Reaction-diffusion with a time-dependent reaction rate: the single-species diffusion-annihilation process

2004/07/31 by L. Turban
Physics and Astronomy · #cond-mat.stat-mech

paper · pdf · doi:10.1088/0305-4470/37/35/005

published as J. Phys. A 37 (2004) 8467 · 11 pages, 9 figures, minor corrections

arxiv created 2004/08/20 · arxiv updated 2009/12/01

Abstract

We study the single-species diffusion-annihilation process with a time-dependent reaction rate, lambda(t)=lambda₀ t^-omega. Scaling arguments show that there is a critical value of the decay exponent omega_c(d) separating a reaction-limited regime for omega > omega_c from a diffusion-limited regime for omega < omega_c. The particle density displays a mean-field, omega-dependent, decay when the process is reaction limited whereas it behaves as for a constant reaction rate when the process is diffusion limited. These results are confirmed by Monte Carlo simulations. They allow us to discuss the scaling behaviour of coupled diffusion-annihilation processes in terms of effective time-dependent reaction rates.

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