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A Gauge-Covariant Semiclassical Limit from the magnetic Hartree--Fock equation to the magnetic Vlasov--Poisson equation

  • Jacky J. Chong
  • Zhuohui You
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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.

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Cite

BibTeXRIS
BibTeX
@misc{chong2026gaugecovariant,
  title = {{A Gauge-Covariant Semiclassical Limit from the magnetic Hartree--Fock equation to the magnetic Vlasov--Poisson equation}},
  author = {Jacky J. Chong and Zhuohui You},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16511},
  eprint = {2609.16511},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16511},
}
RIS
TY  - UNPB
TI  - A Gauge-Covariant Semiclassical Limit from the magnetic Hartree--Fock equation to the magnetic Vlasov--Poisson equation
AU  - Jacky J. Chong
AU  - Zhuohui You
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.16511
UR  - https://arxiv.org/abs/2609.16511
AB  - 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.
ER  -