Van der Waals Interaction in Cylindrical Structures

After a section in which we adapt the general formalism presented in Chap. 7 to cylindrical structures in neglect of retardation we start by introducing the basic structure elements: a single cylindrical interface, a cylindrical shell, a thin diluted cylindrical gas film, and a 2D cylindrical film. A general cylindrical structure can then be constructed by stacking these elements coaxially. The thin gas layer is special; it is used to find the interaction on an atom at a general position in the cylindrical structure. Then we go through some common structures and present illustrating examples; the examples involve gold cylinders, gold cavities, graphene shells, and lithium atoms. We furthermore rederive the van der Waals interaction between two atoms by comparing the full result in the diluted limit with that from the summation of pair interactions.