We derive an exact analytic expression for the high-temperature limit of the Casimir interaction between two Drude spheres of arbitrary radii. Specifically, we determine the Casimir free energy by using the scattering approach in the plane-wave basis. Within a round-trip expansion, we are led to consider the combinatorics of certain partitions of the round trips. The relation between the Casimir free energy and the capacitance matrix of two spheres is discussed. Previously known results for the special cases of a sphere-plane geometry as well as two spheres of equal radii are recovered. An asymptotic expansion for small distances between the two spheres is determined and analytical expressions for the coefficients are given.

中文翻译：

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两个任意半径的Drude球的经典卡西米尔自由能：平面波方法

我们推导了任意半径的两个Drude球之间的Casimir相互作用的高温极限的精确解析表达式。具体而言，我们通过在平面波基础上使用散射方法确定卡西米尔自由能。在往返扩展中，我们被引导考虑往返的某些分区的组合。讨论了卡西米尔自由能与两个球的电容矩阵之间的关系。对于球面几何形状以及两个相等半径的球的特殊情况，恢复了先前已知的结果。确定了两个球之间的小距离的渐近展开，并给出了系数的解析表达式。