Semiclassical spectral correlator in quasi one-dimensional systems

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.