Quantum statistical information, entropy, Maximum Entropy Principle in various quantum random matrix ensembles

TL;DR

This paper explores quantum statistical information, entropy, and the maximum entropy principle across various quantum random matrix ensembles, providing theoretical insights and deriving distribution functions for these ensembles.

Contribution

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

Findings

Distribution functions derived from maximum entropy principle.

Quantum chaos and integrability measures calculated.

Application to various quantum systems demonstrated.

Abstract

Random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), found applications in literature in study of following quantum statistical systems: molecular systems, nuclear systems, disordered materials, random Ising spin systems, quantum chaotic 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). Entropy is neginformation (opposite of information or minus information. The distribution functions for the random matrix ensembles are derived from the maximum entropy principle.