涨落诱导的紧致物体与平面镜的量子相互作用
Fluctuation induced quantum interactions between compact objects and a plane mirror
摘要：
研究了由于标量场或电磁场的量子涨落引起的紧致物体与无限延伸镜面的相互作用。镜面被假定服从狄利克雷或诺依曼边界条件或完全反射。利用镜像方法，我们推广了最近发展的一种用于无界空间中紧致物体的方法[1，2]，证明了在物体及其镜像的电荷和电流涨落的广泛分离范围内，可以精确地获得物体与镜像平面之间的Casimir相互作用。我们的一般结果的相互作用只依赖于散射矩阵的紧凑的对象。它适用于具有任意边界条件的标量场和与介质物体耦合的电磁场。对于实验上重要的电磁Casimir相互作用之间的理想导电球和平面镜，我们提出的第一个结果，适用于所有的分离。我们得到了邻近力近似的渐近大距离展开式和两个最低阶修正项。将原子和镜面的渐近Casimir-Polder势推广到描述介质球和镜面之间的相互作用，其中涉及到在亚渐近距离处很重要的高阶多极极化率.
英文摘要：
The interaction of compact objects with an infinitely extended mirror plane due to quantum fluctuations of a scalar or electromagnetic field that scatters off the objects is studied. The mirror plane is assumed to obey either Dirichlet or Neumann boundary conditions or to be perfectly reflecting. Using the method of images, we generalize a recently developed approach for compact objects in unbounded space [1,2] to show that the Casimir interaction between the objects and the mirror plane can be accurately obtained over a wide range of separations in terms of charge and current fluctuations of the objects and their images. Our general result for the interaction depends only on the scattering matrices of the compact objects. It applies to scalar fields with arbitrary boundary conditions and to the electromagnetic field coupled to dielectric objects. For the experimentally important electromagnetic Casimir interaction between a perfectly conducting sphere and a plane mirror we present the first results that apply at all separations. We obtain both an asymptotic large distance expansion and the two lowest order correction terms to the proximity force approximation. The asymptotic Casimir-Polder potential for an atom and a mirror is generalized to describe the interaction between a dielectric sphere and a mirror, involving higher order multipole polarizabilities that are important at sub-asymptotic distances.
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