几种简单结构内Casimir力的计算方法

Calculation methods of Casimir force in some simple configurations

阐述了零点能及Casimir力产生的理论依据,着重分析了两平行平面结构、矩形腔结构和两 同心圆柱体结构内的零点能及Casimir力的计算方法,并对计算结果进行分析,讨论了在不同条件 下零点能及Casimir力的不同表现.相同的计算方法下发现,Casimir力与微腔边界的形状有很大的 关系,与几何尺寸成反比,是边界大小、几何形状和拓扑的函数,并且同外界的影响因素如温度、传 导性等密切相关.它可以是引力也可为斥力,而且对于某些结构,它还可在引力和斥力间转换.

With the development of MEMS apparatus, people bring forward new requests for the Casimir force from theory to experiment and to practice. This paper explains the theoretical gist of the Zero-point Energy and Casimir force, analyzes the calculation methods of the Casimir force in configurations of two parallel boards, rectangle cavity and two concentric cylinders. With the same calculation method, we can see the Casimir force has much connection with geometry figure and is a function of geometry figure, boundary sizes and topology. The force can be gravitation, and also can be expulsion. For some configurations, it can be translated between gravitation and expulsion.