Role of divergence of classical trajectories in quantum chaos

TL;DR

This paper investigates how classical trajectory divergence influences quantum chaos, revealing that deviations from universal behavior are governed by the Ehrenfest time, which depends logarithmically on Planck's constant.

Contribution

It provides analytical expressions linking classical divergence to quantum chaos deviations, emphasizing the role of Ehrenfest time in statistical properties.

Findings

Deviations from universality are logarithmic in 44h44 effects.

Ehrenfest time sets the scale for quantum chaos deviations.

Analytical formulas connect classical Lyapunov exponents to quantum statistical deviations.

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.