Artificial crystals of light, consisting of hundreds of thousands of optical microtraps, are
routinely created by interfering optical laser beams. These so-called optical lattices act as …

This article reviews theoretical and experimental developments for one-dimensional Fermi
gases. Specifically, the experimentally realized two-component delta-function interacting …

We discuss a phase space representation of quantum dynamics of systems with many
degrees of freedom. This representation is based on a perturbative expansion in quantum …

We review phase-space techniques based on the Wigner representation that provide an
approximate description of dilute ultra-cold Bose gases. In this approach the quantum field …

We report the observation of strongly damped dipole oscillations of a quantum degenerate
1D atomic Bose gas in a combined harmonic and optical lattice potential. Damping is …

The stability of superfluid currents in a system of ultracold bosons was studied using a
moving optical lattice. Superfluid currents in a very weak lattice become unstable when their …

We discuss interacting and noninteracting one dimensional atomic systems trapped in an
optical lattice plus a parabolic potential. We show that, in the tight-binding approximation …

We extend the projected Gross-Pitaevskii equation formalism of Davis [Phys. Rev. Lett. 87,
160402 (2001)] to the experimentally relevant case of thermal Bose gases in harmonic …

We analyze the stability and decay of supercurrents of strongly interacting bosons on optical
lattices. At the mean-field level, the system undergoes an irreversible dynamic phase …

Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics
in interacting many-body systems. As with all numerical integration of differential equations …