  We study the propagation of a hole in degenerate (paramagnetic) spin
environments. This canonical problem has important connections to a number of
physical systems, and is perfectly suited for experimental realization with
ultra-cold atoms in an optical lattice. At the short-to-intermediate timescale
that we can access using a stochastic-series-type numeric scheme, the
propagation turns out to be distinctly non-diffusive with the proba- bility
distribution featuring minima in both space and time due to quantum
interference, yet the motion is not ballistic, except at the beginning. We
discuss possible scenarios for long-term evolution that could be explored with
an unprecedented degree of detail in experiments with single-atom resolved
imaging.
