Liquid 4He near the superfluid transition in the presence of a heat current and gravity

TL;DR

This paper presents a renormalization-group analysis of liquid helium-4 near its superfluid transition, accounting for heat currents and gravity, and compares theoretical predictions with experimental data.

Contribution

It introduces a self-consistent Hartree approximation based on model F to analyze vortex effects and calculates key thermodynamic quantities across the transition.

Findings

Calculated thermal conductivity and specific heat across T_lambda.

Identified a second correlation length below T_lambda.

Determined the Gorter-Mellink coefficient A.

Abstract

The effects of a heat current and gravity in liquid 4He near the superfluid transition are investigated for temperatures above and below T_lambda. We present a renormalization-group calculation based on model F for the Green's function in a self-consistent approximation which in quantum many-particle theory is known as the Hartree approximation. The approach can handle a zero average order parameter above and below T_lambda and includes effects of vortices. We calculate the thermal conductivity and the specific heat for all temperatures T and heat currents Q in the critical regime. Furthermore, we calculate the temperature profile. Below T_lambda we find a second correlation length which describes the dephasing of the order parameter field due to vortices. We find dissipation and mutual friction of the superfluid-normal fluid counterflow and calculate the Gorter-Mellink coefficient A. We compare our theoretical results with recent experiments.