Green Functions Scattering in the Casimir Effect

Valery N Marachevsky,Arseny A Sidelnikov

doi:10.3390/universe7060195

Abstract

We propose Green functions scattering method to obtain the Casimir–Polder potential between anisotropic atom and one or two planar parallel plates. Lifshitz formula for pressure between two dielectric half-spaces separated by a vacuum slit is derived within the same method. The method is also applied to known conducting systems including graphene which are overviewed.

Highlights

Direct procedure proved useful for evaluation of the Casimir–Polder potential for non-flat geometries including perfectly conducting wedge and dielectric diffraction grating [49,50,51]
We demonstrate how to derive the Casimir force between geometries with flat parallel boundaries within the same formalism and derive general formula for the Casimir–Polder potential of anisotropic atom between two half-spaces with parallel boundaries and given boundary conditions
Non-diagonal components of the matrix Pij do not contribute to the Casimir–Polder potential of a neutral atom interacting with a dielectric half-space

Summary

Introduction

Direct procedure proved useful for evaluation of the Casimir–Polder potential for non-flat geometries including perfectly conducting wedge and dielectric diffraction grating [49,50,51]. We demonstrate how to derive the Casimir force between geometries with flat parallel boundaries within the same formalism and derive general formula for the Casimir–Polder potential of anisotropic atom between two half-spaces with parallel boundaries and given boundary conditions.

Casimir–Polder Potential of Anisotropic Atom above a Dielectric Half-Space

Force between Two Dielectric Half-Spaces

Impedance Boundary Conditions

Discussion