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.
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.
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
@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}, pages = {1031--1076}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {3}, year = {2014}, doi = {10.5802/aif.2873}, zbl = {1315.82015}, mrnumber = {3330163}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2873/} }
TY - JOUR AU - Breteaux, Sébastien TI - A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach JO - Annales de l'Institut Fourier PY - 2014 SP - 1031 EP - 1076 VL - 64 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2873/ DO - 10.5802/aif.2873 LA - en ID - AIF_2014__64_3_1031_0 ER -
%0 Journal Article %A Breteaux, Sébastien %T A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach %J Annales de l'Institut Fourier %D 2014 %P 1031-1076 %V 64 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2873/ %R 10.5802/aif.2873 %G en %F 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, Volume 64 (2014) no. 3, pp. 1031-1076. doi : 10.5802/aif.2873. https://aif.centre-mersenne.org/articles/10.5802/aif.2873/
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