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 nonequilibrium steady states and investigate the relaxation dynamics toward stationarity. Furthermore, we demonstrate that the mean first-passage time to a target exhibits a nonmonotonic dependence on the resetting rate, attaining a minimum at an optimal value. All analytical predictions are corroborated by numerical simulations.