Semiclassical periodic-orbit theory for quantum spectra

TL;DR

This paper explains how Gutzwiller's trace formula connects quantum energy levels in chaotic systems to classical periodic orbits, using a path integral derivation and linking to random matrix theory.

Contribution

It provides a didactic derivation of the trace formula from the Feynman path integral and discusses its application to quantum chaos and spectral statistics.

Findings

Derivation of the trace formula from path integrals

Explanation of universal spectral features via random matrix theory

Overview of related research in quantum chaos

Abstract

Gutzwiller's trace formula has a central place in quantum chaos because it provides semiclassical approximations for quantum energy levels in classically chaotic systems by linking them to classical periodic orbits. In this didactic article, we discuss a derivation of the trace formula starting from the Feynman path integral. We then describe how the trace formula is used to explain universal features in the distribution of the quantum energy levels that are described by random matrix theory, and we give an overview of related work.