  In this paper, we present a detailed study on discrete-time Dirac quantum
walks (DQWs) on triangular and honeycomb lattices. At the continuous limit,
these DQWs coincide with the Dirac equation. Their differences in the discrete
regime are analyzed through the dispersion relations, with special emphasis on
Zitterbewegung. An extension which couples these walks to arbitrary discrete
electromagnetic field is also proposed and the resulting Bloch oscillations are
discussed.

Quantum Physics