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Active Brownian motion in two dimensions under stochastic resetting.

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We investigated active Brownian particle (ABP) movement with stochastic resetting in 2D. Resetting position and orientation leads to a stationary state, with distributions diverging near the reset point for high rates.

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Area of Science:

  • Statistical mechanics
  • Soft matter physics
  • Non-equilibrium systems

Background:

  • Active Brownian particles (ABPs) exhibit self-propelled motion.
  • Stochastic resetting introduces a mechanism to return the system to a specific state.
  • Understanding particle dynamics in confined or resetting environments is crucial.

Purpose of the Study:

  • To analyze the position distribution of a 2D ABP under three distinct stochastic resetting protocols.
  • To determine conditions under which the ABP reaches a stationary state.
  • To characterize the emergent position distributions and dynamics.

Main Methods:

  • Mathematical modeling of ABP dynamics with stochastic resetting.
  • Application of renewal theory to calculate stationary distributions.
  • Perturbative analysis for short-time non-Gaussian behavior.
  • Investigation of limiting cases for resetting rate (r) versus rotational diffusion (DR).

Main Results:

  • Protocols resetting position (with or without orientation) lead to a stationary state.
  • Position distributions can diverge near the resetting point at high resetting rates.
  • Orientation resetting alone does not yield a stationary state but alters dynamics from ballistic to diffusive.
  • Short-time distributions are non-Gaussian and characterized via perturbation.

Conclusions:

  • Stochastic resetting significantly alters ABP spatial and temporal dynamics.
  • The specific resetting protocol dictates the system's emergent statistical properties.
  • Divergent position distributions highlight unique behaviors at high resetting frequencies.