On the generalized Kramers problem with exponential memory friction

Abstract The time-dependent transmission coefficient for the generalized Kramers problem with exponential memory friction has recently been calculated by Kohen and Tannor [D. Kohen, D.J. Tannor, J. Chem. Phys. 103 (1995) 6013] using a procedure based on the method of reactive flux and the phase space distribution function. Their analysis is restricted to the high friction regime or diffusion-limited regime. We recently developed a complementary theory for the low-friction energy-diffusion-limited regime in the Markovian limit [J.M. Sancho, A.H. Romero, K. Lindenberg, J. Chem. Phys. 109 (1998) 9888]. Here, we generalize our method to the case of an exponential dissipative memory kernel. We test our results, as well as those of Kohen and Tannor, against numerical simulations.