Various applications of the random matrix ensembles to the quantum chaotic systems

TL;DR

This paper explores how random matrix ensembles can be applied to quantum chaotic systems, analyzing eigenfunctions in various Hilbert spaces and solving related eigenproblems with physical applications.

Contribution

It introduces a framework for applying random matrix theory to quantum chaos, including solutions to random eigenproblems and connections to physical models.

Findings

Random matrix ensembles effectively model quantum chaotic systems.

Eigenproblems in different Hilbert spaces are solved analytically.

Applications demonstrate relevance to physical quantum systems.

Abstract

The random matrix ensembles are applied to the quantum chaotic systems. 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.