Microscopic chaos and reaction-diffusion processes in the periodic Lorentz gas

摘要

We apply the hypothesis of microscopic chaos to diffusion-controlled reaction which we study in a reactive periodic Lorentz gas. The relaxation rate of the reactive eigenmodes is obtained as eigenvalue of the Frobenius-Perron operator, which determines the reaction rate. The cumulative functions of the eigenstates of the Frobenius-Perron operator are shown to be generalizations of Lebesgue's singular continuous functions. For small enough densities of catalysts, the reaction is controlled by the diffusion. A random-walk model of this diffusion-controlled reaction process is presented, which is used to study the dependence of the reaction rate on the density of catalysts. [References: 32]