isotopes for which there is a slight peak in the 2@xmath116 energies for n=38 and / or the supposed subshell at n=40 , and then a gentle drop in e(2@xmath116 ) beyond n=42 as the @xmath132g@xmath133 orbitals fill and some collectivity is observed ( see fig . 7 ) . however , recent experiments at the ps - booster isolde using the high z - selectivity of laser ionization have made possible decay - studies of very neutron - rich @xmath134mn isotopes , and the determination of detailed nuclear - structure information for their @xmath135fe - daughters . in particular , it was found that contrary to expectations the n=40 isotone @xmath136fe , situated only one proton - pair below double ( semi- ) magic @xmath126ni , is already relatively deformed . from the well - known relationship between e(2@xmath116 ) , b(e2 ) values and collectivity @xcite , we deduce a deformation value of @xmath0@xmath113@xmath650.26 for @xmath136fe . as can be seen from fig . 7 , this trend toward collectivity below @xmath126ni is already observed for @xmath137fe@xmath138 with @xmath0@xmath113@xmath650.18 . needless to say , these data serve as an indication that ` theoretical consensus ' for sphericity in n=40 isotones with z@xmath1728 does not provide a good description of the structure , and consequently also of nuclear masses and decay properties of these nuclides . subsequent data from the ganil / lise spectrometer @xcite in this mass region are in support of our conclusion that the n=40 and adjacent nuclides below @xmath126ni are relatively deformed , with the maximum collectivity presumably centered around @xmath137cr@xmath139 . hence , the use of theoretical results that do not account for deformation of neutron - rich isotopes in this mass region as input data for astrophysical calculations must be approached with caution . already with the use of z - selective laser ionization at the general - purpose separator ( gps ) of cern / isolde , it has been possible to study decay properties of 14-ms @xmath140mn , which is one of the most neutron - rich isotopes with the shortest @xmath0-decay half - life beyond the sd - shell . the prospects are good for an extension of such measurements to even heavier isotopes with lis and the high - resolution separator ( hrs ) , eventually including the study of detailed level structures up to @xmath141fe . combined with ongoing work on neutron - rich @xmath142cu and @xmath129zn at isolde and on @xmath143co and @xmath128ni at other facilities , nuclear - structure information towards the next major neutron - shell closure n=50 will accumulate , to answer e.g. the question about shell - quenching at double - magic @xmath124ni and its ` bottle - neck ' behaviour for the r - process matter flow through n=50 . moreover , the nuclear properties in this region have gained additional importance in the context of the lately discussion of _ two _ distinct r - process components , a ` weak ' r - process below a@xmath65130 , and the ` main ' r - process beyond a@xmath65130 ( see sect . 5.2 ) . the mass region around the far - unstable double - magic nucleus @xmath125sn has long been and still is of particular interest for experimental and theoretical investigations . apart from astrophysical importance ( formation of the a@xmath65130 peak of the n@xmath94 distribution @xcite ) , this region is of considerable shell - structure interest . the neutron - rich isotope @xmath144sn@xmath91 with its pronounced magicity ( only comparable to stable @xmath145pb@xmath96 ) , together with the properties of the nearest - neighbour single - particle ( @xmath146sb@xmath91 and @xmath147sn@xmath148 ) and single - hole ( @xmath149sn@xmath150 and @xmath151in@xmath91 ) nuclides are essential for tests of the shell model , and as input for any reliable future microscopic nuclear - structure calculations towards the neutron drip - line . the bulk of the data so far known in this region have been obtained from @xmath0-decay spectroscopy at the mass - separator facilities osiris ( sweden ) and isolde ( see , e.g. @xcite , and references therein ) . the structures of @xmath152sn ( @xmath132-hole ) and @xmath153sb ( @xmath154-particle ) are fairly well known since more than a decade . more recently , the @xmath132-particle states 2f@xmath155 ( g.s . ) , 3p@xmath156 ( 854 kev ) , 1h@xmath133 ( 1561 kev ) and 2f@xmath157 ( 2005 kev ) , as well as tentatively also the 3p@xmath97-particle ( 1655 kev ) and the 1h@xmath158-hole ( @xmath1203700 kev ) states in @xmath153sn@xmath159 have been identified @xcite at the general purpose separator ( gps ) of the new ps - booster isolde facility . from these data , valuable information on the spin - orbit splitting of the 2f - orbital and tentatively the 3p - state splitting was obtained . these results were compared to mean - field and hfb predictions , and it was found that none of the potentials currently used in _ ab initio _ shell - structure calculations was capable of properly reproducing the ordering and spacing of these states ( see , e.g. @xcite , where also possible astrophysical consequences are given ) . of particular interest in this context are the surprisingly low - lying @xmath132p@xmath156- and @xmath132p@xmath97-states in @xmath153sn . according to the standard nilsson model @xcite , for example , they are expected at 2.89 mev and 4.36 mev , respectively . such lowering of the energies of low - j orbitals ( here , by as much as 2.0 mev and 2.7 mev , respectively ) seems to occur in different mass regions for very neutron - rich nuclides , and has been interpreted , for example , as monopole shifts of single - particle ( sp ) states@xcite . the occurrence of such energy shifts of sp levels has recently also been predicted as a _ neutron - skin _ phenomenon to occur only near the neutron drip - line ( see , e.g. @xcite ) , but not yet in ( n@xmath99 + 1 ) @xmath153sn which is still neutron - bound by s@xmath98@xmath652.4 mev . nevertheless , following the suggestion of dobaczewski @xcite , we have modified the nilsson potential by reducing the strength of the @xmath160-term ( i.e. the spin - orbit interaction ) , in order to study its effect on different orbitals . and indeed , this procedure has led to the desired change in the position and even the ordering of the @xmath132-particle states beyond n=82 , and has thus allowed at least a qualitative reproduction of the experimental observation of low - lying low - j and high - lying high - j orbitals in @xmath153sn . recently , zhang et al . @xcite have proposed a new set of nilsson parameters that correctly reproduce the sp levels in @xmath152sn and @xmath153sn . they compare their new results with the experimental levels and older nilsson parameters , as well as sp levels obtained from relativistic mean - field calculations . the danger with this approach is that the change in parameters may be compensating for underlying deficiencies in the model . consequently , while the results do fit the levels of @xmath153sn , they may not be useful for astrophysical uses where the goal is to determine the structure of nuclides significantly further from stability . with these new data , the @xmath125sn valence - nucleon region is nearly complete . the only missing information are the @xmath154-hole states in @xmath151 in , which can be studied through @xmath0-decay of the very exotic nucleus @xmath152cd@xmath159 . recent lis developments at mainz @xcite and cern / isolde , using a novel frequency - tripling technique for the z - selective resonance ionization of cd , have made possible first test measurements on cd isotopes in the a@xmath65130 region at the gps of the ps - booster isolde . although the data are not yet fully analyzed , we can already present some interesting new results . for example , the complex @xmath0dn - curve at a=130 indicates a half - life component of ( 162@xmath1187 ) ms on top of the @xmath90 in @xmath0dn - activity . we assign this component to the r - process waiting - point isotope @xmath90cd , which we had first identified using non - selective ionization with a somewhat longer half - life @xcite . as weighted average of the two determinations , we now favour a t@xmath97=(168@xmath11812 ) ms . in this experiment , it was also possible to measure , for the first time , a half - life for @xmath152cd@xmath159 . the value of ( 68@xmath1183 ) ms @xcite is considerably shorter , and the estimated @xmath0dn - branch is much lower than might have been expected . it is possible to estimate a forbidden g.s .- to - g.s . @xmath0-branch ( @xmath132f@xmath155 @xmath161 @xmath154g@xmath133 ) with a partial half - life of about 120 ms . this means that the gamow - teller ( gt ) allowed decay must also have a half - life of at least 150 ms , as compared to the earlier qrpa prediction of 943 ms @xcite . as it is unlikely that the log(ft ) value is smaller , this result indcates a significantly larger @xmath0-energy driving the gt decay than predicted by the qrpa . in turn , this means either a significantly larger q@xmath162 ( meaning a less bound 83@xmath163 neutron ) or a significantly lower energy for the daughter states to be populated in @xmath152 in . either of these possibilities is an indication that full understanding of the structure of nuclides along the n=82 closed neutron shell is not complete . in any case , the present results from both detection methods , @xmath0dn - counting and @xmath39-spectroscopy , suggest the need of isobar separation , i.e. the use of the hrs at isolde , in order to discriminate the laser - ionized @xmath107cd from the unavoidable surface - ionized @xmath164 in isobar . another recent study of nuclear - structure development towards n=82 concerns the @xmath0dn- and @xmath39-spectroscopic measurements of neutron - rich ag nuclides at the ps - booster isolde facility ( @xcite ) , using an improved version of the lis system described in @xcite together with new microgating procedures @xcite . this approach was of considerable assistance in minimizing the activities from surface - ionized in and cs isobars . in this context , the additional ` selectivity ' of the spin- and moment - dependent hyperfine ( hf ) splitting was used to enhance the ionization of either the @xmath154p@xmath97-isomer or the @xmath154g@xmath133 g.s .- decay of the ag isotopes . the laser response to hf - splitting was calibrated on the stable j@xmath123=1/2@xmath165 @xmath166ag whose magnetic moment is small ( @xmath167=-0.11 n.m . ) and on the radioactive j@xmath123=7/2@xmath116 isomer that has a large moment of @xmath167=4.4 n.m . ( see upper left part of fig . 8 , and sebastian et al . subsequently , the @xmath0dn - activities were measured as a function of laser frequency for @xmath168ag up to @xmath169ag ( see fig . all ag isotopes show apart from the expected small isotope shift the same global pattern , where the moment of the odd g@xmath133-proton is the dominant source of hf - splitting . for @xmath168ag , previous decay - studies had already indicated the presence of both a low- and a high - spin isomer @xcite . and indeed , apart from the highly split peak that can be associated with a ( @xmath154g@xmath133@xmath132h@xmath158)@xmath170 configuration , another narrow peak shows up in the center that could arise from the ( @xmath154p@xmath97@xmath132d@xmath156)@xmath171 configuration ( see fig . subsequently , both @xmath0dn- and @xmath39-decay from @xmath168ag was studied as a function of laser frequency . as is evident from the partial @xmath39-spectra shown in the lower part of fig . 9 , when the laser is set at the center of the frequency scale , @xmath39-rays from both isomers can be observed . however , when the laser frequency is shifted away from the center ( to 35 units ) , ionization of the low - spin isomer is suppressed , and the @xmath39-spectrum indicates that only the decay of the high - spin isomer is oberved . similarly , when following the @xmath0dn - decay curves as a function of laser frequency , different half - lives are obtained which represent varying admixtures of the two isomers . from a preliminary analysis , we get a half - life of the low - spin isomer of t@xmath97@xmath65550(50 ) ms and a value of t@xmath97@xmath65200(50 ) ms for the high - spin isomer of @xmath168ag @xcite . this experiment clearly demonstrates the sensitivity of ionization to laser frequency and marks the first spectroscopic application of this technique to short - lived isomers . in the meantime , a gross analysis of @xmath39-spectra taken at different laser - frequency settings confirms isomerism also for the heavier ag isotopes up to ( at least ) @xmath172ag . an important nuclear - physics quantity for r - process nucleosynthesis calculations ( in particular for the r - matter flow through the a@xmath65130 region and the n@xmath94 peak shape ) is the @xmath0-decay half - life of the n=82 waiting - point isotope @xmath103ag , situated just below @xmath90cd . qrpa calculations using different q@xmath101-values and sp wave functions resulted in decay rates between 15 ms and 170 ms @xcite . this had left large uncertainties in the reproduction of the a@xmath65130 peak ( see fig . 1 in @xcite , and also fig . 4 in @xcite ) . initial attempts @xcite to observe the @xmath0dn - decay of @xmath103ag , performed with the ( broad - band ) lasers centered with respect to the mean frequency for the stable @xmath154p@xmath97 @xmath166ag , had failed . after the observation of enhanced ionization of the @xmath154g@xmath133 level at an off - center frequency , a new experiment was performed with the laser setting at the left @xmath154g@xmath133 peak value observed for @xmath169ag ( see lowest right part of fig . this approach together with the microgating procedure @xcite mentioned above , finally permitted the unambiguous identification of the @xmath0dn - decay from @xmath154g@xmath133 @xmath173ag ( see fig . the half - life of 46@xmath174 ms is in very good agreement with the recent qrpa prediction of 47 ms @xcite , but is lower than our old waiting - point requirement of about 130 ms @xcite . however , that estimate was based on the earlier half - life measurement of t@xmath97@xmath65195 ms for @xmath90cd , and on the older r - process residuals n@xmath94 of @xcite . however , for a non - equilibrium r - process , or after the breakdown of the @xmath0-flow equilibrium , also the t@xmath97 contribution from the @xmath154p@xmath97 @xmath103ag isomer would be of importance for the ` stellar ' half - life . with the qrpa model of @xcite , it is possible to calculate the gt decay for such an isomer to t@xmath97@xmath65320 ms . when including an estimate for the expected first - forbidden strength ( extrapolated from the decay of the j@xmath123=1/2@xmath165 isomer in isotonic @xmath152 in ) , a minimum value of t@xmath97@xmath65125 ms is suggested . and , indeed , a careful re - examination and comparison of the a=129 @xmath0dn - decay curve taken with the laser at central frequency with the pure @xmath103 in curve from a laser - off run , gave a first indication of a weak , longer - lived @xmath103ag @xmath0dn - component with a half - life of roughly 160 ms . now , it will be important to use isomer - specific laser ionization in combination with isobar separation at isolde - hrs to ascertain the existence of this @xmath154p@xmath97 isomer . the astrophysical half - life of @xmath103ag for non - equilibrium conditions , expected to be a mixture of the g.s and isomer values , might then lead to a better understanding of the bottle - neck behaviour and shape of the a@xmath65130 n@xmath94 peak . based on our present knowledge on level systematics in the @xmath125sn region , neutron - capture @xmath39-decay from s@xmath98@xmath655.6 mev in @xmath103ag would populate the @xmath154p@xmath97 isomer to roughly 35@xmath175 and the @xmath154g@xmath133 ground state to about 65 @xmath175 @xcite . this would result in an average stellar t@xmath97@xmath6580 ms . however , already within the waiting - point approximation requesting only the t@xmath97 of @xmath173ag , an excellent reproduction of the shape of the n@xmath94 peak from a=126 to a=133 is obtained . from this result , we conclude that the effect of neutrino - processing of the n@xmath176 during freeze - out is considerably smaller for the a@xmath65130 peak region than recently postulated by qian et al . @xcite , and that the main effect is rather due to @xmath0dn - branching during the first 100 ms of the freeze - out . in addition to the study of gross @xmath0-decay properties of neutron - rich ag isotopes , also the level systematics of the cd - daughters has been extended up to the r - process path @xcite . first , an alternate source of nuclear structure for neutron - rich isotopes is the investigation of correlated @xmath39-emission of complementary fragments of spontaneous - fission systems . recent data from such studies have revealed surprisingly low 2@xmath116 to 6@xmath116 energies in @xmath177sn ( only two neutrons beyond double - magic @xmath125sn ) , that suggest a reduction of the effects of pairing in very neutron - rich sn nuclides @xcite . for the cd isotopes , however , such fission data extend only up to @xmath168cd . our studies at isolde have now permitted even - even cd structures to be extended six neutrons further out , up to n=80 @xmath178cd . the new results are shown in fig . 11 , together with known e(2@xmath116 ) and e(4@xmath116)/e(2@xmath116 ) level systematics of neighbouring even - z elements . the e(4@xmath116)/e(2@xmath116 ) ratio for the 4n - hole nuclide @xmath172cd is 2.25 , a value almost unchanged relative to that for the 6n - hole isotope @xmath179cd . already this static ratio is in contrast to the larger reduction observed for the z=52 isotones @xmath178te and @xmath90te . for the new 2n - hole nuclide @xmath178cd , the energy of the first 2@xmath116 state at 645 kev is even * lower * than the e(2@xmath116 ) of 657 kev in @xmath172cd , and also the e(4@xmath116)/e(2@xmath116 ) ratio of 2.22 is only insignificantly smaller than those in @xmath179cd and @xmath172cd . as can be seen from the right side of fig . 11 , this trend for the z=48 isotopes clearly deviates from that of the z=50 ( sn ) , 52 ( te ) and 54 ( xe ) isotones . this situation is similar to the hg isotopes below n=126 , where the e(2@xmath116 ) in the 2n - hole nuclide @xmath180hg@xmath181 is with 436.6 kev also slightly lower than the e(2@xmath116)=439.6 kev in the 4n - hole isotope @xmath182hg@xmath183 . for the ee - cd nuclides this indicates an extension of the well - known vibrational character of the lighter isotopes up to n=82 , indicating a weakening of the spherical shell strength below @xmath125sn . for a=130 , we do have an indication for two weak @xmath39-lines at 957 kev and 1395 kev with a tentative assignment to the 4@xmath116 and 2@xmath116 levels in @xmath90cd . if confirmed , this would result in an e(4@xmath116)/e(2@xmath116 ) ratio of 1.69 . as the above results were accomplished with lis and gps - isolde , again there is promise of additional data with hrs . in particular , a study of the decay of isobaric ` clean ' @xmath90ag should permit the identification of excited states of n=82 @xmath90cd up to the 8@xmath116 level in which two aligned g@xmath133 proton holes are coupled to double - magic @xmath125sn . as the structure of @xmath184cd , which has the same two g@xmath133 aligned protons coupled to the double - magic @xmath185sn core , is known , a direct comparison is already available for such a measurment at n=82 . there also exists the possibilty of the presence of a low - spin @xmath154p@xmath97 isomer in @xmath152ag that should populate the @xmath132p@xmath156 state in the @xmath152cd - daughter . as has been mentioned previously , one possible effect of large neutron excess in nuclei is the lowering of the low - j orbitals . hence , an hrs study of @xmath152ag decay could demonstrate if the 854-kev gap between the @xmath132p@xmath156 first excited state and the @xmath132f@xmath155 g.s . in @xmath153sn@xmath159 has narrowed with the removal of two protons in the n=83 ag isotone . under development and testing at isolde is a scheme for laser ionization of sn nuclides @xcite . if past experience is any guide , again , it should be possible with gps and hrs to produce and study the decay of at least six sn isotopes beyond @xmath177sn , the heaviest sn nuclide for which some nuclear properties are known . @xmath186sn is a nucleus with 50 protons and 90 neutrons , a neutron / proton ratio of 1.8 . it would be the most neutron - rich nuclide studied beyond the sd shell ; and if there are to be strong divergences from expected nuclear properties because of the high neutron / proton ratio , the properties of this nuclide should reveal such signatures . moreover , these heavy sn nuclides lie directly in the path of the r - process , and the degree to which they capture neutrons prior to undergoing @xmath0-decay is a measure of how quickly the r - process flow can be established beyond the waiting - point nuclides at n=82 . at this point , all nucleosynthesis calculations use predicted t@xmath97 values which are presumably too long . given the recent , highly interesting results in the @xmath125sn region , one is tempted to re - inspect existing data for additional hidden or so far unrecognized signatures of shell quenching at n=82 . and indeed , first qualitative evidence for such a phenomenon came already from a comparison of the old t@xmath97 measurement of @xmath90cd@xmath91 @xcite with predictions from the original qrpa model of mller and randrup @xcite . when applying q@xmath162-values from the unquenched mass models frdm @xcite and etfsi-1 @xcite , theoretical t@xmath97 values for gt - decay of 1.12 s and 674 ms are obtained , respectively . however , with the quenched mass formulae hfb / skp @xcite and etfsi - q @xcite , shorter values of 246 ms and 364 ms , respectively , are derived which are in better agreement with experiment . another , so far unrecognized indication is given by the measured masses in the @xmath125sn region @xcite . as can be seen from fig . 12 , between the sequence of @xmath93sn and @xmath107cd isotopes there is a significant change in the trend of the experimental and theoretical mass differences ( normalized to the frdm predictions , m@xmath187-m@xmath188 ) . clearly , for the cd isotopic chain the best agreement with the measured masses is obtained with the quenched etfsi - q . all these signatures can , of course , only be taken as first evidence for a quenching of the spherical n=82 shell below @xmath125sn . certainly , much more experimental data , including nuclear masses ( and , as e.g. shown in fig . 4 of @xcite , in particular s@xmath98 values of n=81 and 83 isotones ) , single - neutron levels , as well as spectroscopic factors of transfer and pickup reactions on radioactive isotopes around @xmath125sn , are necessary to quantify the effect of shell quenching . as will be shown in the next section , a vanishing of the classical , spherical n=82 and 126 shell closures would not only be an interesting new nuclear - structure phenomenon close to the neutron drip - line , but may also have important consequences for r - process nucleosynthesis up to the th , u , pu cosmochronometers , and maybe even beyond ( see , e.g. @xcite ) .

the focus of the present review is the production of the heaviest elements in nature via the r - process . experiments at cern / isolde have played a pioneering role in exploring the characteristics of nuclear structure in terms of masses and @xmath0-decay properties . we close with a list of remaining theoretical and experimental challenges needed to overcome for a full understanding of the nature of the r - process , and the role cern / isolde can play in this process . nuclear astrophysics , r - process nucleosynthesis , isotope and isomer separation via hf splitting , laser ion source , nuclear structure , neutron - rich isotopes , ultra - metal - poor halo stars

the focus of the present review is the production of the heaviest elements in nature via the r - process . a correct understanding and modeling requires the knowledge of nuclear properties far from stability and a detailed prescription of the astrophysical environment . experiments at cern / isolde have played a pioneering role in exploring the characteristics of nuclear structure in terms of masses and @xmath0-decay properties . initial examinations paid attention to far unstable nuclei with magic neutron numbers related to r - process peaks , while present activities are centered on the evolution of shell effects with the distance from the valley of stability . we first show in site - independent applications the effect of both types of nuclear properties on r - process abundances . then , we explore the results of calculations related to two different ` realistic ' astrophysical sites , ( i ) the supernova neutrino wind and ( ii ) neutron star mergers . we close with a list of remaining theoretical and experimental challenges needed to overcome for a full understanding of the nature of the r - process , and the role cern / isolde can play in this process . nuclear astrophysics , r - process nucleosynthesis , isotope and isomer separation via hf splitting , laser ion source , nuclear structure , neutron - rich isotopes , ultra - metal - poor halo stars

math0701743

i

for a complex number @xmath0 , let us define the _ @xmath0-polylogarithm _ function @xmath3 by the following series : @xmath4 which is absolutely convergent for @xmath5 . these functions appear in algebraic geometry , number theory , mathematical physics , applied mathematics and the theory of special functions . since @xmath6 we really need to study @xmath3 for @xmath7 . for integer @xmath0 a lot is known about the @xmath0-polylogarithm . for example , @xmath8 , thus implies that for all @xmath9 , @xmath10 is a rational function with a single singularity at @xmath11 . when @xmath12 , the functions @xmath3 were studied in the nineteenth century , forgotten for many years , and rediscovered by the algebraic geometers in the late 1970s ; see for example lewin s book @xcite , bloch s paper @xcite and the survey articles @xcite . it is well known that @xmath3 is a multivalued function defined on @xmath13 with computable monodromy ; see @xcite and @xcite . for @xmath12 , the @xmath0-polylogarithms are special functions that play a key role in algebraic geometry . for @xmath12 , the special values @xmath14 are well - known examples of _ periods _ ; see @xcite . this is not an accident . zagier and deligne conjectured that special values ( at integers ) of @xmath15-functions of algebraic varieties are expressed by the @xmath0-polylogarithm for @xmath12 ; see @xcite and @xcite . a motivic interpretation of @xmath3 for @xmath12 is given in @xcite , as well as a conjecture that the @xmath0-th beilinson - deligne regulator maps are expressed by the @xmath0-polylogarithm for @xmath12 . for integer @xmath0 , _ elliptic polylogarithms _ that resemble @xmath16 were introduced by beilinson - levin in @xcite , and further studied in @xcite in relation to motivic cohomology conjectures for elliptic curves . for a recent survey on the better - known dilogarithm , see @xcite . the @xmath0-polylogarithms for noninteger @xmath0 are also classical and modern objects . they were studied in the eighteenth century by jonquire as a function of two complex variables @xmath0 and @xmath17 ; see @xcite . several approximation formulas were obtained by jonquire and half a century later by truesdell , whose motivation was asymptotic properties of _ polymer structures _ ; see @xcite . further results regarding approximation and analytic continuation were obtained by pickard in the sixties , and more recently by kenyon - wilson in relation to _ resonance _ of some _ statistical mechanical models _ ; see @xcite and also ( * ? ? ? * prop.1 ) . the @xmath0-polylogarithm functions for half - integer @xmath0 appear naturally in the context of an _ euler - maclaurin summation _ , and are also used in proving resurgence of some power series associated to knotted objects ; see @xcite and @xcite . they also play a prominent role in proving analytic continuation of some power series that encode quantum invariants of knotted objects ; see for example ( * ? ? ? * sec.7 ) . in addition , in 1994 , m. kruskal proposed to the first author to study the analytic continuation and the global bahavior of the function @xmath18 . this problem was a motivation for a global reconstruction theorem of resurgent functions from local data , developed by the first author several years ago ( and independently by calle in @xcite ) , and recently written in @xcite . the purpose of this short note is to study the * the analytic continuation * the mittag - leffler decomposition * the asymptotic behavior for large @xmath19 of the polylogarithm function @xmath3 for non - integer @xmath0 . with over a century of history on the fractional polylogarithm , some of our results resemble statements of the above mentioned literature . however , we were not able to find the key equation , nor an explicit computation of the monodromy around @xmath20 and @xmath11 in the literature . the latter does not seem to have a finite dimensional faithful representation , and its motivic or physical origin is unknown when @xmath21 . let us recall first what is a multivalued analytic function on @xmath13 . such functions are examples of _ global analytic functions _ ( see @xcite ) and examples of _ resurgent functions _ in the sense of calle , @xcite . let @xmath22 denote the universal cover of @xmath23 with base point at @xmath24 . as a set , we have : @xmath25 $ of paths $ c$ in } \,\ , \bc\setminus\{0,1\ } \,\ , \text{starting at } \,\ , \frac{1}{2 } \right\}.\ ] ] there is an action of @xmath26 on @xmath22 given by @xmath27=[\gamma.c]$ ] for @xmath28 $ ] and @xmath29 \in x$ ] . by a _ multivalued analytic _ ( in short , _ resurgent _ ) function @xmath30 on @xmath13 we mean an analytic function on @xmath22 . for @xmath29 \in x$ ] , where @xmath31 is a path from @xmath24 to @xmath17 , we write , following @xcite : @xmath32}(z):=f([c]).\ ] ] observe that @xmath33 is a free group on @xmath34 $ ] and @xmath35 $ ] , where @xmath36 are paths around @xmath1 and @xmath2 respectively : @xmath37 in what follows , @xmath0 is _ not _ an integer . let us introduce some useful notation . let @xmath38 denote a _ hankel contour _ that encircles the positive real axis : @xmath39 the next definition uses notation familiar to algebraic geometry . see for example the survey paper @xcite . for @xmath40 , let @xmath41 denote the multivalued function on @xmath13 given by : @xmath42 where @xmath43 for @xmath44 , let us define the twisted multivalued functions @xmath45(z)$ ] for @xmath46 by : @xmath47(z):=m_{\a}(z \ , e^{2 \pi i k})= c_{\a } \ , ( \log z + 2 \pi i k)^{\a-1}.\ ] ] the following theorem converts the series of @xmath3 into an integral , from which we can easily deduce the existence of analytic continuation . \(a ) for @xmath5 and @xmath0 such that @xmath48 , @xmath3 has an integral representation : @xmath49 known as _ appell s integral _ in ( * ? ? ? * sec.2 ) . ( b ) for @xmath5 and @xmath50 , @xmath3 has an integral representation : @xmath51 ( c ) for all @xmath50 , @xmath3 has an analytic continuation to a multivalued function on @xmath13 . more precisely , let @xmath46 and @xmath31 any path from @xmath24 to @xmath17 in @xmath13 . then , we have : @xmath52}(z ) & = \li_{\a}^{[c]}(z ) & \li_{\a}^{[c_1c]}(z ) & = \li_{\a}^{[c]}(z)-(1-e^{2 \pi i \a})m_{\a}^{[c]}(z ) \\ \lbl{eq.m1 } m_{\a}^{[c_0c]}(z ) & = m_{\a}^{[c]}[1](z ) & m_{\a}^{[c_1c]}(z ) & = -(1-e^{2 \pi i \a } ) m_{\a}^{[c]}(z)\end{aligned}\ ] ] ( d ) for @xmath0 such that @xmath53 , @xmath3 has a mittag - leffler type decomposition : @xmath54 where the series is uniformly convergent on compact sets . thus , we have : @xmath55 : = \lim_{n \to \infty } \sum_{k =- n}^n m_{\a}[k].\ ] ] when @xmath0 is a negative integer , the right hand side of is an _ eisenstein series _ ; see @xcite . the mittag - leffler decomposition is an analogue of _ hurwitz s theorem _ ; see @xcite . the mittag - leffler implies is the following corollary . for @xmath0 such that @xmath56 and @xmath17 such that @xmath57 and @xmath58 we have : @xmath59 compare with ( * ? ? ? * prop.1 ) . the integral formula and some stationary phase implies the following estimate for the behavior of the fractional polylogarithms for large @xmath19 . for @xmath60 and @xmath17 large we have : @xmath61 for @xmath12 , this is known ; see ( * ? ? ? * eqn.7 ) . once we convert the series definition of the @xmath0-polylogarithms into an integral formula , analytic continuation follows from a general principle , i.e. , by moving the contour of integration and achieving analytic continuation . if we move the contour of integration to @xmath62 , and the integral vanishes at @xmath62 , collecting residues gives a mittag - leffler type decomposition of @xmath3 for @xmath63 , @xmath64 . an early version of this paper was presented at talks in orsay and the university of maryland in the fall of 2006 . the authors wish to thank j. calle for encouraging conversations . m. kontsevich pointed out to the second author that some aspects of the fractional polylogarithms have been studied independently by m. kontsevich and d. zagier . after the paper was written , j. morava informed us of @xcite , where the fractional polylogarithms are also studied from the point of view of distributions over the real numbers .

the fractional polylogarithms , depending on a complex parameter @xmath0 , are defined by a series which is analytic inside the unit disk . after an elementary conversion of the series into an integral presentation , we show that the fractional polylogarithms are multivalued analytic functions in the complex plane minus @xmath1 and @xmath2 . for non - integer values of @xmath0 , we prove the analytic continuation , compute the monodromy around @xmath1 and @xmath2 , give a mittag - leffler decomposition and compute the asymptotic behavior for large values of the complex variable . the fractional polylogarithms are building blocks of resurgent functions that are used in proving that certain power series associated with knotted objects are resurgent . the motivic or physical interpretation of the monodromy of the fractional polylogarithms for non - integer values of @xmath0 is unknown to the authors .

the fractional polylogarithms , depending on a complex parameter @xmath0 , are defined by a series which is analytic inside the unit disk . after an elementary conversion of the series into an integral presentation , we show that the fractional polylogarithms are multivalued analytic functions in the complex plane minus @xmath1 and @xmath2 . for non - integer values of @xmath0 , we prove the analytic continuation , compute the monodromy around @xmath1 and @xmath2 , give a mittag - leffler decomposition and compute the asymptotic behavior for large values of the complex variable . the fractional polylogarithms are building blocks of resurgent functions that are used in proving that certain power series associated with knotted objects are resurgent . this is explained in a separate publication @xcite . the motivic or physical interpretation of the monodromy of the fractional polylogarithms for non - integer values of @xmath0 is unknown to the authors .

0910.2531

i

the general topic of our study is the statistical properties of the eigenvalues of @xmath9 non - symmetric random matrices with real entries . such matrices will , in general , have both real and complex eigenvalues . in the case that the entries of the matrix are independently chosen as standard gaussians referred to as the real ginibre ensemble after @xcite a result of edelman _ et al _ @xcite tells us that the expected number of real eigenvalues is asymptotically equal to @xmath10 . numerical evidence presented in the same paper indicates that this asymptotic value persists with the standard gaussian replaced by any distribution of zero mean and unit standard deviation . similar properties hold true of the generalised eigenvalues of a pair of @xmath0 random matrices @xmath1 with standard gaussian entries . the generalised eigenvalues @xmath11 are specified as the solutions of @xmath12 , or equivalently , as the eigenvalues of @xmath4 . the statistical properties of the @xmath11 are the specific concern of this paper . our starting point will be to first establish the joint matrix distribution of @xmath13 , which we show in proposition [ prop : elementjpdf ] to be the matrix cauchy distribution @xmath14 studies into the statistical properties of the @xmath11 were initiated in @xcite using a different logic . it was shown , for example , that the expected number @xmath15 of real ( generalised ) eigenvalues has the exact evaluation @xmath16 to derive ( [ eqn : eks_result ] ) , the generalised eigenvalue problem in the case of @xmath5 having standard gaussian elements was placed in the context of integral geometry . first the pair of matrices @xmath1 can be regarded as two vectors in @xmath17 and the corresponding plane spanned by these vectors intersects the sphere @xmath18 to give a great circle . the real generalised eigenvalues correspond to the intersection of this great circle with the set @xmath19 of all @xmath9 singular matrices @xmath20 such that @xmath21 ( thus choose @xmath22 for suitable @xmath23 ) . with @xmath5 having standard gaussian entries , the great circle has uniform measure , so the expected number of real eigenvalues is equal to the expected number of intersections of @xmath19 with a random great circle . another feature of the random generalised eigenvalue problem studied in @xcite is the density @xmath24 of real generalised eigenvalues . by writing @xmath25 the generalised eigenvalue equation reads @xmath26 . using the fact that a pair of standard gaussians @xmath27 is , as a distribution in the plane , invariant under rotation , it was noted that @xmath28 must be distributed uniformly on the unit circle , and so @xmath29 the transformation @xmath25 is the stereographic projection of the real line on to a great circle of the sphere . from the famous circle theorem @xcite relating to eigenvalue densities of large @xmath9 matrices with general iid entries drawn from any distribution with mean zero and fixed @xmath30 , one might similarly expect uniform asymptotic density on the sphere for @xmath31 where @xmath32 also have iid entries from any distribution with zero mean and fixed @xmath30 a kind of spherical law . certainly , in the case of complex gaussian entries , this is true for every value of @xmath33 . indeed , with @xmath34 where @xmath35 such that @xmath36 , one has that @xmath37 has the same distribution as @xmath38 , implying that the corresponding joint eigenvalue distribution is invariant under rotation of the sphere @xcite . in the traditions of random matrix theory for example the circular ensembles of dyson the present real gaussian matrices @xmath31 may be said to form the real spherical ensemble . in @xcite the complex gaussian matrices @xmath31 were referred to as the ( complex ) spherical ensemble . from ( [ eqn : rho ] ) and the fact that with @xmath39 , @xmath40 , we see that as a distribution on the sphere , the density of real eigenvalues is uniform . one can also stereographically project the complex eigenvalues on to the sphere ; it will turn out ( eq . ( [ df ] ) below ) that in the large @xmath33 limit the total eigenvalue distribution is uniform . thus , to leading order , the concentration of real eigenvalues on a great circle of the sphere does not affect the overall eigenvalue distribution . this is analogous to the situation for the real ginibre ensemble , for which the expected number of real eigenvalues is asymptotically @xmath41 , yet the eigenvalue density is to leading order uniform @xcite . also , we remark that there is an analogy with the random polynomials @xmath42.\end{aligned}\ ] ] when stereographically projected onto the sphere there is of order @xmath43 zeros on a great circle corresponding to the real axis @xcite , but for @xmath33 large the density is asymptotically uniform on the sphere @xcite . matrices with the eigenvalues stereographically projected . the great circle of real eigenvalues can be clearly seen . ] so in summary , from the pioneering study of the gaussian real generalised eigenvalue problem of @xcite , we know the expected number of real eigenvalues and the density of real eigenvalues . beginning with ( [ eqn : elementjpdf ] ) , this statistical knowledge will be greatly extended . an essential ingredient in our analysis is to conformally map from the real line and upper half - plane ( _ i.e. _ the domain of the independent eigenvalues of @xmath44 ) to the boundary of the unit disk by the fractional linear transformation @xmath45 for @xmath11 a real eigenvalue , and with @xmath46 , ( [ 7 ] ) reads @xmath47 a key feature is that the corresponding real eigenvalue density is uniform in @xmath48 @xmath49 as follows from ( [ eqn : rho ] ) . in terms of ( [ 7 ] ) and ( [ 14.2 ] ) we show that the explicit form of the joint eigenvalue probability density function ( jpdf ) for @xmath7 real eigenvalues is @xmath50 with @xmath51 and @xmath52^{1/2},\end{aligned}\ ] ] @xmath53 which is the content of proposition [ thm : ainvb_jpdf ] . we use ( [ eqn : q(y ) ] ) to deduce exact statistical properties . as an example , let @xmath6 denote the probability that there are exactly @xmath7 real eigenvalues , and set @xmath54 where the asterisk indicates that the sum over @xmath7 is restricted to values with the same parity as @xmath33 . in proposition [ prop : gen_fn ] , with @xmath33 even , we show @xmath55 where @xmath56 the product form ( [ 3a ] ) for @xmath57 should be contrasted with the simplest known forms in the case of the real ginibre ensemble @xcite , which are determinants of size @xmath58 . it follows from ( [ eqn : z_n ] ) that @xmath59 where we have used the fact that @xmath60 . substituting ( [ 3a ] ) then reclaims ( [ eqn : eks_result ] ) with @xmath33 even . in corollary [ prop : odd_en_var ] we give the odd analogue of ( [ 3.1 ] ) and with ( [ 3a ] ) we again reclaim ( [ eqn : eks_result ] ) . the variance in the distribution of the number of real eigenvalues is , by definition , given by @xmath61 , which , in terms of the generating function , reads @xmath62 substituting ( [ eqn : z_n ] ) and ( [ 3.1 ] ) , we then obtain the explicit evaluation @xmath63 this has large @xmath33 form @xmath64 , which is the same as for the real ginibre ensemble @xcite . recalling ( [ 3 ] ) we can read off the explicit value of @xmath6 . for @xmath65 odd it is a rational number , while for @xmath65 even it is of the form @xmath66 with @xmath67 rational ( proposition [ p310 ] ) . in particular , for @xmath68 , @xmath69 and for @xmath70 , @xmath71 as decimals ( [ 2.2 ] ) reads @xmath72 , @xmath73 . these values , further approximated to @xmath74 and @xmath75 respectively , have been reported in a simulation of the @xmath76 case @xcite . the latter study was motivated by the question of determining the typical rank of a @xmath77 array ( tensor ) ( see , e.g. , @xcite ) . the meaning of a tensor in this setting relates to structures @xmath78 represented as the column vector @xmath79 . as reviewed in @xcite , a point of interest is to find matrices @xmath80 \in \mathbb r^{p \times r}$ ] , @xmath81 \in \mathbb r^{p \times r}$ ] and @xmath82 \in \mathbb r^{2 \times r}$ ] such that @xmath83 for @xmath84 as small as possible . the positive integer @xmath84 is referred to the rank . with both @xmath85 and @xmath86 random matrices , entries chosen from a continuous distribution , one has that @xmath87 if all the eigenvalues of @xmath88 are real , and @xmath89 otherwise . the simple structure of ( [ eqn : z_n ] ) also allows for the computation of the large @xmath33 form of the distribution of the number @xmath7 of real eigenvalues . in proposition [ pab ] we prove that it is a standard gaussian in the scaled variable @xmath90 . further , our method of derivation of ( [ eqn : z_n ] ) , which involves first computing the exact functional form of the eigenvalue jpdf ( [ eqn : q(y ) ] ) , allows for the result ( [ eqn : rho ] ) to be generalised . thus , in theorem [ thm : correlns ] we give a @xmath91 pfaffian formula for the exact @xmath92-point correlation function between @xmath93 real eigenvalues and @xmath94 complex eigenvalues . the simplest case beyond ( [ eqn : rho ] ) is the density of the complex eigenvalues in terms of the coordinates ( [ 7 ] ) . with @xmath95 we find that the complex density @xmath96 depends only on @xmath97 , and is given by @xmath98 the densities ( [ eqn : rhoc ] ) and ( [ eqn : rhor ] ) are related by the sum rule for the total number of eigenvalues @xmath99 where the factor of 2 is required since @xmath100 only refers to one of each complex conjugate pair . section 4 continues with the evaluation of the average of two characteristic polynomials in terms of elements of the correlation kernel . we also compute the scaled limit of the @xmath92-point correlation function , and demonstrate that it agrees with the recently obtained @xcite scaled correlation function for the bulk eigenvalues in the real ginibre ensemble . an analogy with a coulomb gas allows for the formulation of sum rules relating to the screening of the effective charge of a fixed number of eigenvalues , and also allows us to isolate a certain combination of one- and two - point correlations for which the complex moments vanish .

the generalised eigenvalues for a pair of @xmath0 matrices @xmath1 are defined as the solutions of the equation @xmath2 , or equivalently , for @xmath3 invertible , as the eigenvalues of @xmath4 . we show that these correlations satisfy sum rules characteristic of the underlying two - component coulomb gas . * pfaffian point process for the gaussian real generalised eigenvalue problem * + + _ department of mathematics and statistics , university of melbourne , victoria 3010 , australia _

the generalised eigenvalues for a pair of @xmath0 matrices @xmath1 are defined as the solutions of the equation @xmath2 , or equivalently , for @xmath3 invertible , as the eigenvalues of @xmath4 . we consider gaussian real matrices @xmath5 , for which the generalised eigenvalues have the rotational invariance of the half - sphere , or after a fractional linear transformation , the rotational invariance of the unit disk . in these latter variables we calculate the joint eigenvalue probability density function , the probability @xmath6 of finding @xmath7 real eigenvalues , the densities of real and complex eigenvalues ( the latter being related to an average over characteristic polynomials ) , and give an explicit pfaffian formula for the higher correlation functions @xmath8 . a limit theorem for @xmath6 is proved , and the scaled form of @xmath8 is shown to be identical to the analogous limit for the correlations of the eigenvalues of real gaussian matrices . we show that these correlations satisfy sum rules characteristic of the underlying two - component coulomb gas . * pfaffian point process for the gaussian real generalised eigenvalue problem * + + _ department of mathematics and statistics , university of melbourne , victoria 3010 , australia _

quant-ph0508108

i

the potential speedup offered by quantum computers is exemplified by shor s factoring algorithm @xcite , grover s search algorithm @xcite , and algorithms for quantum simulation @xcite . although the origin of this speed - up is not fully understood , there are indications that quantum entanglement plays a crucial role in making quantum algorithms efficient @xcite . in particular , it was shown that quantum algorithms that do not create entanglement can be simulated efficiently on a classical computer @xcite . it is therefore of interest to quantify the entanglement produced by quantum algorithms and examine its correlation with their efficiency . this requires to develop entanglement measures for the quantum states of multiple qubits that appear in quantum algorithms . these include pure states as well as mixed states , which would inevitably show up when decoherence effects are taken into account . the special case of bi - partite entanglement has been studied extensively in recent years and suitable entanglement measures were introduced . it was established that bi - partite entanglement can be considered as a resource for teleportation @xcite . the entanglement of bi - partite pure states can be evaluated by the von neumann entropy of the reduced density matrix , traced over one of the parties . for bi - partite mixed states , several measures were proposed @xcite and for the special case of states of two qubits an exact formula for the entanglement of formation was obtained @xcite . for mixed states of multiple qubits , entanglement measures based on distance measures in hilbert space were proposed @xcite . consider a mixed quantum state @xmath2 of @xmath0 qubits . the state is non - entangled , or separable , if its density matrix can be written in the form @xmath3 where @xmath4 , @xmath5 is a density operator of a pure state of the @xmath6th qubits , namely @xmath7 and @xmath8 . in the special case that @xmath2 is a pure state , all probabilities vanish except for @xmath9 , and the state can be expressed by @xmath10 such states are called tensor - product states . in order to evaluate the entanglement of a quantum state , @xmath2 , one needs a scalar function @xmath11 [ or @xmath12 for pure states ] called an _ entanglement measure _ that satisfies @xcite : ( a ) @xmath13 if and only if @xmath2 is a separable state ; ( b ) assuming that each qubit is held by a different party , it is not possible to increase @xmath11 by local operations and classical communication ( locc ) between the parties . consider the special case of local unitary operators . such operators can not decrease @xmath11 because if they could then the inverse operators ( which are also unitary ) would increase it and thus contradict the second condition above . the conclusion is that local unitary operators can not change @xmath11 . the groverian entanglement measure , @xmath14 , provides an operational measure of entanglement for pure states of multiple qubits @xcite . it is related to the success probability of grover s search algotirhm when the state @xmath15 is used as the initial state . a pre - precessing stage is allowed in which an arbitrary local unitary operator is applied to each qubit . these operators are optimized in order to obtain the maximal success probability of the algorithm , @xmath16 . the groverian measure is given by @xmath17 . the groverian measure was used in order to evaluate the entanglement in certain quantum states of high symmetry as well as in states that are generated during the operation of quantum algorithms @xcite . for example , it was found that grover s iterations generate highly entangled intermediate states , even in case that the initial and the final states are product states . in this paper we generalize the groverian entanglement measure to the case of mixed states . the groverian measure , @xmath18 , of a given mixed state @xmath2 , of @xmath0 qubits , is obtained by its purification into a pure state of @xmath1 qubits . an optimization procedure based on uhlmann s theorem @xcite is then applied before the resulting pure state is fed into grover s algorithm . @xmath18 is then expressed in terms of the maximal success probability @xmath19 , as described above for pure states . in sec . [ sec : algorithm ] we briefly describe grover s search algorithm , in a context suitable to this paper . in sec . [ sec : pure ] we review the groverian entanglement measure for pure states . the generalization to mixed states is presented in sec . [ sec : mixed ] and its operational interpretation is considered . the results are summarized and discussed in sec . [ sec : summary ] .

rev . a 65 , 062312 ( 2002 ) ] is generalized to the case of mixed states , in a way that maintains its operational interpretation . the groverian measure of a mixed state of @xmath0 qubits is obtained by a purification procedure into a pure state of @xmath1 qubits , followed by an optimization process before the resulting state is fed into grover s search algorithm . the groverian measure , expressed in terms of the maximal success probability of the algorithm , provides an operational measure of entanglement of both pure and mixed quantum states of multiple qubits .

the groverian entanglement measure introduced earlier for pure quantum states [ o. biham , m.a . nielsen and t. osborne , phys . rev . a 65 , 062312 ( 2002 ) ] is generalized to the case of mixed states , in a way that maintains its operational interpretation . the groverian measure of a mixed state of @xmath0 qubits is obtained by a purification procedure into a pure state of @xmath1 qubits , followed by an optimization process before the resulting state is fed into grover s search algorithm . the groverian measure , expressed in terms of the maximal success probability of the algorithm , provides an operational measure of entanglement of both pure and mixed quantum states of multiple qubits . these results may provide further insight into the role of entanglement in making quantum algorithms powerful .

1305.0170

i

in 2012 , the lhc discovered a new particle with the mass of 126 gev @xcite . the particle is regarded as the higgs boson predicted in the standard model ( sm ) of elementary particles . the discovery of the higgs boson means that all the particle contents in the sm are completed . the lhc is now searching for indications of new physics , and is trying to measure the deviation in the coupling from the sm . on the other hand , the cosmic observations such as the experiments at wmap and planck have reported the new results @xcite . these experiments measure the temperature fluctuation of the cosmic microwave background precisely , by which we can impose constraints on the models of inflation . cosmic inflation at the early universe @xcite , which is a promising candidate to solve cosmological problems such as the horizon problem and the flatness problem , requires an additional scalar boson , the inflaton . we consider the higgs inflation scenario where the higgs boson plays a role of the inflaton . in the minimal model of this scenario @xcite , we do not have to introduce any other particle in addition to the particle contents in the sm to explain an inflation . however , it would be difficult to realize the higgs inflation scenario in the minimal model . assuming the sm with one higgs doublet , the vacuum stability argument indicates that the model can be well defined only below the energy scale where the running coupling of the higgs self - coupling becomes zero . for the higgs boson mass to be 126 gev with the top quark mass to be 173.1 gev and for the coupling for the strong force to be @xmath0 0.1184 , the critical energy scale is estimated to be around @xmath1 gev using the nnlo calculation , although the uncertainty due to the values of the top quark mass and @xmath2 is not small @xcite . the vacuum seems to be metastable when we assume that the model holds up to the planck scale . this kind of analysis gives a strong constraint on the scenario of the higgs inflation , because the inflation occurs at the energy scale where the vacuum stability is not guaranteed in the sm . recently , a viable model for the higgs inflation has been proposed , in which the higgs sector is extended including an additional scalar field @xcite . there is also another problem in the minimal model , which comes from unitarity argument @xcite . extending the higgs sector from the sm one , we may expect to reveal new physics that can explain phenomena such as neutrino oscillation , existence of dark matter and baryon asymmetry of the universe . here , we extend the higgs inflation model in the framework of a radiative seesaw scenario by e. ma @xcite . the radiative seesaw scenario is a way to explain tiny neutrino masses , where they are radiatively induced at the loop level by introducing @xmath3-odd scalar fields and @xmath3-odd right - handed neutrinos @xcite . an interesting characteristic feature in these radiative seesaw models is that dark matter candidates automatically enter into the model because of the @xmath3 parity . in this work , we discuss a simple model to explain inflation , neutrino masses and dark matter simultaneously , which is based on the simplest radiative seesaw model @xcite . both the higgs boson and neutral components of the @xmath3-odd scalar doublet can satisfy conditions on the slow - roll inflation @xcite and vacuum stability up to the inflation scale . we find that a part of the parameter region where these scalar fields can play a role of the inflaton is compatible with the current lhc results , the current data from neutrino experiments and those of the dark matter abundance as well as the direct search @xcite . a phenomenological consequence of scenario results in a specific mass spectrum of scalar fields , which can be tested at the international linear collider ( ilc ) @xcite .

the higgs inflation scenario is an approach to realize the inflation , in which the higgs boson plays a role of the inflaton without introducing a new particle . we investigate a higgs inflation scenario in the so - called radiative seesaw model proposed by e. ma . we find that a part of parameter regions where additional scalar fields can play a role of an inflaton is compatible with the current lhc results , the current data from neutrino experiments and those of the dark matter abundance as well as the direct search .

the higgs inflation scenario is an approach to realize the inflation , in which the higgs boson plays a role of the inflaton without introducing a new particle . we investigate a higgs inflation scenario in the so - called radiative seesaw model proposed by e. ma . we find that a part of parameter regions where additional scalar fields can play a role of an inflaton is compatible with the current lhc results , the current data from neutrino experiments and those of the dark matter abundance as well as the direct search . we show that we can partially test this model by measuring masses of scalar bosons at the international linear collider .

astro-ph0304331

i

experimental data on solar neutrinos ( @xmath16@xmath17)@xmath18 has accumulated rapidly in the last few years by the operation of several large detector facilities such as super - kamiokande ( sk ) , the sudbury neutrino observatory ( sno ) and kamland . the data from these detectors were precise and informative . the neutral current signals ( nc ) from @xmath3b neutrinos in sno @xcite showed that @xmath16@xmath17 flavor was not conserved because the flavor - blind nc rate explicitly exceeded the charged current ( cc ) @xmath16@xmath17 signal rate . the absolute nc rate was close to the @xmath3b @xmath16@xmath17 flux of the standard solar model ( ssm)@xcite . the ( @xmath16-electron ) scattering ( es ) signal in sk @xcite indicated the _ _ type _ _ of flavor conversion with a highly precise energy - independent es spectrum in the measured window 5 - 15 mev . this result severely restricted the possible @xmath16@xmath17 models . global analyses of solar @xmath16@xmath17 data pinpointed matter conversion ( msw effect ) in the large mixing ( mass ) ( lma - msw ) regime as the most favored model of solar neutrinos@xcite . finally , kamland observed oscillations of _ _ terrestrial _ _ _ _ anti__neutrinos@xcite . the resulting parameters were approximately consistent with lma - msw neutrinos , as expected by the invariance of cpt symmetry . the solar neutrino problem therefore appears resolved . in view of the preponderance of evidence of global consistency for the lma - msw model , why search for an alternate model ? in principle , however , no physical effect specific to lma has yet been observed to prove its _ _ uniqueness . _ _ the nc / cc result from sno@xcite , shows only that the @xmath16@xmath17 s oscillate but it does not specify the mechanism as lma - msw . the lack of a uniqueness proof becomes a central issue ( not just a point of principle ) if an _ _ explicitly testable _ _ competitive model can be invented . in this work i show that such a solar neutrino model can be constructed . the uniqueness of _ _ this _ _ model can be proved or disproved by a variety of effects at signal energies @xmath195 mev . in particular , in contrast to lma - msw , sizable shape distortions are predicted in the 35 mev window in es spectra even though the shape is still flat above 5 mev . such an effect in solar neutrino spectra is predicted for the first time . the 35 mev window is now experimentally observable for the first time in a liquid scintillation device such as the already operational kamland detector ; thus , the above prediction can be readily subjected to experimental test . the physical mechanism of the present model is long wavelength oscillations ( lwo ) in vacuum , discovered by a new approach based on `` spectral engineering '' . although the underlying parameters were previously detected in the general dragnet of global analysis programs @xcite the _ _ experimental effects _ _ of the model are new , unsuspected and distinctly different from those of generic vacuum oscillations . the @xmath15 parameters of the model , very different from lma , imply manifest violation of cpt invariance in view of the kamland results . whether this is a fatal flaw is at present unclear from the standpoint of basic theory . the suggested experimental tests of the new model , however , offer a decisive resolution of the question , thus they are doubly important . the present work has its origins in a question posed in 1994 , if it was possible to conceive a neutrino oscillation model elusive enough to _ _ escape _ _ detection in experiments at the time . the answer was yes , if solar neutrinos oscillated at only the lowest energies . in very long wavelength ( vlwo ) oscillations in vacuum with @xmath11m@xmath20ev@xmath21ev@xmath13 ) , @xmath22b neutrinos are hardly converted ; neutrinos @xmath191 mev are converted , and explain the @xmath23ga results@xcite . thus , the @xmath3b flux deficit observed in the @xmath24cl data can only be produced by an initial flux _ _ reduced astrophysically to @xmath251/3 . _ _ this scenario , called `` just - so 2''@xcite , was the first model to be ruled out @xcite by the sno nc result the initial flux is apparently the full ssm flux , thus , _ _ conversion _ _ is centrally responsible for the flux deficit . such an effect is available via lma - msw especially since it also supplies the crucial undistorted sk spectrum . thus , conversion models at two extremes produce the observed undistorted @xmath3b spectrum in principle , via : 1 ) vlwo with no @xmath3b @xmath16@xmath17 flavor conversion but a flux reduction by a factor @xmath250.36 ; and 2 ) lma - msw with @xmath16@xmath17 survival of @xmath250.36 but the full initial ssm @xmath22b flux . the question then arises whether a scenario could be engineered with a _ _ mixture _ _ of _ _ both _ _ flavor conversion _ _ and _ _ a smaller initial flux that leaves the high energy part of the @xmath3b @xmath16@xmath26 spectrum _ _ shape _ _ _ _ invariant _ _ so that all the experimental consequences ( at @xmath275 mev ) follow automatically . by definition , this does need a smaller initial @xmath3b flux than the ssm / sno value , however , in the spirit of global analyses made so far , one could tolerate in principle a lower flux up to the 2@xmath28 lower limit of the sno nc result , i.e. , @xmath27 75% of the ssm flux . the surprising initial discovery was that a shape invariant high energy @xmath22b neutrino spectrum could indeed be engineered to a high degree of precision ( within a few percent ) by a sensitive choice of the initial flux and mass - mixing parameters in a very narrow band @xmath11m@xmath13= 70 - 80 @xmath29ev@xmath13 , @xmath30 times larger than the vlow - just - so2 regime @xcite . the oscillations in the new regime are thus termed long - wavelength or lwo in this paper . the new mass - mixing band is very different from lma - msw regime . in view of the kamland result , one thus immediately faces the problem of violation of cpt invariance by neutrinos . nevertheless , work proceeded undeterred . recent theoretical ideas appear to allow that the otherwise rigid invariance of cpt may be relaxed in principle in the neutrino sector@xcite .

pursuantly , a new `` astroparticle '' model with the relatively specific parameters @xmath5ev@xmath6 ev@xmath7 ) ; sin@xmath8 0.580.56 ; @xmath9(b ) = 0.830.81@xmath10b : ssm ) coupled with modest changes in the ssm , offers a viable solution consistent with data . because kamland has set @xmath11m@xmath12ev@xmath13 , sin@xmath14 for _ _ anti__@xmath15-e scattering signals in the window 35 mev , even though the spectrum is flat above 5 mev . this window is accessible to experiment for the first time in kamland . r. s. raghavan bell laboratories , lucent technologies , murray hill nj 07974 usa infn laboratori nazionali del gran sasso , italy

the large mixing ( mass ) ( lma ) -msw model of solar neutrinos ( @xmath0 ) is now widely held to be near definitive , based on global consistency with data . no physical effect , however , compels its _ _ uniqueness__. the present search for an explicitly testable competitive model was stimulated by a surprising finding the high energy part of the standard solar model ( ssm ) @xmath1b @xmath2 spectrum can be scaled very precisely to observed flux levels _ without measurable shape distortion _ via sensitive combinations of long wavelength flavor conversion in vacuum and a @xmath3b @xmath2 flux @xmath4(b : ssm ) . pursuantly , a new `` astroparticle '' model with the relatively specific parameters @xmath5ev@xmath6 ev@xmath7 ) ; sin@xmath8 0.580.56 ; @xmath9(b ) = 0.830.81@xmath10b : ssm ) coupled with modest changes in the ssm , offers a viable solution consistent with data . because kamland has set @xmath11m@xmath12ev@xmath13 , sin@xmath14 for _ _ anti__@xmath15-e scattering signals in the window 35 mev , even though the spectrum is flat above 5 mev . this window is accessible to experiment for the first time in kamland . new experiments are proposed to observe the more dramatic charged - current spectral effects . r. s. raghavan bell laboratories , lucent technologies , murray hill nj 07974 usa infn laboratori nazionali del gran sasso , italy

astro-ph0008317

c

before we interpret the properties of ngc 1614 , we need to apply an extinction correction . the extinction to the nucleus of ngc 1614 has been estimated a number of times . some works ( e.g. , neff et al . 1990 ; shier , rieke , rieke 1996 ) have found relatively small values for the visual extinction ( @xmath51mag with a foreground screen model ) from optical and infrared colors , and infrared emission lines . puxley & brand ( 1994 ) used optical and near infrared hydrogen recombination lines , and claimed that the extinction to ngc 1614 could not be modeled with a simple foreground screen model . instead they used a composite model ( mixture of dust and gas , and a foreground screen ) and inferred a total extinction in the optical of @xmath52mag . ho , beck , & turner ( 1990 ) derived a relatively large extinction between br@xmath47 and br@xmath1 , but their result is subject to significant calibration uncertainties ( see also puxley & brand 1994 ) . lccccc 1 & @xmath53 & @xmath54 & 18.7 & 0.56 & @xmath55 + 2 & @xmath56 & @xmath57 & 19.1 & 0.32 & @xmath58 + 3 & @xmath59 & @xmath60 & 18.9 & 0.52 & @xmath61 + 4 & @xmath59 & 0.34 & 17.5 & 0.44 & @xmath62 + 5 & @xmath63 & 1.45 & 16.9 & 0.38 & @xmath64 + 6 & @xmath65 & 2.42 & 18.8 & 0.05 & @xmath66 + 7 & @xmath67 & @xmath68 & 18.6 & 0.36 & @xmath55 + 8 & @xmath69 & 2.41 & 18.2 & 0.69 & @xmath70 + 9 & @xmath71 & 2.04 & 20.0 & 1.94 & @xmath72 + 10 & @xmath73 & 1.37 & 17.9 & 0.28 & @xmath74 + 11 & @xmath75 & 2.81 & 18.9 & 0.39 & @xmath76 + 12 & @xmath27 & @xmath77 & 17.5 & 0.47 & @xmath78 + 13 & 0.07 & 1.70 & 17.0 & 0.84 & @xmath79 + 14 & 0.16 & 1.04 & 18.1 & 0.70 & @xmath80 + 15 & 0.30 & 1.44 & 19.3 & 1.18 & @xmath81 + 16 & 0.52 & @xmath27 & 18.9 & 0.52 & @xmath76 + using the fluxes of the two [ feii ] emission lines at @xmath82 m and @xmath83 m ( whose ratio is largely independent of nebular conditions ) and the hydrogen recombination lines pa@xmath49 and br@xmath47 and a foreground dust screen model , we find values of the extinction to the gas in the @xmath11-band of @xmath84mag , corresponding to @xmath85mag . a comparison of dust models ( from witt , thronson , & capuano 1992 ) with the simple foreground screen model ( c.f . , the analysis of ngc 253 by engelbracht et al . 1998 ) shows that the correction needed for all the infrared lines ( [ feii]@xmath86 m , [ feii]@xmath87 m , pa@xmath49 and br@xmath47 ) and the broad - band colors is similar . thus a foreground dust screen model ( with extinction in the @xmath11-band of @xmath88mag ) is a good approximation for the near - infrared extinction to the ionized gas . this approximation may not give the correct extinction in the optical , but we do not use any optical data for our study of the star formation properties of this galaxy . the infrared @xmath2 color map ( figure 2 and also the close - up in figure 6 ) shows that the actual distribution of the extinction is quite patchy . if we assume an intrinsic color @xmath89 for the stellar population and the rieke & lebofsky ( 1985 ) extinction law , we find values of the @xmath11-band extinction to the stars of @xmath90mag to the east of the center of ngc 1614 , whereas the @xmath11-band extinction to the west is higher , ranging between approximately 0.2 and 1.2mag . the @xmath2 color of the nucleus ( through a 0.76-diameter aperture ) is 0.41 , which would imply a @xmath11-band extinction of @xmath91mag . compared with other dusty starbursts , the levels of extinction in ngc 1614 are low . we can determine the near infrared properties of the nucleus of ngc 1614 reasonably accurately by taking an average extinction of @xmath92mag and making a first order correction by assuming a simple foreground screen of dust . this value for the extinction agrees well with foreground screen model of puxley & brand ( 1994 ) , @xmath93mag . they show that an underestimate of the ly continuum by about 20% may result compared with more sophisticated models . however , from the combination of our slightly higher assumed extinction level and other minor differences , our derived ly continuum is similar to the value they feel is most accurate . in general , if there are regions of very heavy extinction , or where the extinction is optically thick at the wavelengths of our observations , then we would have underestimated the starburst parameters . our conclusions about the galaxy would become stronger with this error corrected . the relatively modest extinction in a face - on starburst is an important advantage for studies of ngc 1614 . the foundation for much of this paper is the resulting possibility to determine the starburst properties more reliably than for most other well - studied examples . the nicmos images provide important new insights to the morphology of the starburst in ngc 1614 . figure 2 presents from the upper left corner and clockwise , the optical wfpc2 f606w image , nic2 f160w ( @xmath10-band ) , nic2 f160w - nic2 f222 m ( @xmath2 color map ) , and continuum subtracted pa@xmath1 image . the field of view of these images is @xmath94 . figure 6 presents close - ups of the central regions ( @xmath95 ) as in figure 2 . the nucleus of ngc 1614 is extremely luminous , with an @xmath10-band absolute magnitude measured through a 0.76-diameter aperture of @xmath96mag ( corrected for extinction ) . the bright infrared nucleus is surrounded by a number of fainter sources and similar sources lie along the spiral arms . these objects are probably stellar clusters . we measured @xmath10-band luminosities ( see table 4 ) ranging up to @xmath97mag for the brightest sixteen clusters ( excluding those located in the vicinity of the bright nucleus ) , similar to the cluster luminosities measured in arp 299 ( alonso - herrero et al . 2000a ) and other luminous and ultraluminous infrared galaxies ( scoville et al . neff et al . ( 1990 ) noted the presence of a knot some 10sw of the nucleus in a @xmath98-band image ( figure 2 in their paper ) , and suggested that it could be interpreted to be fragments of a second galaxy . this knot ( tentatively identified with cluster # 7 , table 4 ) is on the edge of our nic2 f160w image . it is most likely to be another stellar cluster from its observed luminosity . ground - based imaging shows the nucleus of the galaxy to be elongated at position angle 39@xmath99 ( e.g. , mazzarella & boroson 1993 ) . the wfpc2 f606w image resolves the central 2 of ngc 1614 into two prominent sources at a similar position angle ( see figure 6 ) . the brighter of these sources coincides with the infrared nucleus . the other optical source lies at the position of a secondary peak in the infrared images to the ne of the nucleus , but it is far less prominent in the infrared than in the f606w image . its @xmath10-band luminosity is about 30 times fainter than the primary nucleus ( @xmath100mag ; the error accounts for the uncertainty in the determination of the underlying background because of its proximity to the bright nucleus ) . the @xmath10-band absolute magnitude of the secondary peak is a magnitude or more brighter than the brightest of the stellar clusters , suggesting that it is the nucleus of an interacting small galaxy . the small extinction toward the secondary nucleus , as indicated by its blue color from optical to infrared , places it in front of the main nucleus and the activity around it ( see figure 6 ) . the co band in the primary nucleus is very strong as shown by both our spectroscopy ( section 2.3 ) and imaging ( figure 4 ) , much stronger than expected for an old stellar population . the most plausible explanation for this behavior is that the light from this nucleus is dominated by red supergiants that are the product of a starburst of age 10 or more million years . as shown in figure 4 , outside the starburst ring the co index assumes a value appropriate to an old stellar population , presumably that of the underlying galaxy . the pa@xmath1 line emission image reveals a nuclear ring of star formation with an approximate diameter of 650pc . the pa@xmath1 morphology is remarkably similar to the 6 cm radio map ( neff et al . 1990 ) . although the two available mid - infrared images ( keto et al . 1992 ; miles et al . 1996 ) do not agree in detail , they do show that the emission in the central part of the galaxy is confined to a 2 " diameter region . the image of miles et al . ( 1996 ) , which should have higher angular resolution and signal to noise , suggests that the emission arises from the ring seen in pa@xmath1 . comparison of small aperture ( @xmath101 5diameter ) ground - based photometry ( rieke & low 1972 ; lebofsky & rieke 1979 ; carico et al . 1988 ) with the iras fluxes ( in a 45 by 250 beam ) shows that the infrared emission of the entire galaxy is strongly concentrated into the central region . in fact , if approximate corrections are made from the ground - based to iras effective wavelengths and for the wavelength weighting introduced in iras to reduce color corrections to the fluxes , more than 80% of the total infrared flux at 12 @xmath46 m originates in the nucleus , and hence , from the miles et al . ( 1996 ) image , primarily in the circumnuclear ring . at 25@xmath46 m , making similar corrections to the measurement by lebofsky & rieke ( 1979 ) , we find about 75% of the total flux to originate in the nucleus . given the relation between far infrared and radio fluxes , we can also estimate the central concentration in the far infrared from radio data . we compare the survey results by griffith et al . ( 1995 ) in a 4.2 arcmin beam at 6 cm with the vla map of the nucleus reported by neff et al . we have corrected the flux scale in the latter reference upward by 11% , as they suggest . we find that @xmath101 60% of the 6 cm flux lies in the nuclear ring . these three estimates are consistent in stating that about 70% of the far infrared luminosity arises from the nuclear region . in the following , we can ascribe most of the far infrared luminosity to the circumnuclear ring of hii regions . the integrated far infrared luminosity indicates a star formation rate of 52 m@xmath4 yr@xmath15 from equation(3 ) of kennicutt ( 1998 ) . if 70% of this star formation occurs in the nucleus , we predict a level there of 36 m@xmath4 yr@xmath15 . the pa@xmath1 luminosity in the circumnuclear ring ( see table 2 ) indicates , after correction for reddening , a star formation rate of @xmath101 36 m@xmath4 yr@xmath15 from equation ( 2 ) of kennicutt ( 1998 ) , in perfect agreement . the hii regions in the ring of ngc 1614 are extremely luminous with an equivalent ionizing luminosity an order of magnitude greater than that of 30 doradus . a similar rich population of bright hii regions has been found in the luminous starburst in arp 299 ( see alonso - herrero et al . the hii regions in the spiral arms are weaker than those in the ring , but still exceedingly luminous . those listed in table 2 are all similar in luminosity to 30 dor ( for which log l@xmath102 @xmath103erg s@xmath15 ; kennicutt , edgar , & hodge 1989 ) . 30 dor is usually considered the prototype _ super_-hii region . such objects are very uncommon in normal galaxies ( e.g. , kennicutt et al . 1989 ; rozas , beckman , & knapen 1996 ) . the existence of so many comparable to 30 dor and even with greater ionizing luminosity appears to be associated with strong starbursts ( see alonso - herrero et al . 2000a ) . just outside the ring of hii regions , the @xmath2 extinction map shows a partial ring of high extinction . this ring is obliterated to the ne due to the overlying secondary nucleus , but otherwise it can be seen for more than 220@xmath99 . it traces the dense interstellar molecular material as discussed in the following section . the molecular hydrogen appears to extend from the ring of hii regions into the molecular cloud ( see figure 3 ) . the detection of the ( 2 - 1 ) s(3 ) line at @xmath104 m and the ( 2 - 1 ) s(1 ) line at @xmath105 m ( the latter line both in our spectrum and in that of puxley & brand 1994 ) suggests that a significant fraction of the emission is due to fluorescence in low density gas , for which the ratio of these lines to the @xmath106 m line is @xmath107 ( e.g. black & van dishoek 1987 ; sternberg & dalgarno 1989 ) . the relative h@xmath7 line strengths are very similar to those in ngc 253 ( engelbracht et al . 1998 ) , for which we derived that the excitation was probably shared between fluorescence and shocks , with nearly 2/3 of the total near infrared h@xmath7 luminosity from the former mechanism . the morphology suggests that at least some of the h@xmath7 originates at a shock penetrating into the molecular ring from the hii ring . spectra of higher signal to noise and angular resolution will be needed to sort out the excitation conditions for the h@xmath7 in more detail . figure 7 summarizes the distribution of starlight on a large scale . we have used ellipse fitting to generate surface brightness profiles from the nicmos @xmath11-band image ( figure 4 ) and from a ground - based image ( shier et al . these profiles join smoothly and trace the surface brightness to 20 radius ( @xmath108kpc ) . the galaxy is dominated by an exponential disk with a scale length of 6.3 ( @xmath109kpc ) from a radius of 5 ( @xmath110kpc ) outward . within a radius of 3(@xmath111kpc ) , there is a bright central source fitted well by an r@xmath112 law with a scale length of 1.14 or 350pc . at least in the innermost arcsec this region is dominated by the output of the newly formed stars and not by a traditional bulge of old stars . combining the results reported above , ngc 1614 appears to be a textbook example of a propagating starburst that started in the nucleus of a late type , large spiral galaxy , has grown outward to a radius of @xmath101 300 pc , and is potentially still growing into a circumnuclear nuclear ring of molecular material just outside this radius ( see also discussion in section 3.4 ) . this picture will be made more quantitative in a following section where we carry out evolutionary synthesis modeling of the starburst . our data re - emphasize the result of neff et al . ( 1990 ) that the activity in this galaxy is dominated by star formation and not by an agn there is no compact nuclear source either in the near or mid infrared , the emission lines are all narrow , and correlations observed in star forming regions such as the ratio of hydrogen recombination lines to far infrared luminosity appear to hold in ngc 1614 . an interesting additional result is that the starburst is accompanied by a number of _ super_-hii regions in the spiral arms of the galaxy . the presence of a secondary nucleus out of the plane of ngc 1614 suggests that all this activity has been triggered by an interaction with a smaller galaxy , which has by now largely been destroyed . there is further evidence for a merger from the tidal tails in the outer structure of ngc 1614 ( figure 1 ) . an aperture of diameter 2 ( 620pc at the galaxy distance ) includes the starburst and molecular ring . to understand the behavior in these regions , we need to determine the total mass and the mass of various constituents within this aperture . we first estimate the dynamical mass and then show that it is virtually all accounted for by the population of old , pre - starburst stars . the mass budget leaves very little for the starburst and molecular gas , as summarized in table 5 . this budget is strongly incompatible with the standard conversion of co to gas mass and also challenges starburst models using conventional forms of the initial mass function . lcc total dynamical mass & & 13 + @xmath6 from stellar velocity dispersion & 12 & + @xmath6 from pa@xmath1 ring rotation & 14 & + mass in old stars & & 12 + modeled starburst mass & & 5.5 + molecular gas mass & & 3 + @xmath6 from standard co conversion & 48 & + @xmath6 from extinction & @xmath113 & + @xmath6 from toomre q condition & @xmath114 & + @xmath6 for optically thin co & 2 & + shier et al . ( 1996 ) modeled the velocity dispersion measured in the 2.3@xmath46 m co band head to derive the dynamical mass for a 1000pc ( 3 ) diameter region in ngc 1614 . they considered three models for the stellar distribution : two bulge models and a disk model . the mass was only weakly dependent on which model was used for its derivation , although the mass in the disk model would be about twice that in the bulge ones if the disk were assumed to be at the inclination we find for the circumnuclear ring . however , since the @xmath11-band surface brightness profile of the inner 2-arcsec radius is well fitted with an @xmath115 law ( see figure 7 ) , here we adopt the highest value for the spherical geometry ( bulge ) models of shier et al . ( 1996 ) , 1.8 @xmath116 10@xmath117 m@xmath4 , and make an approximate correction in proportion to diameter to the 2 diameter region which is thus indicated to have a mass of 12 @xmath48 4 @xmath116 10@xmath118 m@xmath4 . an independent estimate of the mass in the central region of ngc 1614 can be obtained using the br@xmath47 spectroscopy presented in puxley & brand ( 1999 ) , and our knowledge of the morphology and size of the emitting region ( a ring ) . it is expected that the ring is associated with a lindblad resonance or other similar dynamical feature and is close to round . puxley & brand ( 1999 ) detected two peaks of line emission separated by @xmath119 km s@xmath15 . we have obtained the ring rotational velocity by modeling the line profile expected for a rotating ring , convolved with a gaussian to represent both the instrumental profile ( resolution 39 km s@xmath15 ) and the dispersion within the beam . we find models with dispersions between 38 and 64 km s@xmath15 fit equally well as the double gaussian used by puxley & brand . in all the satisfactory models , the peak rotational velocity is very close to 1.4 times the velocity that would have been deduced just from the separation of the gaussians fitted by puxley and brand . that is , the rotational velocity is 106 km s@xmath15 , uncorrected for inclination . the total rotational velocity is determined by de - projecting for an inclination of @xmath120 ( determined from the observed ellipticity and an assumption that the ring is round ) . from the @xmath10-band morphology we know that the mass is symmetrically distributed inside the hii ring , and therefore we can use the virial theorem in its simplest form to convert the rotational velocity to a mass . the conversion depends weakly on the mass distribution . given the good fit of the r@xmath112 model to the starlight in the center of the galaxy ( see section 3.2 ) , coupled with the large mass represented by these stars ( see next section ) , we have assumed a spherically symmetric mass distribution . we find that the total mass in a region with diameter 2@xmath121 620 pc is @xmath122 . the mass for a spherically symmetric distribution lies midway between the minimum possible value , for a thin disk , and the maximum , for a thin and narrow ring . the total range between these two extremes is a factor of two ( i.e. , @xmath101 @xmath123 ) . both because the situations at the extremes tend to be unstable and because of the observational evidence for a massive stellar spheroid within the ring , the systematic errors in our mass estimate should be much smaller than this range . for the following we adopt the average of the two measures of @xmath101 13 @xmath116 10@xmath118 m@xmath4 as the best estimate of the mass in the starburst region , with an upper limit of 20 @xmath116 10@xmath118 m@xmath4 . not only is this value based on two independent and consistent determinations , but also our extinction data indicate that the galaxy is optically thin at the wavelengths and in the regions critical for the mass determinations . thus , the mass should be measured reliability . to estimate the mass in old stars within the star forming region , we used the @xmath11-band fit to the surface brightness profile outside the ring of star formation ( see figure 7 ) . the exponential disk is assumed to account for the old stars present in the galaxy before the strong episode of star formation seen today . the disk fit was extrapolated to the center of the galaxy to estimate the contribution of old stars hidden by the output of the starburst . no extinction correction was applied , since the extinction to the disk is unknown and in any case is likely to be less than the already modest extinction ( at @xmath11 ) to the nucleus . we estimated 1.2mjy of @xmath11-band light is emitted by the old population within the central 2 " . using the light - to - mass ratio derived for spiral galaxy disks by thronson & greenhouse ( 1988 ) ( corresponding to @xmath124 ) , we find that the old stars account for @xmath125 . there is substantial evidence that the @xmath126 for spiral disks is very similar from galaxy to galaxy and in accordance with the values derived from thronson & greenhouse ( e.g. , bottema 1993 ; 1999 ) . in fact , the widely applied tully - fisher relation probably depends on the uniformity of @xmath126 in spiral disks ( aaronson , mould , & huchra 1979 ) . even if we assume that it is at the extreme low side of the dispersion in the tully fisher relation , the mass in the disk of ngc 1614 is unlikely to be more than 30% lower than our estimate . that is , assuming the lower limit @xmath127 , a lower limit to the disk mass in the nuclear region is 9 @xmath128 . our estimate ignores the mass of any bulge of old stars hidden within the central starburst region , and hence this lower limit is quite conservative . comparison of the mass in old stars with the dynamical mass of 13 @xmath116 10@xmath118 m@xmath4 provides a difficult constraint . this problem can not be relieved significantly by enlarging the region under consideration . for example , within a 3 diameter region , the flux from the exponential disk model is 1.9mjy , corresponding to a lower limit on the mass in old stars of 14.5 @xmath116 @xmath129 , which includes virtually all the dynamical mass within this diameter also . use of the standard procedure for estimating the mass in the interstellar medium from co measurements is strongly inconsistent with the mass budget implied by the dynamics and the old stellar population ; see table 5 . scoville et al . ( 1989 ) made observations of the nuclear region in the @xmath5co j=1 - 0 line . these results have been re - analyzed by scoville et al . ( 1991 ) and bryant & scoville ( 1999 ) ; our discussion is based primarily on the last reference . the nuclear co source is described as being unresolved with a diameter @xmath130 3 . most of the material is probably located in the ring of strong extinction revealed in our @xmath131 images , which is 2 in diameter . bryant & scoville ( 1999 ) use a `` standard '' conversion of co emission to total mass ( h@xmath7 + he ) of molecular gas of n(h@xmath7)/i@xmath132 = 2.25 @xmath116 10@xmath133 @xmath134 ( k km s@xmath15)@xmath15 , corrected by a factor of 1.36 to allow for the mass in helium . they deduce a nuclear molecular mass of 48 @xmath116 10@xmath118 m@xmath4 , nearly four times the total dynamical mass ! further details of the conversion ( but with a slightly higher standard factor ) can be found in sanders , scoville , & soifer ( 1991 ) . the use of the standard conversion factor in intense starbursts has come under question previously . maloney & black ( 1988 ) suggested that it should substantially overestimate the molecular masses because of the relatively high densities and temperatures of the molecular clouds in these regions . shier , rieke , & rieke ( 1994 ) determined the dynamical mass with near infrared spectroscopy of the 2.3@xmath46 m co bandhead in the nuclei of a number of luminous starburst galaxies and found that the masses of gas were overestimated by the standard conversion by factors of @xmath135 . solomon et al . ( 1997 ) and downes & solomon ( 1998 ) concluded the standard factor may be high by a factor of five in starbursts , based on a comparison of the dynamical mass and gas mass from far infrared measures . lisenfeld , isaak , & hills ( 2000 ) used submillimeter measurements of the emission by cold dust to argue that the co - deduced mass is typically @xmath136 times higher than would be deduced from the thermal emission . dunne et al . ( 2000 ) point out that such an increase is one of the possible explanations for apparently large values of m@xmath137/m@xmath138 in some strong merging / starburst galaxies . however , agreement has not been reached as illustrated , for example , by the use of the standard factor by bryant & scoville ( 1996 , 1999 ) . in ngc 1614 , an independent test of the large molecular mass deduced from the standard conversion can be based on the mm - wave co line profile . casoli et al . ( 1991 ) have published a profile in a 44 diameter beam that shows the full width at 20% intensity to be @xmath139 km s@xmath15 . the line profile of sanders et al . ( 1991 ) in a 55 beam has a full width at 20% intensity of 390 km s@xmath15 . scoville et al . ( 1989 ) show that about 30% of the emission in these beams would have been from the central compact source . if the mass of this region were @xmath140m@xmath4 , the line width would be @xmath141 km s@xmath15 or greater for this central 30% component , which would be very difficult to reconcile with the lack of strong , broad wings in the observed profile . we have made another estimate of the amount of molecular gas , based on our discovery of an extinction shadow due to a circumnuclear molecular ring . we use the ratio of @xmath142co emission to h@xmath7 from the study of molecular clouds by goldsmith , bergin , & lis ( 1997 ) and the relation between a@xmath143 and @xmath142co from alves , lada , & lada ( 1999 ) to relate the extinction in this ring to its mass . from our data , we estimate that the shadow of the molecular ring subtends an annulus between radii of 0.5 and 1 with a typical extinction level of a@xmath143 @xmath144mag . because the extinction is only effective in the foreground of the stellar population , we made the assumption that the source is symmetric along the line of sight and therefore doubled the mass estimates derived from the relations cited above . our value should probably be taken as a lower limit : we would underestimate the extinction if stars are mixed with the obscuring gas ( or if some stars lie in front of it , or the obscuration is clumpy ) . also , the reddening at @xmath10 and @xmath11 in the thickest parts of the ring is strong enough that optical depth effects might reduce the apparent extinction . nonetheless , our value of @xmath145 @xmath116 10@xmath118 m@xmath4 is well aligned with the dynamical mass and , in fact , a significantly higher value would create a serious problem in explaining the nuclear properties given the other constituents and their expected contributions to the mass . an upper limit to the mass of interstellar material can be obtained from the discovery that this material is predominantly distributed in a circumnuclear ring , as shown both by the pa@xmath1 morphology and the extinction shadow of a ring sector seen in the color maps . although this ring is currently the site of vigorous star formation as the starburst propagates outward , it must have originally been a semi - stable configuration . the toomre stability parameter for gas in a plane is @xmath146 where @xmath147 is the epicyclic frequency , @xmath148 is the cloud velocity dispersion and @xmath149 is the gas surface density . so that the gas remains in a disk and does not fragment into small clumps , @xmath150 . thus , we can derive an upper limit for @xmath149 : @xmath151 where @xmath152 is the circular velocity and @xmath153 . we have used a maximum value of @xmath154 for a solid body rotation curve . we assume a velocity dispersion of @xmath155 km s@xmath15 . this value was determined by extrapolating the observed cloud size / line width relation ( falgarone , puget , & prault 1992 ) to a size of 100pc and then doubling the width for good measure , to allow for possible extreme conditions in a galaxy nuclear region . taking @xmath156 using @xmath157 pc ( based on the ring width in the extinction shadow ) , we find a maximum mass of @xmath158 . if there is a high dispersion component of material , the actual gas mass could be somewhat higher . another lower limit of m@xmath159 @xmath160 2 @xmath116 10@xmath118 m@xmath4 can be computed by assuming the co emission is optically thin ( bryant & scoville 1996 , equation a4 ) . combining these arguments , the molecular mass in the nucleus is most likely @xmath101 3 @xmath116 10@xmath118 m@xmath4 , about 25% of the dynamical mass in this region . this mass is about 15 times lower than the @xmath161 in molecular mass deduced from co and the standard conversion by bryant and scoville ( 1999 ) . table 5 illustrates how tight the mass budget is . it seems unlikely that the molecular gas can be more than 1/10 the amount estimated from the standard conversion even if the dynamical mass is set to the upper limit of 20 @xmath116 10@xmath118 m@xmath4 and the mass in old stars to its lower limit of 9 @xmath116 10@xmath118 m@xmath4 . in that case , it might be necessary to incorporate a significant change in the starburst initial mass function ( see section 3.5.2 ) . our results are in agreement with those of shier et al . ( 1994 ) , who estimated that the amount of gas in the nucleus of ngc 1614 was a factor of at least nine below the value from the standard conversion . to accompany their estimate of a huge mass of molecular gas , scoville et al . ( 1989 ) inferred the extinction in the nuclear region of ngc 1614 to be @xmath162mag . they argued that much of the `` action '' in this region would be hidden from optical and even infrared observers unless there happened to be a particularly favorable line of sight . this picture of lirgs and ulirgs has gained wide credence , but the observations presented here are a serious caution . not only do we find far less molecular mass , but more significantly for the `` hidden action '' model , we _ do not _ find anything approaching the high extinction deduced from the co observations . an independent indication that the extinction is not hiding any significant action is the close correspondence between the star formation rates deduced from pa@xmath1 and far infrared luminosities , as discussed in section 3.2 . for our analysis of the star formation properties of ngc 1614 , we will use the rieke et al . ( 1993 ) evolutionary synthesis starburst models because they include a careful calibration of the co stellar absorption band strengths against observational data . we have considered gaussian bursts of 5myr duration ( fwhm ) with the peak of star formation at 5myr after the beginning time for the burst . ngc 1614 is a well known wolf - rayet ( wr ) galaxy ( vacca & conti 1992 ; schaerer , contini , & pindao 1999 ) . the presence of wr features in star forming galaxies can only be explained with short bursts of star formation with durations of the order of a few million years ( leitherer & heckman 1995 ) , as used in our fit to the observed properties of the galaxy . we used a truncated salpeter imf from 1 to @xmath163 , and @xmath164 from 0.1 to @xmath165 . ] which is virtually identical to imf8 which rieke et al . ( 1993 ) decided gave the best fit to the properties of m82 , and has since been shown to fit other starburst galaxies well ( engelbracht et al . 1996 , 1998 ) . in table 6 we summarize the properties of the central starburst of ngc 1614 that will be fitted with the evolutionary synthesis models . llll dynamical mass & @xmath3 & ir spectroscopy & this work + infrared luminosity & @xmath166 & iras & goldader et al . ( 1997 ) + ionizing photons ( log ) & 54.5 , @xmath167 & [ neii ] , pa@xmath1 & roche et al . ( 1991 ) , this work + @xmath11 absolute magnitude & @xmath168mag & & engelbracht ( 1997 ) + snr & @xmath169 & [ feii ] & this work + co index & 0.23 & ir spectroscopy & this work + the infrared luminosity will be taken as a lower limit to the bolometric luminosity of the galaxy . this assumption makes two errors in opposite direction . from the aperture measurements discussed in section 3.2 , up to about one third of the infrared luminosity of the galaxy may be produced outside the nuclear region . on the other hand , a significant amount of optical / uv energy must escape from the starburst before it is absorbed and re - emitted in the infrared , particularly given the patchy and relatively low level of extinction . the number of ionizing photons is from both the [ neii]@xmath170 m line flux of roche et al . ( 1991 ) , and the _ pa@xmath1 flux , the latter corrected for an average extinction of @xmath171mag and assuming case b recombination . our estimate of the number of ionizing photons is in good agreement with the value from puxley & brand ( 1994 ) derived from measurements that included br@xmath1 , analyzed through detailed modeling of the extinction . it is also consistent with the upper limit established from the 3@xmath148 non - detection of the radio h@xmath192 hydrogen recombination line ( phookun , anantharamaiah , & goss 1998 ) . to allow for the possibility of absorption of ionizing photons by interstellar dust , in the models we take the derived uv flux as a lower limit . the [ feii ] line ratios are similar to those detected in ngc 253 ( engelbracht et al . 1998 ) and are typical of those in supernova remnants . we estimated the supernova rate ( snr ) from the [ feii]@xmath83 m luminosity ( corrected for extinction ) from this work and a new calibration between these two quantities ( alonso - herrero et al . 2000b , in preparation ) . our best fit to the properties of ngc 1614 with a single burst of star formation is presented in figure 8 ( left panel ) . in this diagram the output of the model is normalized to the properties of ngc 1614 so the target quantity is unity . the model uses a mass in newly formed stars of @xmath172 ( @xmath173 ) . the derived age is between 5myr and 8myr after the peak of star formation , or @xmath174myr measured from the rising half power of the assumed gaussian star formation rate . this age is consistent with our failure to detect the 1.7@xmath46 m he line , which suggests ( although it is not a strong result given the signal to noise ) that there are relatively few stars hotter than 40,000k ( vanzi et al . all the observables except the co index converge at the young age . the observed co index appears to be too deep for such a young population . the strong co of this galaxy is more typical of a stellar population ten million years old or older . the discrepancy with the age of 5 @xmath6 8 myr for the other starburst indicators suggests that this galaxy has experienced a more extended period of star formation than in our single burst . the simplest example would be a double burst . in figure 8 ( right panel ) we show the best fit model obtained with two gaussian bursts ( both with fwhm = 5myr ) separated by 5myr . each burst uses 20% of the dynamical mass . as can be seen from this figure , the fit is excellent . the derived age is @xmath175yr after the peak of star formation of the first burst . a variety of other time dependencies of star formation are also likely to fit the data , but the minimum duration of the episode and the minimum mass required are both well constrained by the double burst model . this starburst model coincides closely with the morphology of the galaxy . we find that the strong co is concentrated in the nucleus ( figure 4 , upper panel ) , and the modeling associates this feature with the older part of the starburst . most of the ionizing flux is produced in the younger part of the starburst , and is physically located in the circumnuclear ring ( figure 6 ) . from the starburst modeling and the diameter of the circumnuclear ring of hii regions , we can roughly estimate that the speed at which the starburst is propagating outward is @xmath176 km s@xmath15 . rieke et al . ( 1980 ) found that evolutionary starburst models using the then - current form for the local imf ( miller & scalo 1979 ) had difficulty fitting the properties of m82 within the available dynamical mass . they suggested that the imf in the starburst might be biased toward massive stars compared with the proposed local form . since the low mass stars contribute most of the total mass in the imf , but have no observable properties in a starburst , reducing their numbers is a plausible way to reconcile the masses . this possibility has been discussed at great length since . rieke et al . ( 1993 ) reconsidered m82 , experimenting with a broad variety of forms for the imf and histories of star formation . they confirmed that the currently proposed forms for the local imf ( e.g. , scalo 1986 ) were inadequate and proposed their `` imf8 '' as a more satisfactory solution , imf8 provides @xmath177 times more stars in the @xmath178 range than does scalo ( 1986 ) but drops toward higher masses to avoid overproduction of oxygen in very massive stars ( rieke et al . 1993 ) . in the last few years , modeling of the ultraviolet spectra of starburst galaxies has led to the conclusion that their imfs have roughly the salpeter slope at high masses ( e.g. , gonzlez - delgado et al . satyapal et al . ( 1997 ) modeled m82 with less complete evolutionary models than used by rieke et al . they claimed that they could account for the @xmath11-band luminosity with a salpeter imf , avoiding the necessity to suppress formation of low mass stars compared with the local imf . a problem with their approach is that they did not demonstrate the simultaneous fitting of all the starburst constraints used by rieke et al . ( 1993 ) ; it is relatively easy to fit a subset of constraints if the rest are ignored . furthermore , because they assumed a foreground screen extinction model , the @xmath11-band luminosity they fitted is in fact a lower limit to the true luminosity , making their fits less demanding . nonetheless , their success with a modified salpeter imf confirms independently the derivation of imf8 to fit m82 by rieke et al . ( 1993 ) , as we show below . lcc imf8 & 14% & 5% + modified salpeter & 13% & 9% + original salpeter & 7% & 5% + miller & scalo 1979 & 6.5% & 3% + scalo 1986 & 3% & 1% + basu & rana 1992 & 3% & 3.5% + the critical aspect of a starburst imf constrained by luminosities and dynamical mass is the proportion of mass it places in the @xmath178 range that dominates the observable aspects of the starburst . table 7 summarizes this proportion and that of more massive stars for the various forms of the imf that have been used to fit starbursts . it shows the similarity of imf8 and the modified salpeter imf , which are equivalent in fitting the primary starburst characteristics . however , imf8 is to be preferred because its factor of two lower portion of very massive stars results in a proportionate reduction in the production of oxygen . keeping the abundance of oxygen within the observational limits is a difficult constraint in starburst models ( rieke et al . 1993 ; wang & silk 1993 ) . the other forms for the imf produce significantly fewer 10 @xmath6 30 m@xmath4 stars . to first order , the dynamical masses required with them are just in the ratio of the proportions of these stars . thus , if m82 can be fitted with 2.5 @xmath116 @xmath129 in a modified salpeter imf , it would require about @xmath179m@xmath4 with a miller - scalo imf , about 70% of the dynamical mass available and unlikely to be an acceptable fit once allowance is made for the mass of other constituents of the nuclear region . for ngc 1614 , the miller - scalo imf would take all the dynamical mass and the scalo ( 1986 ) and basu & rana ( 1992 ) ones would require about twice the dynamical mass , all of which is clearly unacceptable . virtually all studies find the local imf to fall more steeply toward high masses than the salpeter form . even salpeter ( 1955 ) continued the simple power law to high masses only for simplicity , but at the same time called attention to an apparent high mass steepening : `` it is not yet clear whether the steeper drop for masses larger than 10 m@xmath4 is a real effect , since in this region masses and bolometric corrections are not known very accurately and the number of such stars near the galactic plane is small . '' as with the rest of his work this statement has proven prescient . however , a salpeter imf has been shown to be an approximate fit in many situations outside the local neighborhood ( e.g. , scalo 1998 ) . it now appears that a better description of the m82 issue might be that the local imf ( or at least our estimates of it ) may differ from the imf we find in most regions of active star formation , including in starbursts like m82 . we have emphasized that ngc 1614 is particularly well suited to studying starburst properties , given the relatively modest near infrared extinction and our favorable viewing of it at modest inclination . it has a well determined dynamical mass of 13 @xmath116 10@xmath118 m@xmath4 in the starburst region , as discussed in section 3.2 . however , the constituents in this region appear to sum to a significantly greater mass , @xmath160 9 @xmath116 10@xmath118 m@xmath4 for the old stars plus @xmath101 3 @xmath116 10@xmath118 m@xmath4 for the molecular gas plus 5.5 @xmath116 10@xmath118 m@xmath4 for the starburst using either a salpeter imf or imf8 . the total exceeds the dynamical mass by at least 35% . unless there is substantial contamination of the disk outside the starburst by younger stars , these numbers suggest that the mass in the starburst may be overestimated . a further indication in the same direction is that the starburst plus remaining molecular gas in our nominal estimates account for 65% of the dynamical mass . theoretical modeling suggests that instabilities will set in and a starburst will appear once the mass of gas reaches @xmath101 20% of the total in a galaxy nucleus ( wada & habe 1992 ; bekki 1995 ) . these estimates are somewhat uncertain and may not apply strictly to the conditions in ngc 1614 . however , they fall so far below the deduced mass of new stars and residual gas to suggest that the imf in the ngc 1614 starburst is weighted toward massive stars , even compared with imf8 or a modified salpeter function . this behavior should be tested in studies of other extreme starbursts . the mechanism needed to account for the strong star formation in luminous mergers is a matter of debate . the two main competing models are : ( 1 ) cloud - cloud collisions which predict a large population of high mass stars to give rise to the high infrared luminosities ( scoville , sanders , & clemens 1986 ) ( 2 ) gravitational instability in nuclear gas disks , as favored by taniguchi & ohyama ( 1998 ) . the former model would predict a schmidt law , schmidt ( 1959 ) ] with index @xmath180 , whereas the latter model predicts indices @xmath181 as found for isolated galaxies and strong starbursts ( kennicutt 1998 ; taniguchi & ohyama 1998 ) . from the pa@xmath1 luminosity of ngc 1614 ( corrected for extinction ) and using the relation between sfr and h@xmath1 luminosity ( kennicutt 1998 ) we measured a @xmath182 in the ring and a sfr surface density of @xmath183 , similar to , although slightly higher than , the earlier estimate by kennicutt ( 1998 ) from the fir luminosity and somewhat different parameters for the size of the emitting region ( @xmath184 ) . the value of @xmath185 that we found for ngc 1614 is of the same magnitude as that of the giant hii region 30 doradus ( kennicutt 1998 ) , and the global star formation efficiency for this galaxy approaches 100% over a gas consumption period of @xmath186 . based on the standard conversion , kennicutt ( 1998 ) derived @xmath187 . if the mass in molecular gas is only @xmath101 3 @xmath116 10@xmath118 m@xmath4 , with a conversion of co to h@xmath7 mass a factor of @xmath101 15 lower than the standard value , one would derive @xmath188 or more , as discussed by kennicutt ( 1998 ) ( with less gas , higher efficiency is needed ) . thus , our results appear to favor the cloud collision explanation for the high rate of star formation . mihos & hernquist ( 1994 ) explored via numerical simulations the merger of a large and a smaller galaxy , similar to our proposal for ngc 1614 . from their simulation they predicted that in response to the tidal perturbation of the infalling satellite , the disk galaxy develops strong spiral arms . this non - axisymmetric perturbation causes large quantities of material to be funneled into the central regions , and as a result a strong burst of star formation is triggered lasting for up to 60myr . the predicted central starburst is very compact ( @xmath189pc in radius ) and contains some 85% of the total mass in newly formed stars . hernquist & mihos ( 1995 ) carried out further simulations . they showed that the degree of central concentration of gas decreases markedly with the presence of a massive bulge . the relatively low dynamical mass in the central 620 pc of ngc 1614 indicates that it had little bulge prior to the collision , so it would be ideal for a strong central concentration of gas . hernquist & mihos ( 1995 ) state that the resolution of their calculations is inadequate to determine how the gas behaves once it has sunk into the central few hundred pc . however , from the behavior of ngc 1614 , it appears that it must be further concentrated until instability is reached in the bottom of the potential well of the galaxy , leading to the initial stages of massive star formation . as the starburst ages , supernovae begin to explode and winds develop that expand outward , compressing the remaining molecular gas surrounding the nucleus ( e.g. , tenorio - tagle & muoz - tun 1997 ; taniguchi , trentham , & shioya 1998 ) . gravitationally unstable shocked layers of interstellar gas may be produced in cloud cloud collisions and by the impact of these winds on incoming clouds . the resulting star formation appears to favor massive stars ( whitworth et al . 1994 ) , possibly accounting for the suggestion of a high abundance of such stars in extreme starbursts . the evidence we find that the starburst in ngc 1614 has expanded from the nucleus to the ring of hii regions and into the surrounding molecular ring is in agreement with this picture .

deep co stellar absorption , tracing a starburst nucleus about 45pc in diameter ; 2 . ) surrounded by a @xmath0pc diameter ring of supergiant hii regions revealed in pa@xmath1 line emission ; 3 . ) lying within a molecular ring indicated by its extinction shadow in @xmath2 ; 4 . ) all at the center of a disturbed spiral galaxy . the star forming activity may have been initiated by a merger between a disk galaxy and a companion satellite , whose nucleus appears in projection about 300pc to the ne of the nucleus of the primary galaxy . the relation of deep stellar co bands to surrounding ionized gas ring to molecular gas indicates that the luminous starburst started in the nucleus and is propagating outward into the surrounding molecular ring . this hypothesis is supported by evolutionary starburst modeling that shows that the properties of ngc 1614 can be fitted with two short - lived bursts of star formation separated by 5myr ( and by inference by a variety of models with a similar duration of star formation ) . the total dynamical mass of the starburst region of @xmath3 is mostly accounted for by the old pre - starburst stellar population . although our starburst models use a modified salpeter initial mass function ( turning over near 1 m@xmath4 ) , the tight mass budget suggests that the imf may contain relatively more 10 - 30 m@xmath4 stars and fewer low mass stars than the salpeter function . the dynamical mass is nearly 4 times smaller than the mass of molecular gas estimated from the standard ratio of @xmath5co ( 1 @xmath6 0 ) to h@xmath7 .

the modest extinction and reasonably face - on viewing geometry make the luminous infrared galaxy ngc 1614 an ideal laboratory for study of a powerful starburst . _ hst_/nicmos observations show : 1 . ) deep co stellar absorption , tracing a starburst nucleus about 45pc in diameter ; 2 . ) surrounded by a @xmath0pc diameter ring of supergiant hii regions revealed in pa@xmath1 line emission ; 3 . ) lying within a molecular ring indicated by its extinction shadow in @xmath2 ; 4 . ) all at the center of a disturbed spiral galaxy . the luminosities of the giant hii regions in the ring are extremely high , an order of magnitude brighter than 30 doradus ; very luminous hii regions , comparable with 30 dor , are also found in the spiral arms of the galaxy . luminous stellar clusters surround the nucleus and lie in the spiral arms , similar to clusters observed in other infrared luminous and ultraluminous galaxies . the star forming activity may have been initiated by a merger between a disk galaxy and a companion satellite , whose nucleus appears in projection about 300pc to the ne of the nucleus of the primary galaxy . the relation of deep stellar co bands to surrounding ionized gas ring to molecular gas indicates that the luminous starburst started in the nucleus and is propagating outward into the surrounding molecular ring . this hypothesis is supported by evolutionary starburst modeling that shows that the properties of ngc 1614 can be fitted with two short - lived bursts of star formation separated by 5myr ( and by inference by a variety of models with a similar duration of star formation ) . the total dynamical mass of the starburst region of @xmath3 is mostly accounted for by the old pre - starburst stellar population . although our starburst models use a modified salpeter initial mass function ( turning over near 1 m@xmath4 ) , the tight mass budget suggests that the imf may contain relatively more 10 - 30 m@xmath4 stars and fewer low mass stars than the salpeter function . the dynamical mass is nearly 4 times smaller than the mass of molecular gas estimated from the standard ratio of @xmath5co ( 1 @xmath6 0 ) to h@xmath7 . a number of arguments place the mass of gas in the starburst region at @xmath8% of the dynamical mass , nominally about 1/15 and with an upper limit of 1/10 of the amount estimated from @xmath5co and the standard ratio .

astro-ph0008317

i

we have used _ hst_/nicmos and wfpc2 imaging , ground - based near infrared spectra , and information from the literature to study the luminous infrared galaxy ngc 1614 . the modest extinction to its starbursting nucleus , combined with our favorable viewing angle , make this galaxy ideal for probing the properties of its powerful starburst . we show that star formation has propagated outward from the nucleus to a @xmath139pc radius circumnuclear ring of massive hii regions . these circumnuclear hii regions are an order of magnitude more luminous than 30 doradus , and hii regions in the spiral arms are similar in luminosity to 30 dor . these regions are probably younger versions of the luminous stellar clusters also around the nucleus and in the spiral arms . the presence of so many extremely luminous hii regions and stellar clusters is similar to the behavior of other luminous starbursts . the ring of hii regions is surrounded by molecular gas . the mass in molecular gas appears to be @xmath190 the prediction from the standard @xmath5co / h@xmath7 ratio , with an upper limit of 1/10 the standard ratio . the large levels of extinction predicted previously from the standard ratio are absent in ngc 1614 . the mass budget for the starburst is very tight , suggesting that the proportion of massive stars is larger than predicted by a salpeter imf modified to turn over near 1 m@xmath4 , or by the virtually identical imf8 found to fit the starburst in m82 ( rieke et al . 1993 ) . until now , such imfs have been adequate to fit the properties of all known starbursts . the high efficiency needed to convert the available molecular gas density into the observed density of star formation suggests that the starburst is propagating by cloud - cloud interactions and winds . the behavior of ngc 1614 is consistent with simulations for the interaction of a modest sized galaxy with a massive , late type spiral .

the modest extinction and reasonably face - on viewing geometry make the luminous infrared galaxy ngc 1614 an ideal laboratory for study of a powerful starburst . _ the luminosities of the giant hii regions in the ring are extremely high , an order of magnitude brighter than 30 doradus ; very luminous hii regions , comparable with 30 dor , are also found in the spiral arms of the galaxy . luminous stellar clusters surround the nucleus and lie in the spiral arms , similar to clusters observed in other infrared luminous and ultraluminous galaxies . a number of arguments place the mass of gas in the starburst region at @xmath8% of the dynamical mass , nominally about 1/15 and with an upper limit of 1/10 of the amount estimated from @xmath5co and the standard ratio .

the modest extinction and reasonably face - on viewing geometry make the luminous infrared galaxy ngc 1614 an ideal laboratory for study of a powerful starburst . _ hst_/nicmos observations show : 1 . ) deep co stellar absorption , tracing a starburst nucleus about 45pc in diameter ; 2 . ) surrounded by a @xmath0pc diameter ring of supergiant hii regions revealed in pa@xmath1 line emission ; 3 . ) lying within a molecular ring indicated by its extinction shadow in @xmath2 ; 4 . ) all at the center of a disturbed spiral galaxy . the luminosities of the giant hii regions in the ring are extremely high , an order of magnitude brighter than 30 doradus ; very luminous hii regions , comparable with 30 dor , are also found in the spiral arms of the galaxy . luminous stellar clusters surround the nucleus and lie in the spiral arms , similar to clusters observed in other infrared luminous and ultraluminous galaxies . the star forming activity may have been initiated by a merger between a disk galaxy and a companion satellite , whose nucleus appears in projection about 300pc to the ne of the nucleus of the primary galaxy . the relation of deep stellar co bands to surrounding ionized gas ring to molecular gas indicates that the luminous starburst started in the nucleus and is propagating outward into the surrounding molecular ring . this hypothesis is supported by evolutionary starburst modeling that shows that the properties of ngc 1614 can be fitted with two short - lived bursts of star formation separated by 5myr ( and by inference by a variety of models with a similar duration of star formation ) . the total dynamical mass of the starburst region of @xmath3 is mostly accounted for by the old pre - starburst stellar population . although our starburst models use a modified salpeter initial mass function ( turning over near 1 m@xmath4 ) , the tight mass budget suggests that the imf may contain relatively more 10 - 30 m@xmath4 stars and fewer low mass stars than the salpeter function . the dynamical mass is nearly 4 times smaller than the mass of molecular gas estimated from the standard ratio of @xmath5co ( 1 @xmath6 0 ) to h@xmath7 . a number of arguments place the mass of gas in the starburst region at @xmath8% of the dynamical mass , nominally about 1/15 and with an upper limit of 1/10 of the amount estimated from @xmath5co and the standard ratio .

math0511713

i

let @xmath0 be an algebraically closed field provided with a non trivial rank one valuation @xmath1 , where @xmath2 is onto @xmath3 . we have naturally the following map in the algebraic torus : @xmath4 this map is the _ tropicalization _ or _ projection map_. _ tropical varieties _ are then defined as the image of an algebraic variety @xmath5 under the tropicalization map @xmath6 . tropical varieties are polyhedral complexes which are the basic objects of study of tropical geometry . one of the most interesting aspects of tropical varieties is that they inherit relevant geometric properties from their algebraic counterparts . in the present work we try to measure the differences in the behavior of the tropical varieties with respect to the algebraic ones . in particular , we check if incidence theorems of classical projective geometry hold in the tropical context . the origin of this work is the pappus theorem counterexample showed in @xcite . in that paper , it is showed a tropical configuration of points and lines in the shape of pappus theorem hypothesis such that it does not verify pappus thesis . in particular , it implies that this configuration is not the projection of a similar configuration of points and lines in the algebraic plane . the authors provide then another alternative version of the same theorem and claimed that this new version would hold in the tropical context . the key of this new version of pappus theorem is that the hypothesis is given as the result of a geometric construction dealing with points and lines . the correctness of this theorem was showed in @xcite using some precursor techniques on geometric constructions . many incidence theorems can be given as a construction of a configuration of curves and points ( _ hypothesis _ ) and then some information is derived ( the _ thesis _ of the theorem ) . so we will focus on geometric constructions in the plane and how they behave with respect to tropicalization . intuitively , a geometric construction is a procedure that starts with a set of input curves and points and then define other curves and points by either intersecting two available curves or computing a curve defined by a polynomial of fixed support passing through a set of points ( a conic through five points , for example ) . the main algorithm we present consists in : taking a tropical instance of a geometric construction , computing a constructible set @xmath7 over the residual field of the valuation that encodes sufficient conditions for the compatibility of an algebraic geometric construction . we will also show some certificates during the computation to detect if a tropical realization of a geometric constructions is not the projection of any algebraic realization . then , we present the notion of _ admissible geometric construction_. this is a combinatorial notion defined on an associated graph of a geometric construction that ensure that for all tropical realization , the computed set @xmath7 is non empty and dense . that is , we will always be able to compute an algebraic preimage under the tropicalization @xmath6 . this notion can be applied to prove that some incidence theorems hold in the tropical context if we are able to describe their hypothesis as the output of an admissible geometric construction . we provide a notion of _ constructible incidence theorem _ that is compatible with tropicalization . in particular , we will show some theorems of this kind . the notation and basic results are the following : @xmath8 denotes the residual field of @xmath0 by the valuation . after possibly rescaling the valuation , we suppose that @xmath9 . we will also suppose that we have fixed a multiplicative subgroup @xmath10 such that @xmath11 is an isomorphism . @xmath12 denotes the unique element of @xmath13 such that @xmath14 . by the isomorphism , we have that @xmath15 , @xmath16 , @xmath17 . @xmath18 denotes the projection from the valuation ring of @xmath0 onto @xmath8 . let @xmath19 , @xmath20 , then @xmath21 is an element of valuation @xmath22 , so it has a non zero image in the residual field @xmath8 . we write @xmath23 the _ principal coefficient _ of @xmath24 to this residual image . note that the principal coefficient depends on the group @xmath13 chosen . the _ principal term _ of @xmath24 is denoted by @xmath25 . this principal term is only a notation , it is not an element of @xmath0 nor @xmath8 and it can not be , for example , if the valuation is a @xmath26-adic one . it happens that @xmath27 if and only if @xmath28 . usually we will write @xmath29 in order to emphasize the principal term of an element @xmath24 . the valuation group @xmath3 is given a structure of idempotent semifield with the tropical operations @xmath30 , @xmath31 . a tropical polynomial is just a formal sum of monomials @xmath32 where @xmath33 , @xmath34 , @xmath35 . the tropical hypersurface defined by a polynomial is defined as : let @xmath36 $ ] be a tropical polynomial . then the hypersurface defined by @xmath37 is the set of points @xmath38 such that the value @xmath39 is attained for at least two different indices @xmath40 . @xmath41 hypersurfaces defined like this coincide with the projection of algebraic hypersurfaces by @xmath6 @xcite . if @xmath42 $ ] and @xmath43"$ ] , then @xmath44 . this result can be refined by using residual polynomials . let @xmath45 $ ] be a polynomial in @xmath46 variables @xmath47 ; @xmath48 , @xmath49 , @xmath50 , @xmath51 . let @xmath52 be a tropical point . let @xmath53 be the _ residual polynomial over @xmath54_. this is a non zero polynomial in @xmath55 $ ] . given a tropical object @xmath24 ( a point , a curve , a configuration , ) , a _ lift _ or _ preimage _ of @xmath24 is an algebraic element @xmath56 over @xmath0 such that @xmath57 . in particular , the notion of residual polynomial allows us to compute the lift of a point @xmath24 belonging to a tropical hypersurface @xmath58 to an algebraic point @xmath56 belonging to a lift @xmath59 of @xmath58 . for a constructive proof of this theorem we refer to @xcite or @xcite . [ initialserie ] let @xmath60 $ ] and @xmath61 be any point , then there is a root @xmath62 of @xmath63 such that @xmath64 , @xmath65 , if and only if @xmath66 is a zero of the tropical polynomial @xmath37 and @xmath67 is a root of @xmath68 in @xmath69 . given a tropical point @xmath70 , it can be written in projective coordinates @xmath71 . two tuples @xmath72 $ ] , @xmath73\in \mathbb{t}^{n+1}$ ] are identified if and only if there is a @xmath74 such that @xmath75 , @xmath76 . given a tropical polynomial @xmath77 , it defines a regular subdivision on its newton polygon that is combinatorially dual to the hypersurface @xmath78 . let @xmath79 be the convex hull of the set @xmath80 . the upper convex hull of @xmath79 , that is , the set of boundary maximal cells whose outgoing normal vector has its last coordinate positive , projects onto @xmath81 by deleting the last coordinate . this projection defines the regular subdivision on @xmath81 . it is called the _ subdivision of @xmath81 associated to @xmath37 _ ( see @xcite for the details ) . [ newton - dual ] the subdivision of @xmath81 associated to @xmath37 is dual to the set of zeros of @xmath37 . there is a bijection between the cells of @xmath82 and the cells of @xmath78 such that : * every @xmath8-dimensional cell @xmath83 of @xmath81 corresponds to a cell @xmath84 of @xmath78 of dimension @xmath85 such that the affine linear space generated by @xmath84 is orthogonal to @xmath83 . ( in the case where @xmath86 , the corresponding dual cell is a connected component of @xmath87 ) * if @xmath88 , then @xmath89 * if @xmath90 , then @xmath91 * @xmath92 where the union is disjoint . * @xmath84 is not bounded if and only if @xmath93 . in our results , we have to specify families of curves ( lines , conics ) . a first approach could be fixing the newton polygon of the curves . this has a good geometric meaning . however , without further effort in the proofs , we can fix the support of the curves . this has no geometric advantages but is a refinement from an algebraic point of view . [ def_support ] a _ support _ is a finite subset of @xmath94 modulo a translation by an integer vector in @xmath94 . that is , let @xmath95 be the set of finite subsets of @xmath96 and let @xmath97 be the relation @xmath98 if and only if there is an integer vector @xmath99 such that @xmath100 . then , the set of supports @xmath101 of @xmath96 is the set of equivalence classes @xmath102 . given a support @xmath103 , @xmath104 denotes the number of elements of @xmath105 . @xmath106 , the convex hull of @xmath105 in @xmath107 , is the _ newton polytope _ of @xmath105 . note that @xmath108 is invariant by translations , so it is well defined and @xmath81 is well defined up to integer translations . if @xmath58 is a hypersurface defined by a polynomial @xmath109 , the support of @xmath58 is the set of tuples @xmath110 such that @xmath111 effectively appear in @xmath37 modulo integer translations . it is known that in the tropical context , polynomials of different support may define the same hypersurface . so , we will always fix a priori the support of a defining polynomial . sometimes this is not even enough . contrary to the algebraic torus , there may be polynomials @xmath37 , @xmath112 defining the same tropical curve @xmath113 but such that one is not a multiple of the other . that is , there is no monomial @xmath114 such that @xmath115 . however , for some proofs , it is convenient to have a tropical polynomial of fixed support defining a curve that is _ canonical _ in a sense . we use the notion of concave polynomial from @xcite . [ canonic_polynomial ] to a given tropical polynomial @xmath116 , we may associate the function @xmath117 , given by @xmath118 . we say that @xmath119 is concave if for any ( possibly non distinct ) @xmath120 and any @xmath121 with @xmath122 and @xmath123 we have that @xmath124 . if this is the case , we say that @xmath37 is a _ concave polynomial_. fixed the support @xmath105 and a tropical hypersurface @xmath125 defined by a polynomial @xmath112 of support @xmath105 , there is ( up to a multiplication by a laurent monomial ) a unique concave tropical polynomial @xmath37 of support @xmath105 such that @xmath126 . finally , we need a notion that is essential in the geometric construction definition , the notion of stability . given two tropical curves @xmath127 , @xmath128 defined by polynomials @xmath129 , @xmath130 , it may happen that the intersection of the curves is infinite even when they share no common component . however , there is always a finite set of points , called the _ stable intersection _ of @xmath127 and @xmath128 such that it varies continuously as we deform the coefficients of @xmath129 , @xmath130 . this intersection set verifies bernstein - kushnirenko theorem , @xcite . namely , let @xmath131 be two tropical curves defined by polynomials @xmath129 , @xmath130 . let @xmath132 , @xmath133 be the newton polygons of the respective polynomials . denote by @xmath134 the mixed volume of @xmath132 and @xmath133 , then the number of stable intersection points of @xmath135 , counted with multiplicities equals @xmath134 . analogously , given a support @xmath105 and a set @xmath136 of @xmath137 tropical points , it may happen that there are infinitely many curves of support @xmath105 passing through @xmath136 . however , there is always a unique well defined curve of support @xmath105 that passes through @xmath136 and such that it varies continuously as the configuration @xmath136 is perturbed . this curve can be computed using tropical linear algebra , see [ stable_curve_subsection ] and it is called the _ stable curve of support @xmath105 passing through @xmath136_. the paper is structured as follows : in section [ section_construcciones ] we present the notion of geometric construction and show how to deal with the steps of a construction . we provide also a notion of _ points in general position _ inside a tropical curve that will be useful to generalize some results . in section [ section_lift ] we provide the main algorithm of the paper that computes a set of residual sufficient conditions to ensure a correspondence between algebraic and tropical instances of a geometric construction . then , it is shown the limits of the geometric constructions method by a series of examples , we provide some slight generalizations of the notion of admissibility and we provide some certificates for the incompatibility with tropicalization . as well as an example of a construction such that our method can not derive neither the compatibility nor the incompatibility because the residual information is not enough in this case . finally , in section [ section_theorem ] we use the results obtained so far to provide a notion of incidence theorem that is compatible with tropicalization and to show some instances of theorems of this kind .

the notion of geometric construction is introduced . this notion allows to compare incidence configurations in the algebraic and tropical plane . we provide an algorithm such that , given a tropical instance of a geometric construction , it computes sufficient conditions to have an algebraic counterpart related by tropicalization . we also provide sufficient conditions in a geometric construction to ensure that the algebraic counterpart always exists . geometric constructions are applied to transfer classical theorems to the tropical framework , we provide a notion of incidence theorems and prove several tropical versions of classical theorems like converse pascal , fano plane or cayley - bacharach . _

the notion of geometric construction is introduced . this notion allows to compare incidence configurations in the algebraic and tropical plane . we provide an algorithm such that , given a tropical instance of a geometric construction , it computes sufficient conditions to have an algebraic counterpart related by tropicalization . we also provide sufficient conditions in a geometric construction to ensure that the algebraic counterpart always exists . geometric constructions are applied to transfer classical theorems to the tropical framework , we provide a notion of incidence theorems and prove several tropical versions of classical theorems like converse pascal , fano plane or cayley - bacharach . _ keywords : _ tropical geometry , geometric constructions , incidence configurations , classical incidence theorems .

astro-ph0307284

i

continuing disagreement as to whether massive compact halo objects ( machos ) have been detected by microlensing experiments looking towards the magellanic clouds highlights the need for other microlensing targets ( e.g. , kerins 2001 ) . the andromeda galaxy ( m31 ) presents an opportune target in this respect . the disk of m31 is highly inclined ( @xmath2 ) , with the consequence that lines of sight to disk stars in the north - west or near side of m31 are shorter than those to the south - east or far side . microlensing by a spheroidal dark halo will have a characteristic signature with an excess of events on the far side of the m31 disk ( crotts 1992 ; baillon et al.1993 ) . this asymmetric signal is absent for variable stars or stellar microlenses in the disk of m31 . a number of groups ( e.g. , aurire et al . 2001 ; riffeser et al . 2001 ; calchi - novati et al . 2002 ; crotts et al . 2001 ) are now carrying out large - scale surveys of m31 to search for this near - far disk asymmetry . this is a mammoth task as the individual stars in m31 are not resolved , so that new techniques based on the super - pixel method ( ansari et al . 1997 ) or difference imaging ( e.g. , crotts & tomaney 1996 ) have been exploited to measure the flux changes on unresolved stars . nonetheless , convincing candidate events are now being discovered , for example by the point - agape collaboration ( e.g. , aurire et al . 2001 ; paulin - henriksson et al . 2002 , 2003 ) . therefore , this is a timely moment to consider what factors affect the near - far disk asymmetry and how many events are likely to be needed for a convincing detection . the aim of this paper is to estimate the size of candidate event samples needed to detect asymmetry for different halo models . in sections 2 and 3 of the paper we show how the magnitude of the asymmetry signal is affected by the velocity anisotropy and the flattening of the m31 baryonic dark halo respectively . there are few ways known to us for measuring the properties of the orbits of dark objects in the halo of any galaxy or for ascertaining the flattening of the baryonic dark component of the halo . hence , any clues gleaned from pixel lensing experiments will be invaluable . in section 4 , we present some simple , non - parametric statistical estimators of asymmetry and calculate how many candidates are needed to give convincing detections .

there is also a distance asymmetry , in that the events on the far - side are typically further from the major axis . we show that , if this positional information is exploited in addition to number counts , then the number of candidate events required to confirm asymmetry for a range of flattened and anisotropic halo models is achievable , even with significant contamination by variable stars and foreground microlensing events . for pixel - lensing surveys which probe a representative portion of the m31 disk ,

the point - agape collaboration is currently searching for massive compact halo objects ( machos ) towards the andromeda galaxy ( m31 ) . the survey aims to exploit the high inclination of the m31 disk , which causes an asymmetry in the spatial distribution of m31 machos . here , we investigate the effects of halo velocity anisotropy and flattening on the asymmetry signal using simple halo models . for a spherically symmetric and isotropic halo , we find that the underlying pixel - lensing rate in far - disk m31 machos is more than 5 times the rate of near - disk events . we find that the asymmetry is increased further by about 30% if the machos occupy radial orbits rather than tangential orbits , but is substantially reduced if the machos lie in a flattened halo . however , even for haloes with a minor - to - major axis ratio @xmath0 , the numbers of m31 machos in the far - side outnumber those in the near - side by a factor of @xmath12 . there is also a distance asymmetry , in that the events on the far - side are typically further from the major axis . we show that , if this positional information is exploited in addition to number counts , then the number of candidate events required to confirm asymmetry for a range of flattened and anisotropic halo models is achievable , even with significant contamination by variable stars and foreground microlensing events . for pixel - lensing surveys which probe a representative portion of the m31 disk , a sample of around 50 candidates is likely to be sufficient to detect asymmetry within spherical haloes , even if half the sample is contaminated , or to detect asymmetry in haloes as flat as @xmath0 provided less than a third of the sample comprises contaminants . we also argue that , provided its mass - to - light ratio is less than 100 , the recently observed stellar stream around m31 is not problematic for the detection of asymmetry .

astro-ph0307284

c

pixel - lensing experiments targeting m31 are hoping to exploit the favourably high disk inclination in order to detect an asymmetry in the spatial distribution of microlensing events . if such a signal is found , it will provide powerful evidence for the existence of machos . for a spherically symmetric and isotropic halo , the numbers of m31 machos in the far - disk outnumber those in the near - disk by more than 5 to 1 . this asymmetry is increased by about 30% if m31 machos occupy radial orbits rather than tangential ones . the signal is diminished if m31 machos lie in a flattened halo . however , even for haloes as flat as @xmath0 , the numbers of m31 machos in the far side will outnumber those in the near side by a factor of @xmath12 . the key to detecting asymmetry is to isolate microlensing events solely due to m31 machos . there is likely to be significant contamination from other microlensing populations , as well as from variable stars and supernovae mistaken for microlensing , which will dilute the observed signal . the combination of number - count and distance information permits asymmetry to be detected for a wide range of halo models , even in the presence of significant levels of contamination . for models with high levels of asymmetry , such as spherical haloes or haloes with a high degree of radial velocity anisotropy , number count information alone provides a sensitive diagnostic . the addition of distance information allows @xmath115% reduction in the size of samples needed to confirm asymmetry . for models with low levels of asymmetry , such as strongly flattened haloes , distance information can reduce the required size of candidate samples by a factor 2 or more . a sample of 50 events is typically sufficient to detect asymmetry in the m31 macho distribution within spherical haloes , even if only half the sample is due to m31 macho events . for flattened halo models , a sample of 50 candidates would likely allow asymmetry to be seen , provided that the halo axis ratio @xmath117 and the contaminants do not contribute more than a third of the sample . the term `` contaminants '' covers milky way machos , m31 disk stellar lensing events and variable star populations , all of which are assumed to be symmetrically distributed with respect to the major axis . for comparison , paulin - henriksson et al . ( 2003 ) have already found 362 lightcurves compatible with microlensing from the first two years of the point - agape survey , though the contamination factor may still be very large . samples of 50 events with modest contamination are easily achievable with the current generation of pixel - lensing surveys . ( _ solid line _ ) as a function of anisotropy parameter @xmath40 and normalised to the value for the isotropic model @xmath118 . also shown is the m31 macho number asymmetry @xmath39 ( _ dashed line _ ) , the ratio of near - disk to far - disk average durations @xmath37 ( _ dot - dashed line _ ) , and the ratio of projected distances to the major axis @xmath38 ( _ dotted line _ ) ] ( _ dashed line _ ) , the mean vertical distance @xmath38 ( _ dotted line _ ) and the time - scales ( _ dot - dashed line _ ) , shown as a function of flattening . this diagram is drawn using the transformation introduced in section [ tilt ] . ] . _ upper panel _ shows @xmath94 as a function of halo velocity anisotropy for a spherical halo . _ lower panel _ shows @xmath94 for flattened halo models , using the equivalence between the halo flattening parameter @xmath46 and disk inclination @xmath48 discussed in section [ tilt].,title="fig : " ] . _ upper panel _ shows @xmath94 as a function of halo velocity anisotropy for a spherical halo . _ lower panel _ shows @xmath94 for flattened halo models , using the equivalence between the halo flattening parameter @xmath46 and disk inclination @xmath48 discussed in section [ tilt].,title="fig : " ]

we find that the asymmetry is increased further by about 30% if the machos occupy radial orbits rather than tangential orbits , but is substantially reduced if the machos lie in a flattened halo . however , even for haloes with a minor - to - major axis ratio @xmath0 , the numbers of m31 machos in the far - side outnumber those in the near - side by a factor of @xmath12 . a sample of around 50 candidates is likely to be sufficient to detect asymmetry within spherical haloes , even if half the sample is contaminated , or to detect asymmetry in haloes as flat as @xmath0 provided less than a third of the sample comprises contaminants .

the point - agape collaboration is currently searching for massive compact halo objects ( machos ) towards the andromeda galaxy ( m31 ) . the survey aims to exploit the high inclination of the m31 disk , which causes an asymmetry in the spatial distribution of m31 machos . here , we investigate the effects of halo velocity anisotropy and flattening on the asymmetry signal using simple halo models . for a spherically symmetric and isotropic halo , we find that the underlying pixel - lensing rate in far - disk m31 machos is more than 5 times the rate of near - disk events . we find that the asymmetry is increased further by about 30% if the machos occupy radial orbits rather than tangential orbits , but is substantially reduced if the machos lie in a flattened halo . however , even for haloes with a minor - to - major axis ratio @xmath0 , the numbers of m31 machos in the far - side outnumber those in the near - side by a factor of @xmath12 . there is also a distance asymmetry , in that the events on the far - side are typically further from the major axis . we show that , if this positional information is exploited in addition to number counts , then the number of candidate events required to confirm asymmetry for a range of flattened and anisotropic halo models is achievable , even with significant contamination by variable stars and foreground microlensing events . for pixel - lensing surveys which probe a representative portion of the m31 disk , a sample of around 50 candidates is likely to be sufficient to detect asymmetry within spherical haloes , even if half the sample is contaminated , or to detect asymmetry in haloes as flat as @xmath0 provided less than a third of the sample comprises contaminants . we also argue that , provided its mass - to - light ratio is less than 100 , the recently observed stellar stream around m31 is not problematic for the detection of asymmetry .

physics0511093

i

ardm detector currently under construction is a wimp detector prototype based on argon bi - phase technology , see @xcite . in this detector , the detection of the 128 nm argon scintillation light as well as a localized charge readout allow discrimination against gamma / beta backgrounds . a major goal of the project is the proof of scalability of such technology to large target masses . ardm is aiming to be among the first large direct dark matter detectors , with a target mass of the order of one metric ton . in the last two years extensive r@xmath2d has been conducted towards the achievement of this goal . this included investigation of the possibility to reflect vuv photons on al coated mylar foils as a means of light collection . for light detection purposes , the feasibility of using large area avalanche photodiodes ( laapd ) for light read - out was analyzed . this talk presents the results of the measurement of the quantum efficiency of such devices . noble gases are known to provide scintillation light with high yield , up to about 50 photons per kev electron equivalent . detection of this light proves fundamental in many applications in which noble gas is used as medium . difficulties arise from the fact that noble gas emission is peaked in the vacuum ultraviolet ( vuv ) range . to detect such light , wavelength shifter - coated photomultiplier tubes ( pmts ) have often been used , resulting in a low global quantum efficiency , typically @xmath3 . there is interest in knowing if laapds could be a viable alternative , in particular in applications where the radiopurity is a concern . the presented results show that it is in principle possible both to collect vuv light using mirrors , as well as to detect gas scintillation from kr , xe and ar with apds at a quantum efficiency significantly higher than with pmts . the issues related to the signal to noise of apds , to the parallel operation of a large number of apds to increase the sensitive area , and the mechanical problems at potential cryogenic temperatures are not addressed in this paper .

the possibility of efficient collection and detection of vacuum ultraviolet light as emitted by argon , krypton , and xenon gas is studied . absolute quantum efficiencies of large area avalanche photodiodes ( laapds ) are derived at these wavelengths . vuv light of wavelengths down to the 128 nm of ar emission is shown to be detectable with silicon avalanche photodiodes at quantum efficiencies above 42% . vuv light , apd , argon scintillation , quantum efficiency , al+mgf2 .

the possibility of efficient collection and detection of vacuum ultraviolet light as emitted by argon , krypton , and xenon gas is studied . absolute quantum efficiencies of large area avalanche photodiodes ( laapds ) are derived at these wavelengths . vuv light of wavelengths down to the 128 nm of ar emission is shown to be detectable with silicon avalanche photodiodes at quantum efficiencies above 42% . flexible mylar foil overcoated with al+mgf@xmath0 is measured to have a specular reflectivity of @xmath191% at argon emission wavelength . low - pressure argon gas is shown to emit significant amounts of non - uv radiation . the average energy expenditure for the creation of non - uv photons in argon gas at this pressure is measured to be below 378 ev . vuv light , apd , argon scintillation , quantum efficiency , al+mgf2 .

1309.1350

i

it was suggested by wmap that the amplitude of cosmic microwave background ( cmb ) anisotropies has a dipolar directional dependence @xcite . this anomalous signature has been recently confirmed by planck @xcite . although it is possible that this anisotropy is a foreground effect , it is an interesting question whether or not we can explain this feature consistently within the paradigm of the inflationary universe . the basic issue is that a dipolar modulation of the amplitude of the curvature perturbation requires a seed dipolar perturbation . this seed dipolar perturbation itself is known to produce quadrupole and octupole moments of cmb anisotropy , known as the grishchuk - zeldovich ( gz ) effect @xcite . various scenarios that explain the dipolar statistical anisotropy have been proposed @xcite and various features have been investigated @xcite . the proposal in ref . @xcite advocates the use of the super - curvature perturbation @xcite produced in the open inflation scenario as the seed for the dipolar modulation . the amplitudes of monopole , dipole , and quadrupole fluctuations @xmath0 @xmath1 caused by the super - curvature mode of a free scalar field in the small mass limit are , respectively , evaluated by taking the small radius limit of the corresponding normalized mode functions as @xcite @xmath2 where @xmath3 and @xmath4 are the radii of the last scattering surface and the curvature radius in the comoving conformal coordinate , and @xmath5 and @xmath6 are the mass and the hubble expansion rate in the false vacuum before bubble nucleation . thus , one can basically avoid the constraint due to the gz effect by choosing @xmath7 to be sufficiently small . ( although in ref . @xcite a constraint on the amplitude of the super - curvature perturbation was imposed , such a condition on the magnitude of fluctuations beyond the current horizon scale is usually thought to be unnecessary in the context of the inflationary universe . the quasi - open inflation scenario @xcite is a typical example . ) however , we suspect that one important constraint has been overlooked . it is a genuine non - linear effect . if the amplitude of a dipole moment is large , a non - negligible quadrupole moment is naturally induced by non - linearity . taking into account the constraint from the amplitude of this induced quadrupole moment , we find that almost all models proposed so far are almost excluded by observations . in this letter , we propose a simple alternative scenario that can naturally evade this constraint .

the presence of a dipolar statistical anisotropy in the spectrum of cosmic microwave background ( cmb ) fluctuations was reported by the wilkinson microwave anisotropy probe ( wmap ) , and has recently been confirmed in the planck 2013 analysis of the temperature anisotropies . at the same time , the planck 2013 results report a stringent bound on the amplitude of the local - type non - gaussianity . we show that the non - linear effect of the dipolar anisotropy generates not only a quadrupole moment in the cmb but also a local - type non - gaussianity . in particular , most models proposed so far are almost excluded , or are at best marginally consistent with observational data .

the presence of a dipolar statistical anisotropy in the spectrum of cosmic microwave background ( cmb ) fluctuations was reported by the wilkinson microwave anisotropy probe ( wmap ) , and has recently been confirmed in the planck 2013 analysis of the temperature anisotropies . at the same time , the planck 2013 results report a stringent bound on the amplitude of the local - type non - gaussianity . we show that the non - linear effect of the dipolar anisotropy generates not only a quadrupole moment in the cmb but also a local - type non - gaussianity . consequently , it is not easy to build models having a large dipolar modulation and at the same time a sufficiently small quadrupole and level of local bispectral anisotropy to agree with the present data . in particular , most models proposed so far are almost excluded , or are at best marginally consistent with observational data . we present a simple alternative scenario that may explain the dipolar statistical anisotropy while satisfying the observational bounds on both the quadrupole moment and local - type non - gaussianity .

1211.6226

i

as the end products of about 97% of the stars of the galaxy , white dwarf stars offer important clues about their prior evolutionary history . they also provide potentially the age of the galactic disk and of the globular clusters they belong to ( winget et al . 1987 ; harris et al . 2006 ) through the age that can be estimated from cooling sequences ( ruiz & bergeron 2001 ) . however , determining the age of a white dwarf on its cooling sequence requires knowing its fundamental parameters : the total mass , the effective temperature , the luminosity , the fractional mass of the hydrogen and/or the helium outer layers , the core composition , etc . asteroseismology of white dwarfs provides a unique tool to explore their internal structure and determine those fundamental parameters . the method has been successfully applied to the pulsating pre - white dwarf stars of pg 1159 type , the gw vir stars , e.g. the prototype of the group pg 1159 - 035 ( winget et al . 1991 ) , the hottest one rxj 2117 + 3412 ( vauclair et al . 2002 ) and the coolest one pg 0122 + 200 ( fu et al . 2007 , crsico et al . 2007 ) , to the db pulsators , e.g. gd 358 ( winget et al . 1994 , provencal et al . 2009 ) , pg 1351 + 489 ( redaelli et al . 2011 ) , and to the dav stars , either for individual pulsator , e.g. hl tau 76 ( dolez et al . 2006 ) or for global study of the group properties ( castanheira & kepler 2009 ; romero et al . 2012 ) . since @xmath7 80% of the white dwarf stars are of da type , the uncertainties on their fundamental parameters have a strong impact on the derived age estimates . this justifies the effort in determining precise fundamental parameters of da white dwarfs using asteroseimology of the da pulsators , the dav or zz ceti stars . there are presently 148 pulsating da white dwarfs known ( castanheira et al . 2010a , 2010b ) . these stars define a narrow instability strip in the h - r diagram ( or in the log@xmath0-t@xmath8 diagram ) . this instability strip is a pure " instability strip , which means that all the da white dwarfs falling in this domain of the log@xmath0-t@xmath8 diagram do pulsate ( gianninas et al . 2011 ) . this is an indication that the internal structure of the zz ceti white dwarfs as derived from asteroseismology is representative of the da white dwarfs as a whole group . white dwarf stars being the oldest stars in a given stellar population , they can be used to estimate the age of the population they belong to . however , to achieve such a goal one must rely on realistic models of white dwarf stars . the major uncertainties in building such realistic models come from the uncertainty on their total mass and on their hydrogen mass fraction as well as from the approximate treatment of the convection by the mixing length theory parameterized by a mixing length @xmath9 . the asteroseismology is the only method able to determine the value of the hydrogen mass fraction and to give accurate total mass estimates of the zz ceti white dwarfs . in addition , new theoretical developments on the interaction of the pulsations with convection have opened a way to constrain the efficiency of the convection in white dwarf stars ( wu 2001 , montgomery 2005 , montgomery et al . 2010 ) . the difficulty in determining the fundamental parameters of the zz ceti stars from asteroseismology comes from two main sources : 1 ) the zz ceti stars show generally few modes simultaneously , in contrast with the theoretical calculations which predict much more unstable modes than observed , and 2 ) the pulsation amplitudes become increasingly variable as the zz cetis evolve towards the red edge of the instability strip . both effects make difficult to find enough appropriate modes to use the method based on the period spacing which needs a large enough number of pulsation modes to be observed and identified . only zz ceti stars close to the blue edge of the instability strip show constant pulsation amplitude . but in this case , very few modes are unstable since the stars are just entering the instability strip . in those stars , the @xmath10-mechanism due to hydrogen partial ionization is responsible for the instability since the fraction of the flux conveyed by convection is negligible ( dolez & vauclair 1981 , winget et al . as the white dwarfs evolve along their cooling sequence , the fraction of the flux conveyed by convection increases . the light curves become more complex as a result of the interaction of the convection with the pulsations . they show signatures of nonlinear effects like non sinusoidal pulse shapes which reflect into linear combinations of real " frequencies in the fourier spectrum . modeling precisely the light curve resulting from these inteactions can be used to constrain the efficiency of convection ( montgomery 2005 , montgomery et al . the asteroseismological analysis of various zz ceti stars through the instability strip allows to map the convection efficiency . the da white dwarf hs 0507 + 0434b is one of those zz ceti star of particular interest which we intend to study in more details . its parameters as derived from earlier spectroscopy give an effective temperature of 11630@xmath11 k and log@xmath0= 8.17@xmath12 ( fontaine et al . 2003 ; bergeron et al . 2004 ) which placed hs 0507 + 0434b approximately in the middle of the instability strip of the zz ceti pulsators . fontaine et al . ( 2003 ) provide a mass value of 0.71 @xmath13 derived from the models of wood ( 1995 ) for carbon core compositions , helium layers of @xmath14 , and hydrogen layers of @xmath15 , and absolute magnitude in @xmath16 of @xmath17 . more recent high signal / noise ratio spectroscopy and atmospheric analysis by gianninas et al . ( 2011 ) have shifted the zz ceti instability strip to higher effective temperature . with an effective temperature and a surface gravity of 12290 @xmath18 k and log@xmath0= 8.24@xmath12 respectively , hs 0507 + 0434b still lies close to the middle of the new zz ceti instability strip . it is of particular interest because it forms a common proper motion pair with hs 0507 + 0434a , which is a 20000 k da white dwarf ( jordan et al . gianninas et al . ( 2011 ) give also a higher effective temperature of 21550 @xmath19 k for the a component . since both members of the pair must have been formed at the same time , this provides one additional constraint on the modeling of their evolution . hs 0507 + 0434b was discovered to be a zz ceti variable by jordan et al . it has been observed subsequently from single sites only ( kotak et al . 2002 ; handler et al . those observations allowed the detection of 10 independent frequencies identified as @xmath20=1 gravity modes and of 38 linear combinations of these frequencies ( handler et al . the linear combinations of frequencies were interpreted as resulting from the nonlinear interaction of the pulsations with convection . the 10 independent frequencies are formed of three triplets ( i.e. @xmath20=1 modes split by rotation ) plus one single mode . this was clearly insufficient to constrain the star internal structure . to improve this situation , we carried out multisite observation campaigns in 2007 , december 2009 and january 2010 to study hs 0507 + 0434b . the goal of this paper is to improve the determination of the fundamental parameters of hs 0507 + 0434b using the new data collected during the campaigns of 2007 , 2009 and 2010 . it is organized as follows : the observations are described in @xmath21 . @xmath22 analyses the derived amplitude spectrum . a preliminary asteroseismology of hs 0507 + 0434b is presented in @xmath23 where are discussed successively the frequency identification and their linear combinations , in 4.1 , the period distribution and the period spacing , in 4.2 , the rotational splitting and the rate of rotation , in 4.3 , the inclination of the rotation axis , in 4.4 , and the mode trapping in 4.5 . @xmath24 discusses the amplitude variations . from the improved list of pulsation modes resulting from this work , we attempt to constrain the fundamental parameters of hs 0507 + 0434b by building a set of models which are described in @xmath25 , from which we derived one `` best fit '' model . we summarize our results in the conclusions @xmath26 .

the pulsating da white dwarfs ( zz ceti stars ) are @xmath0-mode non - radial pulsators . asteroseismology provides strong constraints on their global parameters and internal structure . since all the da white dwarfs falling in the zz ceti instability strip do pulsate , the internal structure derived from asteroseismology brings knowledge for the da white dwarfs as a whole group . hs 0507 + 0434b is one of the zz ceti stars which lies approximately in the middle of the instability strip for which we have undertaken a detailed asteroseismological study . we carried out multisite observation campaigns in 2007 and from december 2009 to january 2010 . in total , 206 hours of photometric time - series have been collected . [ firstpage ] stars : white dwarfs stars : oscillations stars : individual : hs 0507 + 0434b .

the pulsating da white dwarfs ( zz ceti stars ) are @xmath0-mode non - radial pulsators . asteroseismology provides strong constraints on their global parameters and internal structure . since all the da white dwarfs falling in the zz ceti instability strip do pulsate , the internal structure derived from asteroseismology brings knowledge for the da white dwarfs as a whole group . hs 0507 + 0434b is one of the zz ceti stars which lies approximately in the middle of the instability strip for which we have undertaken a detailed asteroseismological study . we carried out multisite observation campaigns in 2007 and from december 2009 to january 2010 . in total , 206 hours of photometric time - series have been collected . they have been analysed by means of fourier analysis and simultaneous multi - frequency sine - wave fitting . in total , 39 frequency values are resolved including 6 triplets and a number of linear combinations . we identify the triplets as @xmath1=1 @xmath0-modes split by rotation . we derived the period spacing , the rotational splitting and the rotation rate . from the comparison of the observed periods with the theoretical periods of a series of models we estimate the fundamental parameters of the star : its total mass m@xmath2/m@xmath3 = 0.675 , its luminosity l / l@xmath3=3.5@xmath4 , and its hydrogen mass fraction m@xmath5/m@xmath2= 10@xmath6 . [ firstpage ] stars : white dwarfs stars : oscillations stars : individual : hs 0507 + 0434b .

1211.6226

i

we summarize our results as follows : - we have obtained new photometric time - series of the zz ceti star hs 0507 + 0434b in 2007 , 2009 and 2010 . the combined power spectra allow us to identify 18 independent pulsation modes consisting of 6 triplets and one single mode , plus a number of their linear combinations . we identify those triplets as @xmath1=1 @xmath0-modes split by rotation . - we determine an average period spacing of 49.63 s. the period distribution exhibits the signature of mode trapping . - from the frequency shifts measured in the triplets , we determine an average rotational splitting of 3.59 @xmath610.57 @xmath27hz from which we infer an average rotation rate of 1.61 @xmath610.26 days . the amplitude ratio of the triplets components , if interpreted as uniquely due to geometrical effect , could be used to estimate that the angle of the rotation axis on the line of sight is close to @xmath62 . however , the evidence of amplitude variations casts some doubts on the assumption that only geometrical aspect is responsible for the amplitude ratios . - the amplitude of the modes vary on week time - scale and we find that the `` pulsation power '' is also time dependent . - we computed a grid of models and their @xmath1=1 @xmath0-modes in the adiabatic approximation . the comparison of their theoretical periods with the observed periods through @xmath50 tests allows us to estimate the fundamental parameters of a preliminary `` best fit '' model which has a total mass of m@xmath2/m@xmath3 = 0.675 , a luminosity l / l@xmath3=3.5@xmath4 , a thin hydrogen outer layer of m@xmath5/m@xmath2= 10@xmath6 . the periods of other models with `` thick '' hydrogen envelope do not fit as well the observed periods according to their @xmath50 . the `` thin '' hydrogen envelope of the best fit model of hs 0507 + 0434b is in agreement with the fact that its common proper motion companion hs 0507 + 0434a , which must have been formed at the same time and has a similar mass , has a significantly higher effective temperature . this implies that the b component must have a thinner h envelope than the a component for having cooled down to a lower effective temperature during the same cooling time scale . this low value of the hydrogen mass fraction suggests that hs 0507 + 0434b has evolved from a last he thermal pulse episode . further observations of hs 0507 + 0434b are required to refine the modeling , to better constrain the amplitude variation time - scales and identify the physical mechanism driving those variations , and to contribute to the mapping of the convection efficiency through the zz ceti instability strip .

they have been analysed by means of fourier analysis and simultaneous multi - frequency sine - wave fitting . in total , 39 frequency values are resolved including 6 triplets and a number of linear combinations . we identify the triplets as @xmath1=1 @xmath0-modes split by rotation . we derived the period spacing , the rotational splitting and the rotation rate . from the comparison of the observed periods with the theoretical periods of a series of models we estimate the fundamental parameters of the star : its total mass m@xmath2/m@xmath3 = 0.675 , its luminosity l / l@xmath3=3.5@xmath4 , and its hydrogen mass fraction m@xmath5/m@xmath2= 10@xmath6 .

the pulsating da white dwarfs ( zz ceti stars ) are @xmath0-mode non - radial pulsators . asteroseismology provides strong constraints on their global parameters and internal structure . since all the da white dwarfs falling in the zz ceti instability strip do pulsate , the internal structure derived from asteroseismology brings knowledge for the da white dwarfs as a whole group . hs 0507 + 0434b is one of the zz ceti stars which lies approximately in the middle of the instability strip for which we have undertaken a detailed asteroseismological study . we carried out multisite observation campaigns in 2007 and from december 2009 to january 2010 . in total , 206 hours of photometric time - series have been collected . they have been analysed by means of fourier analysis and simultaneous multi - frequency sine - wave fitting . in total , 39 frequency values are resolved including 6 triplets and a number of linear combinations . we identify the triplets as @xmath1=1 @xmath0-modes split by rotation . we derived the period spacing , the rotational splitting and the rotation rate . from the comparison of the observed periods with the theoretical periods of a series of models we estimate the fundamental parameters of the star : its total mass m@xmath2/m@xmath3 = 0.675 , its luminosity l / l@xmath3=3.5@xmath4 , and its hydrogen mass fraction m@xmath5/m@xmath2= 10@xmath6 . [ firstpage ] stars : white dwarfs stars : oscillations stars : individual : hs 0507 + 0434b .

1403.0341

i

the recent discoveries of the massive neutron stars psr j@xmath0 @xcite and psr j@xmath1 @xcite have brought new challenges for theories of dense matter beyond the nuclear saturation density . recently the radio timing measurements of the pulsar psr j@xmath0 and its white dwarf companion have confirmed the mass of the pulsar to be in the range of @xmath7 m@xmath8 at @xmath9 or @xmath10 m@xmath8 at @xmath11 confidence @xcite . this is only the second neutron star(ns ) with a precisely determined mass around 2m@xmath8 , after psr j@xmath1 and has a 3@xmath6 lower mass limit @xmath12 m@xmath8 higher than the latter . it therefore provides the tightest reliable lower bound on the maximum mass of neutron stars . compact stars provide the perfect astrophysical environment for testing theories of cold and dense matter . densities at the core of neutron stars can reach values of several times of @xmath13 . at such high densities , the energies of the particles are high enough to favour the appearance of exotic particles in the core . since the lifetime of neutron stars are much greater than those associated with the weak interaction , strangeness conservation can be violated in the core due to the weak interaction . this would result in the appearance of strange particles such as hyperons . the appearance of such particles produces new degrees of freedom , which results in a softer equation of state ( eos ) in the neutron star interior . the observable properties of compact stars depend crucially on the eos . according to the existing models of dense matter the presence of strangeness in the neutron star interior leads to a considerable softening of the eos , resulting in a reduction of the maximum mass of the neutron star @xcite . therefore many existing theories involving hyperons can not explain the large pulsar masses @xcite . most relativistic models obtain maximum neutron star masses in the range @xmath14 @xcite , when hyperons are included . some authors have tackled this problem by including a strong vector repulsion in the strange sector or by pushing the threshold for the appearance of hyperons to higher densities @xcite . in several studies the maximum neutron star masses were generally found to be lower than @xmath15 @xcite which is in contradiction with observed pulsar masses . however , neutron stars with maximum mass larger than @xmath16 have been obtained theoretically . bednarek @xcite achieved a stiffening of the eos by using a non - linear relativistic mean field ( rmf ) model with quartic terms involving the strange vector meson . lastowiecki @xcite obtained massive stars including a quark matter core . taurines @xcite achieved large neutron star masses including hyperons by considering a model with density dependent coupling constants . the coupling constants were varied nonlinearly with the scalar field . bonanno and sedrakian @xcite also modeled massive neutron stars including hyperons and quark core using a fairly stiff eos and vector repulsion among quarks . authors in ref . @xcite incorporated higher order couplings in the rmf theory in addition to kaonic interactions to obtain the maximum neutron star mass . agrawal @xcite have optimized the parameters of the extended rmf model using a selected set of global observables which includes binding energies and charge radii for nuclei along several isotopic and isotonic chains and the iso - scalar giant monopole resonance energies for the @xmath17zr and @xmath18pb nuclei . weissenborn @xcite investigated the vector meson - hyperon coupling , going from su(6 ) quark model to a broader su(3 ) , and concluded that the maximum mass of a neutron star decreases linearly with the strangeness content of the neutron star core independent of the nuclear eos . on the other hand , h. dapo @xcite found that for several different bare hyperon - nucleon potentials and a wide range of nuclear matter parameters the hyperons in neutron stars are always present . the parameters of the rmf model are fitted to the saturation properties of the infinite nuclear matter and/or the properties of finite nuclei . as a result extrapolation to higher densities and asymmetry involve uncertainties . three of these properties of the infinite nuclear matter are more precisely known : ( a ) the saturation density , ( b ) the binding energy and ( c ) the asymmetry energy , compared to the remaining ones - the effective nucleon mass and the compression modulus of the nuclear matter . the uncertainty in the dense matter eos is basically related to the uncertainty in these two saturation properties . it has been seen that to reproduce the giant monopole resonance ( gmr ) in @xmath18pb , accurately fitted non - relativistic and relativistic models predict compression modulus in the symmetric nuclear matter ( @xmath19 ) that differ by about @xmath20 . the reason for this discrepancy being the density dependence of the symmetry energy . moreover , the alluded correlation between @xmath19 and the density dependence of the symmetry energy results in an underestimation of the frequency of oscillations of neutrons against protons , the so - called isovector giant dipole resonance ( ivgdr ) in @xmath18pb . fsugold is a recently proposed accurately calibrated relativistic parameterization . it simultaneously describes the gmr in @xmath17zr and @xmath18pb and the ivgdr in @xmath18pb without compromising the success in reproducing the ground - state observables @xcite . the main virtue of this parameterization is the softening of both the eos of symmetric nuclear matter and the symmetry energy . this softening appears to be required for an accurate description of different collective modes having different neutron - to - proton ratios . as a result , the fsugold effective interaction predicts neutron star radii that are too large and a maximum stellar mass that is too small @xcite . the indiana university - florida state university ( iufsu ) interaction , is a new relativistic parameter set , derived from fsugold . it is simultaneously constrained by the properties of finite nuclei , their collective excitations and the neutron star properties by adjusting two of the parameters of the theory - the neutron skin thickness of @xmath21 and the maximum neutron star mass @xcite . as a result the new effective interaction softens the eos at intermediate densities and stiffens the eos at high density . as it stands now , the new iufsu interaction reproduces the binding energies and charge radii of closed - shell nuclei , various nuclear giant ( monopole and dipole ) resonances , the low - density behavior of pure neutron matter , the high - density behavior of the symmetric nuclear matter and the mass - radius relationship of neutron stars . whether this new eos can accommodate the hyperons inside the compact stars , with the severe constraints imposed by the recent observations of @xmath22 pulsars , needs to be explored . in this work we plan to make a detailed study of such a possibility . for this purpose we have extended the iufsu interaction by including the full baryon octet . a new eos is constructed to investigate the neutron star properties with hyperons . [ cols="^,^,^,^,^,^,^,^,^ " , ] the paper is organized as follows . in section 2 , we briefly discuss the model used and the resulting eos . in the next section we use this eos to look at static and rotating star properties . we give a brief summary in section 4 .

the recent discoveries of massive neutron stars , such as psr j@xmath0 and psr j@xmath1 , have raised questions about the existence of exotic matter such as hyperons in the neutron star core . the validity of many established equations of states ( eos s ) like the gm1 and fsugold are also questioned . we investigate the existence of hyperonic matter in the central regions of massive neutron stars using relativistic mean field ( rmf ) theory with the recently proposed iufsu model . the iufsu model is extended by including hyperons to study the neutron star in @xmath2 equilibrium . the effect of different hyperonic potentials , namely @xmath3 and @xmath4 potentials , on the eos and hence the maximum mass of neutron stars has been studied .

the recent discoveries of massive neutron stars , such as psr j@xmath0 and psr j@xmath1 , have raised questions about the existence of exotic matter such as hyperons in the neutron star core . the validity of many established equations of states ( eos s ) like the gm1 and fsugold are also questioned . we investigate the existence of hyperonic matter in the central regions of massive neutron stars using relativistic mean field ( rmf ) theory with the recently proposed iufsu model . the iufsu model is extended by including hyperons to study the neutron star in @xmath2 equilibrium . the effect of different hyperonic potentials , namely @xmath3 and @xmath4 potentials , on the eos and hence the maximum mass of neutron stars has been studied . we have also considered the effect of stellar rotation since the observed massive stars are pulsars . it has been found that a maximum mass of @xmath5 , which is within the 3@xmath6 limit of the observed mass of psr j@xmath0 , can be obtained for rotating stars , with certain choices of the hyperonic potentials . the said star contains a fair amount of hyperons near the core . 0.2 cm

1403.0341

i

to summarize , we have studied the static and rotating axisymmetric stars with hyperons using iufsu model . the original fsugold parameter set has been very successful in describing the properties of finite nuclei . with the discovery of highly massive neutron stars the reliability of this model was questioned . it was then revised in the form of iufsu to accommodate such highly massive stars leaving the low density finite nuclear properties unchanged . in this work we have studied this new parameter set in the context of the possibility of having a hyperonic core in such massive stars . we have included the full octet of baryons in iufsu . the eos gets softened due to the inclusion of hyperons whereas the inclusion of the @xmath25 meson makes the eos stiffer . we have also investigated the influence of @xmath3 and @xmath4 potentials on the eos . for static stars with hyperonic core we get a maximum mass of @xmath122 . so iufsu with hyperons can not reproduce the observed mass of static stars . however , as the observed @xmath22 neutron stars are both pulsars , we compare the results in the rotating limit . in the keplerian limit we get a maximum mass of @xmath137 , which is within the 3@xmath6 limit of the mass of psr j@xmath0 and 1@xmath6 limit of the earlier observation of psr j@xmath1 . we have looked at the particle densities inside the star having the maximum mass and found that a considerable amount of hyperons are present near the core . therefore , our results are consistent with the recent observations of highly massive pulsars confirming the presence of hyperons in the core of such massive neutron stars . to conclude , iufsu model , which reproduces the properties of finite nuclei quite successfully also reproduces the recent observations of @xmath140 stars , in case of stars having exotic core and rotating in the keplerian limit . it will be interesting to see whether such a star can hold a quark core . related work is in progress .

it has been found that a maximum mass of @xmath5 , which is within the 3@xmath6 limit of the observed mass of psr j@xmath0 , can be obtained for rotating stars , with certain choices of the hyperonic potentials . the said star contains a fair amount of hyperons near the core .

the recent discoveries of massive neutron stars , such as psr j@xmath0 and psr j@xmath1 , have raised questions about the existence of exotic matter such as hyperons in the neutron star core . the validity of many established equations of states ( eos s ) like the gm1 and fsugold are also questioned . we investigate the existence of hyperonic matter in the central regions of massive neutron stars using relativistic mean field ( rmf ) theory with the recently proposed iufsu model . the iufsu model is extended by including hyperons to study the neutron star in @xmath2 equilibrium . the effect of different hyperonic potentials , namely @xmath3 and @xmath4 potentials , on the eos and hence the maximum mass of neutron stars has been studied . we have also considered the effect of stellar rotation since the observed massive stars are pulsars . it has been found that a maximum mass of @xmath5 , which is within the 3@xmath6 limit of the observed mass of psr j@xmath0 , can be obtained for rotating stars , with certain choices of the hyperonic potentials . the said star contains a fair amount of hyperons near the core . 0.2 cm

0807.1875

i

since the discovery of high temperature superconductors ( hts ) two decades ago , many anomalous properties have been reported . one of the most interesting properties is the possible existence of the stripe state consisting of one dimensional charge - density modulation coupled with spin ordering @xcite . the first direct experimental evidence @xcite of this stripe state as the ground state is for the non - superconducting @xmath3 with the hole density about @xmath4 per unit cell . since then more evidences of the presence of these have been reported in other cuprate samples @xcite . however it seems that the stripe is much more prominent in the lasrcuo ( lsco ) family near @xmath4 doping @xcite and in particular for @xmath5 ( @xmath6 ) @xcite where the charge density or spin density modulation could be considered as an long - ranged order parameter of a phase with broken symmetries . very recently the high resolution scanning tunneling microscopy ( stm ) has observed unidirectional domains with periodic density of states modulation in two families of @xmath7 and @xmath0 ( bscco ) @xcite . these bond - centered electronic patterns with a width of four lattice constants form the so called electronic cluster glass state with short - ranged modulations . although the modulation is weak , it is still surprising to have the rather high superconducting ( sc ) transition temperature in this glass state . stm spectra also provided the new puzzling result that there are two different types of spectral gaps in those systems . one is a larger gap with a broader distribution and it seems to be related to the pseudogap . inside this gap , there is a smaller gap or the so called sub - gap kink with clear @xmath8-wave like spectra @xcite . these results and the most recent conflicting results reported by angle - resolved - photo - emission spectra ( arpes ) @xcite raise the question whether there are two energy scales related with two different underlying mechanisms separately responsible for the larger pseudogap and the lower - temperature sc transition . but one feature that most experimental results agree is the presence of the linear density of state ( dos ) near the nodal point . it is interesting to note that this has also been reported in the non - superconducting stripe state of @xmath6 @xcite . the observations of these strongly - modulated inhomogeneous states like @xmath6 with almost zero sc transition temperature ( @xmath9 ) or weakly inhomogeneous cluster glass states in bscco with quite high @xmath9 have fueled the idea about the presence of competing interactions and underdoped hts is near the boundary of two distinct phases with different order parameters . the fluctuations @xcite of the order parameters in these adjacent phases could be the mechanism of high temperature superconductivity . thus it seems like a @xmath10 @xmath11 that after two decades we are still faced with a daunting question about the appropriate fundamental interactions to model and to understand the hts . many people are still not convinced by all those successes @xcite claimed by studying the strong coupling hubbard model or its equivalent @xmath2 model . in this model the nearest - neighbor antiferromagnetic ( af ) spin coupling @xmath1 is the only relevant interaction besides the usual kinetic energy of electrons ( represented by the @xmath12 term ) . there are no other competing interactions and certainly no phase boundaries between overdoped and underdoped regimes with different order parameters to be worried . in this paper we will show that interactions represented by @xmath12 and @xmath1 are actually competing with each other . this competition , greatly enhanced by the strong correlation between electrons , has many spatially heterogeneous states almost exactly the same energy as the uniform ground state . the ground state could easily tolerate local spatial modulation of charge density , spin density and even pairing amplitude without much an effect on its sc order parameter . the presence of these very low - energy cluster glass states with a random pattern of short - ranged modulation is an inherent nature of the @xmath2 model . the selection of a particular local electronic pattern as observed in scanning tunneling spectroscopy ( sts ) for hts is most likely determined by the effects of impurities , defects and electron - lattice interaction , etc . random distribution of impurities and defects will not produce long - ranged modulation in the sense of charge - density - wave order or spin - density - wave order unless these is a very strong lattice distortion as demonstrated @xcite by the structural transition observed in @xmath6 . hence our result for the extended @xmath2 model shows that for weakly inhomogeneous cuprates like bscco there is no need to introduce other strong competing interactions with new broken symmetry phases and long - ranged order parameters to produce the observed glass states . the extended @xmath2 model is adequate to explain many of the experimental observations . depending on the particular type of modulations , the local dos could either have a node with linear dos or without a node . these local modulations also produce the sub - gap structures . in addition , these cluster glass states have almost completely suppressed the quasi - particle spectral weight near the antinodal region as observed by arpes for bscco compounds @xcite . before we start with the discussion about the cluster glass states , we should point out that the competition between the kinetic energy represented by @xmath12 and the magnetic energy represented by @xmath1 is not a new idea . it is the main reason for the uniform - state phase diagram obtained by the theory of the resonating - valence - bond ( rvb ) state @xcite . the @xmath1 term prefers the formation of spin pairing , the so called rvb singlet , or the long - ranged antiferromagnetism . because of the strong correlation a spin can only hop by exchanging position with a hole , hence the kinetic energy is proportional to the density of holes . but the more hole the system has , the less number of spin there is . consequently the pairing is also reduced . thus the pairing amplitude reduces when hole doping increases . magnetic energy is reduced while kinetic - energy gain increases . it is shown below this competition also happens in individual unit cell . on the theoretical side the stripe state also has a long history . it was first founded almost two decades ago in the mean - field treatment of the hubbard model @xcite although the validity of the method in treating strong hubbard interaction is questionable . then the extended @xmath2 models were studied by several numerical methods such as the exact diagonalization method @xcite , the density matrix renormalization group method @xcite and the variational monte carlo ( vmc ) method @xcite . but the results are inconsistent . there are indications that stripe is unstable when the second neighbor hopping , @xmath13 , is included in the @xmath2 model . however , a later vmc study of the @xmath14 model @xcite indicates that the stripe has about @xmath15 lower energy than the uniform rvb based @xmath8-wave sc state for most of the negative values of @xmath13 except when @xmath16 is less than @xmath17 . similar results were also reported for the hubbard model @xcite . these results pose a new direct contradiction with the experimental findings . many experimental and theoretical studies have found that @xmath16 is smallest for lsco family @xcite , thus the stripe state should not be favorable . yet as mentioned above , among all the cuprates lsco family has the most solid evidences for the existence of stripe . there are also other problems with the proposed stripe states , such as suppressed pairing correlation and absence of the v - shape dos at low energy , and we will discuss them below . all of the previous works concentrated on studying periodic stripes with a long - ranged order , it is unclear if the result will hold for the cluster glass state . there are also different kinds of stripes to be considered . it is possible to have only charge density modulation , or only spin density modulation , or only pairing amplitude modulation or with the linear combination of any two or all three of them @xcite . furthermore the relation between these modulations could be correlated or anti - correlated . all these issues are addressed below and their results are compared with the experiments .

the recent observation of an electronic cluster glass state composed of random domains with unidirectional modulation of charge density and/or spin density on @xmath0 reinvigorates the debate of existence of competing interactions and their importance in high temperature superconductivity . by using a variational approach , here we show that the presence of the cluster glass state is actually an inherent nature of the model based on the antiferromagnetic interaction ( @xmath1 ) only , _ i.e. _ the well known @xmath2 model . there is no need yet to introduce a competing interaction to understand the existence of the cluster glass state . the modulation also produces subgap structures inside the `` coherent '' peaks of the local density of states .

the recent observation of an electronic cluster glass state composed of random domains with unidirectional modulation of charge density and/or spin density on @xmath0 reinvigorates the debate of existence of competing interactions and their importance in high temperature superconductivity . by using a variational approach , here we show that the presence of the cluster glass state is actually an inherent nature of the model based on the antiferromagnetic interaction ( @xmath1 ) only , _ i.e. _ the well known @xmath2 model . there is no need yet to introduce a competing interaction to understand the existence of the cluster glass state . the long - range pairing correlation is not much influenced by the disorder in the glass state which also has nodes and linear density of states . in the antinodal region , the spectral weight is almost completely suppressed . the modulation also produces subgap structures inside the `` coherent '' peaks of the local density of states .

1507.00054

i

entanglement is a central topic in quantum information theory . it is viewed as a resource for manipulating quantum information and accomplishing quantum computing tasks . in an isolated pure state @xmath0 , entanglement is manifested as quantum correlations between its partitions @xmath1 and @xmath2 . that is , the results of measurements done on a partition , say @xmath1 , are statistically distributed according to the reduced density operator @xmath3 , where the partial trace @xmath4 is a quantum average done over a complete set of states for the complementary partition @xmath2 . for these bipartite pure states , @xmath5 and @xmath6 have identical spectra ( eigenvalues ) and hence entanglement measures can be calculated from either reduced density operator . when the partitions @xmath1 and @xmath2 are _ unentangled _ both @xmath5 and @xmath6 are projectors onto a single state vector . on the other hand , when @xmath1 and @xmath2 are _ maximally entangled _ @xmath5 and @xmath6 correspond to uniform distributions over their respective eigenvectors . that is , there is more entanglement in @xmath7 when there is less certainty in the state of a given partition when the effects of its complement are averaged over . a similar relationship between the uncertainty in knowing the ( reduced ) state of a subsystem and the strength of its coupling with its complement or environment is well - established in statistical mechanics @xcite . the main pedagogical objective in this article is the presentation of several key concepts of quantum information theory using the language of statistical mechanics and thermodynamics . the construction of effective thermal models for a partition is a very useful concept that underlies more advanced ideas such as the emergence of area laws in the scaling of entanglement entropy @xcite and the replica trick of quantum field theory @xcite . the systems under consideration here are also particularly illustrative : for example , uncertainty and fluctuations in a mode - partitioned squeezed state are identical to that of a harmonic oscillator at thermal equilibrium . some of the results given in this paper have been demonstrated in the past @xcite , but here we emphasize the consonance of the quantum information and statistical mechanics perspectives . additionally , we also present some new exact results such as the detailed calculation of the rnyi entanglement entropy in bosonic two - mode squeezed states and a multi - mode silbey harris state @xcite , and the identification of the single - copy entanglement @xcite as a free energy analogue @xcite for these systems . for a broader overview of the research on entanglement in many - particle systems , the reader may refer to extensive technical reviews found in the literature @xcite as well as others at a more introductory level @xcite . the mode - entangled examples studied here involve coherent ( displaced ) and squeezed boson modes that are encountered in , for example , quantum optical systems @xcite , ultracold coherent matter systems @xcite , and nanomechanical systems @xcite . we partition these composite states with respect to the mode indices @xmath1 and @xmath2 and analytically obtain the reduced density operator for a partition @xmath5 . this allows us to calculate entanglement measures ( ) for these bipartite pure states , such as the rnyi entanglement entropy @xcite and entanglement spectrum @xcite . the entanglement spectrum is further used to construct effective thermal models that yield identical fluctuations in observables that are local to a given partition ( mode - local ) . we first consider several cases of two - mode coherent and squeezed states ( ) and then proceed to the case of the multi - mode silbey harris state ( ) .

the rnyi entanglement entropy is calculated exactly for mode - partitioned isolated systems such as the two - mode squeezed state and the multi - mode silbey harris polaron ansatz state . effective thermodynamic descriptions of the correlated partitions are constructed to present quantum information theory concepts in the language of thermodynamics .

the rnyi entanglement entropy is calculated exactly for mode - partitioned isolated systems such as the two - mode squeezed state and the multi - mode silbey harris polaron ansatz state . effective thermodynamic descriptions of the correlated partitions are constructed to present quantum information theory concepts in the language of thermodynamics . boltzmann weights are obtained from the entanglement spectrum by deriving the exact relationship between an effective temperature and the physical entanglement parameters . the partition function of the resulting effective thermal theory can be obtained directly from the single - copy entanglement .

1703.09714

c

we presented the application of our selection method for photometric white dwarfs candidates @xcite to the latest internal data release of the vst atlas survey combined with proper motions from apop . the resulting catalogue contains @xmath7atlas sources with computed @xmath54 . using a small number of sdss spectroscopically confirmed white dwarfs and contaminants we calculated that a confidence cut at @xmath55 produces a sample of white dwarfs that is 96 per cent complete with an efficiency of 87 per cent . we estimate that our catalogue contains @xmath1 high - confidence white dwarf candidates the majority of which have not yet received spectroscopic follow - up . only @xmath23 per cent of the white dwarfs known to date are located in the southern hemisphere and our catalogue therefore constitute a significant improvement on the current north - south knowledge gap . among these thousands of new white dwarfs we expect to find several systems of particular interest : metal polluted white dwarfs ( most likely more than 1000 in the final atlas footprint ) which will improve current statistics on planetary debris abundances , a few tens of white dwarfs with detectable debris discs which can be identified combining our catalogue with ir data from the vista hemisphere survey ( vhs , @xcite ) and wise @xcite , several magnetic white dwarfs and white dwarfs with rare atmospheric composition ( e.g. dq ) like those already identified in our limited spectroscopic follow - up ( sect.[spec_follow ] ) , and more pulsating white dwarfs ( sect.[pulse ] ) . the application of our catalogue to most white dwarfs population studies will ultimately require spectroscopic follow - up . the possibility to rely on the @xmath54s allows one to tailor future spectroscopic observations prioritising efficiency ( and therefore high @xmath54 targets ) for single target observations or completeness in large scale campaigns .

we make use of the vst atlas survey , one of the first surveys obtaining deep , optical , multi - band photometry over a large area of the southern skies , to remedy this situation . applying the colour and proper - motion selection developed in @xcite to the most recent internal data release ( 2016 april 25 ) of vst atlas we created a catalogue of @xmath1 moderately bright ( @xmath2 ) , high - confidence southern white dwarf candidates , which can be followed up individually with both the large array of southern telescopes or in bulk with forthcoming multi - object spectrographs . [ firstpage ] white dwarfs - surveys - catalogues - proper motions

the sloan digital sky survey ( sdss ) has created a knowledge gap between the northern and the southern hemispheres which is very marked for white dwarfs : only @xmath0 of the known white dwarfs are south of the equator . here we make use of the vst atlas survey , one of the first surveys obtaining deep , optical , multi - band photometry over a large area of the southern skies , to remedy this situation . applying the colour and proper - motion selection developed in @xcite to the most recent internal data release ( 2016 april 25 ) of vst atlas we created a catalogue of @xmath1 moderately bright ( @xmath2 ) , high - confidence southern white dwarf candidates , which can be followed up individually with both the large array of southern telescopes or in bulk with forthcoming multi - object spectrographs . [ firstpage ] white dwarfs - surveys - catalogues - proper motions

1211.6364

i

the interference of scattering amplitudes in quantum mechanics arises from the indistinguishability of alternative scattering paths , as in the interference of the paths of a photon passing through the celebrated double - slits of young . for example , a modern variation on the young experiment @xcite shows spatial fringes in the intensity of light scattered from two trapped ions ; but only so long as the scattering can not be traced to one ion or the other @xcite . even in the latter situation , other measurements might be found which can not distinguish between the paths , hence recovering the interference . typically they involve higher - order moments of the field @xcite , or post - selection , _ i.e. _ , partitioning of scattering events into subensembles @xcite . such a measurement strategy is termed a `` quantum eraser '' , since it recovers interference by `` erasing '' the information that identifies the path . a time - domain analogue of double - slit interference can occur inside multi - level atoms , where photon emission via parallel transitions can result in a modulation of the emission intensity at the frequency of a level splitting the phenomenon of quantum beats " ( see , _ e.g. _ , @xcite ) . a distinction has traditionally been drawn between `` type - i '' or `` v '' atomic systems , where decay of a superposition of upper levels yields beats at the transition difference frequency ; and the inverted `` type - ii '' or `` @xmath0 '' systems , where decay to a superposition of lower levels _ does not _ yield beats @xcite . the typical argument for the latter outcome is that a measurement of the ground - state population could always , in principle , determine in which of the two available states the electron landed ; as there is no sum over alternative paths to one and the same final state , there are no `` ground - state quantum beats '' @xcite . nevertheless , as with spatial fringes , a quantum eraser - type strategy can recover time - domain interference in the ground state . zajonc @xcite proposed one such implementation in a `` type - ii '' atomic system , basing his proposal on two - photon scattering . in this case the second scattered photon erases the path information written by the first amplitudes for the scattering of two photons in sequence interfere . we recently published experimental results showing quantum beats in spontaneous emission at the frequency of the ground - state zeeman splitting in rb , @xmath1 ground - state quantum beats seen in spontaneous emission @xcite . oscillations appear in the second - order intensity autocorrelation function only , not in the average intensity , as follows from the indistinguishability requirement above . the presence of a similar oscillation hidden within the noise of spontaneous emission was demonstrated in 1955 by forrester _ et al . _ they mixed two incoherent light sources a zeeman doublet on a photocathode , and used a resonant microwave cavity to enhance the beat signal extracted from the photocurrent noise . the interference in this case is classical , though the oscillation is recovered from noise through intensity correlation . more than 50 years later , using coherent excitation and single - photon detectors , we have realized a time - resolved measurement of the ground - state quantum beat recovered from spontaneous emission noise . the oscillation in our system arises as a complicated mixture of quantum eraser - type interferences within single atoms , pair - wise interference between emission from different atoms , and a homodyne contribution due to the superposition of a weak coherent background ( similar to @xcite ) generated by birefringence in the cavity mirrors . by coupling spontaneous emission into an optical cavity at moderate dipole coupling strength , we overcome the signal - to - noise limitations set by a small coherence area in free space @xcite , and enforce indistinguishability among different atoms emitting into a common spatial mode . moreover , we show below that the complicated level structure of @xmath2rb actually aids in the survival of ground - state coherence , counter to the conventional strategy of protecting coherence by limiting the state space through which population can diffuse . we distinguish here between ground - state coherences imposed by an external drive and those arising spontaneously , selected through the detection process , as in our experiment . in the former case , an external magnetic or optical drive couples two ground states directly , with the resulting coherence read out optically in forward scattering ( see @xcite for many examples . ) in the latter , levels couple only through the vacuum , with no external drive to enforce coherence . the fact that spontaneous decay can generate coherence is evident from the observation of quantum beats at the intermediate level splitting in cascade decay @xcite ; that the same process occurs in transitions to ground or meta - stable states is not therefore surprising . schubert et al . @xcite measured such a coherence in the bichromatic cross - correlation of fluorescence from a single ion , where detection of a first photon left the ion in a superposition of meta - stable states . when considering isotropic emission , however , spontaneously created coherences tend to vanish on the average , and for this reason are often left out of density matrix calculations @xcite . the recent interest follows a 1992 paper @xcite in which specific measurable consequences were claimed ; various arrangements have been explored theoretically @xcite . a publication as recent as 2005 @xcite claims evidence of the first serious experimental consequences of spontaneously - generated coherence , this in a quantum dot system . other experiments are surprisingly few . we direct the interested reader to ref . @xcite for an overview . in this article we expand upon the results presented in @xcite . in particular , we seek to explain the origin of the various individual components of the beat signal , show which experimental conditions are necessary for the robust survival and detection of beats , and explore their sensitivity to various experimental controls . the paper is organized as follows . section [ sc : theoreticalmodel ] introduces the theoretical model , starting with a single atom fixed in space and moving to a full atomic beam with realistic fluctuations . section [ sc : experiment ] presents the details of our experimental method , from the atomic source and optics to the detection apparatus . section [ sc : results ] summarizes the evolution of the beat signal as we explore parameter space and compares experiment with theory . the paper concludes in section [ sc : conclusions ] .

the spontaneous creation and persistence of ground - state coherence in an ensemble of intracavity rb atoms has been observed as a quantum beat . our system realizes a quantum eraser , where the detection of a first photon prepares a superposition of ground - state zeeman sublevels , while detection of a second erases the stored information . beats appear in the time - delayed photon - photon coincidence rate ( intensity correlation function ) . although beats arise most simply through single - atom - mediated quantum interference , scattering pathways involving pairs of atoms interfere also in our intracavity experiment .

the spontaneous creation and persistence of ground - state coherence in an ensemble of intracavity rb atoms has been observed as a quantum beat . our system realizes a quantum eraser , where the detection of a first photon prepares a superposition of ground - state zeeman sublevels , while detection of a second erases the stored information . beats appear in the time - delayed photon - photon coincidence rate ( intensity correlation function ) . we study the beats theoretically and experimentally as a function of system parameters , and find them remarkably robust against perturbations such as spontaneous emission . although beats arise most simply through single - atom - mediated quantum interference , scattering pathways involving pairs of atoms interfere also in our intracavity experiment . we present a detailed model which identifies all sources of interference and accounts for experimental realities such as imperfect pre - pumping of the atomic beam , cavity birefringence , and the transit of atoms across the cavity mode .