Quantum information and entropy in random matrix ensembles

TL;DR

This paper explores the application of Gaussian and Ginibre random matrix ensembles to quantum systems, defining measures of quantum chaos and integrability, and deriving distribution functions from the maximum entropy principle.

Contribution

It introduces a framework linking random matrix ensembles to quantum chaos measures and derives related distribution functions using maximum entropy principles.

Findings

Distribution functions derived from maximum entropy.

Measures of quantum chaos and integrability defined.

Application to nuclear, molecular, and electron systems.

Abstract

The random matrix ensembles (RME), especially Gaussian random matrix ensembles GRME and Ginibre random matrix ensembles, are applied to following quantum systems: nuclear systems, molecular systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum integrability with respect to eigenergies of quantum systems are defined and calculated. The distribution function for the random matrix ensembles is derived from the maximum entropy principle. Information functional is defined as negentropy (opposite of entropy or minus entropy).