Role of divergence of classical trajectories in quantum chaos

Abstract

We study logarithmical in $\hbar$ effects in the statistical description of quantum chaos. We found analytical expressions for the deviations from the universality in the weak localization corrections and the level statistics and showed that the characteristic scale for these deviations is the Ehrenfest time, $t_E= \lambda^{-1}|\ln\hbar|$, where $\lambda$ is the Lyapunov exponent of the classical motion.