The theory of a fermi liquid (the properties of liquid 3He at low temperatures)

The review gives the general theory of an isotropic Fermi liquid constructed by L. D. Landau, and continued by the authors of the present article. The results of the theory are compared with the experimental data on the properties of liquid helium 3 at low temperatures. The contents of the review are set out in the following order. After a short introduction (§ 1), § 2 gives the basic premises of L. D. Landau's theory, and in particular the energy of excitations and the interaction function f are derived. § 3 gives the derivation from Galileo's principle of a relation which expresses the effective mass of the excitations in terms of the mass of the atoms and the zeroth harmonic of the function f . § 4 is devoted to the derivation of the specific heat of a Fermi liquid, and an expression for the magnetic susceptibility is deduced in § 5. The exchange interaction of the excitations plays a considerable role in this expression. § 6 gives the kinetic equation for the excitations and this is used to find expressions for the momentum and energy flux. The results of § 6 are applied in § 7 to the calculation of the coefficient of viscosity, and in § 8 the coefficient of thermal conductivity is found by an analogous method. § 9 is concerned with the problem of the velocity of sound. In particular, this section contains the result obtained by L. D. Landau concerning the possibility of propagating the so-called `zero sound' in a Fermi liquid at sufficiently low temperatures. § 10 considers the problem of dispersion and absorption of sound. § 11 deduces the average fluctuations of the distribution function and this result is used to calculate the scattering of light. An expression is given for the total intensity of scattered light, and the frequency and angular distributions are also given. The Appendix shows how the basic premises of the theory of a Fermi liquid can be derived from microscopic considerations. § A1 considers the properties of a rarefied Fermi gas. § A2 gives the microscopic basis of the energy spectrum of a Fermi liquid in the general case, and also gives a relation between the function f and the scattering amplitude of excitations.