Casimir energy due to inhomogeneous thin plates

FOSCO, C.D.; MAZZITELLI, F.D.

Physical Review D

APS

Año: 2020 vol. 101

2470-0010

We study the Casimir energy due to a quantum real scalar field coupled to two planar, infinite, zero-width, parallel mirrors with nonhomogeneous properties. These properties are represented, in the model weuse, by scalar functions defined on each mirror?s plane. Using the Gelfand-Yaglom?s theorem, we constructa Lifshitz-like formula for the Casimir energy of such a system. Then we use it to evaluate the energyperturbatively, for the case of almost constant scalar functions, and also implementing a derivativeexpansion, under the assumption that the spatial dependence of the properties is sufficiently smooth. Wepoint out that, in some particular cases, the Casimir interaction energy for nonplanar perfect mirrors can bereproduced by inhomogeneities on planar mirrors