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

2021/11/16 by Priyanka Rao, Rao, Priyanka, Manan Vyas +3
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Physics (quant-ph) #Spectroscopy and Quantum Chemical Studies #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2111.08820

openalex publication_date 2021/11/16 · openalex created_date 2021/11/22 · openalex updated_date 2026/07/28

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 (l_H) 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.

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