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

Abstract

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 ${\gamma }_{\mathrm{opt}}$ at which the MTA is a minimum, where $r_c=\sqrt{d/\left(d+4\right)}R$ and $R$ is the radius of sphere. As $r$ increases, ${\gamma }_{\mathrm{opt}}$ exhibits a continuous transition from zero to nonzero at $r=r_c$. Furthermore, we consider that the particle lies in between two two-dimensional or three-dimensional concentric spheres, and obtain the domain in which resetting expedites the MTA, which is $(R_1,r_{c_1})\cup (r_{c_2},R_2)$, with $R_1$ and $R_2$ being the radius of inner and outer spheres, respectively. Interestingly, when $R_1/R_2$ is less than a critical value, ${\gamma }_{\mathrm{opt}}$ exhibits a discontinuous transition at $r=r_{c_1}$; otherwise, such a transition is continuous. However, at $r=r_{c_2}$, ${\gamma }_{\mathrm{opt}}$ always shows a continuous transition.

9 pages, 9 figures

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