Intrawell Relaxation Time: The Limit of the Adiabatic Approximation

We consider the overdamped motion of a Brownian particle in a potential well and examine the relaxation of its probability distribution. We give a new definition, based on the mean first passage time, for the intrawell relaxation time, which characterizes the relaxation process in the entire well and can be expressed analytically for an arbitrary potential. Further, we show how it can be approximated by other simple quantities in most cases. If the characteristic time scale of some modulation of the potential is much longer than this intrawell relaxation time, the particle's probability distribution can be considered to be adiabatically adjusted to the potential at every instant.