非PT对称Scarf II势相干散射的新解析形式
An update on coherent scattering from complex non-PT-symmetric Scarf II potential with new analytic forms
摘要：
多功能和精确可解的Scarf II一直在预测，确认和演示复杂PT对称扇区中的有趣现象，最令人印象深刻。然而，对于非PT对称部门，它没有得到充分利用。在这里，我们提出了最简单的散射系数$(T(k),R(k),|\det S(k)|)$的解析形式。一方面，这些形式证明了早期效应，并证实了近期效应。另一方面，他们做出了新的预测--所有这些都是简单的、分析性的。我们展示了两个非PT扇区（势）中的自对偶和非自对偶谱奇点（NSDSS）的可能性。前者不伴随时间反演相干完全吸收（CPA），并产生了参数控制分裂的SS在一个有限数量的复共轭对的本征值（CCPE）。后者（NSDSS）的行为正好相反：CPA，但没有分裂的SS。我们证明了一个没有不可见性的片面无反射。最重要的是，我们提出了一个令人惊讶的共存的真实离散谱和一个单一的SS在一个固定的潜力。尽管如此，到目前为止，还不知道复杂的Scarf II在$η(x)$类型的度量下是伪埃尔米特（$η^{-1} Hη=H^\dagger$）。
英文摘要：
The versatile and exactly solvable Scarf II has been predicting, confirming and demonstrating interesting phenomena in complex PT-symmetric sector, most impressively. However, for the non-PT-symmetric sector it has gone underutilized. Here, we present most simple analytic forms for the scattering coefficients $(T(k),R(k),|\det S(k)|)$. On one hand, these forms demonstrate earlier effects and confirm the recent ones. On the other hand they make new predictions - all simply and analytically. We show the possibilities of both self-dual and non-self-dual spectral singularities (NSDSS) in two non-PT sectors (potentials). The former one is not accompanied by time-reversed coherent perfect absorption (CPA) and gives rise to the parametrically controlled splitting of SS in to a finite number of complex conjugate pairs of eigenvalues (CCPEs). The latter ones (NSDSS) behave just oppositely: CPA but no splitting of SS. We demonstrate a one-sided reflectionlessness without invisibility. Most importantly, we bring out a surprising co-existence of both real discrete spectrum and a single SS in a fixed potential. Nevertheless, the complex Scarf II is not known to be pseudo-Hermitian ($η^{-1} Hη=H^\dagger$) under a metric of the type $η(x)$, so far.
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