  Propagation in quantum walks is revisited by showing that very general 1D
discrete-time quantum walks with time- and space-dependent coefficients can be
described, at the continuous limit, by Dirac fermions coupled to
electromagnetic fields. Short-time propagation is also established for
relativistic diffusions by presenting new numerical simulations of the
Relativistic Ornstein-Uhlenbeck Process. A geometrical generalization of Fick's
law is also obtained for this process. The results suggest that relativistic
diffusions may be realistic models of decohering or random quantum walks. Links
with general relativity and geometrical flows are also mentioned.
