In this thesis, we study the effects of both disorder and low carrier density in low-dimensional systems, employing a variety of analytical and numerical methods. The work is structured in two main parts, each addressing a distinct research direction.

The first part focuses on the impact of disorder in one-dimensional and quasi-one dimensional systems. Using tools such as bosonization, renormalization group techniques, and exact diagonalization, we investigate two key aspects. First, we explore how specific spatial correlations in the disorder affect the properties of the metallic-insulating transition in a one-dimensional system, uncovering significant deviations from the behaviour typically associated with uncorrelated disorder. Second, we examine the effects of different types of disorder on a quasi-one-dimensional singlet superconductor, where we recover Anderson’s theorem under certain conditions and observe a competition between disorder and interactions.

The second part of the thesis examines magneto-transport in two-dimensional, locally correlated materials. Using a microscopic quantum theory, we demonstrate pronounced deviations of the Hall constant and the conductivities of the system from their semiclassical predictions, in regimes where the Fermi energy is no longer the dominant energy scale.