Herglotz变分原理在有耗散电磁系统中的应用
Application of Herglotz's Variational Principle to Electromagnetic Systems with Dissipation
摘要：
这项工作适用于接触形式主义的经典力学和经典场论，介绍了Herglotz和后来发展的接触几何的背景下，描述电磁系统的耗散。特别是，我们研究了一个电子在一个非完美的导体和变化的回旋辐射。为了将接触形式应用于受洛伦兹力支配的系统，必须推广经典电磁规范并在拉格朗日量中增加一项。我们还适用于经典场的k-接触理论来模拟外部阻尼下电磁场本身的行为。特别是，我们展示了该理论如何描述在某些情况下介质中电磁场的演化。导出了相应的坡印廷定理。我们讨论了它的适用性的洛伦兹偶极子模型和高阻电介质。
英文摘要：
This work applies the contact formalism of classical mechanics and classical field theory, introduced by Herglotz and later developed in the context of contact geometry, to describe electromagnetic systems with dissipation. In particular, we study an electron in a non-perfect conductor and a variation of the cyclotron radiation. In order to apply the contact formalism to a system governed by the Lorentz force, it is necessary to generalize the classical electromagnetic gauge and add a term in the Lagrangian. We also apply the k-contact theory for classical fields to model the behaviour of electromagnetic fields themselves under external damping. In particular, we show how the theory describes the evolution of electromagnetic fields in media under some circumstances. The corresponding Poynting theorem is derived. We discuss its applicability to the Lorentz dipole model and to a highly resistive dielectric.
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