Casimir energy due to inhomogeneous thin plates
- URL: http://arxiv.org/abs/1912.12651v2
- Date: Fri, 24 Jan 2020 16:53:07 GMT
- Title: Casimir energy due to inhomogeneous thin plates
- Authors: Cesar D. Fosco and Francisco D. Mazzitelli
- Abstract summary: We study the Casimir energy due to a quantum real scalar field coupled to two parallel mirrors with non-homogeneous properties.
In some particular cases, the Casimir interaction energy for non-planar perfect mirrors can be reproduced by inhomogeneities on planar mirrors.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study the Casimir energy due to a quantum real scalar field coupled to two
planar, infinite, zero-width, parallel mirrors with non-homogeneous properties.
These properties are represented, in the model we use, by scalar functions
defined on each mirror's plane. Using the Gelfand-Yaglom's theorem, we
construct a Lifshitz-like formula for the Casimir energy of such a system. Then
we use it to evaluate the energy perturbatively, for the case of almost
constant scalar functions, and also implementing a Derivative Expansion, under
the assumption that the spatial dependence of the properties is sufficiently
smooth. We point out that, in some particular cases, the Casimir interaction
energy for non-planar perfect mirrors can be reproduced by inhomogeneities on
planar mirrors.
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