Repulsive Casimir Force of the Free and Harmonically Trapped Bose Gas in the Bose-Einstein Condensate Phase

Abstract

In this study, ideal free and harmonically trapped Bose gases confined by two plates in thex-y-plane in-between distancedare considered. The Casimir potential is obtained from the grand canonical potential of these quantum Bose gases for the Zaremba and the anti-periodic boundary conditions. The Casimir force is then obtained for the Bose-Einstein condensate phaseT Tc. It is shown that Casimir forces are repulsive for these boundary conditions. Additionally, it is shown that Casimir forces exponentially decay in the non-condensate phaseT>Tcwith the decay lengths. These decay lengths were discussed and compared for different boundary conditions. As a result, new results are obtained for harmonically trapped Bose gas and the free gas results are compared with previous results.