There have been a number of recent investigations of diffusing particles in the presence of traps. Among many applications of this process, we find phenomena such as reaction rates, biological models, and dielectric 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 results 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 excellent agreement for symmetric and nonsymmetric switching-time densities.

• Received 25 April 1995

DOI:https://doi.org/10.1103/PhysRevE.52.3462