Response to glassy disorder in coin on spread of quantum walker

Abstract: 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.