  We analyze the response to incorporation of glassy disorder in the coin
operation of a discrete-time quantum walk in one dimension. We find that the
ballistic spread of the disorder-free quantum walker is inhibited by the
insertion of disorder, for all the disorder distributions that we have chosen
for our investigation, but remains faster than the dispersive spread of the
classical random walker. Beyond this generic feature, there are significant
differences between the responses to the different types of disorder. In
particular, the falloff from ballistic spread can be slow (Gaussian) or fast
(parabolic) for different disorders, when the strength of the disorder is still
weak. The cases of slow response always pick up speed after a point of
inflection at a mid-level disorder strength. The disorder distributions chosen
for the study are Haar-uniform, spherical normal, circular, and two types of
spherical Cauchy-Lorentz.
