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

Abstract: Popular Abstract in English Nowadays, cutting-edge technologies require devices to be small, ultrafast, and operational in a wide range of regimes. To fulfill these requirements we need to go beyond the traditional materials, i.e. to solids with novel, unconventional and tailorable properties. Great progress in this direction is conjectured to stem from materials in which the effect of inter-particle interactions (e.g. among electrons or between electrons and atomic vibrations) strongly affects the dynamical behavior. That is, the expectation is that "unforeseen" useful properties are most likely to be found in systems exhibiting a complex behavior, which cannot be reduced to a picture where particles act if they were mutually independent. A theoretical description of these systems is not easy: in spite of the potentially huge technological pay-off, our understanding is rather incomplete, especially in the out-of-equilibrium regime. This challenging state of affairs is what motivates the strong ongoing effort in the scientific community to develop theories for systems out of equilibrium. Often, when knowledge is at an early stage, simplified descriptions are rewarding for preliminary insight. This strategy is used in this thesis, where we investigate several simple models lattice systems via density-functional theory. The latter is a well established theoretical technique (in fact, it is the current method of choice) for investigations of real materials, which is used here in a rather novel way. The model used by us here is the Hubbard model (see Figure). It is one of the simplest pictures of interacting fermions on a discrete lattice, and yet it exhibits a fascinating and rich physical behavior, useful for deep qualitative insight into the properties of real materials where the independent-particle picture fails (materials where electron-electron interactions make an independent-particle picture not possible, are commonly referred to as strongly correlated materials/systems). This thesis concern some intriguing and little-understood properties and behavior of nonequilibrium fermions. One of them is the expansion dynamics of clouds of cold atoms. Within density-functional theory, we studied the the so-called melting of the Mott insulator, a dynamical process due to a complicated interplay among many-body interactions, kinetic energy, and spatial confinement. We simulated large 3D systems (125000 lattice sites, with the effect of disorder also taken into account), and also considered collisions between atomic clouds. Our results showed interesting features, which depend on dimensionality of the system and the strength of interactions and/or disorder. We also investigated the electronic conduction in model nanodevices with disorder, interactions and lattice vibrations. Our main conclusion there was the evidence of a competing behavior between interactions and disorder. By including lattice vibrations in the picture, we showed how it is possible to manipulate in a controlled way the nuclear dynamics of a molecular device via fast electronic external fields, a result of potential interest for technologies employing mechanical motors at the nanoscale. These brief remarks give an idea of the contents and the scope of this thesis. As an outlook, if our work represents or not a small step towards a better understanding of nonequilibrium fermions, it is not for us to decide, and not at this stage. In any case, we vividly hope that it will stimulate further investigations in this challenging and beautiful area of Physics.