Transition rates of a non-Markovian Brownian particle in a double well potential

The transition rate of a non-Markovian Brownian particle in a double well potential is determined analytically by means of asymptotic methods and compared with both current theories and numerical simulations by Straub, Borkovec, and Berne [J. Chem. Phys. 83, 3172 (1985)]. We obtain good agreement with these simulations. The ranges of validity for the different current theories which we find do, however, not exhaust the complete parameter range. In particular, for large static friction we identify a region of bath correlation times in which the rate differs grossly from the value predicted by either Grote–Hynes theory or non-Markovian energy diffusion. Additionally, corrections to the Grote–Hynes rate are determined and an analytical expression for the non-Markovian energy diffusion rate is obtained.