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Poissonian pair correlations for the three-particle Sutherland model

  • Christopher Lutsko
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Abstract

We prove a Berry-Tabor theorem for the repulsive three-particle trigonometric Sutherland Hamiltonian. For fixed total momentum, its relative spectrum is an affine translate of the positive-definite A2-form. For a Diophantine coupling, the desymmetrized spectrum has Poissonian pair correlation. The proof reduces the problem to a finite-congruence and Weyl-sector version of Marklof's theorem on inhomogeneous quadratic forms.

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Cite

BibTeXRIS
BibTeX
@misc{lutsko2026poissonian,
  title = {{Poissonian pair correlations for the three-particle Sutherland model}},
  author = {Christopher Lutsko},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03112},
  eprint = {2609.03112},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03112},
}
RIS
TY  - UNPB
TI  - Poissonian pair correlations for the three-particle Sutherland model
AU  - Christopher Lutsko
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.03112
UR  - https://arxiv.org/abs/2609.03112
AB  - We prove a Berry-Tabor theorem for the repulsive three-particle trigonometric Sutherland Hamiltonian. For fixed total momentum, its relative spectrum is an affine translate of the positive-definite A_2-form. For a Diophantine coupling, the desymmetrized spectrum has Poissonian pair correlation. The proof reduces the problem to a finite-congruence and Weyl-sector version of Marklof's theorem on inhomogeneous quadratic forms.
ER  -