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Classical Loschmidt echo in chaotic many-body systems.

Gregor Veble1, Tomaz Prosen

  • 1Physics Department, FMF, University of Ljubljana, Ljubljana, Slovenia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2005
PubMed
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A new theory explains Loschmidt echoes in chaotic systems. Doubly exponential decay is observed, with rates linked to the largest Lyapunov exponent and initial density properties.

Area of Science:

  • Statistical mechanics
  • Quantum chaos
  • Dynamical systems theory

Background:

  • Loschmidt echoes probe the sensitivity of dynamical systems to perturbations.
  • Chaotic systems with many degrees of freedom exhibit complex dynamics.
  • Understanding echo decay is crucial for characterizing system stability.

Purpose of the Study:

  • To develop a general theoretical framework for classical Loschmidt echoes in many-body chaotic systems.
  • To analyze the decay rates and their dependence on system parameters.
  • To investigate the role of initial phase-space density properties.

Main Methods:

  • Development of a general theoretical approach.
  • Analysis of perturbations affecting all degrees of freedom.

Related Experiment Videos

  • Investigation of scaling laws for decay rates.

    • Main Results:

    • A doubly exponential decay of Loschmidt echoes is predicted.
    • The decay rate is determined by the largest Lyapunov exponent.
    • The scaling of the decay rate depends on the continuity of the initial phase-space density.

    Conclusions:

    • The developed theory provides a unified understanding of Loschmidt echoes in chaotic systems.
    • Lyapunov exponents are key indicators of echo decay.
    • Initial state properties significantly influence the system's response to perturbations.