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Modified Scattering for Infinite-Rank Hartree--Fock Equations

  • Masaki Kawamoto
  • Jinyeop Lee
  • Changhun Yang
  • Chanjin You
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Abstract

We study the long-time behavior of the Hartree--Fock equation with Coulomb interaction in dimensions d≥2 for small initial density matrices of possibly infinite rank. We prove global well-posedness and modified scattering governed by a resonant Hartree-Fock equation. Our approach is based on the half-density formulation and a final-state construction for the resonant dynamics. We also characterize the stationary states of the resonant Hartree--Fock equation and prove that ordinary linear scattering fails when the initial density matrix has rank at least two. These results extend long-range modified scattering to genuinely operator-valued infinite-rank Hartree-Fock evolution. Despite cancellation between the direct and exchange terms, the long-range effect persists, with resonant dynamics evolving on the same logarithmic time scale as in the Hartree equation.

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Cite

BibTeXRIS
BibTeX
@misc{kawamoto2026modified,
  title = {{Modified Scattering for Infinite-Rank Hartree--Fock Equations}},
  author = {Masaki Kawamoto and Jinyeop Lee and Changhun Yang and Chanjin You},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38676},
  eprint = {2610.38676},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38676},
}
RIS
TY  - UNPB
TI  - Modified Scattering for Infinite-Rank Hartree--Fock Equations
AU  - Masaki Kawamoto
AU  - Jinyeop Lee
AU  - Changhun Yang
AU  - Chanjin You
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38676
UR  - https://arxiv.org/abs/2610.38676
AB  - We study the long-time behavior of the Hartree--Fock equation with Coulomb interaction in dimensions d≥2 for small initial density matrices of possibly infinite rank. We prove global well-posedness and modified scattering governed by a resonant Hartree-Fock equation. Our approach is based on the half-density formulation and a final-state construction for the resonant dynamics. We also characterize the stationary states of the resonant Hartree--Fock equation and prove that ordinary linear scattering fails when the initial density matrix has rank at least two. These results extend long-range modified scattering to genuinely operator-valued infinite-rank Hartree-Fock evolution. Despite cancellation between the direct and exchange terms, the long-range effect persists, with resonant dynamics evolving on the same logarithmic time scale as in the Hartree equation.
ER  -