PT -symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model
PT -symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model
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DOI：
10.1103/physreva.93.032129
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发表时间：
2015-10
影响因子：
2.9
通讯作者：
Baogang Zhu;R. Lu;Shu Chen
中科院分区：
文献类型：
--
作者：
Baogang Zhu;R. Lu;Shu Chen
本文研究了一维非厄米密结晶格模型的对称性破缺问题，该模型的增益和损失分布在相邻的两个位置上。在散射过程中，随着复电位振幅的增加，系统经历了从精确的$\mathcal{PT} $-对称相位到自发破坏$\mathcal{PT} $-对称相位的转变。利用s矩阵方法，导出了一种精确判别法，可用于区分不同的对称相位，并解析确定对称破缺的异常点。在$\mathcal{PT} $-对称破缺区，我们也证实了在这个简单的非厄米晶格模型中出现了独特的特征，即相干完全吸收激光。对这种简单模型的散射问题的研究，为揭示非厄米数学{PT} $对称势的物理效应提供了一个新的途径。
We study the $\mathcal{PT} $-symmetry breaking for the scattering problem in a one-dimensional (1D) non-Hermitian tight-binding lattice model with balanced gain and loss distributed on two adjacent sites. In the scattering process the system undergoes a transition from the exact $\mathcal{PT} $-symmetry phase to the phase with spontaneously breaking $\mathcal{PT} $-symmetry as the amplitude of complex potentials increases. Using the S-matrix method, we derive an exact discriminant, which can be used to distinguish different symmetry phases, and analytically determine the exceptional point for the symmetry breaking. In the $\mathcal{PT} $-symmetry breaking region, we also confirm the appearance of the unique feature, i.e., the coherent perfect absorption Laser, in this simple non-Hermitian lattice model. The study of the scattering problem of such a simple model provides an additional way to unveil the physical effect of non-Hermitian $\mathcal{PT} $-symmetric potentials.