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Abstract: The Casimir effect in an inhomogeneous dielectric is investigated usingLifshitz-s theory of electromagnetic vacuum energy. A permittivity functionthat depends continuously on one Cartesian coordinate is chosen, bounded oneach side by homogeneous dielectrics. The result for the Casimir stress isinfinite everywhere inside the inhomogeneous region, a divergence that does notoccur for piece-wise homogeneous dielectrics with planar boundaries. A Casimirforce per unit volume can be extracted from the infinite stress but it divergeson the boundaries between the inhomogeneous medium and the homogeneousdielectrics. An alternative regularization of the vacuum stress is consideredthat removes the contribution of the inhomogeneity over small distances, wheremacroscopic electromagnetism is invalid. The alternative regularization yieldsa finite Casimir stress inside the inhomogeneous region, but the stress andforce per unit volume diverge on the boundaries with the homogeneousdielectrics. The case of inhomogeneous dielectrics with planar boundaries thusfalls outside the current understanding of the Casimir effect.

Author: T.G. Philbin, C. Xiong, U. Leonhardt


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