Thermally activated barrier crossing and stochastic resonance of a flexible polymer chain in a piecewise linear bistable potential

We study the stochastic resonance (SR) of a flexible polymer chain crossing over a piecewise linear bistable potential. The dependence of signal to noise ratio $SNR$ on noise intensity $D$, coupling constant $k$ and polymer length $N$ is studied via two state approximation. We find that the response of signal to the background noise strength is significant at optimum values of $D_{opt}$, $k_{opt}$ and $N_{opt}$ which suggests novel means of manipulating proteins or vesicles. Furthermore, the thermally activated barrier crossing rate $r_{k}$ for the flexible polymer chain is studied. We find that the crossing rate $r_{k}$ exhibits an optimal value at an optimal coupling constant $k_{opt}$; $k_{opt}$ decreases with $N$. As the chain length $N$ increases, the escape rate for the center of mass $r_{k}$ monotonously decreases. On the other hand, the crossing rate for the portion of polymer segment $r_s$ increases and saturates to a constant rate as $N$ steps up.