A model for the λ-transition of helium

Abstract

Summary. --Guided by the analogy to the Bose-Einstein condensation of the ideal Bose gas (IBG) we propose a new model for the ~-transition of liquid helium. Deviating from the IBG our model uses phase-ordered and localized single-particle functions. This means that finite groups of particles are assumed to be phase-locked. These phase correlations can be related to the singularity at the transition point and to the occurrence of the superfluid density. The model leads to the following results: 1) a possible explanation of the logarithmic singularity of the specific heat, 2) a characteristic functional form for the superfluid density which yields excellent fits to the experimental data, 3) a quantitative prediction of a small nonzero entropy content of the superfluid component.PACS 67.20 -Quantum effects on the structure and dynamics of nondegenerate fluids (e.g., normal phase liquid helium 4).

Velocity of the fourth sound in liquid helium II via extended thermodynamics

“…These equations are in accord with the theoretical microscopic motivations in favour of a small superfluid entropy advanced in [36,37].…”

The two-fluid model with superfluid entropy

“…With (12) fitted to the experimental superfluid density, the entropy of the contibuting non-condensed particles can be calculated. The resulting prediction [11] of this superfluid entropy S s is shown in Fig. 1.…”

“…Prediction[11] of the superfluid density S s (T, P SVP ) as a function of the temperature and at saturated vapour pressure.…”

Asymptotic temperature dependence of the superfluid density in liquid4He

“…This motion is superfluid if the velocity u s = ∇Φ/m is sufficiently small. Equations (4) and (5) are a well-known description 2 for a superfluid motion in the IBG. In this description the superfluid fraction ρ s /ρ equals the condensate fraction n 0 /N = ρ 0 /ρ.…”