Time scales of overdamped nonlinear Brownian motion in arbitrary potential profiles.
This paper presents a new approach and new results concerning the problem of the rate of the nonlinear Brownian motion in a field of force. Within the scope of one-dimensional overdamped Brownian motion the exact values of time scales are obtained in detail for three types of arbitrary dimensionless potential profiles varphi(x) which differ from one another by their limiting values at x=+/- infinity. Three time scales, the relaxation time, the decay time of a metastable state and the life time of a nonstable state, are found via given potential profiles varphi(x) by explicit quadrature formulae, as it takes place for the well-known mean first passage times. Specific examples are considered. (c) 1997 American Institute of Physics.
Malakhov
A. N.
AN
Radiophysical Department, Nizhniy Novgorod State University, 23 Gagarin Avenue, Nizhniy Novgorod, 603600, Russia.