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The transport of magnetization is analyzed for the classical Heisenberg chainat and especially above the isotropic point. To this end, the Hamiltonianequations of motion are solved numerically for initial states realizingharmonic-like magnetization profiles of small amplitude and with random phases.Above the isotropic point, the resulting dynamics is observed to be diffusivein a hydrodynamic regime starting at comparatively small times and wavelengths. In particular, hydrodynamic regime and diffusion constant are bothfound to be in quantitative agreement with close-to-equilibrium results fromquantum S=1/2 autocorrelations at high temperatures. At the isotropic point,the resulting dynamics turns out to be non-diffusive at the considered timesand wave lengths.

Spin transport in the XXZ model at high temperatures: Classical dynamics versus quantum S=1/2 autocorrelations