Dresden 2011 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 15: ISPS Intersectional Poster Session

DY 15.25: Poster

Dienstag, 15. März 2011, 18:00–20:00, P1

Boltzmann approach to transport in weakly interacting fermionic 1-d systems — •Christian Bartsch and Jochen Gemmer — Fachbereich Physik, Universität Osnabrück, Barbarastrasse 7, D-49069 Osnabrück, Germany

We investigate the transport behavior of a system of weakly interacting 1-d (spinless) fermions featuring nearest and next nearest neighbor hopping and nearest neighbor interaction. By means of a leading order TCL (time-convolutionless) projection operator approach we set up a master equation for certain momentum mode occupation numbers and interpret the resulting rate matrix as scattering term of a linear(ized) quantum Boltzmann equation, from which one may extract a diffusion coefficient. One numerically finds that both the diffusion coefficient itself and the time scale, on which the diffusion coefficient becomes constant, are larger for smaller next nearest neighbor hoppings. In the absence of next nearest neighbor hopping (, in this case the model corresponds to an anisotropic Heisenberg spin chain in terms of a Jordan-Wigner-transformation,) this time scale diverges, which may indicate ballistic transport or a diffusion coefficient scaling in higher orders of the interaction strength that are beyond this leading order approach.