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Abstract In this thesis the quantum conductance characteristics of a mesoscopic device aare studied under the effect of an external electric field. Two different models are considereda The 2DEG is constrained to a QID-channel, separated from the superconducting reservoirs L and R by quantum point contact controlled by the gates. The superconducting reservoirs are deposited on top of the system. The gates allow the coupling strength between the two superconducting reservoirs and the ballistic channel to be controlled, due to confinement both transverse and longitudinal motion of the quasiparticles in the quasi-ID channel are quantized, giving rise to a set of distinct energy levels. (b) The second model is constructed as a semicondaCtor quantum dot based heterostructure coupled to a superconducting leads via a quantum point contact. This junction is characterized by the interplay of many different energy scales. The transport of quasiparticles takes place through a single resonant level. |