The electrical and thermal conductance and the Seebeck coefficient are calculated for one-dimensional systems, and their behavior as a function of temperature and chemical potential is investigated. It is shown that the conductances are proportional to an average of the transmission probability around the Fermi level with the average taken for the thermal conductance being over a wider range. This has the effect of creating less well-defined plateaus for thermal-conductance quantization experiments. For weak non-linearities, the charge and entropy currents across a quantum point contact are expanded as a series in powers of the applied bias voltage and the temperature difference. After that, the expansions of the Seebeck voltage in temperature difference and the Peltier heat in current are obtained. Also, it is shown that the linear thermal conductance of a quantum point contact displays a half-plateau structure, almost flat regions appearing around half-integer multiples of the conductance quantum. This structure is investigated for the saddle-potential model.

Electron transport in mesoscopic systems, such as quantum point contacts and Aharonov-Bohm rings are investigated numerically in a tight-binding language with a recursive Green's function algorithm. The simulation reveals among other things the quantized nature of the conductance in point contacts, the Hall conductance, the decreasing sensitivity to scattering impurities in a magnetic field, and the periodic magnetoconductance in an Aharonov-Bohm ring. Furthermore, the probability density distributions for some different setups are mapped, making the transmission coefficients, the quantum Hall effect, and the cyclotron radius visible, where the latter indicates the correspondance between quantum mechanics and classical physics on the mesoscopic scale.

The aim of the study presented in this thesis is to explore the electrical and physical properties of films of tin and lead clusters. Understanding the novel conductance properties of cluster films and related phenomenon such as coalescence is important to fabricate any cluster based devices. Coalescence is an important phenomenon in metallic cluster films. Due to coalescence the morphology of the films changes with time which changes their properties and could lead to failure in cluster devices. Coalescence is studied in Sn and Pb cluster films deposited on Si$_3$N$_4$ surfaces using Ultra High Vacuum (UHV) cluster deposition system. The conductance of the overall film is linked to the conductance of the individual necks between clusters by simulations. It is observed that the coalescence process in Sn and Pb films follows a power law in time with an exponent smaller than reported in literature. These results are substantiated by the results from previous experimental and Kinetic Monte Carlo (KMC) simulation studies at UC. Percolating films of Sn show unique conductance properties. These films are characterized using various electrode configurations, applied voltages and temperatures. The conductance measurements are performed by depositing clusters on prefabricated gold electrodes on top of Si$_3$N$_4$ substrates. Sn cluster films exhibit a variety of conductance behaviours during and after the end of deposition. It is observed that the evolution of conductance during the onsets at percolation threshold is dependent on the film morphology. Samples showing difference responses in onset also behave differently after the end of deposition. Therefore all samples were categorized according to their onset behaviour. After the end of deposition, when a bias voltage is applied, the conductance of Sn films steps up and down between various well-defined conductance levels. It is also observed that in many cases the conductance levels between which these devices jump are close to integral multiples of the conductance quantum. There are many possible explanations for the steps in conductance. One of the explanations is formation and breaking of conducting paths in the cluster films by electric field induced evaporation and electromigration respectively. The stepping behaviour is similar to that in non-volatile memory devices and hence very interesting to explore due to potential applications.

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