Mécanique statistique hors d'équilibre de systèmes déterministes non-hyperboliques
(2010)
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- Authors
- Supervisors
- Bricmont, Jean
- Abstract
- (en) This thesis is made of two distinct parts. First, the behavior of a gas of non-interacting particles is analyzed. It is well known that a diffusion process may take place when the dynamic is hyperbolic (e.g. Lorentz gas), but very little is known for polygonal obstacles (e.g. Ehrenfest model). Here one analyzes a very simple model, where particles evolve according to some irrational rotation on the circle. Diffusion is not possible in that case, but, somehow surprisingly, one has been able to exhibit a diffusion process for some suitable time subsequences. A link with the hyperbolic case is also established. The second part of this dissertation deals with the much harder case of interacting particles. In particular, one is interested in a mechanical derivation of Fourier's law, governing heat transport in many kind of materials. An impure one-dimensional solid may be modeled by a chain of unequal masses, coupled between nearest neighbors. When the interaction is harmonic, the system is integrable, and many quantities can then be computed analytically. However, since the masses may be all different, a non-trivial and interesting localization phenomenon occur. With O. Ajanki (University of Helsinki), we obtained some new results on the product of random matrices, allowing us to rigorously establish the thermal conductivity in some models, among which the celebrated Casher-Lebowitz model.
- Affiliations
Citations
Huveneers, F. (2010). Mécanique statistique hors d’équilibre de systèmes déterministes non-hyperboliques. https://hdl.handle.net/2078.5/148288