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arXiv · 2308.16074

Derivation of the Vlasov-Maxwell system from the Maxwell-Schr\"odinger equations with extended charges

Nikolai Leopold·Chiara Saffirio
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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.

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Nikolai Leopold, Chiara Saffirio. 2023-08-30. Derivation of the Vlasov-Maxwell system from the Maxwell-Schr\"odinger equations with extended charges. https://arxiv.org/abs/2308.16074

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