Classical limit for semi-relativistic Hartree systems
Mathematical Physics
2009-11-13 v1 Astrophysics
Analysis of PDEs
math.MP
Abstract
We consider the three-dimensional semi-relativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the initial density matrix as a (fully) mixed quantum state we prove, using Wigner transformation techniques, that its classical limit yields the well known relativistic Vlasov-Poisson system. The result holds for the case of attractive and repulsive mean-field interaction, with an additional size constraint in the attractive case.
Keywords
Cite
@article{arxiv.0810.5457,
title = {Classical limit for semi-relativistic Hartree systems},
author = {Gonca L. Aki and Peter A. Markowich and Christof Sparber},
journal= {arXiv preprint arXiv:0810.5457},
year = {2009}
}
Comments
10 pages