Reaction dynamics in non-Markovian systems with non-monotonically decaying memory

Abstract

Whereas the effect of monotonically decaying memory kernels on reaction dynamics has been studied extensively, the effect of oscillatory memory, observed for widely different systems, is much less explored. We analyze non-Markovian barrier-crossing dynamics in the presence of a single exponentially decaying oscillatory friction memory kernel by simulations and analytical theory. We identify three scaling regimes: two in which the mean first-passage time $τ_{\mathrm{MFP}}$ scales quartically and linearly with the memory kernel decay time $τ_{\mathrm{o}}$, respectively, and a third in which $τ_{\mathrm{MFP}}$ scales quartically with the oscillation period $τ_φ$ of the memory kernel. Our results are relevant to a broad class of many-body dynamical systems such as dihedral isomerization processes and chemical reactions in solvents.