非对易欧氏李代数型系统的自发PT对称破缺
Spontaneous PT-symmetry breaking for systems of noncommutative Euclidean Lie algebraic type
摘要：
我们提出了一个非交换的欧几里德李代数$E_2$。几种类型的非厄米特哈密顿系统表示的通用组合，这个代数进行了研究。使用的明确构建的Dyson映射作为一个criterium的故障，我们确定的域中的参数空间中的哈密顿有真正的能量谱和确定的例外点，标志着交叉到不同类型的自发破PT对称区域的复共轭特征值对。我们发现例外点保持不变的变形下，以及例外点成为依赖于变形参数的代数。
英文摘要：
We propose a noncommutative version of the Euclidean Lie algebra $E_2$. Several types of non-Hermitian Hamiltonian systems expressed in terms of generic combinations of the generators of this algebra are investigated. Using the breakdown of the explicitly constructed Dyson maps as a criterium, we identify the domains in the parameter space in which the Hamiltonians have real energy spectra and determine the exceptional points signifying the crossover into the different types of spontaneously broken PT-symmetric regions with pairs of complex conjugate eigenvalues. We find exceptional points which remain invariant under the deformation as well as exceptional points becoming dependent on the deformation parameter of the algebra.
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