Projection-operator approach to master equations for coarse-grained occupation numbers in nonideal quantum gases

Autor(en): Bartsch, Christian
Steinigeweg, Robin 
Gemmer, Jochen 
Stichwörter: DERIVATION; IMPURITIES; LOCALIZATION; Physics; Physics, Fluids & Plasmas; Physics, Mathematical; RESIDUAL RESISTIVITY; TRANSPORT
Erscheinungsdatum: 2010
Herausgeber: AMER PHYSICAL SOC
Journal: PHYSICAL REVIEW E
Volumen: 81
Ausgabe: 5, 1
Zusammenfassung: 
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.
ISSN: 15393755
DOI: 10.1103/PhysRevE.81.051115

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