On the Kohn-Sham Approach to Time-Dependent Problems in a Density-Functional Framework

Predictivity of the Kohn-Sham approach to dynamical problems, when regarded as an initial value problem in a time-dependent density functional framework, is analysed for a class of models for which the argument devised in the work of Maitra et al. (Phys. Rev. A 78, 056501 (2008), arXiv:cond-mat/0710.0018) for the standard electronic many-body problem does not apply. The original argument is here extended and revised. As a result, predictivity for this class of problems seems possible only at the price of introducing extra unknown functionals in the corresponding Kohn-Sham equation. Furthermore, the same argument, when applied to original electronic problem, suggests that the Hartree-exchange-correlation potential is not unambiguously identified by the contemporary and past densities and initial states, but also requires knowledge of the divergence of the contemporary Kohn-Sham current.

Flavour Condensate and the Dark Sector of the Universe

This thesis is devoted to the development of a nonperturbative quantum field theoretical approach to flavour physics, with special attention to cosmological applications. Neutrino flavour oscillation is nowadays a fairly well-established experimental fact. However, the formulation of flavour oscillations in a relativistic field theoretical framework presents non-trivial difficulties. A nonperturbative approach for building flavour states has been proposed by Blasone, Vitiello and coworkers. The formalism implies a non-trivial physical vacuum (called flavour vacuum), which might act as a source of Dark Energy. Furthermore, such a vacuum has been recognized as the effective vacuum state arising in the low energy limit of a string theoretical model, D-particle Foam Model. In the attempt of probing the observable phenomenology of the D-particle foam model, a simple toy model (two scalars with mixing `a la Blasone & Vitiello on a adiabatically expanding background) has been studied, proving that the flavour vacuum might behave as Dark Energy under certain assumptions. The first work presented in this thesis represents a development of this approach. A more realistic model is considered, which includes two flavoured Dirac fermions on a generic Friedmann-Robertson-Walker universe. In this framework we show that the flavour vacuum presents different features, which are incompatible with Dark Energy. Motivated by this discrepancy, we next embark on the analysis of a simple supersymmetric model in flat spacetime (free Wess-Zumino), proving that the bosonic component of flavour vacuum acts as Dark Energy, whereas the fermionic as a source of Dark Matter. Finally we develop a new method of calculation that open the way to a nonperturbative extension of these results for interactive theories.