| In this thesis we investigate the effects of randomness and dissipation on several low dimensional quantum systems.; In chapter 2 we discuss the ground state correlations of the random transverse field Ising chain, which exhibits a ferro-to-paramagnetic infinite randomness quantum-critical point. We extend the real-space renormalization method and derive the end to-end energy correlations of the model. In Chapter 3 we present and analyze, using the real-space RG, a novel quantum phase transition of the spin-3/2 random Heisenberg chain. We find that at strong randomness, the chain forms a spin-3/2 random-singlet state, whereas at weak randomness it forms a spin-1/2 random-singlet state on top of a valence-bond solid. In between lies a new infinite-randomness fixed point, in which the chain has an unusual effective spin distribution: half the chain consists of spin-1/2 sites, a third is spin-1, and a sixth is spin-3/2.; In Chapters 4--6 we focus on the destruction of superconductivity in nanowires and chains of mesoscopic grains, which are connected to each other by weak links. The weak links are modeled as resistively-shunted Josephson junctions, and the grains are modeled using a two-fluid model (see Sec. 4.2), which assumes that each grain contains both normal electrons and superconducting Cooper pairs, which are out of equilibrium and can equilibrate by flowing through a conversion-resistance r. In chapters 4, 5, and 6 we analyze (respectively) a two-junction system with a single two-fluid grain, infinite chains, and a finite chain of mesoscopic grains. Despite the differences, we find that all these systems undergo a quantum phase transition, which is tuned by the conversion-resistance r, between two superconducting states: the fully superconducting phase (FSC) and the SC* phase, in which grains are normal, but phase coherence is maintained between the two end-electrodes. While the FSC-normal transition is tuned by the local resistance of each weak link, the SC*-normal transition is tuned by the total resistance between the two electrodes. We also apply our analysis to superconducting nanowires (see Sec. 5.9 and 5.10), experiments on which presented the initial motivation for this work. |
