平面层状结构间的卡西米尔力：有限温度下的van Kampen-Schram方法
Casimir force between plane-layered structures: van Kampen-Schram approach for finite temperature
AI总结：
本研究采用van Kampen-Schram方法推导平面层状结构间卡西米尔力公式，发现Lifshitz公式未计入的围道积分在低温下贡献显著，给出金属板相互作用实例，完善了有限温度卡西米尔力的理论。
AI中文摘要：
基于van Kampen-Schram方法，得到了两个平面层状结构间卡西米尔力的公式，该公式包含Matsubara频率的求和与一个围道积分。研究表明，Lifshitz公式未考虑该围道积分；在高温下，当Lifshitz公式近似成立时，计入该围道积分仅贡献很小；但在低温下，其贡献显著，且有限温度下的Lifshitz公式无法过渡到零温度下的Lifshitz公式。文中还给出了金属板相互作用的实例。
英文摘要：
Based on the van Kampen-Schram method, a formula for the Casimir force between two plane-layered structures is obtained, which includes the sum of the Matsubara frequencies and a contour integral. It is shown that the contour integral is not taken into account in the Lifshitz formula. Taking it into account gives a small contribution at high temperatures when the Lifshitz formula is approximately correct. However, at low temperatures, its contribution is significant, and the Lifshitz formula for the finite temperature does not transform into the Lifshitz formula at zero temperature. An example of interaction of metal plates is considered.1
