Divergence of classical trajectories and quantum chaos

This paper reviews our recent studies of the logarithmical in (h) over bar effects in the statistical description of quantum chaos. We concentrate on the deviations from the universality in the level statistics and in the quantum correction to the conductivity. For the latter, we find that the weak localization correction to the current response is delayed by the large time t(E) = lambda(-1)\ln (h) over bar, where lambda is the Lyapunov exponent of the classical motion. For the former, we find the new contribution oscillating with the period pi/t(E). (C) 1997 Elsevier Science Ltd.