Diffusion in a potential landscape with stochastic resetting

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, the 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.