Escape Rates for Coupled Particles in a Stochastic Environment

A particle placed in a deterministic, overdamped potential well will move towards an attractor located at the bottom of the well. Once the particle reaches the attractor, it remains there forever since no other forces are acting on the particle. However, if weak stochasticity is introduced, the particle will fluctuate around the attractor. As a rare event, the noise can organize itself in such a way that a large fluctuation is created that causes the particle to escape from the basin of attraction. The escape rates/escape times can be found both analytically and numerically. Furthermore, it is possible to predict the most probable trajectory of escape, called the optimal escape path, for the particle. In this work, we investigate the noise-induced escape of a single particle as well as two coupled particles from an overdamped double-well potential. For the coupled particles problem, we have developed new analytical tools needed to study the escape problem for different values of coupling, and our results are confirmed numerically