Semiclassical universality of parametric spectral correlations

Details Semiclassical universality of parametric spectral correlations Semiclassical universality of parametric spectral correlations

2006-08-07

arxiv.org/abs/nlin/0608008v1

J. Phys. A 40 (2007) 935

Nonlinear Sciences

Chaotic Dynamics

18 pages, no figures

Scientific paper

10.1088/1751-8113/40/5/005

We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor $K(\tau,x)$ which depends on a scaled parameter difference $x$. For parameter variations that do not change the symmetry of the system we show by using semiclassical periodic orbit expansions that the small $\tau$ expansion of the form factor agrees with Random Matrix Theory for systems with and without time reversal symmetry.

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