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Abstract Recent advance of nanotechnology has stimulated much interest in the study of quantum transport in mesoscopic structures. The present thesis is divided into two parts. In the first part of the thesis, the spin current through a quantum dot system is calculated using a quantum master equation approach in the weak-coupling regime. To be able to efficiently calculate, also at low temperatures, the time evolution of the reduced density matrix in the present approach which includes a sum over Matsubara terms, a high-temperature approximation was derived which proves to be rather accurate in comparison to the exact results. In the present model it is assumed that the energy levels of the dot are split by a constant magnetic field. An additional external (laser) field is used to control the currents of the two spin polarizations. This is either done using the phenomenon of coherent destruction of tunneling or optimal control theory. Scenarios are studied in which the spin current is reversed while the charge current is kept constant. The aim of the second part is to study the quantum transport properties of a mesoscopic device in the presence of an external microwave field. A model for such mesoscopic device is proposed and it is formed of a superconductor quantum dot coupled to two ferromagnetic reservoirs via two quantum point contacts. An expression for the conductance was derived using Landauer-Büttiker i formula. The effect of an external magnetic field was taken into consideration. Also, the spin polarization is expressed in terms of both Andreev-reflection probabilities for spin-up and spin-down. Numerical calculations are performed for the present proposed nanoscale device. This device operates in the mesoscopic regime as indicated from the dependence of the conductance on the temperature. from the results, two peaks appeared due to the Zeeman splitting of the quasiparticle density of states. The dependence of spin polarization on the considered parameters confirms that the spin flip of electrons when Andreev-reflection tunneling occurs through the junction. The spin polarization of the tunneled electrons through the junction gives rise to a non-equilibrium spin density in the superconductor and also due to Zeeman splitting of the quasiparticle density of states. Both equations for the conductance and spin polarization show a dependence on the magnetic field, the geometrical dimensions of the device, temperature, bias voltage and charging energy of the quantum dot. Supervisors Prof. Mohamed Abd Allah Semary........................Prof. Bernhard Kramer Signuture................................................................Signature Prof. Adel Helmy Phillips......................................Dr. Ayman Saleh Atallah Signature................................................................Signature Prof. Gamal Abd El Nasser Signature: Chairman of physics department |