Casimir Physics beyond the Proximity Force Approximation: The Derivative Expansion

Physics Pub Date : 2024-02-27 DOI:10.3390/physics6010020
C. Fosco, F. Lombardo, F. Mazzitelli
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Abstract

We review the derivative expansion (DE) method in Casimir physics, an approach which extends the proximity force approximation (PFA). After introducing and motivating the DE in contexts other than the Casimir effect, we present different examples which correspond to that realm. We focus on different particular geometries, boundary conditions, types of fields, and quantum and thermal fluctuations. Besides providing various examples where the method can be applied, we discuss a concrete example for which the DE cannot be applied; namely, the case of perfect Neumann conditions in 2+1 dimensions. By the same example, we show how a more realistic type of boundary condition circumvents the problem. We also comment on the application of the DE to the Casimir–Polder interaction which provides a broader perspective on particle–surface interactions.
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超越接近力近似的卡西米尔物理学:导数展开
我们回顾了卡西米尔物理学中的导数展开(DE)方法,这是一种扩展了接近力近似(PFA)的方法。在介绍和激励卡西米尔效应以外的导数展开法之后,我们介绍了与该领域相对应的不同示例。我们将重点放在不同的特定几何形状、边界条件、场类型以及量子和热波动上。除了提供可以应用该方法的各种例子外,我们还讨论了一个无法应用 DE 的具体例子,即 2+1 维中完全诺依曼条件的情况。通过同一例子,我们展示了一种更现实的边界条件是如何规避这一问题的。我们还评论了 DE 在卡西米尔-波德尔相互作用中的应用,这为粒子-表面相互作用提供了更广阔的视角。
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