Fluctuations of Quantum Statistical Two-Dimensional Systems of Electrons

TL;DR

This paper explores the application of random matrix ensembles to quantum statistical two-dimensional electron systems, analyzing quantum chaos, integrability, and information measures through maximum entropy principles.

Contribution

It introduces measures of quantum chaos and integrability for these systems and derives their distribution functions using maximum entropy principles, connecting random matrix theory with quantum statistical analysis.

Findings

Distribution functions derived from maximum entropy principle.

Measures of quantum chaos and integrability defined.

Quantum statistical information functional as negentropy.

Abstract

The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em 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 (either opposite of entropy or minus entropy). The distribution function for the random matrix ensembles is derived from the maximum entropy principle.