Escape rate from a metastable state weakly interacting with a heat bath driven by external noise

Based on a system-reservoir model, where the reservoir is driven by an external stationary, Gaussian noise with arbitrary decaying correlation function, we study the escape rate from a metastable state in the energy diffusion regime. For the open system we derive the Fokker-Planck equation in the energy space and subsequently calculate the generalized non-Markovian escape rate from a metastable well in the energy diffusion domain. By considering the dynamics in a model cubic potential we show that the results obtained from numerical simulation are in good agreement with the theoretical prediction. It has been also shown numerically that the well-known turnover feature can be restored from our model.

Figure 1

Turnover phenomenon for an external-color-noise-driven bath. Parameters used are $k_{B}T=0.1$, $D_e=1.0$, ${\kappa }_0^2=5.0$, $\alpha =1.0$, $A=0.5$, and $E_b=5.0$ (scale arbitrary).

Figure 2

Barrier crossing rate in the low-friction regime $(0.001⩽g_0^2⩽0.01)$, a comparison between the theoretical prediction, Eq. (4.17) (solid lines) and Langevin simulation. Parameters used are $k_{B}T=0.1$, $D_e=1.0$, ${\kappa }_0^2=5.0$, $\alpha =1.0$, $A=0.5$, and $E_b=5.0$ (scale arbitrary).