Diffusion in a potential landscape with stochastic resetting

TL;DR

This paper investigates how stochastic resetting affects the steady states and transient behavior of a Brownian particle in various potential landscapes, revealing different classes of nonequilibrium states and confirming findings through simulations.

Contribution

It provides a comprehensive analysis of steady states in diffusive systems with resetting across different potential types, including analytical and numerical verification.

Findings

Stable potentials lead to well-defined steady states.

Unstable potentials may not sustain steady states.

Numerical simulations confirm analytical predictions.

Abstract

The steady state of a Brownian particle diffusing in an arbitrary potential under the stochastic resetting mechanism has been studied. We show that there are different classes of nonequilibrium steady states depending on the nature of the potential. In the stable potential landscape, the system attains a well defined steady state however existence of the steady state for the unstable landscape is constrained. We have also investigated the transient properties of the propagator towards the steady state under the stochastic resetting mechanism. Finally, we have done numerical simulations to verify our analytical results.