\(^3\)He Viscosity Apart From Fermi Liquid Mode

Since the 1940 s, intensive studies of \(^3\)He viscosity have demonstrated the ultra-low-temperature behavior \(T^{-2}\) predicted by Landau’s Fermi liquid(FL) theory. Unexpectedly, it turns out that within one order of magnitude in temperature up to \(^3\)He evaporation, the experimental data obey a mysterious power law \(T^{-1/3}\) out of any theoretical ground. Based on conventional Fermi gas approach we consider a small but important fraction of fermions located in the thermal vicinity of the Fermi energy and, then directly find the fermion-fermion mean free path. Subsequent calculation of viscosity reveals a puzzling dependence of the negative one-third on temperature. We compare our results with longstanding experimental findings. For two-dimensional electron gas an negative one-half law on temperature is predicted.