[Untitled]

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.