Landau theory Fermi liquids

The kernel is a well known quantity that appears in several branches of theoretical physics. For example, evaluated for the electron gas, /xc is, up to a factor, the local field correction . To emphasize the correspondence to the effective interaction of Landau s Fermi-liquid theory, to which it reduces in the appropriate limit, /xc plus the bare Coulomb interaction is sometimes called the effective interaction , while in the theory of classical liquids the same quantity is referred to as the Ornstein-Zernicke function. 

A detailed quantitative understanding of liquid He at low temperatures requires the application of Landau s Fermi liquid theory, which takes explicit account of the interactions, and parameterises them in the form of a small number of dimensionless constants known as Landau parameters. For most purposes, only three of these parameters are needed (usually written as 7q, F and G ) and almost all of the properties of the interacting Fermi liquid can be calculated in terms of them. Numerical values of the Landau parameters are not predicted by the theory but are to be found by experiment. The crucial test of the theory—a requirement that consistent values of the Landau parameters should be obtained from widely differing kinds of experiment—is convincingly fulfilled. 

The properties of the two helium isotopes in the liquid state are strongly influenced by quantum effects. In Fig. 2.8, the specific heat of 3He, calculated from the ideal gas Fermi model (Tp = 4.9 K) with the liquid 3He density, is compared with the experimental data. The inadequacy of this model is evident. A better fit, especially at the lower temperatures, is obtained by the Landau theory [25]. 

Note that the exchange term is of the form / y(r,r ) h(r )dr instead of the y (r) (r) type. Equation (1.12), known as the Hartree-Fock equation, is intractable except for the free-electron gas case. Hence the interest in sticking to the conceptually simple free-electron case as the basis for solving the more realistic case of electrons in periodic potentials. The question is how far can this approximation be driven. Landau s approach, known as the Fermi liquid theory, establishes that the electron-electron interactions do not appear to invalidate the one-electron picture, even when such interactions are strong, provided that the levels involved are located within kBT of Ep. For metals, electrons are distributed close to Ep according to the Fermi function f E) ... 

Once the Landau Fermi-liquid theory is set up and the assumption (22) made about the density of states, explicit calculaiions of M(H) and C (H) can be made. Quantitative agreement is found with all of the experimental results including not only (19), (20), and (21), but the full field dependence of M(H) and C (H) once cA is fixed. These are striking successes, and one would like to have a deeper microscopic understanding of what is going on than is afforded by the assumptions 7. and 8. 

Calculations for finite nuclei will be discussed which demonstrate that the distribution of sp strength in the experimentally accessible energy region can be qualitatively understood. In addition, it becomes possible to interpret both theoretical and experimental results in terms of quasiparticle excitations, the basic concept of Landau s theory of Fermi liquids [19-21]. In contrast to an infinite liquid, the sp basis must be appropriate for the finite system under study and is not composed of the sp momentum states. Apart from this obvious requirement, most notions carry over rather straightforwardly. The ability to calculate the sp strength distribution and compare to experimental data presents an advantage over the approach initiated by Migdal [22,23]. 

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