The Casimir Effect in a Dilute Bose Gas in Canonical Ensemble within Improved Hartree–Fock Approximation

The Casimir effect in a dilute Bose gas confined between two parallel plates is investigated at zero temperature by means of Cornwall–Jackiw–Tomboulis effective action approach within the improved Hartree–Fock approximation in the canonical ensemble, in which the particle number is fixed. In comparison with those in the grand canonical ensemble, where the particle number can be changed, the fixation of the particle number leads to the significant changes in the Casimir energy and the resulting Casimir force. The most interesting result is that the Casimir energy and Casimir force decay in accordance with a half-integer power law instead of an integer power law in the grand canonical ensemble. Moreover, the scattering length dependence of the Casimir force is also considered.