A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field

Sébastien Breteaux (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is geometric and involves coherent states and semi-classical calculus.

Mots clés: Linear Boltzmann equation; Processes in random environments; Quantum field theory; Coherent states; Kinetic theory of gases

Domaines: Physique mathématique [math-ph]

Sébastien Breteaux. A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field. Annales de l'Institut Fourier, 2014, 64 (3), pp.1031-1076. ⟨hal-00605919v2⟩