Computing the Casimir force and energy between objects is a classical problem of quantum theory going back to the 1940s. Several different approaches have been developed in the literature often based on different physical principles. Most notably a representation of the Casimir energy in terms of determinants of boundary layer operators makes it accessible to a numerical approach. In this paper, we first give an overview of the various methods and discuss the connection to the Krein-spectral shift function and computational aspects. We propose variants of Krylov subspace methods for the computation of the Casimir energy for large-scale problems and demonstrate Casimir computations for several complex configurations. This allows for Casimir energy calculation for large-scale practical problems and significantly speeds up the computations in that case.

中文翻译：

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声散射中卡西米尔能量计算的数值方面


计算物体之间的卡西米尔力和能量是量子理论的一个经典问题，可以追溯到 20 世纪 40 年代。文献中已经开发了几种不同的方法，通常基于不同的物理原理。最值得注意的是，卡西米尔能量以边界层算子的决定因素表示，使其可以通过数值方法实现。在本文中，我们首先概述各种方法，并讨论与克雷因谱位移函数和计算方面的联系。我们提出了 Krylov 子空间方法的变体来计算大规模问题的卡西米尔能量，并演示了几种复杂配置的卡西米尔计算。这允许对大规模实际问题进行卡西米尔能量计算，并显着加快这种情况下的计算速度。