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 inter/intra subsystem 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 behaviour. This observation may help to clarify some qualitative features of the curvature distributions observed experimentally in acoustic resonances of quartz blocks.