Real-time broadening of nonequilibrium density profiles and the role of the specific initial-state realization

The real-time broadening of density profiles starting from nonequilibrium states is at the center of transport in condensed-matter systems and dynamics in ultracold atomic gases. Initial profiles close to equilibrium are expected to evolve according to the linear response, e.g., as given by the current correlator evaluated exactly at equilibrium. Significantly off equilibrium, the linear response is expected to break down and even a description in terms of canonical ensembles is questionable. We unveil that single pure states with density profiles of maximum amplitude yield a broadening in perfect agreement with the linear response, if the structure of these states involves randomness in terms of decoherent off-diagonal density-matrix elements. While these states allow for spin diffusion in the XXZ spin-1/2 chain at large exchange anisotropies, coherences yield entirely different behavior.