具有两个可积极限的配对模型中量子简并的意外特征
Unexpected features of quantum degeneracies in a pairing model with two integrable limits
摘要：
研究了具有两种不同可积极限的不可积对模型中能级交叉和例外点的演化模式。其中一个可积极限有两个独立的与参数有关的运动积分。我们证明，并说明在我们的模型中，量子可积性的一个系统与一个以上的参数依赖的运动积分总是由一个复杂的扩展哈密顿的水平交叉信号。我们还发现，可积性意味着减少例外点的数量。这两个性质可以唯一地刻画小希尔伯特空间中的量子可积性。
英文摘要：
The evolution pattern of level crossings and exceptional points is studied in a non-integrable pairing model with two different integrable limits. One of the integrable limits has two independent parameter-dependent integrals of motion. We demonstrate, and illustrate in our model, that quantum integrability of a system with more than one parameter-dependent integral of motion is always signaled by level crossings of a complex-extended Hamiltonian. We also find that integrability implies a reduced number of exceptional points. Both properties could uniquely characterize quantum integrability in small Hilbert spaces.
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