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arXiv · 0906.2113

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

Robin Steinigeweg·Hannu Wichterich·Jochen Gemmer
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Abstract

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.

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Robin Steinigeweg, Hannu Wichterich, Jochen Gemmer. 2009-10-13. Density dynamics from current auto-correlations at finite time- and length-scales. https://doi.org/10.1209/0295-5075/88/10004

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