On The Weak-Coupling Limit for Bosons and Fermions
Abstract
In this paper we consider a large system of Bosons or Fermions. We start with an initial datum which is compatible with the Bose-Einstein, respectively Fermi-Dirac, statistics. We let the system of interacting particles evolve in a weak-coupling regime. We show that, in the limit, and up to the second order in the potential, the perturbative expansion expressing the value of the one-particle Wigner function at time , agrees with the analogous expansion for the solution to the Uehling-Uhlenbeck equation. This paper follows in spirit the companion work [\rcite{BCEP}], where the authors investigated the weak-coupling limit for particles obeying the Maxwell-Boltzmann statistics: here, they proved a (much stronger) convergence result towards the solution of the Boltzmann equation.
Cite
@article{arxiv.math/0503319,
title = {On The Weak-Coupling Limit for Bosons and Fermions},
author = {Dario Benedetto and François Castella and Raffaele Esposito and M. Pulvirenti},
journal= {arXiv preprint arXiv:math/0503319},
year = {2007}
}