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 planar walls is investigated in the canonical ensemble at zero temperature by means of Cornwall-Jackiw-Tomboulis effective action approach within the improved Hartree-Fock approximation. Our results show that: (i) the Casimir energy and the resulting Casimir force in the canonical ensemble remarkably differ from those in the grand canonical ensemble; (ii) when the distance between two planar walls increases, the Casimir energy and Casimir force decay in accordance with a half-integer power law in the canonical ensemble instead of an integer power law in the grand canonical ensemble.