entropy of random quantum states the authors use a simple generating function to calculate exactly the entropy of random quantum states for finite dimensional hilbert spaces over real complex and quaternionic scalars this allows them to extend their previous formula for the quantum correlation information of a state determination apparatus to include real and quaternionic von neumann analysers

a recursive approach to local mesh refinement in two and three dimensions abstract the newest vertex strategy for local refinement in two dimensions is reviewed and discussed a recursive algorithm for local refinement of tetrahedral meshes in three dimensions based on similar bisection strategy is described the recursive approach requires certain restrictions on the initial mesh on the other hand under this condition the refinement process can be kept as local as needed and it can be fully inverted simple data structures and derefinement algorithms are also outlined

a priori probabilities of separable quantum states zyczkowski horodecki sanpera and lewenstein zhsl recently proposed a natural measure on the n dimensional quantum systems but expressed surprise when it led them to conclude that for n 2 2 disentangled separable systems are more probable 0 632 0 002 in nature than entangled ones we contend however that zhsl s rejected intuition has in fact a sound theoretical basis and that the a priori probability of disentangled 2 2 systems should more properly be viewed as considerably less than 0 5 we arrive at this conclusion in two quite distinct ways the first based on classical and the second quantum considerations both approaches however replace in whole or part the zhsl product measure by ones based on the volume elements of monotone metrics which in the classical case amounts to adopting the jeffreys prior of bayesian theory only the quantum theoretic analysis which yields the smallest probabilities of disentanglement uses the minimum number of parameters possible that is n2 1 as opposed to n2 n 1 although this over parametrization as recently indicated by byrd should be avoidable however despite substantial computation we are not able to obtain precise estimates of these probabilities and the need for additional possibly supercomputer analyses is indicated particularly so for higher dimensional quantum systems such as the 2 3 ones which we also study here

noise dressing of financial correlation matrices we show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series the central result of the present study which focuses on the case of financial price fluctuations is the remarkable agreement between the theoretical prediction based on the assumption that the correlation matrix is random and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the s 500 or other major markets in particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management

large deviation eigenvalue density for the soft edge laguerre and jacobi β ensembles we analyze the eigenvalue density for the laguerre and jacobi ensembles in the cases that the corresponding exponents are extensive in particular we obtain the asymptotic expansion up to terms o 1 in the large deviation regime outside the limiting interval of support as found in recent studies of the large deviation density for the gaussian ensemble and laguerre ensemble with fixed exponent there is a scaling from this asymptotic expansion to the right tail asymptotics for the distribution of the largest eigenvalue at the soft edge

exact evaluation of the collapse phase boundary for two dimensional directed polymers the phase boundary of the collapsed phase for a directed polymer on a square lattice in the presence of an attractive wall and monomer monomer interactions is calculated exactly using transfer matrix techniques the position of the multicritical point is also identified

distributions of singular values for some random matrices the singular value decomposition is a matrix decomposition technique widely used in the analysis of multivariate data such as complex space time images obtained in both physical and biological systems in this paper we examine the distribution of singular values of low rank matrices corrupted by additive noise past studies have been limited to uniform uncorrelated noise using diagrammatic and saddle point integration techniques we extend these results to heterogeneous and correlated noise sources we also provide perturbative estimates of error bars on the reconstructed low rank matrix obtained by truncating a singular value decomposition 1999 the american physical society

realigning random states we study how the realignment criterion also called computable cross norm criterion succeeds asymptotically in detecting whether random states are separable or entangled we consider random states on cd cd obtained by partial tracing a haar distributed random pure state on cd cd cs over an ancilla space cs we show that for large d typically the realignment criterion is successful in detecting entanglement if and only if s 83 2d2 in this sense the realignment criterion is asymptotically weaker than the partial transposition criterion

uncertainty for spin systems a modified definition of quantum mechanical uncertainty for spin systems which is invariant under the action of su 2 is suggested its range is shown to be 2j 2j j 1 within any irreducible representation j of su 2 and its mean value in hilbert space computed using the fubini study metric is determined to be mean 2j j 1 2 the most used sets of coherent states in spin systems coincide with the set of minimum uncertainty states

global entangling properties of the coupled kicked tops we study global entangling properties of the system of coupled kicked tops testing various hypotheses and predictions concerning entanglement in quantum chaotic systems in order to analyze the averaged initial entanglement production rate and the averaged asymptotic entanglement various ensembles of initial product states are evolved two different ensembles with natural probability distribution are considered product states of independent spin coherent states and product states of random states it appears that the choice of either of these ensembles results in significantly different averaged entanglement behavior we investigate also a relation between the averaged asymptotic entanglement and the mean entanglement of eigenvectors of the evolution operator lower bound on the averaged asymptotic entanglement is derived expressed in terms of the eigenvector entanglement

random matrix approach to cross correlations in financial data we analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory rmt using two large databases we calculate cross correlation matrices c of returns constructed from i 30 min returns of 1000 us stocks for the 2 yr period 1994 1995 ii 30 min returns of 881 us stocks for the 2 yr period 1996 1997 and iii 1 day returns of 422 us stocks for the 35 yr period 1962 1996 we test the statistics of the eigenvalues lambda i of c against a null hypothesis a random correlation matrix constructed from mutually uncorrelated time series we find that a majority of the eigenvalues of c fall within the rmt bounds lambda lambda for the eigenvalues of random correlation matrices we test the eigenvalues of c within the rmt bound for universal properties of random matrices and find good agreement with the results for the gaussian orthogonal ensemble of random matrices implying a large degree of randomness in the measured cross correlation coefficients further we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the rmt bound display systematic deviations from the rmt prediction in addition we find that these deviating eigenvectors are stable in time we analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks our analysis of the remaining deviating eigenvectors shows distinct groups whose identities correspond to conventionally identified business sectors finally we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return less

statistical mechanics of multipartite entanglement we characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions we search for those maximally multipartite entangled states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics

recursion for the smallest eigenvalue density of β wishart laguerre ensemble the statistics of the smallest eigenvalue of wishart laguerre ensemble is important from several perspectives the smallest eigenvalue density is typically expressible in terms of determinants or pfaffians these results are of utmost significance in understanding the spectral behavior of wishart laguerre ensembles and among other things unveil the underlying universality aspects in the asymptotic limits however obtaining exact and explicit expressions by expanding determinants or pfaffians becomes impractical if large dimension matrices are involved for the real matrices beta 1 edelman has provided an efficient recurrence scheme to work out exact and explicit results for the smallest eigenvalue density which does not involve determinants or matrices very recently an analogous recurrence scheme has been obtained for the complex matrices beta 2 in the present work we extend this to beta wishart laguerre ensembles for the case when exponent alpha in the associated laguerre weight function lambda alpha e beta lambda 2 is a non negative integer while beta is positive real this also gives access to the smallest eigenvalue density of fixed trace beta wishart laguerre ensemble as well as moments for both cases moreover comparison with earlier results for the smallest eigenvalue density in terms of certain hypergeometric function of matrix argument results in an effective way of evaluating these explicitly exact evaluations for large values of n the matrix dimension and alpha also enable us to compare with tracy widom density and large deviation results of katzav and castillo we also use our result to obtain the density of the largest of the proper delay times which are eigenvalues of the wigner smith matrix and are relevant to the problem of quantum chaotic scattering

asymptotic analysis of singular values of rectangular complex matrices in the laguerre and fixed trace ensembles we present for the first time the asymptotic expressions of the one body distribution functions of singular values for the laguerre ensemble and the fixed trace ensemble in a systematic and unified way these expressions can be utilized in a wide range of research fields such as data mining time series analysis and quantum information where finite size effects play a crucial role the asymptotic analysis is performed based on our finding of systems of partial differential equations for the confluent selberg kaneko integral and the simplex type selberg kaneko integral both of which are introduced in kubotani et al 2008 phys rev lett 100 240501 and adachi et al 2009 ann phys ny 324 2278 thus we demonstrate that the systems provide us with new resources of special functions with multiple variables which can be valuable for analytic studies in various areas

singularities of electromagnetic fields in polyhedral domains in this paper we investigate the singular solutions of time harmonic maxwell equations in a domain which has edges and polyhedral corners it is now well known that in the presence of non convex edges the solution fields have no square integrable gradients in general and that the main singularities are the gradients of singular functions of the laplace operator 4 5 we show how this type of result can be derived from the classical mellin analysis and how this analysis leads to sharper results concerning the singular parts which belong to h 1 for the singular functions we exhibit simple and explicit formulas based on generalized dirichlet and neumann singularities for the laplace operator these formulas are more explicit than the results announced in our note 10

inclusion relations among separability criteria we revisit the application of different separability criteria by recourse to an exhaustive monte carlo exploration involving the pertinent state space of pure and mixed states the corresponding chain of implications of different criteria is in such a way numerically elucidated we also quantify for a bipartite system of arbitrary dimension the proportion of states that can be distilled according to a definite criterion our work can be regarded as a complement to the recent review paper by terhal b 2002 theor comput sci 287 313 some questions posed there receive an answer here

measuring dynamical randomness of quantum chaos by statistics of schmidt eigenvalues we study statistics of entanglement generated by quantum chaotic dynamics using an ensemble of the very large number 10 7 of quantum states obtained from the temporally evolving coupled kicked tops we verify that the estimated one body distribution of the squared schmidt eigenvalues for the quantum chaotic dynamics can agree surprisingly well with the analytical one for the universality class of the random matrices described by the fixed trace ensemble fte in order to quantify this agreement we introduce the l 1 norm of the difference between the one body distributions for the quantum chaos and fte and use it as an indicator of the dynamical randomness as we increase the scaled coupling constant the l 1 difference decreases when the effective planck constant is not small enough the decrease saturates which implies quantum suppression of dynamical randomness on the other hand when the effective planck constant is small enough the decrease of the l 1 difference continues until it is masked by statistical fluctuation due to finiteness of the ensemble furthermore we carry out two statistical analyses the 2 goodness of fit test and an autocorrelation analysis on the difference between the distributions to seek for dynamical remnants buried under the statistical fluctuation we observe that almost all fluctuating deviations are statistical however even for well developed quantum chaos unexpectedly we find a slight nonstatistical deviation near the largest schmidt eigenvalue in this way the statistics of schmidt eigenvalues enables us to measure dynamical randomness of quantum chaos with reference to the random matrix theory of fte

induced measures in the space of mixed quantum states we analyse several product measures in the space of mixed quantum states in particular we study measures induced by the operation of partial tracing the natural rotationally invariant measure on the set of all pure states of a n k composite system induces a unique measure in the space of n n mixed states or in the space of k k mixed states if the reduction takes place with respect to the first subsystem for k n the induced measure is equal to the hilbert schmidt measure which is shown to coincide with the measure induced by singular values of non hermitian random gaussian matrices pertaining to the ginibre ensemble we compute several averages with respect to this measure and show that the mean entanglement of n n pure states behaves as lnn 1 2

generalized entanglement as a framework for complex quantum systems purity versus delocalization measures we establish contact between the delocalization properties of pure quantum states as quantified by their number of principal components and the average generalized entanglement properties as quantified by purity measures relative to different observable sets we find that correlations between products of state vector components with respect to hamming distance play an important role in the structure of subsystem based purity measures in particular we derive general conditions under which the amount of global multipartite entanglement relates to the inverse participation ratio averaged over a maximal set of mutually unbiased product bases furthermore we provide a method for computing the expected amount of generalized entanglement with respect to an arbitrary observable set for random pure states specific examples and an explicit application to a disordered quantum spin chain are discussed

random matrix ensembles with an effective extensive external charge recent theoretical studies of chaotic scattering have encountered ensembles of random matrices in which the eigenvalue probability density function contains a one body factor with an exponent proportional to the number of eigenvalues two such ensembles have been encountered an ensemble of unitary matrices specified by the so called poisson kernel and the laguerre ensemble of positive definite matrices here we consider various properties of these ensembles jack polynomial theory is used to prove a reproducing property of the poisson kernel and a certain unimodular mapping is used to demonstrate that the variance of a linear statistic is the same as in the dyson circular ensemble for the laguerre ensemble the scaled global density is calculated exactly for all even values of the parameter while for random matrices with unitary symmetry the neighbourhood of the smallest eigenvalue is shown to be in the soft edge universality class

classical statistical mechanics approach to multipartite entanglement we characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions we search for maximally multipartite entangled states whose average purity is minimal and recast this optimization problem into a problem of statistical mechanics by introducing a cost function a fictitious temperature and a partition function by investigating the high temperature expansion we obtain the first three moments of the distribution we find that the problem exhibits frustration

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

robust and efficient generator of almost maximal multipartite entanglement quantum chaotic maps can efficiently generate pseudorandom states carrying almost maximal multipartite entanglement as characterized by the probability distribution of bipartite entanglement between all possible bipartitions of the system we show that such multipartite entanglement is robust in the sense that when realistic noise is considered distillable entanglement of bipartitions remains almost maximal up to a noise strength that drops only polynomially with the number of qubits

spectral statistics for the difference of two wishart matrices in this work we consider the weighted difference of two independent complex wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite dimension scenario using two distinct approaches the first derivation involves the use of unitary group integral while the second one relies on applying the derivative principle the latter relates the joint probability density of eigenvalues of a matrix drawn from a unitarily invariant ensemble to the joint probability density of its diagonal elements exact closed form expressions for an arbitrary order correlation function are also obtained and spectral densities are contrasted with monte carlo simulation results analytical results for moments as well as probabilities quantifying positivity aspects of the spectrum are also derived additionally we provide a large dimension asymptotic result for the spectral density using the stieltjes transform approach for algebraic random matrices finally we point out the relationship of these results with the corresponding results for difference of two random density matrices and obtain some explicit and closed form expressions for the spectral density and absolute mean

an adaptive edge finite element method for electromagnetic cloaking simulation in this paper we develop an adaptive edge finite element method based on a reliable and efficient recovery type a posteriori error estimator for time harmonic maxwell equations the asymptotically exact a posteriori error estimator is based on the superconvergence result proved for the lowest order edge element on triangular grids where most pairs of triangles sharing a common edge form approximate parallelograms the efficiency and robustness of the proposed method is demonstrated by extensive numerical experiments for electromagnetic cloaking problems with highly anisotropic permittivity and permeability

computing the entropy of a large matrix given a large real symmetric positive semidefinite matrix the goal of this paper is to show how a numerical approximation of the von neumann entropy of the matrix can be computed in an efficient way without relying on matrix diagonalization an application from quantum optics dealing with the entanglement between photons illustrates the new algorithm

convergence of an aefem for time harmonic maxwell equations with variable coefficients abstract an adaptive edge finite element method aefem for three dimensional indefinite time harmonic maxwell equations with variable coefficients is proved to be convergent and arbitrary order nedelec edge elements are considered a posteriori upper bound quasi orthogonality and the contraction of the error estimator are provided to prove the contraction of the sum of the energy error and the scaled error estimator between two consecutive adaptive loops numerical experiments are presented to support the theoretical results

area law for random graph states random pure states of multi partite quantum systems associated with arbitrary graphs are investigated each vertex of the graph represents a generic interaction between subsystems described by a random unitary matrix distributed according to the haar measure while each edge of the graph represents a bipartite maximally entangled state for any splitting of the graph into two parts we consider the corresponding partition of the quantum system and compute the average entropy of entanglement first in the special case where the partition does not cross any vertex of the graph we show that the area law is satisfied exactly in the general case we show that the entropy of entanglement obeys an area law on average this time with a correction term that depends on the topologies of the graph and of the partition the results obtained are applied to the problem of distribution of quantum entanglement in a quantum network with prescribed topology

a posteriori error estimates for maxwell equations maxwell equations are posed as variational boundary value problems in the function space h curl and are discretized by nedelec finite elements in beck et al 2000 a residual type a posteriori error estimator was proposed and analyzed under certain conditions onto the domain in the present paper we prove the reliability of that error estimator on lipschitz domains the key is to establish new error estimates for the commuting quasi interpolation operators recently introduced in j schoberl commuting quasi interpolation operators for mixed finite elements similar estimates are required for additive schwarz preconditioning to incorporate boundary conditions we establish a new extension result

the dirichlet problem for singularly perturbed quasilinear elliptic equations assuming a c solution holland 9 used probabilistic methods to verify the regular and boundary layer expansions for 1 2 in case the fj arc independent of u and z e r van harten 141 proved the correctness of formal approximations for solutions of 1 2 with h 0 i n in case the boundary values are given on an n sphere howes 11 12 has obtained existence and asymptotic estimates for solutions of various boundary value problems associated with 1 2 in case the equation h z u 0 has a smooth solution a0 which satisfies certain stability conditions and such that the characteristic curves for the equation

composed ensembles of random unitary matrices composed ensembles of random unitary matrices are defined via products of matrices each pertaining to a given canonical circular ensemble of dyson we investigate statistical properties of spectra of some composed ensembles and demonstrate their physical relevance we also discuss the methods of generating random matrices distributed according to invariant haar measure on the orthogonal and unitary group

singularly perturbed quadratically nonlinear dirichlet problems on etudie le probleme de dirichlet pour des equations elliptiques a perturbation singuliere de la forme e u a x u u u b x u u c x u dans e u on montre l existence de solutions pour e 0

hall normalization constants for the bures volumes of the n state quantum systems we report the results of certain integrations of quantum theoretic interest relying in this regard upon recently developed parametrizations of boya et al 1998 preprint quant ph 9810084 of the n n density matrices in terms of squared components of the unit n 1 sphere and the n n unitary matrices firstly we express the normalized volume elements of the bures minimal monotone metric for n 2 and 3 thereby obtaining bures prior probability distributions over the two and three state systems then as a first step in extending these results to n 3 we determine that the hall normalization constant cn for the marginal bures prior probablity distribution over the n 1 dimensional simplex of the n eigenvalues of the n n density matrices is for n 4 equal to 71 680 2 since we also find that c3 35 it follows that c4 is simply equal to 211c3 c2 itself is known to equal 2 the constant c5 is also found it too is associated with a remarkably simple decomposition involving the product of the eight consecutive prime numbers from 3 to 23 we also preliminarily investigate several cases n 5 with the use of quasi monte carlo integration we hope that the various analyses reported will prove useful in deriving a general formula which evidence suggests will involve the bernoulli numbers for the hall normalization constant for arbitrary n this would have diverse applications including quantum inference and universal quantum coding

singularly perturbed dirichlet problems with subquadratic nonlinearities on donne une theorie de couche limite et de couche interieure pour une classe de problemes de dirichlet a perturbation singuliere avec des non linearites sous quadratiques dans les termes derives

the ppt square conjecture holds generically for some classes of independent states let be a random pure state on where is a random unit vector uniformly distributed on the sphere in let be a random induced state whose distribution is and let be a random induced state following the same distribution independent of let be a random state induced by the entanglement swapping of and we show that the empirical spectrum of converges almost surely to the marcenko pastur law with parameter c 2 as and as an application we prove that the state is separable generically if are ppt entangled

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

geometries of quantum states the quantum analog of the fisher information metric of a probability simplex is searched and several riemannian metrics on the set of positive definite density matrices are studied some of them appeared in the literature in connection with cramer rao type inequalities or the generalization of the berry phase to mixed states they are shown to be stochastically monotone here all stochastically monotone riemannian metrics are characterized by means of operator monotone functions and it is proven that there exist a maximal and a minimal among them a class of metrics can be extended to pure states and a constant multiple of the fubini study metric appears in the extension

bures volume of the set of mixed quantum states we compute the volume of the n2 1 dimensional set n of density matrices of size n with respect to the bures measure and show that it is equal to that of an n2 1 dimensional hyper hemisphere of radius 1 2 for n 2 we obtain the volume of the uhlmann hemisphere s3 4 we find also the area of the boundary of the set n and obtain analogous results for the smaller set of all real density matrices an explicit formula for the bures hall normalization constants is derived for an arbitrary n

feynman graphs and the large dimensional limit of multipartite entanglement in this paper we extend the analysis of multipartite entanglement based on techniques from classical statistical mechanics to a system composed of n d level parties qudits we introduce a suitable partition function at a fictitious temperature with the average local purity of the system as hamiltonian in particular we analyze the high temperature expansion of this partition function prove the convergence of the series and study its asymptotic behavior as d we make use of a diagrammatic technique classify the graphs and study their degeneracy we are thus able to evaluate their contributions and estimate the moments of the distribution of the local purity

convergence and optimality of adaptive edge finite element methods for time harmonic maxwell equations we consider a standard adaptive edge finite element method aefem based on arbitrary order nedelec edge elements for three dimensional indefinite time harmonic maxwell equations we prove that the aefem gives a contraction for the sum of the energy error and the scaled error estimator between two consecutive adaptive loops provided the initial mesh is fine enough using the geometric decay we show that the aefem yields the best possible decay rate of the error plus oscillation in terms of the number of degrees of freedom the main technical contribution of the paper is in the establishment of a quasi orthogonality and a localized a posteriori error estimator

a nonconforming finite element method for a two dimensional curl curl and grad div problem a numerical method for a two dimensional curl curl and grad div problem is studied in this paper it is based on a discretization using weakly continuous p 1 vector fields and includes two consistency terms involving the jumps of the vector fields across element boundaries optimal convergence rates up to an arbitrary positive epsilon in both the energy norm and the l 2 norm are established on graded meshes the theoretical results are confirmed by numerical experiments

functional form for the leading correction to the distribution of the largest eigenvalue in the gue and lue the neighbourhood of the largest eigenvalue max in the gaussian unitary ensemble gue and laguerre unitary ensemble lue is referred to as the soft edge it is known that there exists a particular centring and scaling such that the distribution of max tends to a universal form with an error term bounded by 1 n2 3 we take up the problem of computing the exact functional form of the leading error term in a large n asymptotic expansion for both the gue and lue two versions of the lue are considered one with the parameter a fixed and the other with a proportional to n both settings in the lue case allow for an interpretation in terms of the distribution of a particular weighted path length in a model involving exponential variables on a rectangular grid as the grid size gets large we give operator theoretic forms of the corrections which are corollaries of knowledge of the first two terms in the large n expansion of the scaled kernel and are readily computed using a method due to bornemann we also give expressions in terms of the solutions of particular systems of coupled differential equations which provide an alternative method of computation both characterisations are well suited to a thinned generalisation of the original ensemble whereby each eigenvalue is deleted independently with probability 1 in sec v we investigate using simulation the question of whether upon an appropriate centring and scaling a wider class of complex hermitian random matrix ensembles have their leading correction to the distribution of max proportional to 1 n2 3 the neighbourhood of the largest eigenvalue max in the gaussian unitary ensemble gue and laguerre unitary ensemble lue is referred to as the soft edge it is known that there exists a particular centring and scaling such that the distribution of max tends to a universal form with an error term bounded by 1 n2 3 we take up the problem of computing the exact functional form of the leading error term in a large n asymptotic expansion for both the gue and lue two versions of the lue are considered one with the parameter a fixed and the other with a proportional to n both settings in the lue case allow for an interpretation in terms of the distribution of a particular weighted path length in a model involving exponential variables on a rectangular grid as the grid size gets large we give operator theoretic forms of the corrections which are corollaries of knowledge of the first two terms in the large n expansion of the scaled kernel and are readily computed using a method due to bornemann we also

random matrix theory analysis of cross correlations in financial markets we confirm universal behaviors such as eigenvalue distribution and spacings predicted by random matrix theory rmt for the cross correlation matrix of the daily stock prices of tokyo stock exchange from 1993 to 2001 which have been reported for new york stock exchange in previous studies it is shown that the random part of the eigenvalue distribution of the cross correlation matrix is stable even when deterministic correlations are present some deviations in the small eigenvalue statistics outside the bounds of the universality class of rmt are not completely explained with the deterministic correlations as proposed in previous studies we study the effect of randomness on deterministic correlations and find that randomness causes a repulsion between deterministic eigenvalues and the random eigenvalues this is interpreted as a reminiscent of level repulsion in rmt and explains some deviations from the previous studies observed in the market data we also study correlated groups of issues in these markets and propose a refined method to identify correlated groups based on rmt some characteristic differences between properties of tokyo stock exchange and new york stock exchange are found

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

universality of eigenvector statistics of kicked tops of different symmetries the authors show that the eigenvectors of the floquet operators of periodically kicked tops with orthogonal unitary and symplectic canonical transformations conform to the predictions of the respective circular ensembles of random matrices

the monge metric on the sphere and geometry of quantum states topological and geometrical properties of the set of mixed quantum states in the n dimensional hilbert space are analysed assuming that the corresponding classical dynamics takes place on the sphere we use the vector su 2 coherent states and the generalized husimi distributions to define the monge distance between two arbitrary density matrices the monge metric has a simple semiclassical interpretation and induces a non trivial geometry among all pure states the distance from the maximally mixed state proportional to the identity matrix admits the largest value for the coherent states while the delocalized chaotic states are close to this contrasts the geometry induced by the standard trace hilbert schmidt or bures metrics for which the distance from is the same for all pure states we discuss possible physical consequences including unitary time evolution and the process of decoherence we introduce also a simplified monge metric defined in the space of pure quantum states and more suitable for numerical computation

compact support probability distributions in random matrix theory we consider a generalization of the fixed and bounded trace ensembles introduced by bronk and rosenzweig up to an arbitrary polynomial potential in the large n limit we prove that the two are equivalent and that their eigenvalue distribution coincides with that of the canonical ensemble with measure exp ntr v m the mapping of the corresponding phase boundaries is illuminated in an explicit example in the case of a gaussian potential we are able to derive exact expressions for the one and two point correlator for finite n having finite support

purity distribution for bipartite random pure states analytic expressions for the probability density distribution of the linear entropy and the purity are derived for bipartite pure random quantum states the explicit distributions for a state belonging to a product of hilbert spaces of dimensions p and q are given for p 3 and any q 3 as well as for p q 4

continuous frequency entanglement effective finite hilbert space and entropy control we examine the quantum structure of continuum entanglement and in the context of short pulse down conversion we answer the open question of how many of the uncountably many frequency modes contribute effectively to the entanglement we derive a set of two photon mode functions that provide an exact discrete and effectively finite basis for characterizing pairwise entanglement our analysis provides a basis for entropy control in two photon pulses generated from down conversion

diagonal quantum discord quantum discord measures quantum correlation by comparing the quantum mutual information with the maximal amount of mutual information accessible to a quantum measurement this paper analyzes the properties of diagonal discord a simplified version of discord that compares quantum mutual information with the mutual information revealed by a measurement that correspond to the eigenstates of the local density matrices in contrast to the optimized discord diagonal discord is easily computable it also finds connections to thermodynamics and resource theory here we further show that for the generic case of non degenerate local density matrices diagonal discord exhibits desirable properties as a preferable discord measure we employ the theory of resource destroying maps liu z w et al 2017 phys rev lett 118 060502 to prove that diagonal discord is monotonically nonincreasing under the operation of local discord nongenerating qudit channels d 2 and provide numerical evidence that such monotonicity holds for qubit channels as well we also show that it is continuous and derive a fannes like continuity bound our results hold for a variety of simple discord measures generalized from diagonal discord