Dielectric formalism for a quasi-one-dimensional electron gas. II. Dielectric functions and potential correlators

The dielectric function of an electron gas confined in a quantum wire is evaluated. The lateral confinement is modeled with a square or parabolic well and the vertical one with a triangular or square well. Screening is treated dynamically, and the electrons are assumed to interact with each other and with an external system taken to be impurities or phonons. Two cases are considered: (i) a homogeneous system and (ii) systems presenting inhomogeneity in one direction such as simple or double heterostructures. The potential correlators and dielectric functions of the external system are also evaluated. The results are useful for describing transport properties using the relevant quantum transport equations and relaxation frequencies.