Renormalization-group theory for rotating 4He near the superfluid transition

The influence of a uniform rotation with frequency Omega on the critical behavior of liquid 4He near T_lambda is investigated. We apply our recently developed approach which is a renormalization-group theory based on model F starting with the calculation of the Green's function in Hartree approximation. We calculate the specific heat, the correlation length, and the thermal resistivity tensor as functions of the temperature T for fixed values of the rotation frequency Omega. For nonzero Omega we find that all physical quantities are smooth near T_lambda so that the superfluid transition is a smooth crossover. We define a frequency-dependent transition temperature T_lambda(Omega) by the maximum of the specific heat and present a power law prediction. For T<T_lambda(Omega) we find mutual friction between the superfluid and the normal-fluid component caused implicitly by the motion of vortex lines and calculate the Vinen coefficients B and B'.Comment: 16 pages, 4 figure

The inversion theorem and Plancherel's theorem in infinite dimensions

Inversion theorem and Plancherels theorem in Banach spac

Renormalization-group calculation of the superfluid/normal-fluid interface of liquid 4He in gravity near T_lambda

The superfluid/normal-fluid interface of liquid 4He is investigated in gravity on earth where a small heat current Q flows vertically upward or downward. We present a local space- and time-dependent renormalization-group (RG) calculation based on model F which describes the dynamic critical effects for temperatures T near the superfluid transition T_lambda. The model-F equations are rewritten in a dimensionless renormalized form and solved numerically as partial differential equations. Perturbative corrections are included for the spatially inhomogeneous system within a self-consistent one-loop approximation. The RG flow parameter is determined locally as a function of space and time by a constraint equation which is solved by a Newton iteration. As a result we obtain the temperature profile of the interface. Furthermore we calculate the average order parameter , the correlation length xi, the specific heat C_Q and the thermal resistivity rho_T where we observe a rounding of the critical singularity by the gravity and the heat current. We compare the thermal resistivity with an experiment and find good qualitative agreement. Moreover we discuss our previous approach for larger heat currents and the self-organized critical state and show that our theory agrees with recent experiments in this latter regime.Comment: 24 pages, 7 figure