Eigenstate structure in many-body bosonic systems: Analysis using random matrices and $q$-Hermite polynomials

Abstract

We analyze the structure of eigenstates in many-body bosonic systems by modeling the Hamiltonian of these complex systems using Bosonic Embedded Gaussian Orthogonal Ensembles (BEGOE) defined by a mean-field plus k-body random interactions. The quantities employed are the number of principal components (NPC), the localization length (lH) and the entropy production S(t). The numerical results are compared with the analytical formulas obtained using random matrices which are based on bivariate q-Hermite polynomials for local density of states F k (E|q) and the bivariate q-Hermite polynomial form for bivariate eigenvalue density ρ biv:q (E, E k ) that are valid in the strong interaction domain. We also compare transport efficiency in many-body bosonic systems using BEGOE in absence and presence of centrosymmetry. It is seen that the centrosymmetry enhances quantum efficiency.

Applications of q-Hermite Polynomials to Subclasses of Analytic and Bi-Univalent Functions

“…The q-Hermite polynomial was first introduced by Rogers [12] (see also [13,14]) and is usually defined by means of their generating function as follows:…”