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The transport properties of low dimensional systems (especially wires) are investigated when the dominant scattering is due to the impurities and is elastic. Such a situation is expected to be relevant to experiments carried out at very low (liquid Helium) temperatures.\ud \ud Initially a Boltzmann formalism is used to illustrate the effects of multiple sub-band occupancy. Structure is found in the electrical conductivity, thermal conductivity and thermopower when plotted as a function of chemical potential, due to the lateral quantisation of the electron states. These quantum size effects (QSE) are most pronounced in the thermopower, which is expected to show sign changes when the chemical potential sweeps through a sub-band minimum.\ud \ud A more sophisticated treatment based on Green's function methods reveals the importance of lifetime broadening in quasi-one-dimensional systems, which smears out the single-particle density of states and the QSE. The type of behaviour expected of realistic devices is explored, and it is shown that the thermopower offers the best chance of observing confinement effects.\ud \ud The formal theory may also be applied to the weak localisation corrections in multi-sub-band systems. An expression for the correction term is obtained which is valid for arbitrary channel width, and enables the crossover from a linear to logarithmic scaling in L. to be demonstrated. A transverse inelastic length is derived, and shown to be the length scale which controls the system dimensionality rather than Lφ. The implication for experiment in narrow channels is discussed.\ud \ud Weak localisation corrections are also calculated for the thermopower and the thermal conductivity. This corrects a result due to Ting et al (1982) that there are no weak localisation corrections to the thermopower in 2D. These results are shown to be a consequence of a rather general scaling theory of thermal transport which has wider implications, such as for the behaviour expected near a Metal-Insulator transition for example. Comparison with the single parameter scaling theory of the zero temperature conductance is made. Fluctuation effects for thermal transport in mesoscopic samples are also explored (both numerically and analytically), and the analogue of universal conductance fluctuations explicitly demonstrated. |
