Abstract
An exact solution is obtained for the survival fraction in the one-dimensional diffusion problem with randomly distributed deep traps. The time decay is studied both with and without a bias field. The small concentration (x) long time (t) decay behaves as exp[-(x 2 t/t 0)1/3]. The exact results are compared with the coherent potential approximation (CPA) and the first passage time approach (FPT). We find that in most cases of practical interest the FPT is superior to the CPA.
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Movaghar, B., Sauer, G.W. & Würtz, D. Time decay of excitations in the one-dimensional trapping problem. J Stat Phys 27, 473–485 (1982). https://doi.org/10.1007/BF01011087
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DOI: https://doi.org/10.1007/BF01011087