Studying Superfluid Transition of a Dilute Bose Gas by Conserving Approximations

Abstract

We consider the Bose-Einstein transition of homogeneous weakly interacting spin-0 particles based on the normal-state Φ-derivable approximation. Self-consistent calculations of Green's function and the chemical potential with several approximate Φ'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 ∆Tc/T 0 c = can 1/3 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 Φ's predict a first-order transition challenges us to clarify whether or not the transition is really continuous.

Comparative studies of many-body corrections to an interacting Bose-Einstein condensate

“…In the RPA, however, the first-order behavior is less marked than the mean-field result. The order of phase transition in these results agree with the recent work [33], which approaches T c from the normal state.…”

“…All the approximations (MBTA, RPA, s-RPA, and GRPA) give the enhancement of T c by the repulsive interaction U (Fig. 6), which is consistent with the previous work [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

“…The critical temperature shift has been evaluated at most in the static limit ( [26] and the references therein). The order of the phase transition has been discussed also in the static limit based on the many-body theory above T c [33]. We assess these problems using our formalism below T c .…”

“…In a trapped gas, T c is lowered, because the density profile spreads out by a repulsive interaction, leading to the decrease in the central particle density [12][13][14][15]. In the uniform system, the enhancement of T c has been predicted in the region of small gas parameter [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. In particular, Monte-Carlo simulations give (T c − T 0 c )/T 0 c = c 1 an 1/3 with c 1 ≃ 1.3 [20,22,28].…”

$1/N$-expansion for the critical temperature of the Bose gas

“…On the other hand, the summation of the particle-particle ladder diagrams [17] gives a twice larger value of this coefficient. The calculations in the so-called fluctuation-exchange approximation [18] which incorporates both particle-particle and particlehole bubbles lead to c = 2.94. The next-to-leading order in the 1/N term of c lowers the result by 26% (for a single component Bose system) [19] which particularly signals a good convergence of the large-N expansion.…”