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Asymptotic quantum behavior of classically anomalous maps.

R Artuso1, M Rusconi

  • 1International Centre for the Study of Dynamical Systems and Dipartimento di Scienze Chimiche, Fisiche e Matematiche, Università dell'Insubria, Via Lucini 3, 22100 Como, Italy. artuso@fis.unico.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 20, 2001
PubMed
Summary

Dynamical localization occurs even with anomalous diffusion, a phenomenon previously studied in classical chaos. The quantum scaling remains consistent, irrespective of the diffusion type.

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Area of Science:

  • Quantum chaos
  • Statistical mechanics
  • Dynamical systems

Background:

  • Dynamical localization is crucial in quantum chaos, linking localization length to diffusion and Planck's constant.
  • Previous studies confirmed this in classically chaotic systems.

Purpose of the Study:

  • Investigate quantum behavior under anomalous diffusion where classical diffusion is undefined.
  • Determine if dynamical localization persists and how it scales with quantum parameters.

Main Methods:

  • Theoretical analysis of quantum systems.
  • Numerical simulations (implied from abstract).

Main Results:

  • Dynamical localization is shown to occur even when classical dynamics exhibit anomalous diffusion.

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  • The scaling of localization with the quantum parameter remains the same as in the classically diffusive case.

    • Conclusions:

    • Dynamical localization is a robust phenomenon in quantum chaos, extending beyond classically diffusive regimes.
    • The quantum parameter's scaling is invariant to the nature of classical diffusion (diffusive vs. anomalous).