Faster than Lyapunov decays of classical Loschmidt echo (量子力学とカオス--基礎的問題からナノサイエンスまで)

Gregor Veble, Tomaž Prosen

Ignacio García-Mata, Diego A. Wisniacki

Giuliano Benenti, Giulio Casati, Gregor Veble

Gregor Veble, Tomaž Prosen

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.

Ignacio García-Mata, Diego A. Wisniacki

The Loschmidt echo (LE) 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 directly related to the anomalous—unexpected—behaviour of the LE.

Fernando Cucchietti