ar X iv : c on d - m at / 9 80 20 44 v 1 4 F eb 1 99 8 Ginzburg - Landau Theory for Impure Superfluid

Liquid 3 He at low temperatures is an ideal substance to study because of its natural purity. The superfluid state, which appears at temperatures below 3 mK, has many unusual and exciting properties. These have extensively been studied experimentally, and the results are in many cases well understood theoretically using quasiclassical approximation. In this work we study the case that liquid 3 He is inside of aerogel. Aerogel is a very porous substance, where 98% of the volume can be empty. The purpose is to understand how the properties of the superfluid are modified when the quasiparticles are scattered from an impurity, such as aerogel. We study extensively the homogeneous scattering model. From it we derive the Ginzburg-Landau theory of impure superfluid 3 He. We give expressions for measurable quantities and compare them with experiments. We consider random anisotropy and its effect on the NMR properties. More sophisticated scattering models are briefly discussed.