非Hermitian Friedrichs-Fano-Anderson模型的谱奇异性
Spectral singularities in a non-Hermitian Friedrichs-Fano-Anderson model
摘要：
预测发生在非厄米扩展的弗里德里希-法诺-安德森模型描述耦合到一个连续的模式的离散状态$|a >$的衰减光谱奇异性。该模型的物理实现，基于电子或光子输运在一个半无限紧束缚晶格与一个假想的杂质网站在晶格边界，提出。示出的光谱奇异性的发生对应于一个发散的反射概率（放大杂质）或消失的反射概率（吸收杂质）从晶格边界。在前一种情况下，光谱奇异性的预解也是负责的状态$|a>$到连续的非衰减，尽管没有绑定状态。
英文摘要：
Spectral singularities are predicted to occur in a non-Hermitian extension of the Friedrichs-Fano-Anderson model describing the decay of a discrete state $|a >$ coupled to a continuum of modes. A physical realization of the model, based on electronic or photonic transport in a semi-infinite tight-binding lattice with an imaginary impurity site at the lattice boundary, is proposed. The occurrence of the spectral singularities is shown to correspond either to a diverging reflection probability (for an amplifying impurity) or to a vanishing reflection probability (for an absorbing impurity) from the lattice boundary. In the former case, the spectral singularity of the resolvent is also responsible for the non-decay of state $|a>$ into the continuum, in spite of the absence of bound states.
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