Trapping and Lifshitz Tails in Random Media, Self-Attracting Polymers, and the Number of Distinct Sites Visited: A Renormalized Instanton Approach in Three Dimensions
- 23 January 1989
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 62 (4) , 357-360
- https://doi.org/10.1103/physrevlett.62.357
Abstract
Diffusion processes are studied which occur in three-dimensional media with traps at quenched random positions. For the first time, aspects of survival at intermediate times are derived, given that the concentration of traps is small. A first-order phase transition is found at zero concentration. The predictions are in good agreement with recent numerical data. They also have new implications for the Lifshitz band-edge singularity of the density of states of random binary mixtures, for a model of selfattracting polymers, and for the distribution of the number of distinct sites visited in a random walk.Keywords
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