Derivation of the Vlasov-Maxwell system from the Maxwell-Schrödinger equations with extended charges

2023/08/30 by Leopold, Nikolai, Saffirio, Chiara
#35Q41 #35Q83 #81Q20 #82C10 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2308.16074

Abstract

We consider the Maxwell-Schrödinger 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-Schrödinger 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-Schrödinger equations and for the Vlasov-Maxwell system for extended charges.

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