Exact results for Casimir interactions between dielectric bodies: The weak-coupling or van der Waals Limit

Abstract

In earlier papers we have applied multiple scattering techniques to calculate Casimir forces due to scalar fields between different bodies described by delta function potentials. When the coupling to the potentials became weak, closed-form results were obtained. We simplify this weak-coupling technique and apply it to the case of tenuous dielectric bodies, in which case the method involves the summation of van der Waals (Casimir-Polder) interactions. Once again exact results for finite bodies can be obtained. We present closed formulas describing the interaction between spheres and between cylinders, and between an infinite plate and a retangular slab of finite size. For such a slab, we consider the torque acting on it, and find non-trivial equilibrium points can occur.

4 pages, 3 figures

References in corpus (18)

• New Developments in the Casimir Effect
• Casimir forces between arbitrary compact objects
• Worldline algorithms for Casimir configurations
• Casimir Forces between Compact Objects: I. The Scalar Case
• Casimir Effects: An Optical Approach I. Foundations and Examples
• Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder
• Casimir energy between a plane and a sphere in electromagnetic vacuum
• Computation and visualization of Casimir forces in arbitrary geometries: non-monotonic lateral forces and failure of proximity-force approximations
• Observability of the Bulk Casimir Effect: Can the Dynamical Casimir Effect be Relevant to Sonoluminescence?
• Casimir forces and non-Newtonian gravitation
• Multiple Scattering Methods in Casimir Calculations
• Casimir force for a sphere in front of a plane beyond Proximity Force Approximation
• Repulsive, nonmonotonic Casimir forces in a glide-symmetric geometry
• Casimir forces between arbitrary compact objects: Scalar and electromagnetic field
• Non-contact gears: II. Casimir torque between concentric corrugated cylinders for the scalar case
• Exact Casimir Interaction Between Semitransparent Spheres and Cylinders
• Non-contact gears: I. Next-to-leading order contribution to lateral Casimir force between corrugated parallel plates
• The Casimir effect as scattering problem

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