Decay of the Loschmidt echo in a time-dependent environment

FERNANDO M. CUCCHIETTI; CAIO H. LEWENKOPF; HORACIO M. PASTAWSKI

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

American Physical Society

Lugar: Ridge N.Y.; Año: 2006 vol. 74 p. 26207 - 26217

1063-651X

We study the decay rate of the Loschmidt echo or fidelity in a chaotic system under a time-dependentperturbation V
q, t with typical strength
/V. The perturbation represents the action of an uncontrolledenvironment interacting with the system, and is characterized by a correlation length 0 and a correlation time0. For small perturbation strengths or rapid fluctuating perturbations, the Loschmidt echo decays exponentiallywith a rate predicted by the Fermi ?golden rule,? 1/?=c /V2 , where cmin0 ,0 /v and v is the typicalparticle velocity. Whenever the rate 1/? is larger than the Lyapunov exponent of the system, a perturbationindependent Lyapunov decay regime arises. We also find that by speeding up the fluctuations
while keepingthe perturbation strength fixed the fidelity decay becomes slower, and hence one can protect the system againstdecoherence.DOI: 10.1103/PhysRevE.74.026207