Interacting Brownian Motion with Resetting

Abstract

We study two Brownian particles in dimension $d=1$, diffusing under an interacting resetting mechanism to a fixed position. The particles are subject to a constant drift, which biases the Brownian particles toward each other. We derive the steady-state distributions and study the late time relaxation behavior to the stationary state.

13 pages, 4 figures

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• Non-renewal resetting of scaled Brownian motion
• Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement
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• Transport properties and first arrival statistics of random searches with stochastic reset times
• Invariants of motion with stochastic resetting and space-time coupled returns
• Stochastic resetting in underdamped Brownian motion
• Continuous-time random walks with reset events: Historical background and new perspectives
• Stochastic resetting in interacting particle systems: A review
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• Mean-performance of sharp restart I: Statistical roadmap
• Anomalous diffusion in random-walks with memory-induced relocations
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• Unusual stationary state in Brownian systems with Lorentz force
• Capture of a diffusing lamb by a diffusing lion when both return home
• Cross-over between diffusion-limited and reaction-limited regimes in the coagulation-diffusion process
• Emerging correlations between diffusing particles evolving via simultaneous resetting with memory
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• Ising Model with Power Law Resetting
• An exactly solvable predator prey model with resetting