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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika // Archive

TMF, 2019 Volume 200, Number 2, Pages 361–377 (Mi tmf9674)

This article is cited in 9 papers

Critical dynamics of the phase transition to the superfluid state

Yu. A. Zhavoronkova, M. V. Komarovaa, Yu. G. Molotkova, M. Yu. Nalimova, J. Honkonenb

a St. Petersburg State University, St. Petersburg, Russia
b National Defence University, Helsinki, Finland

Abstract: 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, $\lambda$ point, stochastic dynamics, quantum field theory, quantum-field renormalization group, $(4-\epsilon)$-expansion.

Received: 13.12.2018
Revised: 27.01.2019

DOI: 10.4213/tmf9674


 English version:
Theoretical and Mathematical Physics, 2019, 200:2, 1237–1251

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