Applications of methods of quantum statistical mechanics to two-dimensional electron systems

TL;DR

This paper applies random matrix theory to quantum statistical models of two-dimensional electron systems, analyzing eigenfunctions and operators to connect mathematical methods with physical phenomena.

Contribution

It introduces a novel application of random matrix ensembles to quantum two-dimensional electron systems, including solutions to random eigenproblems and physical examples.

Findings

Random matrix ensembles effectively model quantum 2D electron systems.

Solutions to random eigenproblems provide insights into physical properties.

Connections established between mathematical models and physical phenomena.

Abstract

The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the systems act on these Hilbert spaces and they are treated as random matrices in generic bases of the eigenfunctions. The random eigenproblems are presented and solved. Examples of random operators are presented with connection to physical problems.