Logarithmic corrections in the survival probability for random walks in random trapping environments

✍ Scribed by J. Köhler

• Publisher: Elsevier Science
• Year: 1990
• Tongue: English
• Weight: 534 KB
• Volume: 167
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(90)90284-y

✦ Synopsis

We study the survival probability of a particle that performs a random walk in a medium with traps where the trapping strength V is distributed randomly. We use an approach which is asymptotically exact and brings Wn(s), the number of distinct sites s visited after n steps, into play. Particularly in one dimension Wn(s) is known exactly and the survival probability for arbitrary potentials can be calculated. We find that for all distributions starting with a power law the survival probability is affected by universal logarithmic corrections, consistent with recent findings of Nieuwenhuizen and Luck. In the one-dimensional case we also give the prefactor and perform Monte Carlo simulations. We also study the survival probability for arbitrary dimensions and diffusion in lattice gases analytically for t---~ 00.