论文标题
极度破碎的广义$ \ Mathcal {pt} $对称性
Extremely broken generalized $\mathcal{PT}$ symmetry
论文作者
论文摘要
我们讨论了具有反对称对称性的非热门操作员的一些简单的Hückel样矩阵表示，其中包括通用$ \ Mathcal {pt} $（均等转换，然后是时间逆转）对称性。其中一个表现出极度破碎的反对称对称性（对于模型参数的所有非平凡值的复杂特征值），因为操作员在Hermitian极限中的堕落性。这些示例说明了点组对称对非热门操作员光谱的影响。我们通过非热门操作员的简单图形表示来构建必要的统一矩阵。
We discuss some simple Hückel-like matrix representations of non-Hermitian operators with antiunitary symmetries that include generalized $\mathcal{PT}$ (parity transformation followed by time-reversal) symmetry. One of them exhibits extremely broken antiunitary symmetry (complex eigenvalues for all nontrivial values of the model parameter) because of the degeneracy of the operator in the Hermitian limit. These examples illustrate the effect of point-group symmetry on the spectrum of the non-Hermitian operators. We construct the necessary unitary matrices by means of simple graphical representations of the non-Hermitian operators.
