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Decoherence and the Loschmidt echo

F. M. Cucchietti·D. A. R. Dalvit·J. P. Paz·W. H. Zurek
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Abstract

Environment--induced decoherence causes entropy increase. It can be quantified using, e.g., the purity $ς={\rm Tr}ρ^2$. When the Hamiltonian of a quantum system is perturbed, its sensitivity to such perturbation can be measured by the Loschmidt echo $\bar M(t)$. It is given by the average squared overlap between the perturbed and unperturbed state. We describe the relation between the temporal behavior of $ς(t)$ and $\bar M(t)$. 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 $\bar M$ has a regime where it is dominated by the classical Lyapunov exponents

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F. M. Cucchietti, D. A. R. Dalvit, J. P. Paz, W. H. Zurek. 2003-06-20. Decoherence and the Loschmidt echo. https://doi.org/10.1103/physrevlett.91.210403

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