  Natural and artificial honeycomb lattices are of great interest because the
band structure of these lattices, if properly constructed, contains a Dirac
point. Such lattices occur naturally in the form of graphene and carbon
nanotubes. They have been created in the lab in the form of semiconductor
2DEGs, optical lattices, and photonic crystals. We show that, over a wide
energy range, gases (of electrons, atoms, or photons) that propagate through
these lattices are Lorentz gases and the corresponding classical dynamics is
chaotic. Thus, honeycomb lattices are also of interest for understanding
eigenstate thermalization and the conductor-insulator transition due to dynamic
Anderson localization.
