  We discuss zero-frequency transport properties of various spin-1/2 chains. We
show, that a careful analysis of Quantum Monte-Carlo (QMC) data on the
imaginary axis allows to distinguish between intrinsic ballistic and diffusive
transport. We determine the Drude weight, current-relaxation life-time and the
mean-free path for integrable and a non-integrable quantum-spin chain. We
discuss, in addition, some phenomenological relations between various
transport-coefficients and thermal response functions.
