Order and transport in interacting disordered low-dimensional systems

The subject of this thesis is order and transport in interacting disordered low-dimensional systems, namely Luttinger liquids and thin superconducting films. The disorder is produced by point impurities in Luttinger liquids and by magnetic dots in thin films. In the second chapter we consider the influence of dissipation on the transport properties of a Luttinger liquid. In the presence of a single impurity we find an exponential suppression of the conductance as a function of applied voltage and temperature at sufficiently low voltages and temperatures. In the third chapter we study a Luttinger liquid in the presence of two impurities and of an external magnetic field. The magnetic field splits the electrons with respect to their spin. We show that this system exhibits spin-filtering effect due to the resonance tunneling effect, which can also be achieved in this particular case, similarly to the case without the field. By tuning a single parameter, one may reach the resonance points when the transmission of spins with one spin-direction is dominating at low temperatures and voltages. The fourth chapter is related to the question of the competition of a periodic and random potential in a Luttinger liquid. The periodic potential alone produces a Mott-insulating state at sufficiently small amount of quantum fluctuations, measured by the interaction parameter K. The random potential alone leads to the Anderson-insulating state for small values of K. In the presence of both potentials and when the interaction is short-ranged, we do not find an intermediate Mott-glass phase, contrary to some studies. The fifth chapter deals with a thin superconducting film with a magnetic dot placed on top of it. We calculate the configurations of vortex-antivortex ground states for such system, finding a diversity of vortex-antivortex states as a function of parameters of the dot. The sixth chapter studies a thin superconducting film covered by magnetic dots of random magnetization. We show that this system is a realization of the two-dimensional XY model with random phase shifts. The latter model helps us to determine the phase diagram of our system