Non-equilibrium Thermodynamical Description of Superfluid Transition in Liquid Helium

In previous papers a phase field model for λ-transition in 4He was proposed, which is able to describe the influence of the heat flux on the temperature transition. The model presented here generalizes previous results taking into account of a homogeneous presence of quantized vortices below the λ-transition. As parameter that controls the transition, a dimensionless field f linked to the modulus of the condensate wave function is used. In addition to the field f , the resulting model chooses the following field variables: Density, velocity, temperature and heat flux. Nonlocal terms to describe inhomogeneities in the field variables and dissipative effects of mechanical and thermal origin are also taken into account. Under the hypothesis that the liquid is at rest, the second sound propagation near the superfluid transition is studied. It is seen that the order parameter modifies the speed and the attenuation of the second sound, as well as the presence of a small tangle of vortices. This shows that the influence of the order parameter is not restricted to the description of the lambda transition, but its presence influences also other features, as the second sound speed and attenuation. In addition to the second sound a new mode is present, corresponding to a perturbation in the order parameter f , which is attenuated within a short number of wavelengths..