Abstract:
It is shown that the exchange-correlation part of the action functional $A_{xc}[\rho (\vec r,t)]$ in time-dependent density functional theory , where $\rho (\vec r,t)$ is the time-dependent density, is invariant under the transformation to an accelerated frame of reference $\rho (\vec r,t) \to \rho ' (\vec r,t) = \rho (\vec r + \vec x (t),t)$, where $\vec x (t)$ is an arbitrary function of time. This invariance implies that the exchange-correlation potential in the Kohn-Sham equation transforms in the following manner: $V_{xc}[\rho '; \vec r, t] = V_{xc}[\rho; \vec r + \vec x (t),t]$. Some of the approximate formulas that have been proposed for $V_{xc}$ satisfy this exact transformation property, others do not. Those which transform in the correct manner automatically satisfy the ``harmonic potential theorem", i.e. the separation of the center of mass motion for a system of interacting particles in the presence of a harmonic external potential. A general method to generate functionals which possess the correct symmetry is proposed.

Abstract:
I show that the so-called causality paradox of time-dependent density functional theory arises from an incorrect formulation of the variational principle for the time evolution of the density. The correct formulation not only resolves the paradox in real time, but also leads to a new expression for the causal exchange-correlation kernel in terms of Berry curvature. Furthermore, I show that all the results that were previously derived from symmetries of the action functional remain valid in the present formulation. Finally, I develop a model functional theory which explicitly demonstrates the workings of the new formulation.

Abstract:
We show that the time-dependent particle density $n(\vec r,t)$ and the current density ${\vec j}(\vec r,t)$ of a many-particle system that evolves under the action of external scalar and vector potentials $V(\vec r,t)$ and $\vec A(\vec r,t)$ and is initially in the quantum state $|\psi (0)>$, can always be reproduced (under mild assumptions) in another many-particle system, with different two-particle interaction, subjected to external potentials $V'(\vec r,t)$ and $\vec A'(\vec r,t)$, starting from an initial state $|\psi' (0)>$, which yields the same density and current as $|\psi (0)>$. Given the initial state of this other many-particle system, the potentials $V'(\vec r,t)$ and $\vec A'(\vec r,t)$ are uniquely determined up to gauge transformations that do not alter the initial state. As a special case, we obtain a new and simpler proof of the Runge-Gross theorem for time-dependent current density functional theory. This theorem provides a formal basis for the application of time-dependent current density functional theory to transport problems.

Abstract:
The Coulomb interaction between electrons of opposite spin orientations in a metal or in a doped semiconductor results in a negative off-diagonal component of the electrical resistivity matrix -- the so-called "spin-drag resistivity". It is generally quite difficult to separate the spin-drag contribution from more conventional mechanisms of resistivity. In this paper I discuss two methods to accomplish this separation in a spin-valve device.

Abstract:
In the absence of an external field, the Rashba spin-orbit interaction (SOI) in a two-dimensional electron gas in a semiconductor quantum well arises entirely from the screened electrostatic potential of ionized donors. We adjust the wave functions of a quantum well so that electrons occupying the first (lowest) subband conserve their spin projection along the growth axis (Sz), while the electrons occupying the second subband precess due to Rashba SOI. Such a specially designed quantum well may be used as a spin relaxation trigger: electrons conserve Sz when the applied voltage (or current) is lower than a certain threshold V*; higher voltage switches on the Dyakonov-Perel spin relaxation.

Abstract:
We calculate the spectral function of a smooth edge of a quantum Hall system in the lowest Landau level by means of a bosonization technique. We obtain a general relationship between the one electron spectral function and the dynamical structure factor. The resulting I-V characteristics exhibit, at low voltage and temperature, power law scaling, generally different from the one predicted by the chiral Luttinger liquid theory, and in good agreement with recent experimental results.

Abstract:
We present a study of ground state energies and densities of quantum dots in a magnetic field, which takes into account correlation effects through the Current-density functional theory (CDFT). The method is first tested against exact results for the energy and density of 2 and 3 electrons quantum dots, and it is found to yield an accuracy better than $ 3 \%. $ Then we extend the study to larger dots and compare the results with available experimental data. The orbital and spin angular momenta of the ground state, and the evolution of the density profile as a function of the magnetic field are calculated. Quantitative evidence of edge reconstruction at high magnetic field is presented.

Abstract:
The frequency-dependent exchange-correlation potential, which appears in the usual Kohn-Sham formulation of a time-dependent linear response problem, is a strongly nonlocal functional of the density, so that a consistent local density approximation generally does not exist. This problem can be avoided by choosing the current-density as the basic variable in a generalized Kohn-Sham theory. This theory admits a local approximation which, for fixed frequency, is exact in the limit of slowly varying densities and perturbing potentials.

Abstract:
We present a density-functional theory (DFT) approach to the study of the phase diagram of the maximum density droplet (MDD) in two-dimensional quantum dots in a magnetic field. Within the lowest Landau level (LLL) approximation, analytical expressions are derived for the values of the parameters $N$ (number of electrons) and $B$ (magnetic field) at which the transition from the MDD to a ``reconstructed'' phase takes place. The results are then compared with those of full Kohn-Sham calculations, giving thus information about both correlation and Landau level mixing effects. Our results are also contrasted with those of Hartree-Fock (HF) calculations, showing that DFT predicts a more compact reconstructed edge, which is closer to the result of exact diagonalizations in the LLL.

Abstract:
It is shown that, contrary to widely held beliefs, the potentials of spin-density-functional theory (SDFT) are not unique functionals of the spin densities. Explicit examples of distinct sets of potentials with the same ground-state densities are constructed, and general arguments that uniqueness should not occur in SDFT and other generalized density-functional theories are given. As a consequence, various types of applications of SDFT require significant corrections or modifications.