  We compare quantum dynamics in the presence of Markovian dephasing for a
particle hopping on a chain and for an Ising domain wall whose motion leaves
behind a string of flipped spins. Exact solutions show that on an infinite
chain, the transport responses of the models are nearly identical. However, on
finite-length chains, the broadening of discrete spectral lines is much more
noticeable in the case of a domain wall.
