Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 15, Issue 12, Pages 1811-1843Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202505000984
Keywords
uehling-uhlenbeck equation; quantum systems; weak coupling
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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 t, agrees with the analogous expansion for the solution to the Uehling-Uhlenbeck equation. This paper follows the same spirit as the companion work,(2) 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.
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