Dielectric formalism for a quasi-one-dimensional electron gas. I. Quantum transport equations

The quantum kinetic equation for the one-particle distribution function, pertinent to a quasi-one-dimensional electron gas, is derived from first principles. The electrons are assumed to interact weakly with an external system, e.g., impurities, phonons, and/or with each other. Correlations between the fluctuations of the density operator and of the scattering potential are taken into account in a manner equivalent to the polarization approximation. The derived collision integral allows for screening and is expressed in terms of the dielectric functions and potential correlators. The results are valid for weak scattering potentials of arbitrary type. From the kinetic equation energy and momentum balance equations are derived. The relevant energy and momentum relaxation rates, with the help of model distribution functions, can be expressed in terms of the dielectric functions and take a simple form suitable for practical applications.