Boltzmann-type approach to transport in weakly interacting one-dimensional fermionic systems

Autor(en): Bartsch, Christian
Gemmer, Jochen 
Stichwörter: Physics; Physics, Fluids & Plasmas; Physics, Mathematical
Erscheinungsdatum: 2012
Herausgeber: AMER PHYSICAL SOC
Journal: PHYSICAL REVIEW E
Volumen: 85
Ausgabe: 4, 1
Zusammenfassung: 
We investigate transport properties of one-dimensional fermionic tight binding models featuring nearest and next-nearest neighbor hopping, where the fermions are additionally subject to a weak short range mutual interaction. To this end we employ a pertinent approach which allows for a mapping of the underlying Schrodinger dynamics onto an adequate linear quantum Boltzmann equation. This approach is based on a suitable projection operator method. From this Boltzmann equation we are able to numerically obtain diffusion coefficients in the case of nonvanishing next-nearest neighbor hopping, i.e., the nonintegrable case, whereas the diffusion coefficient diverges without next-nearest neighbor hopping. For the latter case we analytically investigate the decay behavior of the current with the result that arbitrarily small parts of the current relax arbitrarily slowly which suggests anomalous diffusive transport behavior within the scope of our approach.
ISSN: 15393755
DOI: 10.1103/PhysRevE.85.041103

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