非厄米$PT-$对称Bose-哈伯德模型：高阶例外点开折的特征值环
A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
摘要：
我们研究了一个非厄米$PT-$对称推广的$N$粒子，双模玻色-哈伯德系统，例如一个玻色-爱因斯坦凝聚体在一个双阱势耦合到一个连续体通过一个阱中的汇和一个源在其他的。粒子相互作用和非厄米性之间的相互作用对光谱的特征的影响进行了分析，特别注意例外点（EPs）的发生和展开。我们发现，对于消失的粒子相互作用，只有两个EPs的顺序$N+1$扰动下展开成$[(N+1)/2]$本征值对（和$N+1$奇数的情况下，到一个额外的零本征值）或本征值三元组（三阶本征值环）和$(N+1)\mod 3$单本征值，这取决于在参数空间中的扰动方向。这种行为是用微扰技术分析描述的。更一般的EP展开到本征值环高达$(N+1)$ th阶表示。
英文摘要：
We study a non-Hermitian $PT-$symmetric generalization of an $N$-particle, two-mode Bose-Hubbard system, modeling for example a Bose-Einstein condensate in a double well potential coupled to a continuum via a sink in one of the wells and a source in the other. The effect of the interplay between the particle interaction and the non-Hermiticity on characteristic features of the spectrum is analyzed drawing special attention to the occurrence and unfolding of exceptional points (EPs). We find that for vanishing particle interaction there are only two EPs of order $N+1$ which under perturbation unfold either into $[(N+1)/2]$ eigenvalue pairs (and in case of $N+1$ odd, into an additional zero-eigenvalue) or into eigenvalue triplets (third-order eigenvalue rings) and $(N+1)\mod 3$ single eigenvalues, depending on the direction of the perturbation in parameter space. This behavior is described analytically using perturbational techniques. More general EP unfoldings into eigenvalue rings up to $(N+1)$th order are indicated.
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