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We study logarithmic-in- effects in the statistical description of quantum chaos. We found analytical expressions for the deviations from the universality in the weak localization correction and in the level statistics and showed that the characteristic scale for these deviations is the Ehrenfest time t₄=^-1|ln |, where is the Lyapunov exponent of the classical motion.
Aleǐner et al. (1997) studied this question.