Quantum fluctuations of systems of interacting electrons in two spatial dimensions

TL;DR

This paper explores quantum fluctuations in two-dimensional electron systems using random matrix ensembles, defining measures of quantum chaos and integrability, and deriving distribution functions from maximum entropy principles.

Contribution

It applies random matrix theory to analyze quantum fluctuations and chaos in 2D electron systems, introducing new measures and deriving distribution functions from maximum entropy.

Findings

Measures of quantum chaos and integrability are defined and calculated.

Distribution functions for ensembles are derived from maximum entropy.

Quantum statistical information is characterized by negentropy.

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.