Ehrenfest times for classically chaotic systems

Details Ehrenfest times for classically chaotic systems Ehrenfest times for classically chaotic systems

2001-11-19

arxiv.org/abs/nlin/0111042v1

Phys.Rev.E 65, 035208(R) (2002)

Nonlinear Sciences

Chaotic Dynamics

4 pages

Scientific paper

10.1103/PhysRevE.65.035208

We describe the quantum mechanical spreading of a Gaussian wave packet by means of the semiclassical WKB approximation of Berry and Balazs. 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 $\tau=\fr{7}{6}\lambda^{-1}\ln(A/\hbar)$, with $\lambda$ the Lyapunov exponent and $A$ a typical classical action.

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