On The Weak-Coupling Limit for Bosons and Fermions

2005/03/16 by Dario Benedetto, François Castella, Benedetto, Dario +5 · 2 citations
Mathematics · Physics and Astronomy · #35B40 #35C20 #35J05 #78A40 #81F30 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35B40 #msc:35C20 #msc:35J05 #msc:78A40 #msc:81F30

paper · pdf · doi:10.48550/arxiv.math/0503319

arxiv created 2005/03/16 · arxiv updated 2009/12/01

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 t, agrees with the analogous expansion for the solution to the Uehling-Uhlenbeck equation. This paper follows in spirit the companion work [\rciteBCEP], 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.

Cited by

• From the quantum Boltzmann operator to the quantum Landau operator
• The Incompressible Navier-Stokes-Fourier Limits from Boltzmann-Fermi-Dirac Equation for Low Regularity Data

Related

• From the quantum Boltzmann operator to the quantum Landau operator
• Linear Boltzmann Equation as the Weak Coupling Limit of a Random Schrodinger Equation
• Extended Weak Coupling Limit for Pauli-Fierz Operators
• Hartree-Fock dynamics for weakly interacting fermions
• Exponential decay of the number of excitations in the weakly interacting Bose gas