Semiclassical spectral correlator in quasi one-dimensional systems

TL;DR

This paper analyzes the spectral statistics of chaotic quasi-one-dimensional systems using semiclassical methods, deriving both oscillatory and non-oscillatory contributions to the spectral correlation function, and confirming agreement with disordered systems theory.

Contribution

It introduces a semiclassical approximation that captures both oscillatory and non-oscillatory spectral correlations in quasi-1D chaotic systems, extending previous work.

Findings

Derived spectral correlation functions including oscillatory terms

Confirmed agreement with disordered systems theory

Applicable to systems with and without time-reversal symmetry

Abstract

We investigate the spectral statistics of chaotic quasi one dimensional systems such as long wires. To do so we represent the spectral correlation function $R(\epsilon)$ through derivatives of a generating function and semiclassically approximate the latter in terms of periodic orbits. In contrast to previous work we obtain both non-oscillatory and oscillatory contributions to the correlation function. Both types of contributions are evaluated to leading order in $1/\epsilon$ for systems with and without time-reversal invariance. Our results agree with expressions from the theory of disordered systems.