Abstract
Multiple phases occurring in a Bose gas with finite-range interaction are investigated. In the vicinity of the onset of Bose-Einstein condensation (BEC), the chemical potential and the pressure show a van der Waals-like behavior indicating a first-order phase transition although there is no long-range attraction.
Furthermore, the equation of state becomes multivalued near the BEC transition. For a Hartree-Fock or Popov (Hartree-Fock-Bogoliubov) approximation, such a multivalued region can be avoided by the Maxwell construction.
For sufficiently weak interaction, the multivalued region can also be removed using amany-body T-matrix approximation. However, for strong interactions there remains a multivalued region even for the T-matrix approximation and after the Maxwell construction, which is interpreted as a density hysteresis.
This unified treatment of normal and condensed phases becomes possible due to the recently found scheme to eliminate self-interaction in the T-matrix approximation, which allows one to calculate properties below and above the critical temperature.