Recent Progress in Confined Atoms and Molecules: Superintegrability and Symmetry Breakings

This review article has the antecedents of Jaskolski’s 1996 Physics Report Confined Many-electron Systems , the fifteen chapters on the Theory of Confined Quantum Systems in Vols. 57 and 58 of 2009 Advances in Quantum Chemistry, and the nine chapters of the 2014 Monograph “Electronic Structure of Confined Quantum Atoms and Molecules”. In this contribution the last two sets of reviews are taken as the points of reference to illustrate some advances in several lines of research in the elapsed periods. The recent progress is illustrated on the basis of a selection of references from the literature taking into account the confined quantum systems, the confining environments and their modelings; their properties and processes, emphasizing the changes due to the confinement; the methods of analysis and solutions, their results including confiability and accuracy; as well as applications in other areas. The updated and current works of the Reviewer are also presented. The complementary words in the title apply to the simplest atom in its free configuration and to the harmonic oscillator quantum dot because they admit more exact solutions than the number of their degrees of freedom; and to their many-electron and confined counterparts, due to their additional interactions and changes in boundary conditions.

SURFACE PHONON AND CONFINED PHONON POLARITONS IN WURTIZTE NITRIDE THIN-FILM STRUCTURES

The polar phonon polariton modes in a wurtzite thin-film structure have been theoretically investigated in the present paper. It has been confirmed that there are two types of phonon polariton modes, i.e., the surface phonon polariton (SPP) modes and the confined phonon polariton (CPP) modes in wurtzite thin-film systems. The frequency ranges of the SPP and CPP modes have been discussed in detail. The dispersive equations for the two types of polarition modes are also deduced. Numerical calculations on a GaN thin-film structure reveal that, for a given free wavenumber kt in x-direction, there are two branches of SPP modes in general. The width of the wurtizte thin film has important influence on the dispersive properties of the polariton modes, especially the width d is small. Our calculated result agrees well with the recent experimental observation in GaN thin-film system. Furthermore, we confirm that the SPP modes observed (at about the frequency of 700 cm-1) is the low-frequency SPP modes. The CPP modes appear in two frequency ranges of [ωzT, GaN ,ωtT, GaN ] and [ωzL, GaN ,ωtL, GaN ]. There are infinite branches of CPP modes in each range. The low-frequency branch, in contrast to the high-frequency branch, is more dispersive. Moreover, the dispersion of lower-order CPP modes is more obvious than that of higher-order CPP ones. At last, the distribution properties of the electric field components Ex(z) for the SPP and CPP modes are discussed and analyzed. It is found that Ex(z) are either symmetrical, or antisymmetrical. The electric field components [Formula: see text] for SPP modes are mainly localized at the surfaces. The distribution properties of electric field components [Formula: see text] are quite analogous to the behaviors of bound electronic states in confined quantum systems. In terms of these features, the CPP modes in the GaN thin film structures are distinguished and labeled.