Volume 88, Number 1, October 2009
Article Number 10004
Number of page(s) 5
Section General
Published online 22 October 2009
EPL, 88 (2009) 10004
DOI: 10.1209/0295-5075/88/10004

Density dynamics from current auto-correlations at finite time- and length-scales

R. Steinigeweg, H. Wichterich and J. Gemmer

Fachbereich Physik, Universität Osnabrück - Barbarastrasse 7, D-49069 Osnabrück, Germany, EU

received 8 July 2009; accepted in final form 17 September 2009; published October 2009
published online 22 October 2009

We consider the increase of the spatial variance of some inhomogeneous, non-equilibrium density (particles, energy, etc.) in a periodic quantum system of condensed-matter type. This is done for a certain class of initial quantum states which is supported by static linear response and typicality arguments. We directly relate the broadening to some current auto-correlation function at finite times. Our result is not limited to diffusive behavior, however, in that case it yields a generalized Einstein relation. These findings facilitate the approximation of diffusion constants/conductivities on the basis of current auto-correlation functions at finite times for finite systems. Pursuing this, we quantitatively confirm the magnetization diffusion constant in a spin chain which was recently found from non-equilibrium bath scenarios.

05.60.Gg - Quantum transport.
05.30.-d - Quantum statistical mechanics.
05.70.Ln - Nonequilibrium and irreversible thermodynamics.

© EPLA 2009