  Using quantum Monte Carlo, we study the non-equilibrium transport of
magnetization in large open strongly correlated quantum spin $\frac{1}{2}$
systems driven by purely dissipative processes that conserve the uniform or
staggered magnetization. We prepare both a low-temperature Heisenberg
ferromagnet and an antiferromagnet in two parts of the system that are
initially isolated from each other. We then bring the two subsystems in contact
and study their real-time dissipative dynamics for different geometries. The
flow of the uniform or staggered magnetization from one part of the system to
the other is described by a diffusion equation that can be derived
analytically.
