Abstract
The Loschmidt echo measures the sensitivity to perturbations of quantum evolutions. We study its short-time decay in classically chaotic systems. Using perturbation theory and throwing out all correlation imposed by the initial state and the perturbation, we show that the characteristic time of this regime is well described by the inverse of the width of the local density of states. This result is illustrated and discussed in a numerical study in a two-dimensional chaotic billiard system perturbed by various contour deformations and using different types of initial conditions. Moreover, the influence to the short-time decay of sub-Planck structures developed by time evolution is also investigated.
Highlights
Quantum irreversibility studies have become a very active research topic due to a direct connection with quantum computers and mesoscopics physics1,2͔
Using perturbation theory and throwing out all correlation imposed by the initial state and the perturbation, we show that the characteristic time of this regime is well described by the inverse of the width of the local density of states
Disregarding system specific features and the correlations imposed by the characteristics of initial state, we show via perturbation theory that Ϫ1 is given by the width ⌫ of the LDOS
Summary
Quantum irreversibility studies have become a very active research topic due to a direct connection with quantum computers and mesoscopics physics1,2͔. For a very short time, it is straightforward to show that the LE has a parabolic behavior M (t)ϭ1Ϫ␦x2(⌬HЈ)2t2, with (⌬HЈ) ϭ͉͗HЈ2͉͘Ϫ͉HЈ͘2͔ This decay is better resembled by the Gaussian function expϪ(t/)2͔, with characteristic time ϭ1/(⌬HЈ␦x). Nevetheless, other perturbations do not act in that way and this fact produces a slower decay with Ϫ1Ͻ⌫ In this context, we discuss the influence of an initial time evolution of the wave packet and the corresponding developed structures in phase space in the short-time decay of the LE. If the perturbation produces a decay with Ϫ1ϭ⌫ the developed structures in phase space do not influence the short-time decay. The initial conditions are the evolved Gaussian wave packets in order to study the prediction of Ref.
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