Contributions to the Transport Properties of Many-Body Systems

In this thesis, we study some important problems related to the transport properties of many body systems. It is divided in three parts. First we investigate the effect of dissipation and time - dependent external sources in the phase diagram of a superconducting film at zero and finite temperature. In the presence of time-dependent perturbations, dissipation is essential for the system to attain a steady, time independent state. In order to treat this time dependent problem, we use a Keldysh approach within an adiabatic approximation that allows us to study the phase diagram of this system as a function of the external parameters, including temperature. We also discuss the nature of the quantum phase transitions of the system. Next, we study an important concept in the physics of metallic multi- band systems, that of hybridization, and how it affects the superconducting properties of a material. A constant or symmetric k-dependent hybridization in general acts in detriment of superconductivity. We show here that when hybridization between orbitals in different sites assumes an anti-symmetric character having odd-parity it enhances superconductivity. In chapter 3, we make use of the anti-symmetric property of hybridization to propose a new mechanism to generate Majorana fermions in a superconducting wire, even in the absence of spin-orbit interactions. In the last part of this thesis we study the effect of spin-orbit coupling (SOC) on transport properties in magnetic nanostructures. In this system SOC plays an important role, because surfaces (or interfaces) introduce sym- metry breaking which is a source of spin-orbit interaction. We study the role of Dzyaloshinskii-Moriya (DM) interaction on spin-transport in a 3 layer system. We show that there is a DM interaction between magnetics ions in the layers and spin of conduction electrons. We study the influence of this DM interaction on transport within a simple model where each layer is represented by a point.