Classical diffusion and quantum level velocities: Systematic deviations from random matrix theory

We study the response of the quasienergy levels in the context of quantized chaotic systems through the level velocity variance and relate them to cla ssical diffusion coefficients using detailed semiclassical analysis. The sy stematic deviations from random matrix theory, assuming independence of eig envectors from eigenvalues, are shown to be connected to classical higher-o rder time correlations of the chaotic system. We study the standard map as a specific example, and thus the well-known oscillatory behavior of the dif fusion coefficient with respect to the parameter is reflected exactly in th e oscillations of the variance of the level velocities. We study the case o f mixed phase-space dynamics as well and note a transition in the scaling p roperties of the variance that occurs along with the classical transition t o chaos. [S1063-651X(99)11810-5].