Faster than Lyapunov decays of classical Loschmidt echo

Abstract

We show that the composition of perturbed forward and unperturbed backward hamiltonian evolution can be treated as a time-dependent hamiltonian system. For strongly chaotic systems we derive a cascade of exponential decays for the classical Loschmidt echo, starting with the leading Lyapunov exponent, followed by a sum of two largest exponents, etc.