2009/09/16 by T. G. Philbin, C. Xiong, U. Leonhardt +1
Engineering · Physics and Astronomy · #Casimir effect #Classical mechanics #Dielectric #Mechanical and Optical Resonators #Physics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Regularization (linguistics) #Thermal Radiation and Cooling Technologies #quant-ph
paper · pdf · doi:10.1016/j.aop.2009.11.006
published as Ann. Phys. 325 (2010) 579 · 17 pages
arxiv created 2009/09/16 · openalex publication_date 2009/11/28 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.