First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry

We investigate the first passage properties of a Brownian particle diffusing freely inside a d-dimensional sphere with absorbing spherical surface subject to stochastic resetting. We derive the mean time to absorption (MTA) as functions of resetting rate gamma and initial distance r of the particle to the center of the sphere. We find that when r > r(c) there exists a nonzero optimal resetting rate gamma(opt) at which the MTA is a minimum, where r(c) = root d/(d +4)R and R is the radius of the sphere. As r increases, gamma(opt) exhibits a continuous transition from zero to nonzero at r = r(c). Furthermore, we consider that the particle lies between two two-dimensional or three-dimensional concentric spheres with absorbing boundaries, and obtain the domain in which resetting expedites the MTA, which is (R-1, r(c1)) U (r(c2), R-2), with R-1 and R-2 being the radii of inner and outer spheres, respectively. Interestingly, when R-1/R-2 is less than a critical value, gamma(opt) exhibits a discontinuous transition at r = r(c1) ; otherwise, such a transition is continuous. However, at r = r(c2) the transition is always continuous.