PT对称周期有限能隙系统的谱奇异性
Spectral singularities in PT-symmetric periodic finite-gap systems
摘要：
研究了有限能隙单周期PT对称量子系统中谱奇异性的起源。我们表明，他们出现在一个双周期有限隙系统的带边状态的限制时，虚周期趋于无穷大。在此极限下，能隙收缩消失，能隙边缘的每对相同周期的带态合并并转变为连续谱中的单重态。因此，这些光谱奇异性与非周期系统中的那些类似，在非周期系统中它们表现为零宽度共振。在拓扑结构由非紧变为紧的情况下，我们所研究的周期系统类的谱奇异性转化为例外点。特定的退化有限数量的光谱奇异性和例外点的存在相关的是相干地反映了一个隐藏的，玻色子化的非线性超对称性。
英文摘要：
The origin of spectral singularities in finite-gap singly periodic PT-symmetric quantum systems is investigated. We show that they emerge from a limit of band-edge states in a doubly periodic finite gap system when the imaginary period tends to infinity. In this limit, the energy gaps are contracted and disappear, every pair of band states of the same periodicity at the edges of a gap coalesces and transforms into a singlet state in the continuum. As a result, these spectral singularities turn out to be analogous to those in the non-periodic systems, where they appear as zero-width resonances. Under the change of topology from a non-compact into a compact one, spectral singularities in the class of periodic systems we study are transformed into exceptional points. The specific degeneration related to the presence of finite number of spectral singularities and exceptional points is shown to be coherently reflected by a hidden, bosonized nonlinear supersymmetry.
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