Chaos in the Honeycomb Optical Lattice Unit Cell

TL;DR

This paper demonstrates that gases propagating through honeycomb lattices exhibit chaotic classical dynamics over a wide energy range, linking lattice structure to complex behavior relevant for thermalization and localization phenomena.

Contribution

It reveals that classical dynamics in honeycomb lattices are chaotic, providing new insights into eigenstate thermalization and Anderson localization in these systems.

Findings

Gases in honeycomb lattices behave as Lorentz gases.

Classical dynamics are chaotic over a wide energy range.

Implications for thermalization and localization phenomena.

Abstract

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.