Decoherence and the loschmidt echo

Abstract

Decoherence causes entropy increase that can be quantified using, e.g., the purity [Formula presented]. When the Hamiltonian of a quantum system is perturbed, its sensitivity to such perturbation can be measured by the Loschmidt echo [Formula presented]. It is given by the squared overlap between the perturbed and unperturbed state. We describe the relation between the temporal behavior of [Formula presented] and the average [Formula presented]. In this way we show that the decay of the Loschmidt echo can be analyzed using tools developed in the study of decoherence. In particular, for systems with a classically chaotic Hamiltonian the decay of [Formula presented] and [Formula presented] has a regime where it is dominated by the Lyapunov exponents. © 2003 The American Physical Society.