First-order correction to the Casimir force within an inhomogeneous medium

摘要

For the Casimir piston filled with an inhomogeneous medium, we regularized and expressed the Casimir energy with cylinder kernel coefficients by using the first-order perturbation theory. When the refractive index of the medium is smoothly inhomogeneous (i.e., derivatives of all orders exist), a logarithmically cutoff-dependent term and a quadratically cutoff-dependent term in the Casimir energy are found. We show that in the piston model these terms vanish in the force and thus the Casimir force is always cutoff independent, but these terms will remain in the force in the half-space model and must be removed by additional regularizations. We give explicit benchmark solutions to the first-order corrections of both Casimir energy and Casimir force for an exponentially decaying profile. The present method can be extended to other inhomogeneous profiles. Our results should be useful for future relevant calculations and experimental studies.

关键词