Quasibound states in a triple Gaussian potential.

We derive the transmission probabilities and delay times, and identify quasibound state structures in an open quantum system consisting of three Gaussian potential energy peaks, a system whose classical scattering dynamics we show to be chaotic. Such open quantum systems can serve as models for nanoscale quantum devices and their wave dynamics are similar to electromagnetic wave dynamics in optical microcavities. We use a quantum web to determine energy regimes for which the system exhibits the quantum manifestations of chaos, and we show that the classical scattering dynamics contains a significant amount of chaos.

Signatures of chaos in the Brillouin zone.

When the classical dynamics of a particle in a finite two-dimensional billiard undergoes a transition to chaos, the quantum dynamics of the particle also shows manifestations of chaos in the form of scarring of wave functions and changes in energy level spacing distributions. If we "tile" an infinite plane with such billiards, we find that the Bloch states on the lattice undergo avoided crossings, energy level spacing statistics change from Poisson-like to Wigner-like, and energy sheets of the Brillouin zone begin to "mix" as the classical dynamics of the billiard changes from regular to chaotic behavior.

Chaos in the band structure of a soft Sinai lattice.

We study the effect of broken spatial and dynamical symmetries on the band structure of two lattices with unit cells that are soft versions of the classic Sinai billiard. We find significant signatures of chaos in the band structure of these lattices, in energy regimes where the underlying classical unit cell undergoes a transition to chaos. Broken dynamical symmetries and the presence of chaos can diminish the feasibility of changing and controlling band structure in a wide variety of two-dimensional lattice-based devices, including two-dimensional solids, optical lattices, and photonic crystals.

Chaos in the honeycomb optical-lattice unit cell.

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 laboratory in the form of semiconductor 2DEGs, optical lattices, and photonic crystals.