Poisson-shot-noise induced escape dynamics of a passive particle and a dimer

Abstract

Mean First Passage Time (MFPT) is a crucial quantity that characterizes stochastic processes in various stochastic dynamical systems across different disciplines. The inverse of the MFPT, known as the escape rate, is helpful in the context of Brownian motion and chemical processes. The MFPT dynamics of a passive particle in the presence of active noises presents a fascinating avenue. In this work, we study the dynamics of two different systems: first, a single Brownian particle and second, a dimer (two Brownian particles connected by a spring). In both cases, the systems are kept in contact with a thermal bath and an active bath, and are trapped in a bistable potential. The active bath produces kicks that follow the Poisson distribution. The MFPT of the particle and the dimer is investigated in various scenarios. Analytical results are presented for the small kick variance approximation only. In this approximation, we formulate the MFPT in two scaling regimes: a weak-noise regime characterized by classical Arrhenius scaling for escape rate and a strong-noise regime in which the MFPT scales as a power law in the effective noise strength. For the general case, the problem is solved numerically. Next, under the same approximation, the MFPT of a dimer in the small-bond-strength regime is studied using a sequential-hopping mechanism, and in the large-bond-strength regime, the MFPT is formulated using the adiabatic elimination approach. Motivated by recent studies on speeding up the escape mechanism, the MFPT of the particle and the dimer in the presence of an intermediate barrier is also examined. We deduced from the numerical results that the MFPT can be enhanced and further optimized by selecting a suitable intermediate potential profile.