论文标题
非线性抗（平均时间）对称二聚体
Nonlinear Anti-(Parity-Time) symmetric dimer
论文作者
论文摘要
在目前的工作中，我们提出了一个非线性抗 - $ \ MATHCAL {PT} $ - 对称二聚体，该二聚体在线性级别已在电路谐振器的领域实验创建。我们发现四个溶液家族，即所谓的上和下部分支，无论是对称的还是不对称的（对称性）形式。我们通过分析揭幕并在数值上确认存在此类分支的临界阈值，并探索界定其存在的分叉（例如鞍形节点），以及导致其潜在稳定性交换的跨批评。我们发现，在四个相关分支中，只有一个，上部对称分支，对应于频谱和动态强大的解决方案。随后，我们利用详细的直接数值计算，以探索不同状态的动态，从而证实了我们的光谱分析结果。
In the present work we propose a nonlinear anti-$\mathcal{PT}$-symmetric dimer, that at the linear level has been experimentally created in the realm of electric circuit resonators. We find four families of solutions, the so-called upper and lower branches, both in a symmetric and in an asymmetric (symmetry-broken) form. We unveil analytically and confirm numerically the critical thresholds for the existence of such branches and explore the bifurcations (such as saddle-node ones) that delimit their existence, as well as transcritical ones that lead to their potential exchange of stability. We find that out of the four relevant branches, only one, the upper symmetric branch, corresponds to a spectrally and dynamically robust solution. We subsequently leverage detailed direct numerical computations in order to explore the dynamics of the different states, corroborating our spectral analysis results.
