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.

Abstract (Swedish)

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.

• author: Kartsev, Alexey
• supervisor: Claudio Verdozzi
• opponent: D'Amico, Irene, University of York, UK
• organization: Mathematical Physics
• publishing date: 2013
• type: Thesis
• publication status: published
• subject: Condensed Matter Physics
• keywords: Fysicumarkivet A:2013:Kartsev
• in: Lund-MPh-13/04
• pages: 116 pages
• defense location: Rydbergsalen, Fysiska institutionen
• defense date: 2013-06-12 09:00:00
• external identifiers: other:978-91-7473-562-8 (pdf)
• ISBN: 978-91-7473-561-1
• language: English
• LU publication?: yes
• id: aadf871f-900d-4fe4-abe4-7fc239c21cdc (old id 3737651)
• date added to LUP: 2016-04-04 11:49:47
• date last changed: 2019-05-22 07:01:29