2010/04/29 by Christian Bartsch, Robin Steinigeweg, Jochen Gemmer
Materials Science · Physics and Astronomy · #Quantum and electron transport phenomena #Quantum, superfluid, helium dynamics #Thermal properties of materials #cond-mat.quant-gas #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.81.051115
published as Phys. Rev. E 81, 051115 (2010) · 9 pages, 2 figures, accepted for publication in Phys. Rev. E
arxiv created 2010/04/29 · openalex publication_date 2010/05/12 · arxiv updated 2010/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.