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arXiv 0902.3584physics.plasm-ph
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朗缪尔波包的量子和经典动力学

Quantum and classical dynamics of Langmuir wave packets

Fernando Haas, Padma Kant Shukla

摘要:

导出了三维空间中的量子Zakharov系统及其相应的拉格朗日描述和基本守恒律。在绝热和半经典情况下,量子Zakharov系统简化为包络电场的量子修正矢量非线性薛定谔(NLS)方程。由此产生的矢量NLS方程的拉格朗日结构被用来调查的高斯形本地化解决方案的时间依赖性,通过瑞利-里兹变分方法。形式的经典极限被认为是详细的。的量子校正示出,以防止本地化的朗缪尔包络场的崩溃,在两个和三个空间维度。此外,量子项可以产生近似高斯解的宽度的振荡行为。变分方法被证明保持量子修正向量NLS方程的基本守恒律。

英文摘要:

The quantum Zakharov system in three-spatial dimensions and an associated Lagrangian description, as well as its basic conservation laws are derived. In the adiabatic and semiclassical case, the quantum Zakharov system reduces to a quantum modified vector nonlinear Schrödinger (NLS) equation for the envelope electric field. The Lagrangian structure for the resulting vector NLS equation is used to investigate the time-dependence of the Gaussian shaped localized solutions, via the Rayleigh-Ritz variational method. The formal classical limit is considered in detail. The quantum corrections are shown to prevent the collapse of localized Langmuir envelope fields, in both two and three-spatial dimensions. Moreover, the quantum terms can produce an oscillatory behavior of the width of the approximate Gaussian solutions. The variational method is shown to preserve the essential conservation laws of the quantum modified vector NLS equation.

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