Decoherence and the Loschmidt echo

Details Decoherence and the Loschmidt echo Decoherence and the Loschmidt echo

2003-06-20

arxiv.org/abs/quant-ph/0306142v1

Phys. Rev. Lett. 91, 210403 (2003).

Physics

Quantum Physics

Scientific paper

10.1103/PhysRevLett.91.210403

Environment--induced decoherence causes entropy increase. It can be quantified using, e.g., the purity $\varsigma={\rm Tr}\rho^2$. 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 $\varsigma(t)$ 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 $\varsigma$ and $\bar M$ has a regime where it is dominated by the classical Lyapunov exponents

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