Casimir能量和应力与不稳定性相关的截止依赖性
Inhomogeneity-related cutoff dependence of the Casimir energy and stress
摘要：
利用格林函数方法研究了一维分段光滑非均匀系统的Casimir能量和应力的截止依赖性。得到了能量和应力的渐近柱核展开式，并引入了由非均匀性引起的额外截断项。逐一介绍系统的接口，展示了这些截止项是如何出现的，并阐明了它们的物理解释。在此基础上，我们提出了一个减法方案来解决非均匀介质中Casimir应力的剩余截止依赖性问题，并证明了两个分离体之间的非接触Casimir力是截止无关的。在不均匀性的情况下，发现在理想导电壁附近的表面发散的电和磁的贡献的取消是不完整的。
英文摘要：
The cutoff dependence of the Casimir energy and stress is studied using the Green's function method for a system that is piecewise-smoothly inhomogeneous along one dimension. The asymptotic cylinder kernel expansions of the energy and stress are obtained, with some extra cutoff terms that are induced by the inhomogeneity. Introducing interfaces to the system one by one shows how those cutoff terms emerge and illuminates their physical interpretations. Based on that, we propose a subtraction scheme to address the problem of the remaining cutoff dependence in the Casimir stress in an inhomogeneous medium, and show that the nontouching Casimir force between two separated bodies is cutoff independent. The cancellation of the electric and magnetic contributions to the surface divergence near a perfectly conducting wall is found to be incomplete in the case of inhomogeneity.
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