Reaction-diffusion with a time-dependent reaction rate: the single-species diffusion-annihilation process
نویسنده
چکیده
We study the single-species diffusion-annihilation process with a time-dependent reaction rate, λ(t) = λ0 t−ω . Scaling arguments show that there is a critical value of the decay exponent ωc(d) separating a reaction-limited regime for ω > ωc from a diffusion-limited regime for ω < ωc. The particle density displays a mean-field, ω-dependent, decay when the process is reaction-limited whereas it behaves as for a constant reaction rate when the process is diffusionlimited. These results are confirmed by Monte Carlo simulations. They allow to discuss the scaling behaviour of coupled diffusion-annihilation processes in terms of effective time-dependent reaction rates. PACS numbers: 82.20.-w, 05.40.-a, 05.70.Ln
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