Microscopic chaos and reaction-diffusion processes in the periodic Lorentzgas

We apply the hypothesis of microscopic chaos to diffusion-controlled reacti on which we study in a reactive periodic Lorentz gas. The relaxation rate o f 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 generaliza tions of Lebesgue's singular continuous functions. For small enough densiti es 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 cataly sts.