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Transport in time-dependent random potentials.

Yevgeny Krivolapov1, Shmuel Fishman

  • 1Physics Department, Technion - Israel Institute of Technology, Haifa 32000, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

We studied classical dynamics in random potentials, finding a simple expression for the diffusion coefficient. This work classifies anomalous diffusion into universality classes, with applications in optics and atom optics.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Classical dynamics in random potentials is crucial for understanding chaotic systems.
  • Chirikov resonances are key to comprehending chaos theory.
  • Stationary processes generate time- and space-dependent potentials.

Purpose of the Study:

  • To investigate classical dynamics in potentials random in space and time.
  • To derive a general expression for the diffusion coefficient.
  • To classify anomalous diffusion into universality classes.

Main Methods:

  • Utilizing the Fokker-Planck equation for quantitative analysis.
  • Deriving a diffusion coefficient based on average potential power density.
  • Applying and numerically testing the theory on optical and atom optical systems.

Main Results:

  • A simple expression for the diffusion coefficient was obtained.
  • Anomalous diffusion in velocity was classified into universality classes.
  • The theory was validated through numerical simulations.

Conclusions:

  • The study provides a framework for understanding anomalous diffusion in random potentials.
  • The findings have direct relevance to optics and atom optics.
  • The research contributes to the theory of chaos and statistical mechanics.