Turnover of activationless escape rate for collisional dynamics

We consider the Bhatnagar-Gross-Krook (BGK) model for the dynamics of a par ticle in the phase space. Namely, the particle follows Newtonian trajectori es that are randomly interrupted by collisions which thermalize its velocit y. For this collisional model, we analyze the activationless escape of a fr ee particle from a unit interval as a function of the collision frequency, gamma. Approximate analytic expressions, which compare favorably with simul ations, are derived for the effective and asymptotic rate constants, k and Gamma, that describe the escape kinetics. Both rate constants show a turnov er behavior as functions of gamma similar to the rate constants found when the particle motion is governed by the Langevin dynamics. It is found that as gamma --> 0, k similar to 1/ln(1/gamma) (with an amplitude 1/3 times sma ller than in Langevin dynamics) and Gamma similar to gamma (rather than Gam ma similar to gamma (1/3) in Langevin dynamics) while when gamma --> infini ty both rate constants vanish as gamma -1 like in the Langevin dynamics. (C ) 2001 Elsevier Science B.V. All rights reserved.