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 $\tau =\frac{7}{6}{\lambda }^{-1}\ln (A/ħ),$ with $\lambda$ the Lyapunov exponent and A a typical classical action.

• Received 26 November 2001

DOI:https://doi.org/10.1103/PhysRevE.65.035208