A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach

Sébastien Breteaux[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.

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 3, page 1031-1076
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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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 64.3 (2014): 1031-1076. <http://eudml.org/doc/275529>.

@article{Breteaux2014,
abstract = {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.},
affiliation = {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.},
author = {Breteaux, Sébastien},
journal = {Annales de l’institut Fourier},
keywords = {Linear Boltzmann equation; processes in random environments; quantum field theory; coherent states; kinetic theory of gases; linear Boltzmann equation; Fock space; Weyl quantization; Gaussian random field; random potential; renewal of a random field; a priori estimates},
language = {eng},
number = {3},
pages = {1031-1076},
publisher = {Association des Annales de l’institut Fourier},
title = {A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach},
url = {http://eudml.org/doc/275529},
volume = {64},
year = {2014},
}

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
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 3
SP - 1031
EP - 1076
AB - 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.
LA - eng
KW - Linear Boltzmann equation; processes in random environments; quantum field theory; coherent states; kinetic theory of gases; linear Boltzmann equation; Fock space; Weyl quantization; Gaussian random field; random potential; renewal of a random field; a priori estimates
UR - http://eudml.org/doc/275529
ER -

References

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