Disorder in multi-channel Luttinger liquids

This thesis examines the effects of disorder upon a bundle of coupled one dimensional (ID) systems. Each 1D system is described as a Luttinger liquid, and the coupling between channels is weak enough such that this description remains valid. The coupling can be of either a density-density or current-current type. We consider continuous disorder in each channel, and derive renormalisation group (RG) equations governing the strength of the disorder. We analyse the effects of disorder in two specific examples: a lattice of identical channels, and two distinct channels. In both cases, close to the simultaneous metal-insulator transition, we arrive at coupled Berezinskii-Kosterlitz-Thouless (BKT) equations. Away from the simultaneous transition we analyse the RG equations numerically. Inter-channel interactions are found to shift the metal-insulator boundary, and destroy the mixed insulator-conductor phase close to the simultaneous transition