FIRST PASSAGE TIMES, CORRELATION-FUNCTIONS, AND REACTION-RATES

The mean lifetime of a particle in the presence of an absorbing bounda ry is the mean first passage time to the boundary. For diffusive dynam ics on a one dimensional potential, we establish an exact relation bet ween the mean first passage time to x=a averaged over a (pseudo) equil ibrium distribution in the region a less than or equal to x<infinity, and the time integral of certain equilibrium correlation functions det ermined by dynamics on the entire (-infinity<x<infinity) surface in th e absence of an absorbing boundary at x=a. As an application, we show that the sum of the forward and reverse rate constants for diffusive b arrier crossing obtained using mean first passage times and obtained f rom the time integral of the normalized number correlation function, a re identical for an arbitrary choice of the dividing surface. (C) 1997 American Institute of Physics.