Spectral form factor of hyperbolic systems: leading off-diagonal approximation
Abstract
The spectral fluctuations of a quantum Hamiltonian system with time-reversal symmetry are studied in the semiclassical limit by using periodic-orbit theory. It is found that, if long periodic orbits are hyperbolic and uniformly distributed in phase space, the spectral form factor agrees with the GOE prediction of random-matrix theory up to second order included in the time measured in units of the Heisenberg time (leading off-diagonal approximation). Our approach is based on the mechanism of periodic-orbit correlations discovered recently by Sieber and Richter (Phys. Scr. T 90, 128, 2001). By reformulating the theory of these authors in phase space, their result on the free motion on a Riemann surface with constant negative curvature is extended to general Hamiltonian hyperbolic systems with two degrees of freedom.
Cite
@article{arxiv.nlin/0303051,
title = {Spectral form factor of hyperbolic systems: leading off-diagonal approximation},
author = {Dominique Spehner},
journal= {arXiv preprint arXiv:nlin/0303051},
year = {2009}
}
Comments
22 pages, 5 figures, to be published in J. Phys. A: Math. Gen. Main changes: sections 4,5,6 and appendix A