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Article Dans Une Revue Annales de l'Institut Henri Poincare Physique Theorique Année : 2018

Derivation of an ornstein-uhlenbeck process for a massive particle in a rarified gas of particles

Résumé

We consider the statistical motion of a convex rigid body in a gas of N smaller (spherical) atoms close to thermodynamic equilibrium. Because the rigid body is much bigger and heavier, it undergoes a lot of collisions leading to small deflections. We prove that its velocity is described, in a suitable limit, by an Ornstein-Uhlenbeck process. The strategy of proof relies on Lanford's arguments [17] together with the pruning procedure from [3] to reach diffusive times, much larger than the mean free time. Furthermore, we need to introduce a modified dynamics to avoid pathological collisions of atoms with the rigid body: these collisions, due to the geometry of the rigid body, require developing a new type of trajectory analysis.
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Dates et versions

hal-01609594 , version 1 (04-10-2017)

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Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond. Derivation of an ornstein-uhlenbeck process for a massive particle in a rarified gas of particles. Annales de l'Institut Henri Poincare Physique Theorique, 2018, 19 (6), ⟨10.1007/s00023-018-0674-6⟩. ⟨hal-01609594⟩
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