Revisiting the PT?>-symmetric trimer: bifurcations, ghost states and associated dynamics
Revisiting the PT?>-symmetric trimer: bifurcations, ghost states and associated dynamics
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DOI：
10.1088/1751-8113/46/37/375304
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发表时间：
2013-06
期刊：
影响因子：
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通讯作者：
Kai Li;Panos Kevrekidis;D. Frantzeskakis;C. Rüter;D. Kip
中科院分区：
文献类型：
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作者：
Kai Li;Panos Kevrekidis;D. Frantzeskakis;C. Rüter;D. Kip
在本文中，我们重新审视一个典型的PT？>对称低聚物，即三聚体。我们找到了正则解的所有相关分支，并分析了它们的分岔和不稳定性。我们的工作推广了最近在三聚体的所谓“鬼态”的二聚体的情况下提出的公式，我们也识别并连接到常规状态的对称破坏分岔。我们还研究了不稳定三聚体的动力学，以及在参数状态中发现后者存在的幽灵状态的动力学。最后，我们介绍了目前PT？>对称三聚体，以及增益-损耗-增益三通道波导结构的实验结果。
In this paper, we revisit one of the prototypical PT?>-symmetric oligomers, namely the trimer. We find all the relevant branches of ‘regular’ solutions and analyze the bifurcations and instabilities thereof. Our work generalizes the formulation that was recently proposed in the case of dimers for the so-called ‘ghost states’ of trimers, which we also identify and connect to symmetry-breaking bifurcations from the regular states. We also examine the dynamics of unstable trimers, as well as those of the ghost states in the parametric regime where the latter are found to exist. Finally, we present the current state-of-the-art for optical experiments in PT?>-symmetric trimers, as well as experimental results in a gain–loss–gain three channel waveguide structure.