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Fractal fluctuations in quantum integrable scattering.

Italo Guarneri1, Marcello Terraneo

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 22, 2002
PubMed
Summary

Completely integrable scattering processes can show fractal transmission fluctuations due to spectral properties. This phenomenon also explains recent observations of fractality in dynamical localization systems.

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Area of Science:

  • Physics
  • Quantum Mechanics
  • Complex Systems

Background:

  • Integrable systems possess unique spectral properties.
  • Dynamical localization can lead to complex scattering behaviors.
  • Fractal patterns have been recently observed in scattering processes.

Purpose of the Study:

  • To theoretically and numerically demonstrate fractal transmission fluctuations in integrable scattering.
  • To explain the occurrence of fractality in systems with strong dynamical localization.

Main Methods:

  • Theoretical analysis of spectral properties in integrable systems.
  • Numerical simulations of scattering processes.
  • Investigation of dynamical localization effects on transmission.

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Main Results:

  • Completely integrable scattering processes exhibit fractal transmission fluctuations.
  • Typical spectral properties of integrable systems are responsible for this fractality.
  • Similar fractal properties are observed in scattering with strong dynamical localization.

Conclusions:

  • Fractal transmission fluctuations are a characteristic of completely integrable scattering.
  • The findings provide an explanation for recent numerical observations of fractality in dynamical localization.
  • Spectral properties play a crucial role in the emergence of complex transmission behaviors.