Linear theory of random textures of 3He-A in aerogel

TL;DR

This paper develops a linear theoretical model describing how the orbital part of the order parameter in superfluid helium-3 A-phase behaves in aerogel, analyzing spatial variations and order disruption.

Contribution

It introduces a random walk model for the order parameter's orbital vector in aerogel, providing analytical and numerical insights into order disruption and restoration.

Findings

Correlation function of the order parameter's directions derived

Analytical spatial dependence of order variation obtained

Numerical estimates of length scales and critical anisotropy provided

Abstract

Spacial variation of the orbital part of the order parameter of $^3$He-A in aerogel is represented as a random walk of the unit vector $\mathbf{l}$ in a field of random anisotropy produced by the strands of aerogel. For a range of distances, where variation of $\mathbf{l}$ is small in comparison with its absolute value correlation function of directions of $\mathbf{l}(\mathbf{r})$ is expressed in terms of the correlation function of the random anisotropy field. With simplifying assumptions about this correlation function a spatial dependence of the average variation $\langle\delta\mathbf{l}^2\rangle$ is found analytically for isotropic and axially anisotropic aerogels. Average projections of $\mathbf{l}$ on the axes of anisotropy are expressed in terms of characteristic parameters of the problem. Within the "model of random cylinders" numerical estimations of characteristic length for disruption of the long-range order and of the critical anisotropy for restoration of this order are made and compared with other estimations .