Eur. Phys. J. B 34, 305-319 (2003)
https://doi.org/10.1140/epjb/e2003-00226-0

Classical basis for quantum spectral fluctuations in hyperbolic systems

Fachbereich Physik, Universität Duisburg-Essen, 45117 Essen, Germany

Corresponding author: ^a sebastian.mueller@uni-essen.de

Received: 16 March 2003
Revised: 10 June 2003
Published online: 11 August 2003

Abstract

We reason in support of the universality of quantum spectral fluctuations in chaotic systems, starting from the pioneering work of Sieber and Richter who expressed the spectral form factor in terms of pairs of periodic orbits with self-crossings and avoided crossings. Dropping the restriction to uniformly hyperbolic dynamics, we show that for general hyperbolic two-freedom systems with time-reversal invariance the spectral form factor is faithful to random-matrix theory, up to quadratic order in time. We relate the action difference within the contributing pairs of orbits to properties of stable and unstable manifolds. In studying the effects of conjugate points, we show that almost self-retracing orbit loops do not contribute to the form factor. Our findings are substantiated by numerical evidence for the concrete example of two billiard systems.