Last Passage Time Statistics for Barrier-Crossing Processes

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Abstract

A concept of mean last passage time at the saddle point is proposed in order to compute both the lifetime and the escape rate of a particle in a metastable potential, where the backstreaming across the saddle point is taken into account. It is shown that the mean oscillating time around the saddle point is the longest one among all the time scales at high temperatures and the inverse of the mean last passage time at the saddle point is more close to the steady escape rate.

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