1994/09/13 by John Cardy · 1 citation
Physics and Astronomy · #cond-mat
paper · pdf · doi:10.1088/0305-4470/28/1/004
10 pages, (revised version with abstract included) OUTP-94-35S
arxiv created 1994/09/13 · arxiv updated 2009/11/30
We consider the probability P(t) that a given site remains unvisited by any of a set of random walkers in d dimensions undergoing the reaction A+A→0 when they meet. We find that asymptotically P(t)∼ t-θ with a universal exponent θ=\ffrac12-O(ε) for d=2-ε, while, for d>2, θ is non-universal and depends on the reaction rate. The analysis, which uses field-theoretic renormalisation group methods, is also applied to the reaction kA→0 with k>2. In this case, a stretched exponential behaviour is found for all d≥1, except in the case k=3, d=1, where P(t)∼ \rm e^-\const (ln t)3/2.