Heat conductivity from molecular chaos hypothesis in locally confined billiard systems

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 demonstated by comparing our predictions to the results of numerical simulations performed on a new class of high-dimensional defocusing chaotic billiards.

arXiv comment4 pages, 2 color figures

References in corpus (6)

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Cited by in corpus (10)

• On the derivation of Fourier's law in stochastic energy exchange systems
• Heat transport in stochastic energy exchange models of locally confined hard spheres
• Large deviations of the current in stochastic collisional dynamics
• Persistence effects in deterministic diffusion
• Hot scatterers and tracers for the transfer of heat in collisional dynamics
• A two-stage approach to relaxation in billiard systems of locally confined hard spheres
• Macroscopic fluctuations theory of aerogel dynamics
• Stable and unstable regimes in higher-dimensional convex billiards with cylindrical shape
• Dynamical contribution to the heat conductivity in stochastic energy exchanges of locally confined gases
• Chaos in cylindrical stadium billiards via a generic nonlinear mechanism