Physics – Condensed Matter – Quantum Gases
Scientific paper
2010-04-29
Phys. Rev. E 81, 051115 (2010)
Physics
Condensed Matter
Quantum Gases
9 pages, 2 figures, accepted for publication in Phys. Rev. E
Scientific paper
10.1103/PhysRevE.81.051115
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/solution requires substantial numerical effort. To this we end 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 non-singular, 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 3-dim. Anderson model featuring weak disorder.
Bartsch Christian
Gemmer Jochen
Steinigeweg Robin
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