The steady state distribution for diffusion in a logarithmic-harmonic potential with stochastic resetting

The steady state distribution of the position of a Brownian particle diffusing in logarithmic-harmonic potential with stochastic resetting is obtained analytically. We show that there are two critical conditions that determine the behavior of the stationary distribution function (SDF). We also investigate how the steady state distribution, which occurs due to the nature of the logarithmic-harmonic potential in the absence of reset, changes in the presence of the reset mechanism.