This thesis addresses a variety of systems in which the diffusion is anomalous, mainly motivated by recent experimental developments. The main topics discussed are: * We look at the consequences... Show moreThis thesis addresses a variety of systems in which the diffusion is anomalous, mainly motivated by recent experimental developments. The main topics discussed are: * We look at the consequences that subdiffusion on fractals has for shot noise. * The effects correlations have on superdiffusion in one dimension are examined. * We develop and demonstrate the usefulness of a method to simulate the anomalous diffusion of Dirac fermions in a computer. * A spin precession experiment in topological insulators is proposed and analyzed. * We present the mechanism for the conversion of an ordinary insulator into a topological insulator by disorder which was reported in the literature, on the basis of computer simulations, but had remained unexplained. Show less
The effect of spin-orbit coupling on various quantum transport phenomena is considered. The main topics discussed are: * How spin-orbit coupling can induce shot noise through trajectory splitting. ... Show moreThe effect of spin-orbit coupling on various quantum transport phenomena is considered. The main topics discussed are: * How spin-orbit coupling can induce shot noise through trajectory splitting. * How spin-orbit coupling can degrade electron-hole entanglement (created by a tunnel barrier) by mode mixing. * Mesoscopic Spin Hall effect: longitudinal charge current leads to transverse spin currents in a chaotic electron cavity which has universal fluctuations around a zero mean. * How smooth disorder increases the conductivity of a graphene sheet. In addition a detailed introduction is given to both the origin of spin-orbit coupling and the consequences of time reversal symmetry in quantum systems. Show less
