Critical dynamics of the superfluid phase transition: Multiloop calculation of the microscopic model.

Results and method of a three-loop renormalization-group calculation in the model of a Bose gas with a local density-density interaction in the formalism of time-dependent Green functions at finite temperature are presented. The results provide support to the recent conjecture [J. Honkonen, M.

Superfluid phase transition with activated velocity fluctuations: Renormalization group approach.

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.

Influence of compressibility on scaling regimes of strongly anisotropic fully developed turbulence.

A statistical model of strongly anisotropic fully developed turbulence of the weakly compressible fluid is considered by means of the field theoretic renormalization group. The corrections due to compressibility to the infrared form of the kinetic energy spectrum have been calculated in the leading order in the Mach number expansion. Furthermore, in this approximation the validity of the Kolmogorov hypothesis on the independence of the dissipation length of velocity correlation functions in the inertial range has been proved.