Curvature distribution of chaotic quantum systems: Universality and nonuniversality

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Abstract
The parametric motion of eigenvalues of two chaotic quantum systems, a stadium billiard and a kicked rotator, is studied to investigate the curvature distribution introduced by Gaspard et al. [Phys. Rev. A 42, 4015 (1990)]. By using an average of a statistical quantity over the parameter values along the motion, we obtain the curvature distribution and confirm the predicted universality of its tail behavior. We also show a nonuniversal characteristic at small curvatures, which is attributed to the existence of solitonlike structures.