We propose a new form of the inversion method in terms of a selfenergy expansion to access the phase diagram of the Bose-Einstein transition. The dependence of the critical temperature on the interaction parameter is calculated. This is discussed with the help of a new condition for Bose-Einstein condensation in interacting systems which follows from the pole of the T-matrix in the same way as from the divergence of the medium-dependent scattering length. A many-body approximation consisting of screened ladder diagrams is proposed which describes the Monte Carlo data more appropriately. The specific results are that a non-selfconsistent T-matrix leads to a linear coefficient in leading order of 4.7, the screened ladder approximation to 2.3, and the selfconsistent T-matrix due to the effective mass to a coefficient of 1.3 close to the Monte Carlo data.
We investigate a Bose gas with finite-range interaction using a scheme to eliminate unphysical processes in the T-matrix approximation. In this way the corrected T-matrix becomes suitable to calculate properties below the critical temperature. For attractive interaction, an Evans-Rashid transition occurs between a quasi-ideal Bose gas and a BCS-like phase with a gaped dispersion. The gap decreases with increasing density and vanishes at a critical density where the single-particle dispersion becomes linear for small momenta indicating Bose-Einstein condensation. The investigation of the pressure shows however, that the mentioned quantum phase transitions might be inaccessible due to a preceding first order transition.
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 longrange 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 a many-body T-matrix approximation. However, for strong interactions there remains a multivalued region even for the T-matrix approximation and after the Maxwell construction, what 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 to calculate properties below and above the critical temperature.PACS numbers: 03.75.-b, 67.85.-d
From the many-body T-matrix the condition for a medium-dependent bound state
and its binding energy is derived for a homogeneous interacting Bose gas. This
condition provides the critical line in the phase diagram in terms of the
medium-dependent scattering length. Separating the Bose pole from the
distribution function the influence of a Bose condensate is discussed and a
thermal minimum of the critical scattering length is found
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