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PROPAGATION ESTIMATES FOR THE MANY-BODY BOSON STAR EQUATION

  • Sébastien Breteaux
  • Charlotte Dietze
  • Jérémy Faupin
  • Viviana Grasselli
  • Jinyeop Lee
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Abstract

We study the many-body boson star equation in the mean-field regime. Under a decay assumption on the solution to the effective one-body equation, we prove a uniform-in-time trace-norm estimate comparing the one-particle reduced density matrix of the many-body state with the projection onto the one-body solution. This establishes uniform-in-time mean-field convergence as the particle number goes to infinity. Furthermore, for the many-body dynamics, we establish both a maximal velocity bound, which can be seen as a Lieb-Robinson-type bound, and a minimal velocity bound. As an application, we recover maximal and minimal velocity bounds for the one-body boson star equation by passing to the mean-field limit.

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Cite

BibTeXRIS
BibTeX
@misc{breteaux2026propagation,
  title = {{PROPAGATION ESTIMATES FOR THE MANY-BODY BOSON STAR EQUATION}},
  author = {Sébastien Breteaux and Charlotte Dietze and Jérémy Faupin and Viviana Grasselli and Jinyeop Lee},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36388},
  eprint = {2610.36388},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05844717v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - PROPAGATION ESTIMATES FOR THE MANY-BODY BOSON STAR EQUATION
AU  - Sébastien Breteaux
AU  - Charlotte Dietze
AU  - Jérémy Faupin
AU  - Viviana Grasselli
AU  - Jinyeop Lee
PY  - 2026
DA  - 2026/10/26
PB  - HAL
DO  - 10.48550/arxiv.2610.36388
UR  - https://hal.science/hal-05844717v1
AB  - We study the many-body boson star equation in the mean-field regime. Under a decay assumption on the solution to the effective one-body equation, we prove a uniform-in-time trace-norm estimate comparing the one-particle reduced density matrix of the many-body state with the projection onto the one-body solution. This establishes uniform-in-time mean-field convergence as the particle number goes to infinity. Furthermore, for the many-body dynamics, we establish both a maximal velocity bound, which can be seen as a Lieb-Robinson-type bound, and a minimal velocity bound. As an application, we recover maximal and minimal velocity bounds for the one-body boson star equation by passing to the mean-field limit.
ER  -