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The review considers the peculiarities of symmetry breaking and symmetry transformations and the related physical effects in finite quantum systems. Some types of symmetry in finite systems can be broken only asymptotically. However, with a sufficiently large number of particles, crossover transitions become sharp, so that symmetry breaking happens similarly to that in macroscopic systems. This concerns, in particular, global gauge symmetry breaking, related to Bose-Einstein condensation and superconductivity, or isotropy breaking, related to the generation of quantum vortices, and the stratification in multicomponent mixtures. A special type of symmetry transformation, characteristic only for finite systems, is the change of shape symmetry. These phenomena are illustrated by the examples of several typical mesoscopic systems, such as trapped atoms, quantum dots, atomic nuclei, and metallic grains. The specific features of the review are: (i) the emphasis on the peculiarities of the symmetry breaking in finite mesoscopic systems; (ii) the analysis of common properties of physically different finite quantum systems; (iii) the manifestations of symmetry breaking in the spectra of collective excitations in finite quantum systems. The analysis of these features allows for the better understanding of the intimate relation between the type of symmetry and other physical properties of quantum systems. This also makes it possible to predict new effects by employing the analogies between finite quantum systems of different physical nature.

A non-Boltzmann theory of steady-state transport for two-dimensional systems in a strong electric field is developed, which includes a force- and an energy-balance equation. The electron temperature, impurity-, and phonon-limited mobilities are determined solely from these balance equations. The theory is applied to the calculation of ohmic and nonlinear transport in GaAs-GaAlAs heterojunctions at low temperatures. Temperature-dependent ohmic mobilities are calculated and compared with experiments. Nonlinear effects in electronic transport at low temperatures are discussed and some numerical results are presented. We also compare the present balance equations with those in the carrier temperature model.

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order of experimental error) and of opposite sign to that observed in fluorescence. The phenomenon must thus be due to the centers themselves.The fact that natural light produces polarized emission shows that the elementary oscillators cannot be randomly oriented. 1 Following the dipole theory as applied to the fluorescence in alkali halides 2 "" 4 and diamond, 5 we can try to represent the centers as an array of oscillators all aligned along some direction in the crystal. The polarization depends then upon the elements of a polarizability tensor. It can be shown quite generally that such a model cannot account for the observed results.We can also discard the possibility of the dipoles being oriented along the 12 equivalent directions in the wurtzite lattice. Such an array of dipoles would give rise to a nonvanishing mean square dipole moment only along the c axis and hence would lead to preferential polarization along c. A similar result is obtained in case of centers having the c axis as one of the principal axes of their polarizability tensor (common a zz components) but randomly oriented principal axes in the x-y plane. None of these models can be salvaged by assuming that the exciting radiation is subject to a dichroic absorption by the lattice.It is possible that experimental results can be accounted for by the introduction of separate absorption and emission oscillators, such as have been postulated by Feotilov 2 and others, 1 " 6 in order to explain the dispersion of p. Nevertheless, for a fixed excitation wavelength anisotropic (in particular linear) oscillators are sufficient to explain the results in the halides. The centers in ZnS and CdS must therefore have essentially different features. Our results are qualitatively very similar to those obtained by Dutton 7 on the polarization of edge luminescence in CdS. We have also observed thit the green electroluminescence (involving band to band recombination 8 ) of CdS crystals is polarized preferentially perpendicular to c. Values of p up to -0.3 have been measured although the instability of emission makes it very difficult. As shown by Birman in the accompanying Letter, 9 the polarization in all these cases is consistent with the Lambe-Klick model of luminescence.More detailed work on the effect of crystal structure, crystal disorder, and type and level of doping on the polarization of fluorescence is under way. It is becoming evident that it may provide fundamental information on the nature of luminescent centers and processes.

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