From Hartree dynamics to the relativistic Vlasov equation
Mathematical Physics
2018-03-14 v1 math.MP
Abstract
We derive the relativistic Vlasov equation from quantum Hartree dynamics for fermions with relativistic dispersion in the mean-field scaling, which is naturally linked with an effective semiclassic limit. Similar results in the non-relativistic setting have been recently obtained in [6]. The new challenge that we have to face here, in the relativistic setting, consists in controlling the difference between the quantum kinetic energy and the relativistic transport term appearing in the Vlasov equation.
Keywords
Cite
@article{arxiv.1709.02711,
title = {From Hartree dynamics to the relativistic Vlasov equation},
author = {Elia Dietler and Simone Rademacher and Benjamin Schlein},
journal= {arXiv preprint arXiv:1709.02711},
year = {2018}
}
Comments
30 pages