Level curvature distribution in a model of two uncoupled chaotic subsystems
Abstract
We study distributions of eigenvalue curvatures for a blockdiagonal random matrix perturbed by a full random matrix. The most natural physical realization of this model is a quantum chaotic system with some inherent symmetry, such that its energy levels form two independent subsequences, subject to a generic perturbation which does not respect the symmetry. We describe analytically a crossover in the form of a curvature distribution with a tunable parameter, namely, the ratio of intersubsystem/intrasubsystem coupling strengths. We find that the peak value of the curvature distribution is much more sensitive to the changes in this parameter than the powerlaw tail behavior. This observation may help to clarify some qualitative features of the curvature distributions observed experimentally in acoustic resonances of quartz blocks.
 Publication:

Physical Review E
 Pub Date:
 October 2003
 DOI:
 10.1103/PhysRevE.68.046124
 arXiv:
 arXiv:condmat/0303355
 Bibcode:
 2003PhRvE..68d6124E
 Keywords:

 02.50.r;
 03.65.w;
 05.45.Pq;
 Probability theory stochastic processes and statistics;
 Quantum mechanics;
 Numerical simulations of chaotic systems;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 22 pages, 2 new eps figures, uses revtex4. To appear in Phys. Rev. E