Memory damping and energy-diffusion-controlled escape

A recent refinement by Buttiker, Harris, and Landauer [Phys.Rev. 8 28, 1268 (1983)] of Kramers's theory of activated escape at low damping is extended to the non-Markovian case with memory damping.The dynamics of activated rate processes was treated first in a historic paper by Kramers.Since that time, this important problem has been elaborated on many times resulting in several extensions of Kramers's original approach.In particular, we mention here the extension to a Markovian heat bath interaction described in terms of a master equa- tion, the work based on the concept of the mean first passage time in one-variable systems and multidimensional systems, " the inclusion of physically relevant non- Markovian effects" at moderate and large damping"' as well as the influence of non-Markovian damping on the ex- tremely underdamped case.' ' In another set of papers, the problem of activated escape has been extended to vari- ous situations in nonthermal, driven multistable nonequil- brium systems.' Our concern in this report is yet on another extension of Kramers's work for the underdamped case.Recently, an in- teresting refinement of Kramers's original approach for the underdamped case has been put forward by Buttiker, Harris, and Landauer" (BHL approach).Their theory extends Kramers's work for extremely low damping to the case of low-moderate damping;