Random textures of the order parameter of superfluid $^3$He-B in aerogel

A phenomenological scheme of the observed properties of superfluid $^3$He in aerogel is proposed in the spirit of the Ginzburg-Landau theory. The effect of the aerogel on the order parameter is described by the random tensor field $\eta_{jl}(r)$. The tensor field exerts a considerable disorienting effect on the order parameter in the A phase of $^3$He, but virtually unaffects the orientation of the order parameter in the B phase in zero magnetic field. The change in the texture of the order parameter emerging in the B phase in aerogel in a magnetic field is considered. It is shown that the mean square of the angle between the magnetic field direction and the anisotropy axis of the B phase is proportional to the third power of the magnetic field strength. The fluctuations of the direction of the magnetic anisotropy axis of $^3$He-B are correlated over the familiar «healing length», which is inversely proportional to the field strength and has a macroscopic scale.