Intrawell relaxation time: The limit of the adiabatic approximation

We consider the overdamped motion of a Brownian particle in a potential wel l and examine the relaxation of its probability distribution. We give a new definition, based on the mean first passage time, for the intrawell relaxa tion time, which characterizes the relaxation process in the entire well an d can be expressed analytically for an arbitrary potential. Further, we sho w how it can be approximated by other simple quantities in most cases. If t he characteristic time scale of some modulation of the potential is much lo nger than this intrawell relaxation time, the particle's probability distri bution can be considered to be adiabatically adjusted to the potential at e very instant. [S0031-9007(99)08815-8].