entanglement for multipartite systems of indistinguishable particles we analyze the concept of entanglement for a multipartite system with bosonic and fermionic constituents and its generalization to systems with arbitrary parastatistics we use the representation theory of symmetry groups to formulate a unified approach to this problem in terms of simple tensors with an appropriate symmetry for an arbitrary parastatistics we define the s rank generalizing the notion of the schmidt rank the s rank defined for all types of tensors serves for distinguishing entanglement of pure states in addition for bose and fermi statistics we construct an analog of the jamiolkowski isomorphism

segre maps and entanglement for multipartite systems of indistinguishable particles we elaborate the concept of entanglement for a multipartite system with bosonic and fermionic constituents and its generalization to systems with arbitrary parastatistics the entanglement is characterized in terms of generalized segre maps thus supplementing an algebraic approach to the problem from a more geometric point of view

spectral correlation functions of the sum of two independent complex wishart matrices with unequal covariances we compute the spectral statistics of the sum h of two independent complex wishart matrices each of which is correlated with a different covariance matrix random matrix theory enjoys many applications including sums and products of random matrices typically ensembles with correlations among the matrix elements are much more difficult to solve using a combination of supersymmetry superbosonisation and bi orthogonal functions we are able to determine all spectral k point density correlation functions of h for arbitrary matrix size n in the half degenerate case when one of the covariance matrices is proportional to the identity the recent results by kumar for the joint eigenvalue distribution of h serve as our starting point in this case the ensemble has a bi orthogonal structure and we explicitly determine its kernel providing its exact solution for finite n the kernel follows from computing the expectation value of a single characteristic polynomial in the general non degenerate case the generating function for the k point resolvent is determined from a supersymmetric evaluation of the expectation value of k ratios of characteristic polynomials numerical simulations illustrate our findings for the spectral density at finite n and we also give indications how to do the asymptotic large n analysis

saturation of number variance in embedded random matrix ensembles we study fluctuation properties of embedded random matrix ensembles of noninteracting particles for ensemble of two noninteracting particle systems we find that unlike the spectra of classical random matrices correlation functions are nonstationary in the locally stationary region of spectra we study the number variance and the spacing distributions the spacing distributions follow the poisson statistics which is a key behavior of uncorrelated spectra the number variance varies linearly as in the poisson case for short correlation lengths but a kind of regularization occurs for large correlation lengths and the number variance approaches saturation values these results are known in the study of integrable systems but are being demonstrated for the first time in random matrix theory we conjecture that the interacting particle cases which exhibit the characteristics of classical random matrices for short correlation lengths will also show saturation effects for large correlation lengths

application of approximate matrix factorization to high order linearly implicit runge kutta methods linearly implicit runge kutta methods with approximate matrix factorization can solve efficiently large systems of differential equations that have a stiff linear part e g reaction diffusion systems however the use of approximate factorization usually leads to loss of accuracy which makes it attractive only for low order time integration schemes this paper discusses the application of approximate matrix factorization with high order methods an inexpensive correction procedure applied to each stage allows to retain the high order of the underlying linearly implicit runge kutta scheme the accuracy and stability of the methods are studied numerical experiments on reaction diffusion type problems of different sizes and with different degrees of stiffness illustrate the efficiency of the proposed approach

a stabilized galerkin method for a third order evolutionary problem the periodic initial value problem for the partial differential equa tion ut uxxx s u x 2 u xx euxx outx 0 e o 0 arises in fluidization models the numerical integration of the problem is a difficult task in that many reasonable finite difference and finite element methods give rise to unstable discretizations we show how to modify the standard galerkin technique in order to stabilize it optimal order error estimates are derived and the results of numerical experiments are presented the stabilization technique suggested in the paper can be interpreted as rewriting the problem in sobolev form and would also be useful for other equations involving terms of the form u sulx

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

linearly implicit methods for nonlinear parabolic equations we construct and analyze combinations of rational implicit and explicit multistep methods for nonlinear parabolic equations the resulting schemes are linearly implicit and include as particular cases implicit explicit multistep schemes as well as the combination of implicit runge kutta schemes and extrapolation an optimal condition for the stability constant is derived under which the schemes are locally stable we establish optimal order error estimates

nonlinear periodic waves in a two phase flow model a partial differential equation is presented as a model for a two phase flow a nonlinear analysis is done using perturbation theory formally yielding periodic traveling wave solutions in light of previous work these solutions under certain restrictions are interpreted as linearly unstable waves which have equilibrated

quantum mechanics as an infinite dimensional hamiltonian system with uncertainty structure part ii making reference to the formalism developed in part i to formulate schrodinger quantum mechanics the properties of kahlerian functions in general almost kahlerian manifolds are studied

explicit multistep method for the numerical solution of rlw equation abstract in this paper we present explicit multistep method for regularized long wave rlw equation the discretization in space is based on the galerkin method using linear space finite elements and for the time discretization the explicit multistep method is used propagation of solitary waves and interaction of two solitary waves are simulated using the proposed method to confirm the theoretical results

geometry of quantum systems density states and entanglement various problems concerning the geometry of the space of hermitian operators on a hilbert space are addressed in particular we study the canonical poisson and riemann jordan tensors and the corresponding foliations into k hler submanifolds it is also shown that the space of density states on an n dimensional hilbert space is naturally a manifold stratified space with the stratification induced by the the rank of the state thus the space of rank k states k 1 n is a smooth manifold of real dimension 2nk k2 1 and this stratification is maximal in the sense that every smooth curve in viewed as a subset of the dual to the lie algebra of the unitary group at every point must be tangent to the strata it crosses for a quantum composite system i e for a hilbert space decomposition an abstract criterion of entanglement is proved

a complete set of covariants of the four qubit system we obtain a complete and minimal set of 170 generators for the algebra of sl 2 4 covariants of a binary quadrilinear form interpreted in terms of a four qubit system this describes in particular the algebraic varieties formed by the orbits of local filtering operations in its projective hilbert space also this sheds some light on the local unitary invariants and provides all the possible building blocks for the construction of entanglement measures for such a system

a numerical study of nonlinear waves arising in a one dimensional model of a fluidized bed abstract a third order nonlinear problem which under certain circumstances approximates the flow in a 1 dimensional fluidized bed is solved numerically a petrov galerkin finite element method with piecewise linear trial functions and cubic spline test functions is used for the discretization in space if product approximation is applied to the numerical representation of the nonlinear terms then the scheme is fourth order in space in the finite difference sense second order backward differentiation is used for the time stepping it is found that while certain values of the time step may produce stable results a reduction in the time step introduces instability this is confirmed by a von neumann stability analysis of a simplified case and is also shown to be reasonable in view of the continuous problem which contains stable and unstable modes a set of numerical experiments is presented

exact evaluations of some meijer g functions and probability of all eigenvalues real for the product of two gaussian matrices we provide a proof to a recent conjecture by forrester 2014 j phys a math theor 47 065202 regarding the algebraic and arithmetic structure of meijer g functions which appear in the expression for probability of all eigenvalues real for the product of two real gaussian matrices in the process we come across several interesting identities involving meijer g functions

implicit explicit multistep methods for quasilinear parabolic equations efficient combinations of implicit and explicit multistep methods for nonlinear parabolic equations were recently studied in 1 in this note we present a refined analysis to allow more general nonlinearities the abstract theory is applied to a quasilinear parabolic equation

random matrix ensembles involving gaussian wigner and wishart matrices and biorthogonal structure we consider four nontrivial ensembles involving gaussian wigner and wishart matrices these are relevant to problems ranging from multiantenna communication to random supergravity we derive the matrix probability density as well as the eigenvalue densities for these ensembles in all cases the joint eigenvalue density exhibits a biorthogonal structure a determinantal representation based on a generalization of andreief s integration formula is used to compactly express the r point correlation function of eigenvalues this representation circumvents the complications encountered in the usual approaches and the answer is obtained immediately by examining the joint density of eigenvalues we validate our analytical results using monte carlo simulations

implicit explicit multistep finite element methods for nonlinear parabolic problems we approximate the solution of initial boundary value problems for nonlinear parabolic equations in space we discretize by finite element methods the discretization in time is based on linear multistep schemes one part of the equation is discretized implicitly and the other explicitly the resulting schemes are stable consistent and very efficient since their implementation requires at each time step the solution of a linear system with the same matrix for all time levels we derive optimal order error estimates the abstract results are applied to the kuramoto sivashinsky and the cahn hilliard equations in one dimension as well as to a class of reaction diffusion equations in r v v 2 3

linearly implicit methods for nonlinear evolution equations we construct and analyze combinations of rational implicit and explicit multistep methods for nonlinear evolution equations and extend thus recent results concerning the discretization of nonlinear parabolic equations the resulting schemes are linearly implicit and include as particular cases implicit explicit multistep schemes as well as the combination of implicit runge kutta schemes and extrapolation we establish optimal order error estimates the abstract results are applied to a third order evolution equation arising in the modelling of flow in a fluidized bed we discretize this equation in space by a petrov galerkin method the resulting fully discrete schemes require solving some linear systems to advance in time with coefficient matrices the same for all time levels