2024/11/11 by Nikolai Leopold, Leopold, Nikolai
Physics and Astronomy · #35Q40 #35Q83 #81V10 #82C10 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Laser-Plasma Interactions and Diagnostics #Mathematical Physics (math-ph) #Quantum Chromodynamics and Particle Interactions #Quantum and Classical Electrodynamics
paper · pdf · doi:10.48550/arxiv.2411.07085
openalex publication_date 2024/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
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-Schrödinger 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.