Time-dependent barrier passage of a non-Ohmic damping system.
We consider a particle passing over the saddle point of an inverse harmonic potential, which is described by a generalized Langevin equation with a non-Ohmic damping of power exponent delta. The time-dependent passing probability and transmission coefficient are obtained analytically by using the reaction flux method. It is shown that the overshooting phenomenon for the passing probability appears in the regime 0<delta<1 and the backflow recrossing over the saddle point is observed, where a nonmonotonous time dependence of the passage probability is detected. The long memory aspect of friction is at the origin of this behavior. Thus the steady transmission coefficient is also a nonmonotonous function of delta.
Bao
Jing-Dong
JD
Department of Physics, Beijing Normal University, Beijing 100875, China. jdbao@bnu.edu.cn