非均匀变换介质中Casimir力的佯谬
The paradox of the Casimir force in inhomogeneous transformation media
摘要：
最近有人认为，卡西米尔-利夫希茨力详细取决于系统的微观物理;计算卡西米尔力在非均匀介质中产生的结果是截止依赖。这一结果已被证明是普遍成立的。但假设我们将一种非均匀的超材料引入一个腔体中，它有效地实现了坐标系的简单扭曲。在其“虚拟空间”中考虑，这种材料的光学特性是均匀的，因此不受与非均匀介质相关的截止依赖性的影响。这个结论应该与我们对卡西米尔-李夫希茨力的理解的最新进展相一致。我们考虑这样一个系统的一个例子在这里，并证明，虽然卡西米尔力的大小被修改的非均匀介质，该力是截止独立的，可以准确地说。当我们认识到一种理想化的超材料可以在所有频率下实现虚拟几何时，这种明显的悖论就消失了，这种超材料将没有内部散射，并且不会因此而引起卡西米尔力的截止依赖性。
英文摘要：
It has recently been argued that Casimir-Lifshitz forces depend in detail on the microphysics of a system; calculations of the Casimir force in inhomogeneous media yield results that are cutoff-dependent. This result has been shown to hold generally. But suppose we introduce an inhomogeneous metamaterial into a cavity that effectively implements a simple distortion of the coordinate system. Considered in its 'virtual space', the optical properties of such a material are homogeneous and consequently free from the cutoff-dependency associated with inhomogeneous media. This conclusion should be reconciled with recent advances in our understanding of Casimir-Lifshitz forces. We consider an example of such a system here and demonstrate that, whilst the size of the Casimir force is modified by the inhomogeneous medium, the force is cutoff-independent and can be stated exactly. The apparent paradox dissolves when we recognise that an idealised metamaterial that could implement a virtual geometry for all frequencies would be devoid of internal scattering, and would not give rise to a cutoff-dependency in the Casimir force for that reason.
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