Spectral form factor of hyperbolic systems: leading off-diagonal approximation

Details Spectral form factor of hyperbolic systems: leading off-diagonal approximation Spectral form factor of hyperbolic systems: leading off-diagonal approximation

2003-03-22

arxiv.org/abs/nlin/0303051v2

Nonlinear Sciences

Chaotic Dynamics

22 pages, 5 figures, to be published in J. Phys. A: Math. Gen. Main changes: sections 4,5,6 and appendix A

Scientific paper

10.1088/0305-4470/36/26/304

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.

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