  We study the transport properties of a large class of locally confined
Hamiltonian systems, in which neighboring particles interact through hard core
elastic collisions. When these collisions become rare and the systems large, we
derive a Boltzmann-like equation for the evolution of the probability
densities. We solve this equation in the linear regime and compute the heat
conductivity from a Green-Kubo formula. The validity of our approach is
demonstated by comparing our predictions to the results of numerical
simulations performed on a new class of high-dimensional defocusing chaotic
billiards.
