Random walks with imperfect trapping in the decoupled-ring approximation |
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Authors: | T Aspelmeier J Magnin W Graupner UC Täuber |
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Institution: | (1) Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0435, USA, US |
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Abstract: | We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability
by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical simulations reveal
this solution, which is exact in the limit of perfect traps, to be remarkably robust with respect to a significant lowering
of the trapping probability. We demonstrate that for randomly distributed traps, the long-time asymptotics of our result recovers
the known stretched exponential decay. We also study an anisotropic three-dimensional version of our model. We discuss possible
applications of some of our findings to the decay of excitons in semiconducting organic polymer materials, and emphasize the
crucial influence of the spatial trap distribution on the kinetics.
Received 23 July 2001 / Received in final form 14 May 2002 Published online 13 August 2002 |
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Keywords: | PACS 02 50 Ey Stochastic processes – 05 40 -a Fluctuation phenomena random processes noise and Brownian motion 05 60 -k Transport processes |
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