2016/09/30 by Sören Petrat
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Coulomb #Dynamics (music) #Fermion #Hartree #High-Energy Particle Collisions Research #Kinetic energy #Limit (mathematics) #Quantum Chromodynamics and Particle Interactions #Scaling #math-ph #math.MP #msc:35Q40 #msc:35Q55 #msc:81Q05 #msc:82C10 #quant-ph
paper · pdf · doi:10.1088/1751-8121/aa6e0b
published as Journal of Physics A: Mathematical and Theoretical, 50(24) (2017) · 17 pages, LaTex
openalex publication_date 2017/04/20 · openalex created_date 2017/04/28 · arxiv created 2017/05/24 · arxiv updated 2017/05/26 · openalex updated_date 2026/08/05
Abstract We consider the many-body dynamics of fermions with Coulomb interaction in a mean-field scaling limit where the kinetic and potential energy are of the same order for large particle numbers. In the considered limit the spatial variation of the mean-field is small. We prove two results about this scaling limit. First, due to the small variation, i.e., small forces, we show that the many-body dynamics can be approximated by the free dynamics with an appropriate phase factor with the conjectured optimal error term. Second, we show that the Hartree dynamics gives a better approximation with a smaller error term. In this sense, assuming that the error term in the first result is optimal, we derive the Hartree equations from the many-body dynamics with Coulomb interaction in a mean-field scaling limit.