介质微腔的非厄米性和正交关系守恒
Non-Hermiticity and conservation of orthogonal relation in dielectric microcavity
摘要：
近年来，开放量子系统的非厄米性质及其应用引起了人们的广泛关注。虽然大多数的研究都集中在非厄米特系统的特征性质上，但在这里我们关注以下问题：一个非厄米特系统可以是厄米特系统的一个子系统，正如人们可以在Feshbach投影算子（FPO）形式主义中清楚地看到的那样。在这种情况下，尽管子系统（非厄米特）的本征向量满足双正交条件，但总（厄米特）系统的本征向量的正交性必须保持。因此，我们可以预言，一定存在一些显著的过程，这些过程将非厄米子系统与其余部分联系起来，并最终保持整个系统的厄米性。在本文中，我们研究这样的过程中开放的椭圆微腔。腔的内部是一个非厄米系统，外部是FPO形式的耦合池。我们调查的内部和外部的行为与避免共振交叉（ARC）之间的相关性，并分析结果的自能和集体兰姆位移的相对差异之间的权衡。这些结果来自于全厄米量子系统的正交性守恒。
英文摘要：
Non-Hermitian properties of open quantum systems and their applications have attracted much attention in recent years. While most of the studies focus on the characteristic nature of non-Hermitian systems, here we focus on the following issue: A non-Hermitian system can be a subsystem of a Hermitian system as one can clearly see in Feshbach projective operator (FPO) formalism. In this case, the orthogonality of the eigenvectors of the total (Hermitian) system must be sustained, despite the eigenvectors of the subsystem (non-Hermitian) satisfy the bi-orthogonal condition. Therefore, one can predict that there must exist some remarkable processes that relate the non-Hermitian subsystem and the rest part, and ultimately preserve the Hermiticity of the total system. In this paper, we study such processes in open elliptical microcavities. The inner part of the cavity is a non-Hermitian system, and the outer part is the coupled bath in FPO formalism. We investigate the correlation between the inner- and the outer-part behaviors associated with the avoided resonance crossings (ARCs), and analyze the results in terms of a trade-off between the relative difference of self-energies and collective Lamb shifts. These results come from the conservation of the orthogonality in the total Hermitian quantum system.
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