Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime

Details Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime

2010-09-03

arxiv.org/abs/1009.0725v2

J. Phys. A: Math. Theor. 44 315101 (2011)

Nonlinear Sciences

Chaotic Dynamics

16 pages, 6 figures. IOP format. Substantial changes with respect to v1. Accepted in J. Phys. A: Math. Theo

Scientific paper

10.1088/1751-8113/44/31/315101

The Loschmidt echo is a measure of the stability and reversibility of quantum evolution under perturbations of the Hamiltonian. One of the expected and most relevant characteristics of this quantity for chaotic systems is an exponential decay with a perturbation independent decay rate given by the classical Lyapunov exponent. However, a non-uniform decay -- instead of the Lyapunov regime -- has been reported in several systems. In this work we find an analytical semiclassical expression for the averaged fidelity amplitude that can be related directly to the anomalous -- unexpected-- behaviour of the LE.

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