Multiple scattering in random mechanical systems and diffusion approximation (Q382279)

The paper addresses emergent random processes (diffusion limits) that model multiple scattering events in classical dynamical systems of billiard type. Examples considered are: (i) weak scattering between two parallel plates, (ii) scattering on a rough surface. The convergence of associated random map operators to a second-order elliptic differential operator on compactly supported functions is analyzed. It is shown that the associated Markov chain process converges to a diffusion and its generator is derived. Stationary measures are identified as Maxwell-Boltzmann and Knudsen cosine distributions. The approximating diffusion processes are specified as the Maxwell-Boltzmann (post-collision) diffusion and generalized Legendre diffusion. Numerical simulations are implemented to give a visual picture of dynamical phenomena at hand.