色散宇称破缺系统中的调制不稳定性
Modulation instability in dispersive parity-broken systems
AI总结：
本文研究色散宇称破缺与非线性相互作用对调制不稳定性的影响，通过推导奇数重力波和PT对称介电模型中的非线性薛定谔方程，揭示宇称破缺可手性依赖地稳定调制包络动力学。
摘要：
本工作探讨了在两个表现出调制不稳定性（MI）的对比连续动力学系统中，色散宇称破缺与非线性之间的相互作用。我们首先研究深水奇数表面重力波，并利用多尺度方法推导出调制包络动力学的非线性薛定谔方程（NLSE）。奇数重力波中的宇称破缺导致右行波和左行波具有不同的NLSE，从而产生依赖于手性的包络动力学稳定性性质。此外，重力波与奇数粘性诱导的毛细动力学的共振相互作用，在其中一个手性扇区中创造了一个波数窗口，在该窗口内包络传播保持稳定。在奇数重力结果之后，我们设计了一个一维非互易PT对称介电模型，该模型表现出与二维流体动力学中的奇数粘性项类似的宇称破缺效应。在极化动力学具有三次非线性的情况下，我们推导出相应的NLSE。我们再次观察到，宇称破缺稳定了下极化激元带中的调制包络动力学。然后，我们比较了这种情况与奇数重力波情况之间的异同。
英文摘要：
This work explores the interplay between dispersive parity breaking and non-linearity in two contrasting continuous dynamical systems that exhibit Modulation Instability (MI). We begin by examining deep water odd surface gravity waves and derive the non-linear Schrödinger equation (NLSE) for the modulated envelope dynamics using the method of multiple scales. The parity breaking in the odd gravity waves results in distinct NLSEs for the right and the left mover, leading to chirality-dependent stability properties for the envelope dynamics. Moreover, the resonant interaction of gravity waves and odd viscosity-induced capillary dynamics creates a window of wave numbers in one of the chiral sectors where the envelope propagation remains stable. Following the odd gravity results, we design a one-dimensional non-reciprocal PT-symmetric dielectric model that exhibits parity-breaking effects that are analogous to the odd viscosity term in 2D hydrodynamics. With cubic non-linearity in the polarization dynamics, we derive the corresponding NLSE. Once again, we observe that parity breaking stabilizes the modulated envelope dynamics in the lower polariton bands. We then compare the similarities and differences between this case and that of odd gravity waves.
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