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Lyapunov decoherence rate in classically chaotic systems.

Marcus V S Bonança1

  • 1Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany. marcus.bonanca@ufabc.edu.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 24, 2011
PubMed
Summary

We show that the decoherence rate for a chaotic particle interacting with a heat bath equals its Lyapunov exponent. This finding characterizes quantum decoherence using purity in a semiclassical approximation for weak dissipation.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Chaos theory

Background:

  • Decoherence describes the loss of quantum properties due to environmental interaction.
  • Classically chaotic systems exhibit sensitive dependence on initial conditions.
  • Heat baths induce decoherence by interacting with quantum systems.

Purpose of the Study:

  • To investigate the decoherence process in a single particle with classically chaotic dynamics.
  • To establish a relationship between the decoherence rate and the Lyapunov exponent.
  • To provide a path integral treatment of decoherence induced by a heat bath.

Main Methods:

  • Path integral treatment of decoherence.
  • Semiclassical calculation of purity within the diagonal approximation.
  • Modeling the heat bath as a single random potential for weak dissipation and high temperatures.

Main Results:

  • The decoherence rate is found to be equal to the Lyapunov exponent.
  • Purity is used to characterize the loss of coherence.
  • The heat bath is simplified to a random potential, valid for short times.

Conclusions:

  • The Lyapunov exponent quantifies the decoherence rate in classically chaotic systems.
  • The study provides a semiclassical method to calculate decoherence.
  • Results are applicable to systems with weak dissipation and high temperatures over limited timescales.