Information functional for quantum random matrix ensembles

TL;DR

This paper introduces an information functional based on negentropy for quantum random matrix ensembles, deriving their distribution functions from the maximum entropy principle to analyze quantum chaos and integrability.

Contribution

It defines an information functional for quantum random matrix ensembles and derives their distribution functions using the maximum entropy principle, linking to quantum chaos and integrability.

Findings

Distribution functions derived from maximum entropy principle.

Measures of quantum chaos and integrability calculated.

Information functional based on negentropy introduced.

Abstract

Random matrix ensembles (RME) of quantal statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), had been applied in literature in study of following quantal statistical systems: molecular systems, nuclear systems, disordered materials, random Ising spin systems, quantal chaotic systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum integrability with respect to eigenergies of quantal systems are defined and calculated. 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.