Mo. Caceres et al., THEORY OF THE ABSORPTION PROBABILITY DENSITY OF DIFFUSING PARTICLES IN THE PRESENCE OF A DYNAMIC TRAP, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 52(4), 1995, pp. 3462-3468
There have been a number of recent investigations of diffusing particl
es in the presence of traps. Among many applications of this process,
we find phenomena such as reaction rates, biological models, and diele
ctric relaxation. In this paper we present a theory for the absorption
probability density for a walker in the presence of a dynamic trap by
using the multistate continuous-time random-walk approach. The result
s are exact for every switching-time probability density of the trap.
The deterministic and Markovian cases can be obtained by selecting the
appropriate switching-time density for the trap, Siegert's result is
reobtained in the static case. We perform Monte Carlo simulations, and
compare these results with our analytical prediction, finding excelle
nt agreement for symmetric and nonsymmetric switching-time densities.