Superfluid Phase Transition with Activated Velocity Fluctuations: Renormalization Group Approach

TL;DR

This paper develops a quantum field model for superfluid phase transitions incorporating velocity fluctuations, using renormalization group techniques to analyze the impact of turbulence on critical behavior and exponents.

Contribution

It introduces a generalized model combining critical dynamics with velocity fluctuations and analyzes the effects of turbulence on phase transition properties.

Findings

Critical exponents are significantly altered by turbulence.

One-loop calculations are insufficient for fixed point stability.

Effective viscosity scaling exponent is 4/3.

Abstract

A quantum field model that incorporates Bose-condensed systems near their phase transition into a superfluid phase and velocity fluctuations is proposed. The stochastic Navier-Stokes equation is used for a generation of the velocity fluctuations. As such this model generalizes model F of critical dynamics. The field-theoretic action is derived using the Martin-Siggia-Rose formalism and path integral approach. The regime of equilibrium fluctuations is analyzed within perturbative renormal- ization group method. The double $(\epsilon ,\delta)$-expansion scheme is employed, where is a deviation from space dimension $4$ and $\delta$ describes scaling of velocity fluctuations. The renormalization procedure is performed to the leading order. The main corollary gained from the analysis of the thermal equilibrium regime suggests that one-loop calculations of the presented models are not sufficient to make a definite conclusion about the stability of fixed points. We also show that critical exponents are drastically changed as a result of the turbulent background and critical fluctuations are in fact destroyed by the developed turbulence fluctuations. The scaling exponent of effective viscosity is calculated and agrees with expected value $4/3$.