Spin diffusion and other transport properties of liquid He3

The Landau theory of a Fermi liquid is described and discussed, and the transport equation of the theory is used to obtain an expression for the coefficient of self-diffusion D in liquid He3. It is found that D = A/T2, with A ≈ 4.2 x 10^-6 cm sec^-1 degrees^2; T is the temperature in degrees Kelvin. This is within the estimated probable error of the experimental result: A = 1.54 x 10^-6 cm 2 sec^-1 degrees^2. However, the Landau theory is valid only under certain restricted conditions, In order to understand the nature of the theory more thoroughly and to be able to consider corrections to it, we investigate the formal properties of the exact solution. This is done by a consideration of the thermodynamic Green's functions of the system, as suggested by Kadanoff and Baym. The transport coefficients can be expressed in terms of these Green’s functions, and such an expression is derived for the coefficient of self-diffusion D. The Landau theory result for D is shown to correspond to the Hartree Fock approximation plus the assumption of a constant lifetime for the quasi-particles of the system. Other approximations might be more readily motivated by a consideration of a response function rather than the Green’s functions. Thus the relationship between D and the dynamic magnetic susceptibility χ(k, ω) is demonstrated. The random phase approximation, suitably modified to take account of the hard cores, is shown to give again the Landau result. Finally, the example of the T-matrix approximation is given as a means of determining the value of the constant quasi-particle lifetime at the Fermi surface. This treatment, actually valid only for a dilute fermion gas, is shown to give the qualitative results expected--in particular, a T^- 2 dependence for D. However, He3 is far too dense a liquid for this approximation to be quantitatively valid. It is concluded that the Landau theory gives excellent results for the transport properties of liquid He3; it is extremely difficult to investigate corrections to it in or near the region where the theory is valid.published or submitted for publicationU of I Onlythesi