Thermal activation by power-limited coloured noise

Abstract

We consider thermal activation in a bistable potential in the presence of correlated (Ornstein–Uhlenbeck) noise. Escape rates are discussed as a function of the correlation time of the noise at a constant variance of the noise. In contrast to a large body of previous work, where the variance of the noise decreases with increasing correlation time of the noise, we find a bell-shaped curve for the escape rate with a vanishing rate at zero and infinite correlation times. We further calculate threshold crossing rates driven by energy-constrained coloured noise.