A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach  [ Une dérivation géométrique de l’équation de Boltzmann linéaire pour une particule en interaction avec un champ aléatoire gaussien, utilisant l’espace de Fock ]
Annales de l'Institut Fourier, Tome 64 (2014) no. 3, p. 1031-1076
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.
DOI : https://doi.org/10.5802/aif.2873
Classification:  82C10,  60K37,  81Exx,  81Sxx,  81D30,  82B44,  82C40
Mots clés: Équation de Boltzmann linéaire, processus dans des environnements aléatoires, théorie quantique des champs, états cohérents, théorie cinétique des gaz
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {3},
     year = {2014},
     pages = {1031-1076},
     doi = {10.5802/aif.2873},
     zbl = {1315.82015},
     mrnumber = {3330163},
     zbl = {06387300},
     language = {en},
     url = {http://http://www.numdam.org/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) no. 3, pp. 1031-1076. doi : 10.5802/aif.2873. http://www.numdam.org/item/AIF_2014__64_3_1031_0/

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