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Space-dependent diffusion with stochastic resetting: A first-passage study.

Somrita Ray1

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

The Journal of Chemical Physics
|December 23, 2020
PubMed
Summary
This summary is machine-generated.

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Stochastic resetting affects particle diffusion with bias. Resetting speeds up first-passage for attractive potentials (ν > 0) when ν < 3, but slows it down for ν > 3, revealing a key transition point.

Area of Science:

  • Statistical Physics
  • Non-equilibrium Systems
  • Complex Systems

Background:

  • Diffusion processes are fundamental in physics and biology.
  • Spatially dependent diffusion and external potentials significantly alter particle dynamics.
  • Stochastic resetting introduces non-Markovian behavior, impacting first-passage times.

Purpose of the Study:

  • To investigate the influence of stochastic resetting on first-passage properties of biased diffusion with space-dependent diffusion coefficients.
  • To analytically derive survival probabilities and first-passage time distributions.
  • To characterize dynamical transitions and phase diagrams influenced by resetting.

Main Methods:

  • Analytical derivation of survival probability in Laplace space.

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  • Analysis of first-passage time distribution in a limiting case.
  • Construction of a phase diagram based on the parameter ν = (1 + μD0-1).

    • Main Results:

    • An exact expression for survival probability and first-passage time distribution was derived.
    • The system exhibits dynamical transitions governed by the parameter ν.
    • A resetting transition occurs at ν = 3, altering the efficiency of first-passage.
    • For repulsive potentials (ν < 0), the origin is unreachable; for attractive potentials (ν > 0), it is eventually reached.

    Conclusions:

    • Stochastic resetting introduces a tunable transition point (ν = 3) that can either accelerate or hinder first-passage.
    • The interplay between drift, diffusion, and resetting dictates the system's long-term behavior.
    • This work provides a foundation for studying resetting phenomena in more complex, inhomogeneous diffusion systems.