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Steklov Institute of Mathematics at St.Petersburg

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PREPRINT 14/1996

C. MALYSHEV
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HIGHER CORRECTIONS TO THE MASS CURRENT
IN THE WEAKLY
INHOMOGENEOUS $^{3}$He --A

This preprint was accepted December 1996.

Contact: ` C. Malyshev `

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 $\hl$. A self-contained integral formula for
the total supplementary term is deduced, 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. Bibliography--30.

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