We analyze the scattering dynamics and spectrum of a quantum particle on a tight-binding lattice subject to a non-Hermitian (purely imaginary) local potential. The reflection, transmission, and absorption coefficients are studied as a function of the strength of this absorbing potential. The system is found to have an exceptional point at a certain strength of the potential. Unusually, all (or nearly all) of the spectrum pairs up into mutually coalescing eigenstate pairs at this exceptional point. At large potential strengths, the absorption coefficient decreases and the effect of the imaginary potential is similar to that of a real potential. We quantify this similarity by utilizing properties of a localized eigenstate.

中文翻译：

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紧束缚格上的非埃尔米特散射

我们分析了在非赫米特（纯虚数）局部势能作用下的紧密结合晶格上量子粒子的散射动力学和光谱。研究反射，透射和吸收系数与该吸收电位强度的关系。发现该系统在一定潜力的强度上具有一个例外。异常地，所有（或几乎所有）光谱对在这个例外点都变成相互合并的本征态对。在大的电位强度下，吸收系数减小，并且虚电位的影响类似于真实电位。我们通过利用局部本征态的性质来量化这种相似性。