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Fractional Hydrodynamic Memory and Superdiffusion in Tilted Washboard Potentials.

Igor Goychuk1

  • 1Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam-Golm, Germany.

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|November 26, 2019
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Summary
This summary is machine-generated.

Including fractional hydrodynamics memory effects in tilted washboard potentials significantly enhances diffusion. This leads to stronger resonance effects and prolonged superdiffusion, including Richardson-like diffusion and ballistic supertransport.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Diffusion in periodic potentials can exhibit anomalous behavior, exceeding free diffusion.
  • Inertial effects in the underdamped regime further amplify diffusion.
  • Fractional hydrodynamics, specifically Basset-Boussinesq friction, introduces memory effects.

Purpose of the Study:

  • To investigate the impact of fractional hydrodynamics memory effects on diffusion in tilted washboard potentials.
  • To determine if these memory effects enhance already observed diffusion anomalies.
  • To explore the characteristics and duration of transient superdiffusion regimes.

Main Methods:

  • Accurate numerical simulations were employed.
  • The study focused on the interplay between potential landscape, inertia, and memory effects.
  • Analysis of velocity autocorrelation functions and mean squared displacements was performed.

Main Results:

  • A resonance-like enhancement of normal diffusion was observed to be significantly stronger and sharper.
  • A long-lasting transient regime of superdiffusion was revealed.
  • Specific superdiffusion behaviors, including Richardson-like diffusion (⟨δx^{2}(t)⟩∝t^{3}) and ballistic supertransport (⟨δx(t)⟩∝t^{2}), were identified.

Conclusions:

  • Fractional hydrodynamics memory effects substantially amplify diffusion anomalies in tilted potentials.
  • These effects lead to more pronounced and extended periods of superdiffusion.
  • The findings highlight the importance of considering hydrodynamic memory in understanding complex diffusion phenomena.