Kramers problem for a dimer: effect of noise correlations

Kramers problem for a dimer in a bistable piecewise linear potential is studied in the presence of correlated noise processes. The distribution of first passage times from one minima to the basin of attraction of the other minima is found to have exponentially decaying tails with the parameter dependent on the amount of correlation and the coupling between the particles. Strong coupling limit of the problem is analyzed using adiabatic elimination, where it is found that the initial probability density relaxes towards stationary value on the same time scale as the mean escape time. The implications towards polymer dynamics in a potential are discussed.