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

TL;DR

This paper investigates how the rate of thermally activated barrier crossing in a coupled dimer system depends on parameters, revealing effects of system rigidity and external forces on escape rates and signal-to-noise ratio.

Contribution

It introduces a new model and approach that generalizes previous results, showing how fast variable elimination leads to an effective Kramers potential and analyzing escape dynamics.

Findings

Escape rate decreases with increasing coupling constant for rigid dimers.

Signal-to-noise ratio peaks at specific barrier heights under time-varying forces.

Systematic elimination of fast variables simplifies the analysis of barrier crossing.

Abstract

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 $U_{0}$.