title: Projection-operator approach to master equations for coarse-grained occupation numbers in nonideal quantum gases.
abstract: We aim at deriving an equation of motion for specific sums of momentum mode occupation numbers from models for electrons in periodic lattices experiencing elastic scattering, electron-phonon scattering, or electron-electron scattering. These sums correspond to "grains" in momentum space. This equation of motion is supposed to involve only a moderate number of dynamical variables and/or exhibit a sufficiently simple structure such that neither its construction nor its analyzation or solution requires substantial numerical effort. To this end we compute, by means of a projection operator technique, a linear(ized) collision term which determines the dynamics of the above grain sums. This collision term results as nonsingular finite-dimensional rate matrix and may thus be inverted regardless of any symmetry of the underlying model. This facilitates calculations of, e.g., transport coefficients, as we demonstrate for a three-dimensional Anderson model featuring weak disorder.
authors.affiliation: Fachbereich Physik, Universität Osnabrück, Barbarastrasse 7, D-49069 Osnabrück, Germany. cbartsch@uos.de
authors.forename: Christian
authors.initials: C
authors.lastname: Bartsch
authors.forename: Robin
authors.initials: R
authors.lastname: Steinigeweg
authors.forename: Jochen
authors.initials: J
authors.lastname: Gemmer