Universal behaviour of N-body decay processes

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Abstract
The authors present a scaling approach to investigate the kinetics of the diffusion-controlled multiparticle reactions A1+A2+. . .+AN to inert, and NA to inert, for a random initial distribution of particles. For the first reaction, if the initial densities of all the particle species are equal, the particle density decays with time t as t- alpha , where alpha =1/4d, and d is the spatial dimension. This exponent values is independent of N below an upper critical dimension of dc=4/(N-1), while for d>or=dc, alpha assumes the mean-field value of 1/N(N-1). For the decay NA to inert, alpha =1/2d, again independent of N, for dc=2/(N-1). These universal decays stem from the reaction kinetics being governed by the decay of spatial fluctuations, an effect which is insensitive to the details of the reaction. The author's predictions are tested by extensive computer simulations. They also examine in detail the reaction A1+A2+A3 to inert for arbitrary initial densities of the three reactants and elucidate a number of interesting asymptotic properties.

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