Casimir stress in an inhomogeneous medium
arXiv:0909.2998 · doi:10.1016/j.aop.2009.11.006
Abstract
The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz's theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wise homogeneous dielectrics with planar boundaries. A Casimir force per unit volume can be extracted from the infinite stress but it diverges on the boundaries between the inhomogeneous medium and the homogeneous dielectrics. An alternative regularization of the vacuum stress is considered that removes the contribution of the inhomogeneity over small distances, where macroscopic electromagnetism is invalid. The alternative regularization yields a finite Casimir stress inside the inhomogeneous region, but the stress and force per unit volume diverge on the boundaries with the homogeneous dielectrics. The case of inhomogeneous dielectrics with planar boundaries thus falls outside the current understanding of the Casimir effect.
17 pages
References in corpus (3)
Cited by in corpus (20)
- Casimir effect from macroscopic quantum electrodynamics
- Electromagnetic description of three-dimensional time-reversal invariant ponderable topological insulators
- Canonical quantization of electromagnetism in spatially dispersive media
- Casimir stress inside planar materials
- Lifshitz theory of the cosmological constant
- Casimir forces in inhomogeneous media: renormalization and the principle of virtual work
- Casimir stress in materials: hard divergency at soft walls
- Born-series approach to the calculation of Casimir forces
- Numerical Regularization of Electromagnetic Quantum Fluctuations in Inhomogeneous Dielectric Media
- The energy level shifts and the decay rate of an atom in the presence of a conducting wedge
- The cutoff-dependence of the Casimir force within an inhomogeneous medium
- Inhomogeneity-related cutoff dependence of the Casimir energy and stress
- Spontaneous emission in dispersive media without point-dipole approximation
- First-order correction to the Casimir force within an inhomogeneous medium
- Casimir self-stress in a dielectric sphere
- Electromagnetic Casimir densities for a cylindrical shell on de Sitter space
- Scarf for Lifshitz
- Quantum Electromagnetic Fluctuations in Inhomogeneous Dielectric Media
- On the computation of Casimir stresses in open media and Lifshitz theory
- Aspects of Quantum Energy and Stress in Inhomogeneous Unbounded Dielectric Continua