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Journal of Statistical Physics, VoL 43, Nos. 3/4, 1986 Diffusion with Random Traps: Transient
 

Summary: Journal of Statistical Physics, VoL 43, Nos. 3/4, 1986
Diffusion with Random Traps: Transient
One-Dimensional Kinetics in a Linear Potential
Noam Agmon I
Received August 21, 1985, final December 23, 1985
The problem of one-dimensional diffusion with random traps is solved without
and with a constant field of force. Using an eigenvalue expansion for long times
and the method of images for short times we give an exact, straightforward
solution for the time dependence of the mean survival probability and the mean
probability density for returning to the origin. Using the backward equation
approach, we determine the mean survival time and the mean residence time
density at the origin. We comment on the relation between these solutions and
those for one-dimensional diffusion with random reflectors.
KEY WORDS: Diffusion; random traps; random reflectors; survival
probability; mean survival, residence and relaxation times; method of images.
1. INTRODUCTION
There has recently been considerable interest in the temporal properties of
a random walk or a diffusion process among a random distribution of
stationary sinksJ 1 20) The main properties investigated were (1 17) (a)the
survival probability, (b) the probability density for returning to the origin,

  

Source: Agmon, Noam - Institute of Chemistry, Hebrew University of Jerusalem

 

Collections: Chemistry