We consider two-dimensional stochastic differential equations, describing the motion
of a slowly and periodically forced overdamped particle in a double-well potential,
subjected to weak additive noise. We give sharp asymptotics of Eyring–Kramers type
for the expected transition time from one potential well to the other one. Our results
cover a range of forcing frequencies that are large with respect to the maximal
transition rate between potential wells of the unforced system. The main
difficulty of the analysis is that the forced system is nonreversible, so that
standard methods from potential theory used to obtain Eyring–Kramers laws
for reversible diffusions do not apply. Instead, we use results by Landim,
Mariani and Seo that extend the potential-theoretic approach to nonreversible
systems.
Keywords
stochastic exit problem, diffusion exit, first-exit time,
limit cycle, large deviations, potential theory,
semiclassical analysis, cycling, Gumbel distribution
