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In this thesis, we develop a first principle technique to study linear AC and the nonlinear DC quantum transport in diffusive conductors. Starting from Buttiker's theory for AC and DC transport, the emittance and nonlinear DC conductance are found in terms of the scattering matrix and it's functional derivative. New theoretical tools are developed to compute the functional derivative of the scattering matrix, which would otherwise be unaccessible. These results allows us to compute the linear AC and the nonlinear DC conductance for a diffusive conductor from first principles, for the first time in literature. The sample-to-sample AC conductance fluctuations are computed for a diffusive conductor. In this regime the dynamic response of the conductor can either be capacitive or inductive, depending on impurity configuration. Our results also suggest a crossover for the AC conductance distribution, from a symmetric to a non symmetric distribution function as the number of impurities increases. A degree of generic behavior is discovered, in that the AC fluctuation amplitudes become independent of the strength of the impurities, although it depends on the impurity density. A sample-to-sample analysis of the nonlinear conductance fluctuations, in the diffusive regime, is also reported. In this situation the distribution function is found to be a symmetric Gaussian like function for small disorder and a symmetric exponentially decaying function for large disorder. An interesting result is that the conductance fluctuations increase in an exponential fashion with N, the number of impurities. / We also considered in this thesis the magneto-conductance fluctuations of a quasi-1D quantum wire with artificial impurities (antidots). This problem can only be solved numerically because of the finite size of the artificial impurities. We develop a novel transfer matrix technique to solve the quantum scattering problem by computing the scattering wave function, as a function of the external magnetic field. The Landauer-Buttiker equation is used to compute the magneto-conductance. This work is motivated by the experimental study [1], where several conductance fluctuations anomalies were reported. Our numerical results give good quantitative agreement with the experimental data and confirms the physical picture obtained from the experiment.

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Measurements of the spin-lattice relaxation time, T1, and spin-spin relaxation time, T2, of potassium ferricyanide diluted by potassium coba1ticyanide were made by the CW saturation method. Crystals of two concentrations of Fe3+ in K3Co(CN)6 were investigated: 0.5% and 1.0%. The results are the same for both concentrations to within the probable error. The mean relaxation times for the two concentrations are quoted to one significant figure, together with the probable errors: T1 =(1 +- 0.15) x 10-4 sec and T2 = (9 +- 0.4) x 10-9 sec. Calculations have been made to determine the angular dependence of the paramagnetic resonance spectra of potassium ferricyanide. Three graphs have been plotted which may be useful for comparison with future measurements.

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