三粒子Sutherland模型的泊松型对关联
Poissonian pair correlations for the three-particle Sutherland model
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中文总结 AI 辅助
本研究证明了排斥性三粒子三角Sutherland哈密顿量的Berry-Tabor定理，发现固定总动量下其相对谱为正定A₂型的仿射平移，丢番图耦合时去对称化谱具有泊松型对关联，证明归结为Marklof相关定理的有限同余与外尔区域版本。
中文摘要 AI 辅助
我们证明了排斥性三粒子三角Sutherland哈密顿量的Berry-Tabor定理。在固定总动量下，其相对谱是正定A₂型的仿射平移。对于丢番图耦合，去对称化谱具有泊松型对关联。该证明将问题归结为Marklof关于非齐次二次型定理的有限同余与外尔区域版本。
英文摘要
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.
