ALTERNATING KINETICS OF ANNIHILATING RANDOM-WALKS NEAR A FREE INTERFACE

The kinetics of annihilating random walks in one dimension, with the h alf-line x > 0 initially filled, is investigated. The survival probabi lity of the nth particle from the interface exhibits power-law decay, S-n(t) similar to t(-alpha n), with alpha(n) approximate to 0.225 for n = 1 and all odd values of n; for all n even, a faster decay with alp ha(n) approximate to 0.865 is observed. From consideration of the even tual survival probability in a finite cluster of particles, the rigoro us bound alpha(1) less than or equal to 1/4 is derived, while a heuris tic argument gives alpha(1) approximate to 3 root 3/8 pi = 0.2067.... Numerically, this latter value appears to be a lower bound for alpha(1 ). The average position of the first particle moves to the right appro ximately as 1.7t(1/2), with a relatively sharp and asymmetric probabil ity distribution.