Derivation of the Vlasov-Maxwell system from the Maxwell-Schr\"odinger equations with extended charges
Mathematical Physics
2024-02-01 v3 Analysis of PDEs
math.MP
Abstract
We consider the Maxwell-Schr\"odinger equations in the Coulomb gauge describing the interaction of extended fermions with their self-generated electromagnetic field. They heuristically emerge as mean-field equations from non-relativistic quantum electrodynamics in a mean-field limit of many fermions. In the semiclassical regime, we establish the convergence of the Maxwell-Schr\"{o}dinger equations for extended charges towards the non-relativistic Vlasov-Maxwell dynamics and provide explicit estimates on the accuracy of the approximation. To this end, we build a well-posedness and regularity theory for the Maxwell-Schr\"odinger equations and for the Vlasov-Maxwell system for extended charges.
Keywords
Cite
@article{arxiv.2308.16074,
title = {Derivation of the Vlasov-Maxwell system from the Maxwell-Schr\"odinger equations with extended charges},
author = {Nikolai Leopold and Chiara Saffirio},
journal= {arXiv preprint arXiv:2308.16074},
year = {2024}
}