Decoherence and the Loschmidt Echo

F. M. Cucchietti, D. A. R. Dalvit, J. P. Paz, and W. H. Zurek
Phys. Rev. Lett. 91, 210403 – Published 21 November 2003

Abstract

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 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 M¯ has a regime where it is dominated by the Lyapunov exponents.

  • Figure
  • Received 20 June 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.210403

©2003 American Physical Society

Authors & Affiliations

F. M. Cucchietti

  • Theoretical Division, MS B213, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA and FaMAF, Universidad Nacional de Córdoba, Haya de la Torre s/n, Córdoba 5000 Argentina

D. A. R. Dalvit, J. P. Paz, and W. H. Zurek

  • Theoretical Division, MS B213, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

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Vol. 91, Iss. 21 — 21 November 2003

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