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Anomalous power law of quantum reversibility for classically regular dynamics

Jacquod, P. ; Adagideli, Inanc ; Beenakker, C.

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The Loschmidt Echo M(t) (defined as the squared overlap of wave packets evolving with two slightly different Hamiltonians) is a measure of quantum reversibility. We investigate its behavior for classically quasi-integrable systems. A dominant regime emerges where M(t) ${\approx}$ t^{-alpha} with alpha=3d/2 depending solely on the dimension d of the system. This power law decay is faster than the result ${\approx}$ t^{-d} for the decay of classical phase space densities.

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