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Related Experiment Videos

Quantum fractal fluctuations.

G Benenti1, G Casati, I Guarneri

  • 1International Center for the Study of Dynamical Systems, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy.

Physical Review Letters
|July 20, 2001
PubMed
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Quantum survival probability fluctuations in chaotic systems show fractal patterns even in deep quantum regimes. This fractal behavior arises from dynamical localization, expanding current theoretical understanding of quantum chaos.

Area of Science:

  • Quantum Chaos
  • Statistical Mechanics
  • Dynamical Systems

Background:

  • Quantum survival probability fluctuations in open, classically chaotic systems are theoretically linked to fractal patterns in quasiclassical regimes with mixed phase space.
  • Previous semiclassical arguments suggested fractal behavior is dependent on specific classical phase space properties.

Purpose of the Study:

  • To numerically investigate quantum survival probability fluctuations in a classical regime of complete chaoticity and a deep quantum regime of strong localization.
  • To determine if fractal patterns in fluctuations persist under conditions deviating from those assumed in prior semiclassical theories.

Main Methods:

  • Numerical analysis of quantum survival probability.
  • Simulation within a fully classical chaotic regime.

Related Experiment Videos

  • Exploration of a deep quantum regime characterized by strong localization.

    • Main Results:

    • Evidence found that quantum survival probability fluctuations exhibit fractal patterns even in the deep quantum regime of strong localization.
    • Fractal behavior is attributed to the slow, purely quantum algebraic decay in time caused by dynamical localization.
    • Findings challenge the necessity of quasiclassical conditions and mixed phase space for fractal fluctuation patterns.

    Conclusions:

    • Fractal nature of quantum survival probability fluctuations is more general than previously thought, extending to strongly localized quantum regimes.
    • Dynamical localization plays a crucial role in generating these fractal patterns through its characteristic algebraic decay.
    • The study significantly broadens the theoretical scope for understanding quantum chaos and localization phenomena.