On the generalized Kramers problem with exponential memory friction

The time-dependent transmission coefficient for the generalized Kramers pro blem with exponential memory friction has recently been calculated by Kohen and Tanner [D. Kohen, D.J. Tanner, J. Chem. Phys. 103 (1995) 6013] using a procedure based on the method of reactive flux and the phase space distrib ution function. Their analysis is restricted to the high friction regime or diffusion-limited regime; We recently developed a complementary theory for the low-friction enegy-diffusion-limited regime in the Markovian limit [J. M. Sancho, A.H. Romero, K. Lindenberg, J. Chem. Phys. 109 (1998) 9888]. Her e, we generalize our method to the case of an exponential dissipative memor y kernel. We test our results, as well as those of Kohen and Tannor, agains t numerical simulations. (C) 1999 Elsevier Science B.V. All rights reserved .