Escape of coupled Brownian particles across a fluctuating barrier

The escape of two harmonically coupled Brownian particles across the fluctuating barrier of a bistable potential is investigated with correlated additive and multiplicative fluctuations. Positive correlations enhance the rate of escape across the barrier when the coupling is effective, whereas for weakly coupled particles, escape becomes difficult. It is found that the system exhibits the phenomenon of resonant activation when the rate of barrier fluctuations is comparable to the relaxation time in the bistable potential. Using a decoupling ansatz, we derive the Markovian limit of the problem in the steady state, under the constraint that the barriers fluctuate on a time scale faster than the relative oscillation of the two particles. Adiabatic elimination of the fast variable of the dynamical system is discussed in appropriate limits.