Residence times in diffusion processes

Noam Agmona*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

84 Scopus citations

Abstract

We generalize the notion of "mean survival time" in diffusion processes, which characterizes the disappearance of probability density from the whole coordinate space into boundaries or sinks, by introducing "mean residence time," characterizing the time spent in a portion of the coordinate space. In particular, the time integral of the transition probability (Green's function) is the average residence time density at a point. It is a function of both initial and final variables and fulfills two differential equations, one for each variable. We demonstrate the solution of these equations and compare it to the time integral of the direct solution of the diffusion equation. We present the general solution for spherically symmetric diffusion, and compare it to results in the literature.

Original languageEnglish
Pages (from-to)3644-3647
Number of pages4
JournalThe Journal of Chemical Physics
Volume81
Issue number8
DOIs
StatePublished - 1984

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