A Gauge-Covariant Semiclassical Limit from the magnetic Hartree--Fock equation to the magnetic Vlasov--Poisson equation
Year: 2026
Type: preprint
Abstract: We study the semiclassical limit from the magnetic Hartree--Fock equation to the magnetic Vlasov--Poisson equation in three spatial dimensions in the presence of a nonuniform, purely space-dependent magnetic field. We first establish propagation of regularity for solutions of the magnetic Vlasov--Poisson equation under exponentially weighted assumptions. Building on this result and a gauge-covariant magnetic Weyl quantization framework, we then derive explicit convergence bounds for the semiclassical limit in semiclassical Schatten norms. In particular, the estimates are formulated in terms of the magnetic field rather than a particular choice of vector potential and are therefore gauge covariant. The resulting semiclassical convergence holds for a suitable class of initial data on any fixed finite time interval.
Source: arXiv (Cornell University)
Authors: Chong, Jacky J., You, Zhuohui
Institutions: Beijing Institute of Technology, Beijing Normal University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213411123