Exploring the dynamics of dimer crossing over a Kramers type potential

We explore the escape rate of a dimer crossing a potential barrier using both analytical and numerical approaches. We find that for small coupling strength k, the barrier hopping can be well approximated by a two step reaction scheme where one monomer hops over the barrier and is then followed by the other. In this regime the escape rate increases with k showing that the cooperativity between monomers enhances the crossing rate. However, in the limit of large coupling strength, applying the method of adiabatic elimination, we find that the escape rate is a decreasing function of k. Thus, we find that the escape rate is a non-monotonic function of the spring constant which is peaked at an optimal coupling strength. Furthermore, in the presence of a weak periodic signal, we show that the system response to the periodic signal is pronounced at a particular spring constant showing the dimer can be transported rapidly across the reaction coordinate in a half period.