标题： 二维材料中等离子体和非线性光学的Madelung流体力学应用 显示英文标题

标题： Application of Madelung Hydrodynamics to Plasmonics and Nonlinear Optics in Two-Dimensional Materials

摘要： 本文探讨了Madelung流体动力学模型在研究二维电子气体中的应用，重点在于非局域等离子体学和非线性光学。 我们首先回顾了Madelung方程的推导。 结合Madelung方程与泊松方程，我们在静电条件下计算磁等离子体子的谱和磁光电导率，并考虑由于费米压力引起的非局域修正。 在没有磁场的情况下，我们分析了非线性和非局域的二次谐波产生，展示了等离子体激发如何增强这一过程。 我们进一步讨论了由非线性驱动的自调制现象的出现，导致等离子体色散的重整化。 值得注意的是，我们表明非线性放大了非局域效应，并利用流体动力学形式，推导出重整化谱的简单解析表达式。 显示英文摘要

摘要： This paper explores the application of Madelung hydrodynamic models to study two-dimensional electron gases, with a focus on nonlocal plasmonics and nonlinear optics. We begin by reviewing the derivation of the Madelung equations. Using the Madelung equations in conjunction with Poisson's equation, we calculate the spectrum of magnetoplasmons and the magneto-optical conductivity in the electrostatic regime, incorporating nonlocal corrections due to the Fermi pressure. In the absence of a magnetic field, we analyze nonlinear and nonlocal second-harmonic generation, demonstrating how plasmon excitation enhances this process. We further discuss the emergence of self-modulation phenomena driven by nonlinearity, leading to the renormalization of the plasmon dispersion. Notably, we show that nonlinearity amplifies nonlocal effects and, leveraging the hydrodynamic formalism, derive a simple analytic expression for the renormalized spectra.