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Loschmidt-echo decay from local boundary perturbations.

Arseni Goussev1, Klaus Richter

  • 1Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
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We studied how boundary changes affect quantum wave packets in chaotic billiards. The Loschmidt echo (LE) decays exponentially, matching classical escape rates, suggesting experimental feasibility.

Area of Science:

  • Quantum chaos
  • Statistical mechanics
  • Wave packet dynamics

Background:

  • Chaotic billiards exhibit complex dynamics.
  • Wave packet evolution is sensitive to system parameters.
  • The Loschmidt echo quantifies sensitivity to perturbations.

Purpose of the Study:

  • Investigate semiclassical wave packet sensitivity to boundary perturbations in 2D chaotic billiards.
  • Analyze the time decay of the Loschmidt echo (LE).
  • Relate LE decay to classical dynamics.

Main Methods:

  • Analytical and numerical approaches.
  • Calculation of the time evolution of semiclassical wave packets.
  • Computation of the Loschmidt echo (LE).

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Main Results:

  • The Loschmidt echo (LE) exhibits exponential time decay.
  • The LE decay rate equals the classical escape rate from an equivalent open billiard.
  • Identified the perturbation-affected boundary region as key.

Conclusions:

  • Local boundary perturbations significantly impact wave packet evolution.
  • LE decay provides a direct measure of this sensitivity.
  • Proposed a framework for experimental verification of LE decay dynamics.