The problem of quantum dynamics in open systems has gained attention in recent decades and not
the least due to the advances made in quantum transport in molecular systems. The main motivation
behind quantum transport and molecular electronics is the futuristic goal to be able at some point to
replace, or to complement, the silicon-based technology and to make the electronic devices faster. On a
fundamental level, one has to deal with time-dependent processes where electron-electron or electron-
phonon interactions are of great importance, and they can cause profound quantitative and qualitative
changes on the physical and dynamical properties of electronic systems compared to the non-interacting
case. Most of the studies of quantum transport have been focused on the steady-state description while
neglecting the short-time dynamics. However, the dynamical effects are of great importance since fast-
switching processes play a pivotal role in the operation of future devices. We
studied the problem of
time-dependent electron transport through the Anderson impurity model by using many-body perturbation
theory (MBPT) together with Keldysh Green’s functions as well as with time-dependent density functional
theory (TDDFT). These methods were compared with numerically exact time-dependent density-matrix
renormalization group (tDMRG) method. We found that the many-body perturbation theory results beyond
Hartree-Fock approximation were in close agreement with tDMRG results. In addition we studied the
possibility of multistablity in the density and current of an interacting nanoscale junction as well as how to
reversibly switch between the multiple solutions in time domain.
An accurate theoretical treatment of electron correlation even in as simple model as an interacting
electron gas at metallic densities still continues to be a challenge; especially description of features in
the photoemission spectra due to electron correlations provides a theoretical challenge. The many-body
perturbation theory yields a systematic way to study electron-electron (electron-phonon) correlations
in various systems. One of the widely used approximations in MBPT is the GW approximation in
which the bare interaction line is replaced with screened interaction line in the first order exchange
diagram. The GW approximation gives good estimates for the band gap values close to experimental
ones but especially the self-consistent GW approximation has a number of deficiencies like washing out
of plasmon features and overestimation of bandwidths compared to experiment. One way to improve
GW calculations is to include vertex corrections. Unfortunately, the straightforward inclusion of vertex
corrections yields negative spectra in some frequency regions. We developed a diagrammatic approach to
construct self-energy approximations with positive spectral properties. Our approach consists of expressing
a self-energy of response diagram as a product of half-diagrams after which a minimal set of additional
diagrams is identified to construct a perfect square. We applied this method to study vertex corrections in
a homogeneous electron gas.
In addition we analyzed the diagrammatic content of photocurrent with density functional theory. The
expression for the photocurrent was obtained as an integral over the Kohn-Sham spectral function
renormalized by effective potentials that depend on the exchange correlation kernel of current density functional theory. The expression for the photocurrent gives us the angular dependence of the photocurrent
but it does not provide a direct access to the kinetic energy distribution of the photoelectrons.
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