Transport Equation for a Fermi Liquid in Random Scattering Centers. I. A Quasiparticle Description in the Macroscopic and Low-Temperature Limit

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Abstract
The transport properties of an interacting fermion gas in the presence of randomly distributed scattering centers and a weak longitudinal force field are studied on the basis of a transport equation for the bare-particle distribution function. This equation, valid for arbitrary wavelength, frequency, and temperature, is derived by a generalization of a simple method due to Résibois. For the case of electrons, the transport equation is given in terms of the mean total electric field in the medium, thereby allowing a direct calculation of the transport coefficients of physical interest. The general theory is applied to the case of a slowly and smoothly varying driving field, low temperatures, and weak and dilute scattering centers. It is shown, up to second order in the interfermion interaction, that a transport equation for a quasiparticle distribution function can be derived. This equation has the form originally suggested by Landau with the interparticle and impurity scattering terms added. The connection between the bare-particle and the quasiparticle distribution functions is also obtained.