Dans cet article, l’équation de Boltzmann linéaire est dérivée pour une particule interagissant avec un champ aléatoire gaussien, dans la limite de faible couplage, avec un renouvellement temporel du champ aléatoire. L’état initial peut être choisi de façon arbitraire. La démonstration est géométrique et fait intervenir des états cohérents et du calcul semi-classique.
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.
@article{AIF_2014__64_3_1031_0,
author = {Breteaux, S\'ebastien},
title = {A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach},
journal = {Annales de l'Institut Fourier},
volume = {64},
year = {2014},
pages = {1031-1076},
doi = {10.5802/aif.2873},
zbl = {06387300},
mrnumber = {3330163},
zbl = {1315.82015},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_2014__64_3_1031_0}
}
Breteaux, Sébastien. A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach. Annales de l'Institut Fourier, Tome 64 (2014) pp. 1031-1076. doi : 10.5802/aif.2873. http://gdmltest.u-ga.fr/item/AIF_2014__64_3_1031_0/
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