Level curvature distribution in a model of two uncoupled chaotic subsystems

We study distributions of eigenvalue curvatures for a block-diagonal 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 power-law tail behavior. This observation may help to clarify some qualitative features of the curvature distributions observed experimentally in acoustic resonances of quartz blocks.