Casimir effect for scalar fields under Robin boundary conditions on plates

TLDR: In this paper, the authors studied the Casimir effect for scalar fields with general curvature coupling subject to mixed boundary conditions (1 + βmnμ∂μ) = 0 at x = am on one (m = 1) and two (m= 1, 2) parallel plates at a distance a ≡ a2 − a1 from each other.

Abstract: We study the Casimir effect for scalar fields with general curvature coupling subject to mixed boundary conditions (1 + βmnμ∂μ) = 0 at x = am on one (m = 1) and two (m = 1, 2) parallel plates at a distance a ≡ a2 − a1 from each other. Making use of the generalized Abel–Plana formula previously established by one of the authors [1], the Casimir energy densities are obtained as functions of β1 and of β1, β2, a respectively. In the case of two parallel plates, a decomposition of the total Casimir energy into volumic and superficial contributions is provided. The possibility of finding a vanishing energy for particular parameter choices is shown and the existence of a minimum to the surface part is also observed. We show that there is a region in the space of parameters defining the boundary conditions in which the Casimir forces are repulsive for small distances and attractive for large distances. This yields the interesting possibility of stabilizing the distance between the plates by using the vacuum forces.