Energy levels and their correlations in quasicrystals

Quasicrystals can be considered, from the point of view of their electronic properties, as being intermediate between metals and insulators. For example, experiments show that quasicrystalline alloys such as AlCuFe or AlPdMn have conductivities far smaller than those of the metals that these alloys are composed from. Wave functions in a quasicrystal are typically intermediate in character between the extended states of a crystal and the exponentially localized states in the insulating phase, and this is also reflected in the energy spectrum and the density of states. In the theoretical studies we consider in this review, the quasicrystals are described by a pure hopping tight binding model on simple tilings. We focus on spectral properties, which we compare with those of other complex systems, in particular, the Anderson model of a disordered metal.Comment: 15 pages including 19 figures. Review article, submitted to Phil. Ma

Giant oscillations of energy levels in mesoscopic superconductors

The interplay of geometrical and Andreev quantization in mesoscopic superconductors leads to giant mesoscopic oscillations of energy levels as functions of the Fermi momentum and/or sample size. Quantization rules are formulated for closed quasiparticle trajectories in the presence of normal scattering at the sample boundaries. Two generic examples of mesoscopic systems are studied: (i) one dimensional Andreev states in a quantum box, (ii) a single vortex in a mesoscopic cylinder.Comment: 4 pages, 3 figure

New Fe II energy levels from stellar spectra

The spectra of B-type and early A-type stars show numerous unidentified lines in the whole optical range, especially in the 5100 - 5400 A interval. Because Fe II transitions to high energy levels should be observed in this region, we used semiempirical predicted wavelengths and gf-values of Fe II to identify unknown lines. Semiempirical line data for Fe II computed by Kurucz are used to synthesize the spectrum of the slow-rotating, Fe-overabundant CP star HR 6000. We determined a total of 109 new 4f levels for Fe II with energies ranging from 122324 cm^-1 to 128110 cm^-1. They belong to the Fe II subconfigurations 3d^6(^3P)4f (10 levels), 3d^6(^3H)4f (36 levels), 3d^6(^3F)4f (37 levels), and 3d^6(^3G)4f (26 levels). We also found 14 even levels from 4d (3 levels), 5d (7 levels), and 6d (4 levels) configurations. The new levels have allowed us to identify more than 50% of the previously unidentified lines of HR 6000 in the wavelength region 3800-8000 A. Tables listing the new energy levels are given in the paper; tables listing the spectral lines with loggf>/=-1.5 that are transitions to the 4f energy levels are given in the Online Material. These new levels produce 18000 lines throughout the spectrum from the ultraviolet to the infrared.Comment: Paper accepted by A&A for publicatio

Experimental energy levels of the water molecule

Experimentally derived energy levels are presented for 12 248 vibration–rotation states of the H2 16O isotopomer of water, more than doubling the number in previous, disparate, compilations. For each level an error and reference to source data is given. The levels have been checked using energy levels derived from sophisticated variational calculations. These levels span 107 vibrational states including members of all polyads up to and including 8v. Band origins, in some cases estimates, are presented for 101 vibrational modes

Energy Levels Of Hydrogen-Like Atomsand Fundamental Constants

The present review includes the description of theoretical methods for the investigations of the spectra of hydrogen-like systems. Various versions of the quasipotential approach and the method of the effective Dirac equation are considered. The new methods, which have been developed in the eighties, are described. These are the method for the investigation of the spectra by means of the quasipotential equation with the relativistic reduced mass and the method for a selection of the logarithmic corrections by means of the renormalization group equation. The special attention is given to the construction of a perturbation theory and the selection of graphs, whereof the contributions of different orders of $\alpha$, the fine structure constant, to the energy of the fine and hyperfine splitting in a positronium, a muonium and a hydrogen atom could be calculated. In the second part of this article the comparison of the experimental results and the theoretical results concerning the wide range of topics is produced. They are the fine and hyperfine splitting in the hydrogenic systems, the Lamb shift and the anomalous magnetic moments of an electron and a muon. Also, the problem of the precision determination of a numerical value of the fine structure constant, connected with the above topics, is discussed.Comment: LaTeX file, 68 pp. (figures are available on request

Illustrative Model for Parity Doubling of Energy Levels

A one-dimensional quantum mechanical model possessing mass gap, a gapless excitation, and an approximate parity doubling of energy levels is constructed basing on heuristic QCD-inspired arguments. The model may serve for illustrative purposes in considering the related dynamical phenomena in particle and nuclear physics.Comment: 8 pages, 1 figur