Detailed parametric study of Casimir forces in the Casimir Polder approximation for nontrivial 3D geometries

Abstract

We present a parametric numerical study conducted with the finite element code CasimirSim developed by ARC Seibersdorf research. This simulation has already been applied to two dimensional geometries in the past and showed agreement with exact theoretical predictions between 100 nm and 10 μm. In the current investigation the code has been enhanced to compute arbitrary, nontrivial, fully three dimensional geometries for any material given by its density and dielectric polarizability. For calculation of the Casimir energy the simple Casimir Polder r ⁻⁷ model is used. This approach is known to be of limited accuracy due to the assumption of perfect additivity of dipole interactions. Nonetheless, it can be used to give approximate predictions for sharply curved geometries inaccessible to other approximative schemes such as for example the established Proximity Force Approximation. In the current study, we show in detail the dependence of errors upon physical and numerical parameters. After verification with the plate–plate geometry experimentally relevant geometries such as sphere over plate or crossed cylinders are assessed. Finally, the simulation is applied to the more sophisticated geometries of stacked spherical shells, a gear wheel, and a cantilever, showing up some interesting properties.