One-species bimolecular reaction kinetics enhanced by anomalous diffusion.

Abstract

We show that L\'evy-walk hyperdiffusion, in which diffusing particles run over all the points of their trajectories, can enhance the kinetics of one-species bimolecular annihilation (A+A\ensuremath{\rightarrow}0) and coagulation (A+A\ensuremath{\rightarrow}A). Simple probabilistic arguments indicate that the asymptotic particle number decay goes as N(t)\ensuremath{\propto}${\mathit{t}}^{\mathrm{\ensuremath{-}}1/\ensuremath{\gamma}}$, with \ensuremath{\gamma} the L\'evy exponent (02). Therefore, for \ensuremath{\gamma}1 those reactions proceed faster than in the usual chemical-kinetics approximation, which predicts N(t)\ensuremath{\propto}${\mathit{t}}^{\mathrm{\ensuremath{-}}1}$. Our results are validated by numerical simulations. \textcopyright{} 1996 The American Physical Society.