Maximum entropy principle and quantum statistical information functional in random matrix ensembles

TL;DR

This paper applies the maximum entropy principle to derive distribution functions for quantum statistical random matrix ensembles, analyzing quantum chaos and integrability in various physical systems.

Contribution

It introduces a quantum statistical information functional based on negentropy and derives distribution functions from the maximum entropy principle for different RME.

Findings

Distribution functions derived from maximum entropy principle.

Measures of quantum chaos and integrability defined and calculated.

Application to nuclear, molecular, and electron systems.

Abstract

The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical 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. Quantum statistical information functional is defined as negentropy (opposite of entropy or minus entropy). The distribution function for the random matrix ensembles is derived from the maximum entropy principle.