Decoherence and the Loschmidt Echo

Decoherence causes entropy increase that can be quantified using, e.g., the purity ς=Trρ². When the Hamiltonian of a quantum system is perturbed, its sensitivity to such perturbation can be measured by the Loschmidt echo M(t). It is given by the squared overlap between the perturbed and unperturbed state. We describe the relation between the temporal behavior of ς(t) and the average M̅ (t). 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 ς and M̅ has a regime where it is dominated by the Lyapunov exponents.