Random walks with imperfect trapping in the decoupled-ring approximation

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• 作者：T. Aspelmeier ; J. Magnin ; W. Graupner and U.C. T?uber
• 关键词：PACS. 02.50.Ey Stochastic processes – ; 05.40. ; a Fluctuation phenomena ; random processes ; noise ; and Brownian motion 05.60. ; k Transport processes
• 刊名：The European Physical Journal B - Condensed Matter
• 出版年：2002
• 出版时间：August 2002
• 年：2002
• 卷：28
• 期：4
• 页码：441-450
• 全文大小：232 KB

文摘

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.