Quantum Chaotic Systems and Random Matrix Theory

TL;DR

This paper reviews the application of random matrix theory to quantum chaos, highlighting its historical development and diverse modern applications across physics, biology, and communication systems.

Contribution

It provides an accessible introduction to RMT and its relevance to quantum chaos, emphasizing its interdisciplinary applications and historical context.

Findings

Random matrix theory effectively models spectra in quantum chaotic systems.

RMT has broad applications in physics, biology, and communication.

The review offers a comprehensive overview suitable for graduate students.

Abstract

This article is an introductory review of random matrix theory (RMT) and its applications, with special focus on quantum chaos. Random matrices were first used by Wigner to understand the spectra of complex nuclei from a statistical perspective. Subsequently there have been novel applications to diverse areas, e.g., atomic and molecular physics, mesoscopic and nanoscopic systems, microwave cavities, econophysics, biological sciences, communication theory. This article is designed to be accessible at the graduate and post-doctoral level.