الفهرس 
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Abstract
In this work the electrical, thermal conductance and the Seebeck coefficient are calculated for two-dimensional systems, under the effect of an external magnetic field. In our studes, three different models are considered: .
(1) Transmission coefficient in the absence and presence of a perpendicular magnetic field is discussed in a quadratic saddle-point potential . Our results agree with the calculation of the transmission coefficient in the Wentzel-Kramers-Brillouin approximation[9], we have expected that for large values of the distance of the closest approach, the electron to the saddle point. Our analysis relies on the fact that the Hamiltonian for this system can be expressed as a sum of two commuting Hamiltonians, one involving only the cyclotron coordinates, and the other involving only the guiding center coordinates describing the oscillations of the electron about the guiding-center position.
(2) The electrical, thermal conductance and the Seebeck coefficient are calculated for two-dimensional systems, of a constriction, defined by a saddle-point potential . We have studies their behavior as a function of cyclotron frequency and dimensionless parameter . We have investigated the solution as a function of temperature and chemical potential. Our results 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 behavoir has the effect of creating less well- defined plateaus for thermal-conductance quantization experiments. A method for measuring the sub-band energies and spin- splitting energies in a bottle-neck of the constriction is also proposed.
(3) 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.
Keywords: Transmission coefficient, quantized conductance, thermopower, thermoelectric effect, Peltier effect, Seebeck effect, quantum point contacts, two-dimensional electron gas.