Ehrenfest times for classically chaotic systems.

We describe the quantum-mechanical spreading of a Gaussian wave packet by means of the semiclassical WKB approximation of Berry and Balazs [J. Phys. A 2, 625 (1979)]. We find that the time scale tau on which this approximation breaks down in a chaotic system is larger than the Ehrenfest times considered previously. In one dimension tau=7/6 lambda(-1)ln(A/Plancks over 2 pi), with lambda the Lyapunov exponent and A a typical classical action.