Strong Coupling Corrections to the Ginzburg-Landau Theory of Superfluid ^{3}He

TL;DR

This paper refines the understanding of strong coupling effects in superfluid helium-3 by analyzing experimental data and proposing a model to determine all relevant thermodynamic coefficients, enhancing the phenomenological theory.

Contribution

It introduces a model combining experimental data and theoretical calculations to determine all fifth-order invariants in the Ginzburg-Landau theory of superfluid helium-3.

Findings

Refined the four experimental coefficients using susceptibility and NMR data.

Proposed a model to determine all five fourth order terms.

Discussed implications for surface tension and novel superfluid states.

Abstract

In the Ginzburg-Landau theory of superfluid $^{3}$He, the free energy is expressed as an expansion of invariants of a complex order parameter. Strong coupling effects, which increase with increasing pressure, are embodied in the set of coefficients of these order parameter invariants\cite{Leg75,Thu87}. Experiments can be used to determine four independent combinations of the coefficients of the five fourth order invariants. This leaves the phenomenological description of the thermodynamics near $T_{c}$ incomplete. Theoretical understanding of these coefficients is also quite limited. We analyze our measurements of the magnetic susceptibility and the NMR frequency shift in the $B$-phase which refine the four experimental inputs to the phenomenological theory. We propose a model based on existing experiments, combined with calculations by Sauls and Serene\cite{Sau81} of the pressure dependence of these coefficients, in order to determine all five fourth order terms. This model leads us to a better understanding of the thermodynamics of superfluid $^{3}$He in its various states. We discuss the surface tension of bulk superfluid $^{3}$He and predictions for novel states of the superfluid such as those that are stabilized by elastic scattering of quasiparticles from a highly porous silica aerogel.