Higher Corrections to the Mass Current in the Weakly Inhomogeneous A-phase of Helium-3

TL;DR

This paper derives new mathematical representations for the mass current in the superfluid A-phase of Helium-3, revealing additional correction terms to the standard expression, especially at zero temperature, with detailed calculations for specific orientations.

Contribution

It introduces two new general representations for the mass current, including higher-order gradient corrections, advancing understanding of superfluid Helium-3's behavior near zero temperature.

Findings

New integral and series representations for mass current

Higher-order gradient correction terms derived

Logarithmic cubic contributions identified

Abstract

Two new general representations (the series and the integral) for the mass current $\vj$ in weakly inhomogeneous superfluid A-phase of Helium--3 are obtained near zero of temperature by solving the Dyson-Gorkov equation. These representations result in additional correcting contribution to the standard leading expression for $\vj$ which is of first order in gradients of the orbital angular momentum vector $\hl$. The total supplementary term is found as integral, and, provided the London limit holds, the procedure is advanced to expand it at T=0 asymptotically by the Laplace method in powers of gradients of $\hl$. Three special static orientations of $\hl$ with respect to its curl are considered to calculate the higher correcting terms up to third order. Coefficients at the quadratic terms are estimated numerically, new cubic contributions are found which contain the logarithm of the London parameter.