Casimir energy for N superconducting cavities: a model for the YBCO (GdBCO) sample to be used in the Archimedes experiment

In this paper we study the Casimir energy of a sample made by N cavities, with N >> 1, across the transition from the metallic to the superconducting phase of the constituting plates. After having characterised the energy for the configuration in which the layers constituting the cavities are made by dielectric and for the configuration in which the layers are made by plasma sheets, we concentrate our analysis on the latter. It represents the final step towards the macroscopical characterisation of a "multi-cavity" (with N large) necessary to fully understand the behaviour of the Casimir energy of a YBCO (or a GdBCO) sample across the transition. Our analysis is especially useful to the Archimedes experiment, aimed at measuring the interaction of the electromagnetic vacuum energy with a gravitational field. To this purpose, we aim at modulating the Casimir energy of a layered structure, the multi-cavity, by inducing a transition from the metallic to the superconducting phase. After having characterised the Casimir energy of such a structure for both the metallic and the superconducting phase, we give an estimate of the modulation of the energy across the transition.