N identical particles under quantum confinement: a many-body dimensional perturbation theory approach

Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional perturbation theory, a powerful set of tools that uses symmetry to yield simple results for studying such many-body systems. We present a detailed discussion of the dimensional continuation of the N-particle Schrödinger equation, the spatial dimension D→∞ equilibrium (D⁰) structure, and the normal-mode (D⁻¹) structure. We use the FG matrix method to derive general, analytical expressions for the many-body normal-mode vibrational frequencies, and we give specific analytical results for three confined N-body quantum systems: the N-electron atom, N-electron quantum dot, and N-atom inhomogeneous Bose-Einstein condensate with a repulsive hard-core potential.     

Spectral enhancement of Polish vowels to improve their identification by hearing impaired listeners

Abnormalities in the cochlear function usually cause broadening of the auditory filters which reduces the speech intelligibility. An attempt to apply a spectral enhancement algorithm has been undertaken to improve the identification of Polish vowels by subjects with cochlear-based hearing-impairment. The identification scores of natural (unprocessed) vowels and spectrally enhanced (processed) vowels has been measured for hearing-impaired subjects. It has been found that spectral enhancement improves vowel scores by about 10% for those subjects, however, a wide variation in individual performance among subjects has been observed. The overall vowels identification scores obtained were 85% for natural vowels and 96% for spectrally enhanced vowels.     

Noetherian PI Hopf algebras are Gorenstein

We prove that every noetherian affine PI Hopf algebra has finite injective dimension, which answers a question of Brown (1998).

     

Synthesis and Raman analysis of 1D-ZnO nanostructure via vapor phase growth

1D-nanostructural zinc oxide (ZnO) with different shapes have been synthesized on p-type Si(1 0 0) and glass substrates via vapor phase growth by heating pure zinc powder at temperatures between 480 and 570 °C. The different ZnO nanostructures depend on the substrates and the growth temperatures. Scanning electron microscopy and X-ray diffraction revealed that a well-aligned nanowires array, which are vertical to the substrate of Si(1 0 0) with 18 sides on their heads, but six sides on their stems, has been formed at 480 °C. Raman study on the ZnO nanostructures shows that the coupling strength between electron and phonon determined by the ratio of the second- to the first-order Raman scattering cross-sections declines with decreasing diameter of the nanowires. However, a little changes of the coupling strength in terms of the width of the nanobelts have been observed.     

Dynamical and Topological Methods in the Theory of Geodesically Equivalent Metrics

We suggest a new, more global, approach to the study of geodesically equivalent metrics which is based on application of the theory of integrable geodesic flows. Bibliography: 17 titles.     

Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures

The vibrational response of finite periodic lattice structures subjected to periodic loading is investigated. Special attention is devoted to the response in frequency ranges with gaps in the band structure for the corresponding infinite periodic lattice. The effects of boundaries, viscous damping, and imperfections are studied by analyzing two examples; a 1-D filter and a 2-D wave guide. In 1-D the structural response in the band gap is shown to be insensitive to damping and small imperfections. In 2-D the similar effect of damping is noted for one type of periodic structure, whereas for another type the band gap effect is nearly eliminated by damping. In both 1-D and 2-D it is demonstrated how the free structural boundaries affect the response in the band gap due to local resonances. Finally, 2-D wave guides are considered by replacing the periodic structure with a homogeneous structure in a straight and a 90° bent path, and it is shown how the vibrational response is confined to the paths in the band gap frequency ranges.     

Hawking Radiation of Dirac Particles in a Nonuniformly Rectilinearly Accelerating Black Hole

The Hawking radiation of Dirac particles on the event horizon of a nonuniformly rectilinearly accelerating black hole is studied in this paper. First, we construct the symmetrized null tetrad from which the spin coefficients and Dirac equation are derived. Next, by proposing generalized tortoise coordinate transformation, the decoupling problem of the Dirac equation with nonzero rest mass is solved. Finally, by analytic continuation, the Hawking thermal spectrum formula of Dirac particle for nonuniformly rectilinearly accelerating black hole is obtained.     

Dynamical exchange corrections to the dielectric function in a two-dimensional electron gas

The effect of dynamical exchange interactions on the dielectric function of a two-dimensional electron gas is studied using a variational approach. Exchange effects are introduced via the local-field correction. The variationally obtained local-field factor is compared to the earlier perturbative result to first order in the electron-electron interaction.