Bistability and Colored Noise in Nonequilibrium Systems: Theory versus Precise Numerics

Abstract

We present novel calculations for the archetypal bistability dynamics driven by a correlated Gaussian random force (colored noise). Our focus is on the behavior at weak noise, which is difficult to solve theoretically as well as numerically. Precise numerical results for the smallest eigenvalue ${\lambda }_1\left(\tau \right)$ [or rate of escape $\Gamma \left(\tau \right)=\frac{1}{2}{\lambda }_1\left(\tau \right)$] at small to moderate to large noise correlation times $\tau$ are compared and interpreted versus a whole set of recent but conflicting theoretical predictions.