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Foundations of the theory of Coulomb drag of ballistic electrons of a quantum nanowire by a flux of monoenergetic heavy ions moving with the same velocity V have been elaborated. The ratio of the drag current to the initial current of the ionic beam has been determined. It has been shown that the drag current is a nonmonotonic function of the velocity V. This function has a sharp maximum at the velocity V = vnF/2, where n is the number of the upper active (i.e., participating in the charge transfer) electron miniband (channel) and vnF is the corresponding Fermi velocity. Thus, it turns out that the phenomenon of giant oscillations of the Coulomb drag current can be used for studying the electron spectra of ballistic nanostructures.

The generation of the Joule heat upon collisionless passage of the direct and alternating electric currents in semiconductor quantum wires connecting two classical reservoirs has been discussed. The transverse dimension of the quantum wire is of the order of the de Broglie wavelength of conduction electrons. The spatial distribution of the Joule heat has been considered. The heat is released in the reservoirs at a distance of the electron mean free path. The total production of the Joule heat has been found to be identical in both reservoirs.

The splitting of electronic levels in quantum wells of semimagnetic semiconductors typically characterized by large effective g factors is analyzed theoretically. They are found to be capable of supporting resonance, provided the Zeeman spin-level splitting is equal to the energy of the longitudinal optical phonon ħω‖. The resonance condition can be written as ħω‖ = gμBB. This condition can be satisfied by choosing the magnetic field Bsuch that the sum of the energies of the lowest spin level and the optical phonon coincides with the energy of the highest level. It is shown that these two degenerate energy levels should experience mutual repulsion. The magnitude of the corresponding splitting depends on both the electron-phonon and spin-orbit interactions in semiconductors; moreover, it turns out substantially lower than the Zeeman energy gμBB. Resonant passage of light through and its reflection from a quantum well are considered as one of possible ways to observe this energy level splitting.