Memory-induced acceleration and slowdown of barrier crossing

We study the mean first-passage time τ_MFP for the barrier crossing of a single massive particle with non-Markovian memory by Langevin simulations in one dimension. In the Markovian limit of short memory time τ_Γ, the expected Kramers turnover between the overdamped (high-friction) and the inertial (low-friction) limits is recovered. Compared to the Markovian case, we find barrier crossing to be accelerated for intermediate memory time, while for long memory time, barrier crossing is slowed down and τ_MFP increases with τ_Γ as a power law $τMFP∼τΓ2$⁠. Both effects are derived from an asymptotic propagator analysis: while barrier crossing acceleration at intermediate memory can be understood as an effective particle mass reduction, slowing down for long memory is caused by the slow kinetics of energy diffusion. A simple and globally accurate heuristic formula for τ_MFP in terms of all relevant time scales of the system is presented and used to establish a scaling diagram featuring the Markovian overdamped and the Markovian inertial regimes, as well as the non-Markovian intermediate memory time regime where barrier crossing is accelerated and the non-Markovian long memory time regime where barrier crossing is slowed down.