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Diffusion in a potential landscape with stochastic resetting.

Arnab Pal1

  • 1Raman Research Institute, Bangalore 560080, India.

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|February 14, 2015
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Summary
This summary is machine-generated.

Stochastic resetting influences Brownian particle diffusion, creating distinct nonequilibrium steady states based on potential landscapes. Stable potentials yield well-defined states, while unstable ones present constraints, verified by simulations.

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Area of Science:

  • Statistical Physics
  • Non-equilibrium Systems

Background:

  • Brownian motion describes random particle movement.
  • Stochastic resetting introduces periodic resets to a particle's position.
  • Non-equilibrium steady states are crucial in systems driven out of equilibrium.

Purpose of the Study:

  • Investigate the steady states of Brownian particles under stochastic resetting.
  • Analyze how potential landscapes affect these steady states.
  • Examine transient dynamics and verify analytical findings.

Main Methods:

  • Analytical calculations for steady-state properties.
  • Analysis of transient dynamics of the propagator.
  • Numerical simulations for verification.

Main Results:

  • Identified distinct classes of non-equilibrium steady states.
  • Demonstrated that stable potentials lead to well-defined steady states.
  • Showed constrained steady-state existence for unstable potentials.

Conclusions:

  • Stochastic resetting leads to diverse steady states in Brownian diffusion.
  • The nature of the potential landscape critically determines steady-state properties.
  • Analytical and numerical results confirm the theoretical framework.