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

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.