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Fractal survival probability fluctuations

Casati1, Guarneri, Maspero

  • 1International Center for the Study of Dynamical Systems, Via Lucini 3, 22100 Como, Italy and Istituto Nazionale di Fisica della Materia, Unita di Milano, Via Celoria 16, 20133 Milano, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Milan.

Physical Review Letters
|October 4, 2000
PubMed
Summary

We explored survival probability fluctuations in open quantum systems. Results show these fluctuations exhibit a fractal structure, linked to classical survival probability decay.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Dynamical systems

Background:

  • Open quantum systems exhibit complex dynamics.
  • Survival probability fluctuations are key indicators of system behavior.
  • Classical maps with mixed phase spaces present challenges in predictability.

Purpose of the Study:

  • To investigate the nature of survival probability fluctuations in an open quantum system.
  • To provide numerical evidence for theoretical predictions regarding these fluctuations.
  • To establish a quantitative relationship between quantum fluctuations and classical dynamics.

Main Methods:

  • Numerical simulations of an open quantum system.
  • Analysis of survival probability.
  • Characterization of fractal structures in fluctuations.

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  • Comparison with classical survival probability decay.

    • Main Results:

    • Observed fluctuations in survival probability.
    • Demonstrated a fractal structure in these fluctuations.
    • Established a quantitative link between fractal dimension and algebraic decay.
    • Provided the first numerical support for theoretical predictions.

    Conclusions:

    • Survival probability fluctuations in this system possess a fractal nature.
    • The fractal structure is quantitatively related to classical survival probability decay.
    • Numerical results align with theoretical predictions for open quantum systems.