The Steady-State Distribution for Diffusion in a Logarithmic-Harmonic Potential with Stochastic Resetting

We study the motion of a Brownian particle diffusing in a logarithmic-harmonic potential under stochastic resetting. We derive an exact analytical expression for the steady-state position distribution and contrast it with the equilibrium distribution obtained in the absence of resetting. By exploring the parameter space, we identify distinct regimes characterizing the resulting non-equilibrium steady states and investigate the relaxation dynamics toward stationarity. Furthermore, we demonstrate that the mean first-passage time to a target exhibits a non-monotonic dependence on the resetting rate, attaining a minimum at an optimal value. All analytical predictions are corroborated by numerical simulations.