物质中的电磁本征模。范德瓦尔斯-伦敦-卡西米尔力
Electromagnetic eigenmodes in matter. van der Waals-London and Casimir forces
摘要：
我们通过计算电磁场与两个半无限体（空间的两半）相互作用的本征模，推导出范德华力和卡西米尔力，两个半无限体具有距离为d的平行表面。我们采用简单的模型，金属和金属，众所周知的基本理论的分散。在非延迟（库仑）极限，我们得到一个d^{-3}-力（范德华-伦敦力），产生于表面等离子体振子模式的零点能量（真空涨落）。当延迟包括在内时，我们得到d^{-4}-（卡西米尔）力，其产生于金属的表面等离子体激元-极化激元模式（消逝模式）的零点能量，以及产生于相同介电常数的传播（极化激元）模式。同样的Casimir力也得到了“固定表面”的边界条件，无论对机构。该方法是基于极化和电磁势的运动方程，从而导致耦合积分方程。求解这些方程，并确定其相关的本征频率分支。
英文摘要：
We derive van der Waals-London and Casimir forces by calculating the eigenmodes of the electromagnetic field interacting with two semi-infinite bodies (two halves of space) with parallel surfaces separated by distance d. We adopt simple models for metals and dielectrics, well-known in the elementary theory of dispersion. In the non-retarded (Coulomb) limit we get a d^{-3}-force (van der Waals-London force), arising from the zero-point energy (vacuum fluctuations) of the surface plasmon modes. When retardation is included we obtain a d^{-4}-(Casimir) force, arising from the zero-point energy of the surface plasmon-polariton modes (evanescent modes) for metals, and from propagating (polaritonic) modes for identical dielectrics. The same Casimir force is also obtained for "fixed surfaces" boundary conditions, irrespective of the pair of bodies. The approach is based on the equation of motion of the polarization and the electromagnetic potentials, which lead to coupled integral equations. These equations are solved, and their relevant eigenfrequencies branches are identified.
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