Short time decay of the Loschmidt echo

Details Short time decay of the Loschmidt echo Short time decay of the Loschmidt echo

2002-08-28

arxiv.org/abs/nlin/0208044v2

Phys. Rev. E 67, 016205 (2003)

Nonlinear Sciences

Chaotic Dynamics

7 pages, 7 figures, published version

Scientific paper

10.1103/PhysRevE.67.016205

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 2-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.

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