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We study the transport properties of a large class of locally confinedHamiltonian systems, in which neighboring particles interact through hard coreelastic collisions. When these collisions become rare and the systems large, wederive a Boltzmann-like equation for the evolution of the probabilitydensities. We solve this equation in the linear regime and compute the heatconductivity from a Green-Kubo formula. The validity of our approach isdemonstated by comparing our predictions to the results of numericalsimulations performed on a new class of high-dimensional defocusing chaoticbilliards.

Heat conductivity from molecular chaos hypothesis in locally confined billiard systems