Casimir forces in Bose-Einstein condensates: finite size effects in three-dimensional rectangular cavities

Recently, the Casimir pressure was calculated for infinitely thin and infinitely repulsive parallel plates due to quantum fluctuations of the quasiparticle vacuum in a zero-temperature dilute Bose-Einstein condensate (BEC). We generalize this result and obtain an expression for the Casimir pressure in a three-dimensional rectangular cavity with Dirichlet boundary conditions and arbitrary lengths. We then calculate finite size corrections to the parallel plate scenario