Approach to Asymptotic Behaviour in the Dynamics of the Trapping Reaction

Details Approach to Asymptotic Behaviour in the Dynamics of the Trapping Reaction Approach to Asymptotic Behaviour in the Dynamics of the Trapping Reaction

2004-01-09

arxiv.org/abs/cond-mat/0401148v2

J. Phys. A: Math. Gen. 37 (2004) 8407-8419

Physics

Condensed Matter

Statistical Mechanics

8 pages, 2 figures; minor changes

Scientific paper

10.1088/0305-4470/37/35/001

We consider the trapping reaction A + B -> B in space dimension d=1, where the A and B particles have diffusion constants D_A, D_B respectively. We calculate the probability, Q(t), that a given A particle has not yet reacted at time t. Exploiting a recent formulation in which the B particles are eliminated from the problem we find, for t -> \infty, $Q(t) \sim \exp[-(4/\sqrt{\pi})(\rho^2 D_Bt)^{1/2} - (C \rho^2 D_A t)^{1/3} + ...]$, where $\rho$ is the density of B particles and $C \propto D_A/D_B$ for $D_A/D_B << 1$.

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