Faster than Lyapunov decays of the classical Loschmidt echo |
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Authors: | Veble Gregor Prosen Tomaz |
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Affiliation: | Physics Department, FMF, University of Ljubljana, Ljubljana, Slovenia. |
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Abstract: | We show that in the classical interaction picture the echo dynamics, namely, the composition of perturbed forward and unperturbed backward Hamiltonian evolution, can be treated as a time-dependent Hamiltonian system. For strongly chaotic (Anosov) systems we derive a cascade of exponential decays for the classical Loschmidt echo, starting with the leading Lyapunov exponent, followed by a sum of the two largest exponents, etc. In the loxodromic case a decay starts with the rate given as twice the largest Lyapunov exponent. For a class of perturbations of symplectic maps the echo dynamics exhibits a drift resulting in a superexponential decay of the Loschmidt echo. |
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