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

TL;DR

This paper uses a renormalization-group approach to analyze the superfluid/normal-fluid interface of liquid helium-4 under gravity and heat flow, revealing critical behavior and matching experimental results.

Contribution

It introduces a local space- and time-dependent RG calculation based on model F for the superfluid transition near T_lambda, including perturbative corrections and numerical solutions.

Findings

Temperature profile of the interface obtained

Good qualitative agreement with experimental thermal resistivity data

Discussion of self-organized critical state at larger heat currents

Abstract

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 <psi>, 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.