$\mathcal{PT}$对称环的谱、本征态和输运性质
Spectra, eigenstates and transport properties of a $\mathcal{PT}$-symmetric ring
摘要：
我们研究，解析和数值，一个简单的$\mathcal{PT}$对称紧束缚环与现场能量$a$的增益和损失的网站。我们表明，如果$a\neq 0$，系统一般表现出不间断的$\mathcal{PT}$对称相。我们研究的频谱的性质在复杂的参数空间中的奇异性，以及在大的增益和损耗强度值的本征态的行为。我们发现，除了通常的例外点，有“恶魔点”，逆例外点，复特征值重新转换为实特征值。我们还研究了通过该系统的传输。我们计算从源到漏的总通量，以及它如何沿着环的分支分裂。我们发现，虽然通常的密度流从源极到漏极，对于某些本征态的一个固定的“回流”的密度从漏极到源极沿一个分支可以发生。我们还确定了两种类型的奇异本征态，即不依赖于增益和损耗的强度的状态，并根据它们的输运性质对它们进行分类。
英文摘要：
We study, analytically and numerically, a simple $\mathcal{PT}$-symmetric tight-binding ring with an onsite energy $a$ at the gain and loss sites. We show that if $a\neq 0$, the system generically exhibits an unbroken $\mathcal{PT}$-symmetric phase. We study the nature of the spectrum in terms of the singularities in the complex parameter space as well as the behavior of the eigenstates at large values of the gain and loss strength. We find that in addition to the usual exceptional points, there are "diabolical points", and inverse exceptional points at which complex eigenvalues reconvert into real eigenvalues. We also study the transport through the system. We calculate the total flux from the source to the drain, and how it splits along the branches of the ring. We find that while usually the density flows from the source to the drain, for certain eigenstates a stationary "backflow" of density from the drain to the source along one of the branches can occur. We also identify two types of singular eigenstates, i.e. states that do not depend on the strength of the gain and loss, and classify them in terms of their transport properties.
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