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Decoherence and the Loschmidt echo.

F M Cucchietti1, D A R Dalvit, J P Paz

  • 1Theoretical Division, MS B213, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

Physical Review Letters
|December 20, 2003
PubMed
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Quantum decoherence increases entropy, measured by purity. The Loschmidt echo quantifies system sensitivity to perturbations, revealing connections between decoherence and echo decay, especially in chaotic systems.

Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Chaos theory

Background:

  • Decoherence leads to entropy increase, quantifiable via purity (sigma).
  • System sensitivity to Hamiltonian perturbations is measured by the Loschmidt echo (M(t)).

Purpose of the Study:

  • To describe the relationship between purity temporal behavior (sigma(t)) and average Loschmidt echo (Mmacr;(t)).
  • To demonstrate that Loschmidt echo decay analysis can utilize decoherence study tools.

Main Methods:

  • Quantifying entropy increase using purity (sigma = Tr(rho^2)).
  • Measuring system perturbation sensitivity with the Loschmidt echo (M(t)).
  • Analyzing the temporal behavior of sigma(t) and Mmacr;(t).

Main Results:

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  • A direct relation is established between sigma(t) and Mmacr;(t).
  • Tools from decoherence studies are applicable to Loschmidt echo decay.
  • For classically chaotic Hamiltonians, sigma and Mmacr; decay is governed by Lyapunov exponents.

Conclusions:

  • Loschmidt echo decay can be effectively analyzed using decoherence frameworks.
  • Lyapunov exponents play a key role in the decay dynamics of purity and Loschmidt echo in chaotic systems.