Geodesic
Critical dynamics of the~phase transition to the~superfluid state
Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 2, pp. 361-377

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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.
Keywords: superfluidity, stochastic dynamics, quantum field theory, quantum-field renormalization group, $(4-\epsilon)$-expansion.
Mots-clés : $\lambda$ point 
@article{TMF_2019_200_2_a13,
     author = {Yu. A. Zhavoronkov and M. V. Komarova and Yu. G. Molotkov and M. Yu. Nalimov and J. Honkonen},
     title = {Critical dynamics of the~phase transition to the~superfluid state},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {361--377},
     publisher = {mathdoc},
     volume = {200},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_200_2_a13/}
}
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Yu. A. Zhavoronkov; M. V. Komarova; Yu. G. Molotkov; M. Yu. Nalimov; J. Honkonen. Critical dynamics of the~phase transition to the~superfluid state. Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 2, pp. 361-377. http://geodesic.mathdoc.fr/item/TMF_2019_200_2_a13/