We have studied the electrical conductivity of an electron gas in parallel electric and magnetic fields directed along the plane of a parabolic quantum well ͑across the profile of the potential͒. We found a general expression for the electrical conductivity applicable for any magnitudes of the magnetic field and the degree of degeneration of the electron gas, taking into account electronic scattering with spin flip. A mechanism of generation of the negative magnetoresistance has been revealed. It has been shown that in a parabolic quantum well with a nondegenerated electron gas the negative magnetoresistance results from spin splitting of the oscillator levels and electronic scattering with spin flip.

Analytical expressions are found for the mobility of a degenerate electron gas in a quantum wire for three scattering mechanisms: on ionized impurities and on piezoacoustic and deformation acoustic phonons. The expressions allow one to analyze the concentration, temperature, and dimensional dependences of the electron mobility.

We have studied transverse thermomagnetic effects in a quantum well (QW) with parabolic potential in the presence of a magnetic field parallel to the two-dimensional electron gas layer. The calculation was carried out for the case of elastic electron scattering on short-range potential for degenerate and non-degenerate electron gas. It is shown that the reviewed mechanism of charge carriers' relaxation is essential for the electroconductivity at low temperatures. In the quantum limit, the dependencies of the transverse Nernst–Ettingshausen coefficient and the thermopower on the magnetic field strength, the temperature and the carrier density are determined and analyzed. We have showed that the magnetothermopower is not determined by the entropy only, as is the case for bulk specimens.

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