Thermally activated barrier crossing rate for a coupled system moving in a ratchet potential

We explore the dependence of the thermally activated barrier crossing rate on various model parameters for a dimer that undergoes a Brownian motion on a piecewise linear bistable potential employing the method of adiabatic elimination of fast variable. By introducing a different model system and approaches than the previous works \cite{c4,c5}, not only we recapture the previous results but we further show that systematic elimination of the fast changing variable leads to an effective Kramers type potential. It is shown that for rigid dimer, the escape rate $R$ monotonously decreases with $k$. On the other hand, in the presence of time varying force, the signal to noise ratio (SNR) attains a pronounced peak at particular barrier height $U_{0}$.