We investigate the properties of two anti-parity-time (anti-$\mathcal{PT}$)-symmetric four-site scattering centers. The anti-$\mathcal{PT}$-symmetric scattering center may have imaginary couplings, real couplings, and real on-site potentials. The only difference between the two scattering centers is the coupling between two central sites of the scattering center, which plays a crucial role in determining the parity of anti-$\mathcal{PT}$ symmetry and significantly affects the scattering properties. For the imaginary coupling, the even-parity anti-$\mathcal{PT}$-symmetric scattering center possesses nonunitary scattering and the difference between the reflection and transmission is unity; for the real coupling, the odd-parity anti-$\mathcal{PT}$-symmetric scattering center possesses unitary scattering and the sum of the reflection and transmission is unity. The coupling-induced different scattering behaviors are verified in the numerical simulations. Our findings reveal that a significant difference in the dynamics can be caused by a slight difference between two similar anti-$\mathcal{PT}$-symmetric non-Hermitian scattering centers.

中文翻译：

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反对PT对称非厄米系统中耦合引起的非酉和酉散射

我们研究了两个反奇偶校验时间（anti-$\mathcal{PT}$)-对称四点散射中心。反$\mathcal{PT}$-对称散射中心可能具有虚耦合、实耦合和实现场电位。两个散射中心之间的唯一区别是散射中心两个中心位置之间的耦合，这在确定抗性的奇偶性方面起着至关重要的作用。$\mathcal{PT}$对称性并显着影响散射特性。对于虚耦合，偶校验反$\mathcal{PT}$-对称散射中心具有非幺正散射，反射与透射之差为一；对于实际耦合，奇偶校验反$\mathcal{PT}$-对称散射中心具有单一散射，反射与透射之和为一。在数值模拟中验证了耦合引起的不同散射行为。我们的研究结果表明，动态的显着差异可能是由于两种类似的抗$\mathcal{PT}$对称非厄米散射中心。