On the Generalized Kramers Problem with Exponential Memory Friction

The time-dependent transmission coefficient for the generalized Kramers problem with exponential memory friction has recently been calculated by Kohen and Tannor [D. Kohen and D. J. Tannor, J. Chem. Phys. 103, 6013 (1995)] 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 [Sancho et al., to appear in J. Chem. Phys.; cond-mat/9806001]. 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. Abbreviated Running Title: ON THE GENERALIZED KRAMERS PROBLEM Corresponding author. Department of Chemistry and Biochemistry 0340, UCSD, 9500 Gilman Dr., La Jolla, CA 92093-0340. Phone: (619) 534-3285. FAX: (619) 534-7244. Email: [email protected]