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Diffusion with resetting in a logarithmic potential.

Somrita Ray1, Shlomi Reuveni1

  • 1School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, and The Ratner Center for Single Molecule Science, Tel Aviv University, Tel Aviv 69978, Israel.

The Journal of Chemical Physics
|June 24, 2020
PubMed
Summary
This summary is machine-generated.

Resetting diffusion in a logarithmic potential shows distinct behaviors based on potential strength. Resetting can speed up particle arrival to the origin for certain potential values, but not others.

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Area of Science:

  • Statistical Physics
  • Non-equilibrium Systems
  • Stochastic Processes

Background:

  • Diffusion processes are fundamental in physics and biology.
  • Resetting mechanisms introduce non-equilibrium dynamics to diffusion.
  • Logarithmic potentials are relevant in various physical phenomena.

Purpose of the Study:

  • To investigate the impact of resetting on diffusion in a logarithmic potential.
  • To analyze the transitions and behaviors of the system as a function of potential strength and resetting rate.
  • To generalize existing models of diffusion with resetting.

Main Methods:

  • Analytical treatment of a particle diffusing in a logarithmic potential with a constant resetting rate.
  • Characterization of non-equilibrium steady states for repulsive potentials.
  • Derivation of closed-form expressions for first-passage time distributions for attractive/weakly repulsive potentials.

Main Results:

  • A strongly repulsive logarithmic potential (βU₀ < -1) leads to a non-equilibrium steady state upon resetting.
  • For weakly repulsive or attractive potentials (βU₀ > -1), resetting can expedite arrival at the origin.
  • A resetting transition occurs at βU₀ = 5, where resetting is beneficial for -1 < βU₀ < 5 but detrimental for βU₀ > 5.

Conclusions:

  • The study provides a comprehensive analysis of diffusion with resetting in a logarithmic potential.
  • The findings reveal critical transitions and a resetting transition point, offering insights into optimizing search strategies.
  • This work extends the applicability of resetting diffusion models to more complex potential landscapes.