辐射耦合量子介质中的电荷和电流求和规则II
Charge and Current Sum Rules in Quantum Media Coupled to Radiation II
摘要：
本文是以前研究的延续[Šamaj，L.：J. Stat. Phys.{ \bf 137}，1-17（2009）]，其中通过使用Rytov的波动电动力学导出了耦合到辐射的无限（体）量子介质中的平衡电荷和电流密度关联函数的求和规则序列。在这里，我们将以前的结果扩展到非均匀的情况下，特别是两个联合半无限介质的三维界面几何。电荷-电荷密度相关性的总和规则表示以前的概括，有关的界面偶极矩和长程尾的表面电荷密度关联函数沿接触的导体与惰性（不波动）电介质壁的界面，两个波动的半无限介质的任何一种。据我们所知，这里得到的电荷-电流和电流-电流求和规则是新的。电流-电流求和规则指示由接口打破对角电流-电流相关性的方向不变性。的总和规则明确表示在经典的高温极限（静态的情况下），并为jeldom模型（随时间变化的情况下）。
英文摘要：
This paper is a continuation of the previous study [Šamaj, L.: J. Stat. Phys. {\bf 137}, 1-17 (2009)], where a sequence of sum rules for the equilibrium charge and current density correlation functions in an infinite (bulk) quantum media coupled to the radiation was derived by using Rytov's fluctuational electrodynamics. Here, we extend the previous results to inhomogeneous situations, in particular to the three-dimensional interface geometry of two joint semi-infinite media. The sum rules derived for the charge-charge density correlations represent a generalization of the previous ones, related to the interface dipole moment and to the long-ranged tail of the surface charge density correlation function along the interface of a conductor in contact with an inert (not fluctuating) dielectric wall, to two fluctuating semi-infinite media of any kind. The charge-current and current-current sum rules obtained here are, to our knowledge, new. The current-current sum rules indicate a breaking of the directional invariance of the diagonal current-current correlations by the interface. The sum rules are expressed explicitly in the classical high-temperature limit (the static case) and for the jellium model (the time-dependent case).
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