Direct Lattice Shaking of Bose Condensates: Finite Momentum Superfluids.

We address band engineering in the presence of periodic driving by numerically shaking a lattice containing a bosonic condensate. By not restricting to simplified band structure models we are able to address arbitrary values of the shaking frequency, amplitude, and interaction strengths g. For "near-resonant" shaking frequencies with moderate g, a quantum phase transition to a finite momentum superfluid is obtained with Kibble-Zurek scaling and quantitative agreement with experiment. We use this successful calibration as a platform to support a more general investigation of the interplay between (one particle) Floquet theory and the effects associated with arbitrary g. Band crossings lead to superfluid destabilization, but where this occurs depends on g in a complicated fashion.

Phase imprinting in equilibrating Fermi gases: the transience of vortex rings and other defects.

We present numerical simulations of phase imprinting experiments in ultracold trapped Fermi gases, which were obtained independently and are in good agreement with recent experimental results. Our focus is on the sequence and evolution of defects using the fermionic time-dependent Ginzburg-Landau equation, which contains dissipation necessary for equilibration. In contrast to other simulations, we introduce small, experimentally unavoidable symmetry breaking, particularly that associated with thermal fluctuations and with the phase-imprinting tilt angle, and we illustrate their dramatic effects. As appears consistent with experiment, the former causes vortex rings in confined geometries to move to the trap surface and rapidly decay into more stable vortex lines. The latter aligns the precessing and relatively long-lived vortex filaments, rendering them difficult to distinguish from solitons.

Implementation and Validation of Fully Relativistic GW Calculations: Spin-Orbit Coupling in Molecules, Nanocrystals, and Solids.

We present an implementation of G0W0 calculations including spin-orbit coupling (SOC) enabling investigations of large systems, with thousands of electrons, and we discuss results for molecules, solids, and nanocrystals. Using a newly developed set of molecules with heavy elements (called GW-SOC81), we find that, when based upon hybrid density functional calculations, fully relativistic (FR) and scalar-relativistic (SR) G0W0 calculations of vertical ionization potentials both yield excellent performance compared to experiment, with errors below 1.9%. We demonstrate that while SR calculations have higher random errors, FR calculations systematically underestimate the VIP by 0.1 to 0.2 eV. We further verify that SOC effects may be well approximated at the FR density functional level and then added to SR G0W0 results for a broad class of systems. We also address the use of different root-finding algorithms for the G0W0 quasiparticle equation and the significant influence of including d electrons in the valence partition of the pseudopotential for G0W0 calculations. Finally, we present statistical analyses of our data, highlighting the importance of separating definitive improvements from those that may occur by chance due to a limited number of samples. We suggest the statistical analyses used here will be useful in the assessment of the accuracy of a large variety of electronic structure methods.