Boltzmann-type approach to transport in weakly interacting one-dimensional fermionic systems
Year: 2012
Type: article
Abstract: 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 Schrödinger 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.
Source: Physical Review E
Authors: Christian Bartsch, Jochen Gemmer
Institution: Osnabrück University
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2000786219