Renormalization Group in Non-Relativistic Quantum Statistics

Juha Honkonen,Yu G Molotkov,Yu A Zhavoronkov,M V Komarova,M Yu Nalimov,Gh Adam,M Hnatič,J Buša

doi:10.1051/epjconf/202022601005

Juha Honkonen, Yu G Molotkov + Show 6 more

Open Access

https://doi.org/10.1051/epjconf/202022601005

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Abstract

Dynamic behaviour of a boson gas near the condensation transition in the symmetric phase is analyzed with the use of an effective large-scale model derived from time-dependent Green functions at finite temperature. A renormalization-group analysis shows that the scaling exponents of critical dynamics of the effective multi-charge model coincide with those of the standard model A. The departure of this result from the description of the superfluid transition by either model E or F of the standard phenomenological stochastic models is corroborated by the analysis of a generalization of model F, which takes into account the effect of compressible fluid velocity. It is also shown that, contrary to the single-charge model A, there are several correction exponents in the effective model, which are calculated at the leading order of the ɛ= 4 − d expansion.

Highlights

The analysis of the critical dynamics of the superfluid transition has a long history
A renormalization-group analysis shows that the scaling exponents of critical dynamics of the effective multi-charge model coincide with those of the standard model A
The departure of this result from the description of the superfluid transition by either model E or F of the standard phenomenological stochastic models is corroborated by the analysis of a generalization of model F, which takes into account the effect of compressible fluid velocity

Summary

Introduction

The analysis of the critical dynamics of the superfluid transition has a long history. The attempts to derive critical scaling behaviour with the aid of microscopic models [1] and phenomenological stochastic models [2, 3] have given different results. An unambiguous result for the dynamic critical exponent at the physically relevant value of the expansion parameter has been elusive in the stochastic setup [6, 7]. Critical exponents describing corrections to scaling are shown to be different from those of the model A. In the effective model there are three correction exponents determined by the eigenvalues of the Jacobi matrix of the RG β functions. All these correction exponents have been calculated at the leading order of the = 4 − d expansion

Real-time Green functions at finite temperature

Renormalization-group analysis of the effective model

Stochastic model with density fluctuations

Conclusion