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Related Experiment Videos

Decay of the classical Loschmidt echo in integrable systems.

Giuliano Benenti1, Giulio Casati, Gregor Veble

  • 1Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria and Istituto Nazionale per la Fisica della Materia, Unità di Como, Via Valleggio 11, 22100 Como, Italy. giuliano.benenti@uninsubria.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
Summary

We investigated how classical motion fidelity decays in integrable systems. Two decay types, algebraic and ballistic, were identified, depending on initial conditions and perturbation shape, not size.

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Area of Science:

  • Physics
  • Classical Mechanics
  • Dynamical Systems

Background:

  • Integrable systems exhibit predictable classical motion.
  • Understanding deviations from integrability is crucial for complex system analysis.
  • Fidelity decay quantifies the loss of predictability in perturbed systems.

Purpose of the Study:

  • To analytically and numerically investigate the fidelity decay of classical motion in integrable systems.
  • To identify the different behaviors and underlying mechanisms of fidelity decay.
  • To determine the factors influencing the type and rate of decay.

Main Methods:

  • Analytical treatment of fidelity decay in perturbed integrable systems.
  • Numerical simulations using models like the twist map, rectangular billiard, and kicked rotor.

Related Experiment Videos

  • Analysis of perturbation effects on tori shape and frequencies.

    • Main Results:

    • Identified two distinct fidelity decay behaviors: algebraic and ballistic.
    • Algebraic decay arises from tori shape perturbation; ballistic decay from frequency perturbation.
    • Decay type depends on initial conditions and perturbation shape, not perturbation size (for small perturbations).

    Conclusions:

    • The study reveals fundamental insights into the dynamics of perturbed integrable systems.
    • The findings provide a framework for understanding chaos and predictability in classical mechanics.
    • The results have implications for fields relying on classical dynamics, such as celestial mechanics and statistical physics.