Inhomogeneity-related cutoff dependence of the Casimir energy and stress

Abstract

The cutoff dependence of the Casimir energy and stress is studied using the Green's function method for a system that is piecewise-smoothly inhomogeneous along one dimension. The asymptotic cylinder kernel expansions of the energy and stress are obtained, with some extra cutoff terms that are induced by the inhomogeneity. Introducing interfaces to the system one by one shows how those cutoff terms emerge and illuminates their physical interpretations. Based on that, we propose a subtraction scheme to address the problem of the remaining cutoff dependence in the Casimir stress in an inhomogeneous medium, and show that the nontouching Casimir force between two separated bodies is cutoff independent. The cancellation of the electric and magnetic contributions to the surface divergence near a perfectly conducting wall is found to be incomplete in the case of inhomogeneity.

10 pages, 1 figure

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• Casimir forces in inhomogeneous media: renormalization and the principle of virtual work
• Casimir stress in materials: hard divergency at soft walls
• Inhomogeneity-Induced Casimir Transport of Nanoparticles
• Quantum propulsion and trapping of nano-objects by inhomogeneity-induced lateral Casimir forces
• Casimir-Polder forces in inhomogeneous backgrounds
• Scarf for Lifshitz