Casimir forces beyond the proximity approximation

Abstract

The proximity force approximation (PFA) relates the interaction between\nclosely spaced, smoothly curved objects to the force between parallel plates.\nPrecision experiments on Casimir forces necessitate, and spur research on,\ncorrections to the PFA. We use a derivative expansion for gently curved\nsurfaces to derive the leading curvature modifications to the PFA. Our methods\napply to any homogeneous and isotropic materials; here we present results for\nDirichlet and Neumann boundary conditions and for perfect conductors. A Pad\\'e\nextrapolation constrained by a multipole expansion at large distance and our\nimproved expansion at short distances, provides an accurate expression for the\nsphere-plate Casimir force at all separations.\n