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Casimir stress in an inhomogeneous medium | T.G. Philbin
; C. Xiong
; U. Leonhardt
; | Date: |
16 Sep 2009 | 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. | Source: | arXiv, 0909.2998 | Services: | Forum | Review | PDF | Favorites |
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