Critical dynamics of the phase transition to the superfluid state

In papers devoted to superfluidity, the generally accepted statement that the dynamics of the corresponding phase transition is described by the stochastic model F or E can be frequently found. Nevertheless, the dynamical critical index has not been found even in the leading order of the perturbation theory. It is also unknown which model, E or F, in fact corresponds to this system. We use two different approaches to study this problem. First, we study the dynamics of the critical behavior in a neighborhood of the $\lambda$ point using the renormalization group method based on a quantum microscopic model in the formalism of the time-dependent Green's functions at a finite temperature. Second, we study the stochastic model F to find whether it is stable under compressibility effects. Both approaches lead to the same very unexpected result: the dynamics of the phase transition to the superfluid state are described by the stochastic model A with a known dynamical critical index.