Casimir potential of a compact object enclosed by a spherical cavity

Abstract

We study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects' scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. When the enclosing object is an otherwise empty metallic spherical shell, much larger than the internal object, and the two are sufficiently separated, the Casimir force can be expressed in terms of the static electric and magnetic multipole polarizabilities of the internal object, which is analogous to the Casimir-Polder result. Although it is not a simple power law, the dependence of the force on the separation of the object from the containing sphere is a universal function of its displacement from the center of the sphere, independent of other details of the object's electromagnetic response. Furthermore, we compute the exact Casimir force between two metallic spheres contained one inside the other at arbitrary separations. Finally, we combine our results with earlier work on the Casimir force between two spheres to obtain data on the leading order correction to the Proximity Force Approximation for two metallic spheres both outside and within one another.

12 pages, 6 figures

References in corpus (20)

• Casimir forces between arbitrary compact objects
• Scattering Theory Approach to Electrodynamic Casimir Forces
• Casimir Effect on the Worldline
• Casimir forces in a T operator approach
• Casimir effect for curved geometries: PFA validity limits
• Casimir Forces between Compact Objects: I. The Scalar Case
• The Casimir Effect and Geometric Optics
• Exact Casimir interaction between eccentric cylinders
• Casimir energy between a plane and a sphere in electromagnetic vacuum
• Fluctuation induced quantum interactions between compact objects and a plane mirror
• Casimir interaction of two plates inside a cylinder
• Casimir force for a sphere in front of a plane beyond Proximity Force Approximation
• The Casimir Problem of Spherical Dielectrics: Numerical Evaluation for General Permittivities
• Casimir manipulations: The orientation dependence of fluctuation-induced forces
• The Casimir Problem of Spherical Dielectrics: Quantum Statistical and Field Theoretical Approaches
• Casimir energy and dilute dielectric ball
• Casimir spring and compass: Stable levitation and alignment of compact objects
• Casimir interactions of an object inside a spherical metal shell
• Casimir energy and realistic model of dilute dielectric ball
• Casimir energy and geometry : beyond the Proximity Force Approximation

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• Mode summation approach to Casimir effect between two objects
• Casimir Energy for concentric $\delta$-${\delta }^{\prime }$ spheres
• Scalar Casimir effect between two concentric spheres
• Effect of Curvature and Confinement on the Casimir-Polder Interaction
• Repulsive Casimir-Lifshitz pressure in closed cavities
• Casimir interaction of concentric spheres at finite temperature
• Casimir-Lifshitz pressure on cavity walls