Time evolution in a two-component systems with catalytic reactions

We study the time evolution of a large system consisting of two kinds of particles that can be transformed into each other by (a) an external potential with momentum mixing and (b) a uniform and random distribution of static, short-ranged scattering centers. Integral eqautions are solved exactly for separable interactions. For weak potentials we again find an oscillatory time evolution in the particle density with stronger damping but qualitatively similar to previous results in a model with a constant external field.