  We study magnetization transport at high temperatures in several spin ladder
systems as well as in next-nearest-neighbor coupled spin chains. In the
integrable ladder considered we analytically show that the transport is
ballistic in sectors with nonzero average magnetization, while numerical
simulations of a nonequilibrium stationary setting indicate an anomalous
transport in the zero magnetization (half-filling) sector. For other systems,
isotropic Heisenberg ladder and spin chains, showing eigenlevel repulsion
typical of quantum chaotic systems, numerical simulations indicate diffusive
transport.
