Kramers problem for a dimer: Effect of noise correlations

The Kramers problem for a dimer in a bistable piecewise linear potential is studied in the presence of correlated noise processes. The effect of such a correlation is to redistribute the thermal power between the dynamical degrees of freedom, and this leads to significant deviations in the dynamics of the system from the case of independent 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. The strong coupling limit of the problem is analyzed using adiabatic elimination, where it is found that the initial probability density relaxes towards a stationary value on the same time scale as the mean escape time when the noise intensity of the system is low. For higher noise fluctuations, the relaxation towards the stationary state is slower in comparison to escape times. In the extreme limit of perfect anticorrelation, the random dynamical system behaves as a deterministic system in a steady state in which the center of mass starting from the unstable maxima moves down the hill and gets trapped in the potential minima. The implications for polymer dynamics in a potential are discussed.