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The Diffusion of Passive Tracers in Laminar Shear Flow
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Logarithmic subdiffusion from a damped bath model.

Thomas Guff1, Andrea Rocco1,2

  • 1University of Surrey, School of Mathematics and Physics, GU2 7XH Guildford, United Kingdom.

Physical Review. E
|May 16, 2026
PubMed
Summary
This summary is machine-generated.

Researchers modified a damped oscillator heat bath model, introducing frequency-dependent damping. This resulted in subdiffusive behavior, characterized by a 1/t memory kernel and diffusion scaling as t/ln(t).

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Theoretical Physics

Background:

  • Standard heat bath models utilize constant damping.
  • Previous models did not consider memory kernels with non-finite integrals.

Purpose of the Study:

  • To modify a damped oscillator heat bath model with frequency-dependent damping.
  • To investigate the resulting subdiffusive behavior and memory kernel properties.

Main Methods:

  • Modification of the damped oscillator heat bath model.
  • Numerical simulation to analyze diffusion and memory kernel behavior.
  • Calculation of the velocity correlation function.

Main Results:

  • A frequency-dependent damping leads to a memory kernel k(t) ~ 1/t.
  • The system exhibits subdiffusion due to the non-finite integral of the memory kernel.
  • Numerical results show diffusion scaling as <ΔQ²(t)> ~ t/ln(t).

Conclusions:

  • The modified model presents a boundary case for memory kernel behavior.
  • The study confirms subdiffusion in the asymptotic regime.
  • Numerical calculations validate the theoretical findings on subdiffusion.