实能量下复散射势的谱奇异性与无限反射系数和透射系数
Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
摘要：
谱奇点是破坏某些非厄米哈密顿算子本征函数完备性的谱点。我们确定了复散射势的光谱奇异性，其反射和透射系数趋于无穷大的实能量，即，它们对应于具有零宽度的谐振。我们表明，波导建模使用这样的潜在的操作像一个谐振器在频谱奇点的频率。作为一个具体的例子，我们探讨了一个假想的PT对称势垒势的谱奇异性，并证明了上述共振现象的特定电磁波波导。
英文摘要：
Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width. We show that a wave guide modeled using such a potential operates like a resonator at the frequencies of spectral singularities. As a concrete example, we explore the spectral singularities of an imaginary PT-symmetric barrier potential and demonstrate the above resonance phenomenon for a certain electromagnetic wave guide.
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