Quantum Birkhoff Normal Form in the $\sigma$-Bruno-R\"{u}ssmann non-resonant condition

Huanhuan Yuan; Yixian Gao; Yong Li

Quantum Birkhoff Normal Form in the $\sigma$-Bruno-R\"{u}ssmann non-resonant condition

Mathematical Physics 2026-01-12 v2 math.MP

Authors: Huanhuan Yuan , Yixian Gao , Yong Li

Abstract

The aim of this paper is to construct a Gevrey quantum Birkhoff normal form for the $h$ -differential operator $P_{h}(t),$ where $t\in(-\frac{1}{2},\frac{1}{2})$ , in the neighborhood of the union $\Lambda$ of KAM tori. This construction commences from an appropriate Birkhoff normal form of $H$ around $\Lambda$ and proceeds under the $\sigma$ -Bruno-R\"{u}ssmann condition with $\sigma>1$ .

Keywords

quantum Birkhoff normal form sigma-Bruno-Rüssmann condition Gevrey regularity h-differential operator KAM tori non-resonant condition

Cite

@article{arxiv.2501.05041,
  title  = {Quantum Birkhoff Normal Form in the $\sigma$-Bruno-R\"{u}ssmann non-resonant condition},
  author = {Huanhuan Yuan and Yixian Gao and Yong Li},
  journal= {arXiv preprint arXiv:2501.05041},
  year   = {2026}
}

Quantum Birkhoff Normal Form in the $\sigma$-Bruno-R\"{u}ssmann non-resonant condition

Abstract

Keywords

Cite

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