Dynamical aspects of spin chains at infinite temperature for different spin quantum numbers

For infinite temperature we exactly calculate the coefficients of the short-time expansion of the spin-pair correlations in one-dimensional spin models. For spin quantum numbers s = 1 we present the coefficients up to order t18 and t22, for classical spins up to order t16 and t18 for the isotropic Heisenberg chain and the isotropic XY-chain, respectively. These coefficients are used together with recently determined ones for s = 12 to compute bounds on the autocorrelation functions, to approximate the associated spectral densities and to bound the spatial variances of pair correlations. The results are compared with those obtained from simulation data of Gerling and Landau (Phys. Rev. B 42 (1990) 8214) for classical spin chains. Over the available time region, we find a rather smooth dependence of the dynamics on the spin quantum number and see some evidence for spin diffusion.