Non-equilibrium fermions within lattice density functional theory: quantum transport and ultracold-atom phenomena

Abstract: Cutting-edge technology needs small, ultrafast devices, operational in a wide range of regimes. This calls for solids with novel, unconventional and tailorable properties. Great progress is expected from materials in which electron-electron and electron-phonon correlations strongly affect the dynamics ( i.e. "unforeseen" useful properties are expected to be most likely found in systems with complex behavior). In spite of the potentially huge technological pay-off, our understanding of these systems is rather incomplete, especially in non-equilibrium. Often, with knowledge of systems or phenomena at an early stage, it is rewarding to resort to model, simplified descriptions. This strategy is used in this thesis, where we study several models lattice systems via density-functional theory. The latter is a well established approach (in fact, it is the current method of choice) for investigations of real materials. In our research, we focussed on little understood properties of interacting many-particle systems, such as the time-dependent conduction properties of electronic devices in the presence of interactions, disorder, and lattice vibrations, or the expansion of ultracold fermion clouds in 3D optical lattices. All these systems were described in terms of Hubbard-type interactions for the electrons, and Holstein-type electron-phonon interactions. Our results show interesting features due to the interactions which depend on dimensionality; they also show a dynamical crossover for several properties, due to the competition between disorder and interaction. Finally, when lattice vibrations are included, we showed how it is possible to manipulate in a controlled way the nuclear dynamics of molecular device via fast electronic external fields, of potential interest for technologies employing nanomolecular motors.