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arXiv · 2411.07085

Derivation of the Maxwell-Schr\"odinger and Vlasov-Maxwell Equations from Non-Relativistic QED

Nikolai Leopold
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Abstract

We study the spinless Pauli-Fierz Hamiltonian in a semiclassical mean-field limit of many fermions. For appropriate initial conditions, we prove, in the trace norm topology of reduced density matrices, that the many-body quantum state converges to a tensor product of a semiclassically structured Slater determinant and a coherent photon state. These evolve according to a fermionic variant of the Maxwell-Schr\"odinger equations. By combining this result with [arXiv:2308.16074] through a suitable regularization of the initial data, we further show that, in the limit of large particle number, the dynamics of the Pauli-Fierz Hamiltonian can be approximately described by the non-relativistic Vlasov--Maxwell system for extended charges.

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Nikolai Leopold. 2024-11-11. Derivation of the Maxwell-Schr\"odinger and Vlasov-Maxwell Equations from Non-Relativistic QED. https://arxiv.org/abs/2411.07085

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