no. 3
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]
Breteaux, Sébastien1
1 IRMAR, UMR-CNRS 6625, Université de Rennes 1, campus de Beaulieu, 35042 Rennes Cedex, France. ENS de Cachan, Antenne de Bretagne, Campus de Ker Lann, Av. R. Schuman, 35170 Bruz, France.
Annales de l'Institut Fourier, Tome 64 (2014) no. 3, pp. 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 : 10.5802/aif.2873
Classification : 82C10, 60K37, 81Exx, 81Sxx, 81D30, 82B44, 82C40
Keywords: Linear Boltzmann equation, processes in random environments, quantum field theory, coherent states, kinetic theory of gases.
Mot clés : Équation de Boltzmann linéaire, processus dans des environnements aléatoires, théorie quantique des champs, états cohérents, théorie cinétique des gaz
Breteaux, Sébastien 1

1 IRMAR, UMR-CNRS 6625, Université de Rennes 1, campus de Beaulieu, 35042 Rennes Cedex, France. ENS de Cachan, Antenne de Bretagne, Campus de Ker Lann, Av. R. Schuman, 35170 Bruz, France. 
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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/articles/10.5802/aif.2873/

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