PT-symmetric oligomers: analytical solutions, linear stability, and nonlinear dynamics.
PT-symmetric oligomers: analytical solutions, linear stability, and nonlinear dynamics.
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DOI：
10.1103/physreve.83.066608
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发表时间：
2011-02
期刊：
影响因子：
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通讯作者：
Kai Li;Panos Kevrekidis
中科院分区：
文献类型：
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作者：
Kai Li;Panos Kevrekidis
在目前的工作中，我们重点关注尊重奇偶时间（PT）对称性的（少数站点）配置的情况，即具有空间奇数增益损失曲线。我们研究了这种“低聚物”的情况，不仅像早期的作品那样具有两个位点，而且还研究了三个和四个位点的情况。虽然在最近实验感兴趣的前一种情况下，现有稳态解及其稳定性的图像相当简单，但后一种情况揭示了解的相当大的额外复杂性，包括三聚体情况下超过线性 PT 对称断点和对称破缺分岔的解，以及四聚体情况下更复杂、甚至不对称的解，其线性稳定性和非线性动力学具有非平凡的特性。讨论了所获得的解的线性化及其不稳定时的动态演化。
In the present work we focus on the case of (few-site) configurations respecting the parity-time (PT) symmetry, i.e., with a spatially odd gain-loss profile. We examine the case of such "oligomers" with not only two sites, as in earlier works, but also the cases of three and four sites. While in the former case of recent experimental interest the picture of existing stationary solutions and their stability is fairly straightforward, the latter cases reveal a considerable additional complexity of solutions, including ones that exist past the linear PT-symmetry breaking point in the case of the trimer, and symmetry-breaking bifurcations, as well as more complex, even asymmetric solutions in the case of the quadrimer with nontrivial properties in their linear stability and in their nonlinear dynamics. The linearization around the obtained solutions and their dynamical evolution, when unstable, are discussed.