Bose condensation: The viscosity critical dimension and developed turbulence

Abstract

We propose a model for studying the mutual influence of critical fluctuations in the vicinity of the critical point of phase transition to a superfluid state and the velocity fluctuations in the developed turbulence regime. We demonstrate the presence of two different regimes: the turbulence regime and the equilibrium regime. We show that the standard critical behavior can break in the turbulence regime. The viscosity becomes an infrared-irrelevant parameter in the equilibrium regime. We justify the assumption that the viscosity critical dimension in this regime is determined by critical indices of the critical behavior statistical model, which are currently known with sufficient accuracy.

Influence of hydrodynamic fluctuations on the phase transition in the E and F models of critical dynamics

“…Such a modification of model E leads to some deviations from the standard field-theoretical approach, and we adopt it. We here continue the investigation begun in [4]. Our aim is to study different scaling regimes of the proposed model.…”

“…are not included in action (5), because it can be shown that they are IR-irrelevant. The renormalization of the proposed model was described in detail in [4]. In the renormalization group analysis, the following properties of the model must be applied:…”

“…A stochastic equation for the critical dynamics of a Bose system in the presence of a random velocity field was proposed in [4]. Such a modification of model E leads to some deviations from the standard field-theoretical approach, and we adopt it.…”

Renormalization group study of superfluid phase transition: effect of compressibility

“…By inspection of the graphs we observe that all nontrivial diagrams in the term m ∂ t m vanish. In [20] it has been demonstrated that the linkage to critical statics is violated due to the inclusion of the velocity field, but the multiplicative renormalization can be recovered by considering a new charge associated with the interaction term m (ψ † ∇ 2 ψ − ψ∇ 2 ψ † ). More precisely, instead of writing this term with the charge g 3 (see Eq.…”

“…In this work, we follow the third option (iii) by means of inclusion into the model description external velocity fluctuations. In this regard several generalization have already been proposed [13,20,21]. It has been shown that incompressible hydrodynamic fluctuations contribute sig-nificantly to the value of the ω w -index, which controls stability of large-scale regimes [9,17].…”