Universal spectral correlations from the ballistic sigma model

TL;DR

This paper uses the ballistic sigma-model to explain universal spectral correlations in quantum chaotic systems, linking semiclassical diagrams with field theory and random matrix universality.

Contribution

It demonstrates how the ballistic sigma-model captures universal spectral correlations and connects semiclassical interference diagrams with field theoretical descriptions.

Findings

The sigma-model reproduces universal spectral correlations.

Semiclassical diagrams correspond to field theory structures.

Universality explained via field theory perspective.

Abstract

We consider the semiclassical ballistic sigma-model as an effective theory describing the quantum mechanics of classically chaotic systems. Specifically, we elaborate on close analogies to the recently developed semiclassical theory of quantum interference in chaotic systems and show how semiclassical 'diagrams' involving near action degenerate sets of periodic orbits emerge in the field theoretical description. We further discuss how the universality phenomenon (i.e. the fact that individual chaotic systems behave according to the prescriptions of random matrix theory) can be understood from the perspective of the field theory.