非线性非厄米特皮肤效应的全局分岔与盆地几何
Global bifurcations and basin geometry of the nonlinear non-Hermitian skin effect
AI总结：
研究揭示了非线性非厄米特皮肤效应中全局分岔与盆地几何对稳态共存窗口的影响，提出盆地分数序参量并揭示了非线性分隔线诱导的物理现象。
摘要：
我们研究了一个连续的Hatano-Nelson模型，该模型具有饱和的非线性非互易性，并通过相关的相空间流分析其稳态。我们揭示了一个由亚临界Hopf分岔和极限环的鞍点分岔共同控制的全局场景，这产生了一个有限的共存窗口。在此窗口中，皮肤模式和扩展态在固定能量E下均稳定，它们在相空间中由非线性盆地分隔线分隔，而非线性系统中传统的谱（运动边）机制。平均振幅方程给出了极限环分支和SNLC阈值的闭合形式预测。基于盆地几何，我们引入了一个盆地分数序参量，其在SNLC处表现出类似一级相变的跳跃。共存窗口中还揭示了 intriguing 的物理现象，如分隔线诱导的长寿命空间暂态和滞后效应。总体而言，我们的发现强调，除了线性谱概念外，全局吸引子-盆地几何为理解非线性非厄米特系统的稳态状态提供了一种强大且互补的视角。
英文摘要：
We study a continuum Hatano--Nelson model with a saturating nonlinear nonreciprocity and analyze its stationary states via the associated phase-space flow. We uncover a global scenario controlled by a subcritical Hopf bifurcation and a saddle-node of limit cycles, which together generate a finite coexistence window. In this window, skin modes and extended states are both stable at a fixed energy $E$, separated by a nonlinear basin separatrix in phase space rather than a spectral (mobility-edge) mechanism in a linear system. An averaged amplitude equation yields closed-form predictions for the limit-cycle branches and the SNLC threshold. Building on the basin geometry, we introduce a basin-fraction order parameter that exhibits a first-order-like jump at SNLC. Intriguing physical phenomena in the coexistence window are also revealed, such as separatrix-induced long-lived spatial transients and hysteresis. Overall, our findings highlight that, beyond linear spectral concepts, global attractor-basin geometry provides a powerful and complementary lens for understanding stationary states in nonlinear non-Hermitian systems.
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