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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