具有δ-位势的周期可积系统
Periodic integrable systems with delta-potentials
摘要：
本文研究了具有两两δ函数相互作用的圆上量子玻色气体的根系推广。基本的对称结构所示的相关的分级的切雷德尼克的（适当过滤）退化的双仿射Hecke代数，由Dunkl型微分反射算子。我们利用Gutkin关于不可穿透玻色气体与自由费米气体之间等价性的推广，导出了Bethe平衡方程和Bethe平衡本征函数。
英文摘要：
In this paper we study root system generalizations of the quantum Bose-gas on the circle with pair-wise delta function interactions. The underlying symmetry structures are shown to be governed by the associated graded of Cherednik's (suitably filtered) degenerate double affine Hecke algebra, acting by Dunkl-type differential-reflection operators. We use Gutkin's generalization of the equivalence between the impenetrable Bose-gas and the free Fermi-gas to derive the Bethe ansatz equations and the Bethe ansatz eigenfunctions.
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