  We analyze transport of local magnetization and develop schemes to control
transport behavior in finite spin-1/2 Heisenberg chains and spin-1/2 Heisenberg
two-leg ladders at zero temperature. By adjusting parameters in the
Hamiltonians, these quantum systems may show both integrable and chaotic
limits. We provide examples of chaotic systems leading to diffusive and to
ballistic transport. In addition, methods of coherent quantum control to induce
a transition from diffusive to ballistic transport are proposed.
