Loschmidt Echo

ARSENI GOUSSEV; RODOLFO A. JALABERT; HORACIO M. PASTAWSKI; D. A. WISNIACKI

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Lugar: Paris; Año: 2012

1941-6016

Loschmidt EchoArseni Goussev1, Rodolfo A. Jalabert2, Horacio M. Pastawski3, and Diego Wisniacki41Max Planck Institute for the Physics of Complex Systems, N¨othnitzer Straße 38, D-01187 Dresden, Germany2Institut de Physique et Chimie des Mat´eriaux de Strasbourg, UMR 7504, CNRS-UdS,23 rue du Loess, BP 43, 67034 Strasbourg Cedex 2, France3Instituto de F´ısica Enrique Gaviola (CONICET-UNC) and Facultad de Matem´atica Astronom´ıa y F´ısica,Universidad Nacional de C´ordoba, Ciudad Universitaria, C´ordoba 5000, Argentina4Departamento de F´ısica, FCEyN, UBA, Ciudad Universitaria, Buenos Aires C1428EGA Argentina June 28, 2012The Loschmidt echo is a measure of the revival occurring when an imperfect time-reversal procedure is applied to a complex quantum system. It allows to quantify the sensitivity of quantum evolution to perturbations.An initial quantum state | 0i evolves during a time t under a Hamiltonian H1 reaching the state | ti. Aiming to recover the initial state | 0i a new Hamiltonian −H2 is applied between t and 2t. Perfect recover of | 0i would be achieved by choosing H2 to be equal to H1. This is not possible in realistic setups, and there always appears a difference between H2 and H1, leading to a non-perfect recovery of the initial state. The forward evolution between t and 2t under the Hamiltonian −H2 is equivalent to a backward evolution from t to 0 under H2, which embodies the notion of time-reversal. The Loschmidt echo studies are focused on the cases wherethe dynamics induced by the Hamiltonians H1 and H2 are non-trivial, or sufficiently complex (like that of a classically chaotic one-particle system or a many-body system).