Loschmidt echo and the local density of states

Natalia Ares and Diego A. Wisniacki
Phys. Rev. E 80, 046216 – Published 26 October 2009

Abstract

Loschmidt echo (LE) is a measure of reversibility and sensitivity to perturbations of quantum evolutions. For weak perturbations its decay rate is given by the width of the local density of states (LDOS). When the perturbation is strong enough, it has been shown in chaotic systems that its decay is dictated by the classical Lyapunov exponent. However, several recent studies have shown an unexpected nonuniform decay rate as a function of the perturbation strength instead of that Lyapunov decay. Here we study the systematic behavior of this regime in perturbed cat maps. We show that some perturbations produce coherent oscillations in the width of LDOS that imprint clear signals of the perturbation in LE decay. We also show that if the perturbation acts in a small region of phase space (local perturbation) the effect is magnified and the decay is given by the width of the LDOS.

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  • Received 7 August 2009

DOI:https://doi.org/10.1103/PhysRevE.80.046216

©2009 American Physical Society

Authors & Affiliations

Natalia Ares and Diego A. Wisniacki*

  • Departamento de Física “J. J. Giambiagi,” FCEN, UBA, Pabellón 1, Ciudad Universitaria, C1428EGA Buenos Aires, Argentina

  • *wisniacki@df.uba.ar

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Vol. 80, Iss. 4 — October 2009

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