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.

10 pages, no figures

References in corpus (9)

• Semiclassical Foundation of Universality in Quantum Chaos
• Periodic-Orbit Theory of Universality in Quantum Chaos
• Periodic-Orbit Theory of Level Correlations
• Spectral Statistics Beyond Random Matrix Theory
• Periodic-Orbit Theory of Anderson Localization on Graphs
• Resummation and the semiclassical theory of spectral statistics
• Localization from sigma-model geodesics
• Anderson localization from the replica formalism
• Anderson localization from classical trajectories