Trapping reaction with mobile traps

Abstract

We present the Monte Carlo results for the two-species trapping reaction A+B-->B with diffusing A and B on lattices in one, two, and three dimensions. We use an algorithm that permits one to simulate the survival probabilities of A particles down to <10(-30) with high accuracy. The results for the survival probability agree much better with the exact asymptotic predictions of Bramson and Lebowitz [Phys. Rev. Lett. 61, 2397 (1988)] than with the heuristics of Kang and Redner [J. Phys. A 17, L451 (1984)]. But there are very large deviations from either, which show that even these simulations are far from asymptotia. This is supported by the rms displacement of A particles, which clearly shows that the asymptotic regime has not been reached, at least for d=2 and d=3.