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Published on: September 5, 2018
Heat conductivity from molecular chaos hypothesis in locally confined billiard systems
Thomas Gilbert1, Raphaël Lefevere
1Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium.
Abstract:
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 demonstrated by comparing our predictions with the results of numerical simulations performed on a new class of high-dimensional defocusing chaotic billiards.
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