对“非均匀介质中Casimir力的截止依赖性”一文的评论
Comment on "Cutoff dependence of the Casimir force within an inhomogeneous medium"
摘要：
Horsley和Simpson [Phys.Rev.A88，013833（2013）]最近声称，活塞模型中的非均匀Casimir压力是截止相关的，并且当去除截止参数时发散（λ->0）。我们证明，有一个错误的计算，在他们的推导，我们的修正结果在截止独立Casimir压力，基于一阶微扰理论。本文给出了一阶微扰非齐次Casimir能量的一般表达式，这为分析发散问题或导出Casimir力提供了方便。讨论了平行波（波矢量平行于Casimir板）的Casimir压力贡献以及极限和求和算子的非对易性，并发现其有助于理解另一篇论文[Phys.Rev.A87，043806（2013）]中声明的非均匀发散。应该强调的是，我们还不能给出一阶扰动以上的非均匀Casimir压力的精确表达式，这是值得进一步研究的。
英文摘要：
Horsley and Simpson [Phys. Rev. A 88, 013833 (2013)] recently claimed that the inhomogeneous Casimir pressure in a piston model is cutoff dependent, and diverges when the cutoff parameter is removed (ξ->0). We demonstrate that, there is a miscalculation in their derivation, and our correction results in a cutoff independent Casimir pressure, based on first-order perturbation theory. We give the general expressions of first-order perturbative inhomogeneous Casimir energy which make it convenient to analyze the divergence problem or to yield the Casimir force. The Casimir pressure contribution of parallel waves (with wave vector parallel to the Casimir plates) together with the non-commutativity of limit and summation operators, are discussed and found to be useful for understanding the inhomogeneous divergence declared in another paper [Phys. Rev. A 87, 043806 (2013)]. We should emphasize that we cannot yet give an exact expression of inhomogeneous Casimir pressure beyond first-order perturbation, which is worth future investigation.
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