Studying Superfluid Transition of a Dilute Bose Gas by Conserving Approximations

TL;DR

This study investigates the superfluid transition of a dilute Bose gas using conserving approximations, revealing that different theoretical approaches predict either continuous or first-order transitions, raising questions about the true nature of the transition.

Contribution

It compares various Phi-derivable approximations to determine their predictions for the Bose-Einstein transition, highlighting discrepancies and challenging existing assumptions.

Findings

Ladder approximation predicts a continuous transition with a specific temperature shift.

Second-order, particle-hole, and fluctuation-exchange approximations suggest a first-order transition.

Standard Phi's may not reliably determine the order of the transition.

Abstract

We consider the Bose-Einstein transition of homogeneous weakly interacting spin-0 particles based on the normal-state Phi-derivable approximation. Self-consistent calculations of Green's function and the chemical potential with several approximate Phi's are performed numerically as a function of temperature near Tc, which exhibit qualitatively different results. The ladder approximation apparently shows a continuous transition with the prefactor c=2.94 for the transition-temperature shift given in terms of the scattering length a and density n. In contrast, the second-order, particle-hole, and fluctuation-exchange approximations yield a first-order transition. The fact that some standard Phi's predict a first-order transition challenges us to clarify whether or not the transition is really continuous.