The geodesic approximation for lump dynamics and coercivity of the Hessian for harmonic maps

The most fruitful approach to studying low energy soliton dynamics in field theories of Bogomol'nyi type is the geodesic approximation of Manton. In the case of vortices and monopoles, Stuart has obtained rigorous estimates of the errors in this approximation, and hence proved that it is valid in the low speed regime. His method employs energy estimates which rely on a key coercivity property of the Hessian of the energy functional of the theory under consideration. In this paper we prove an analogous coercivity property for the Hessian of the energy functional of a general sigma model with compact K\"ahler domain and target. We go on to prove a continuity property for our result, and show that, for the CP^1 model on S^2, the Hessian fails to be globally coercive in the degree 1 sector. We present numerical evidence which suggests that the Hessian is globally coercive in a certain equivariance class of the degree n sector for n>1. We also prove that, within the geodesic approximation, a single CP^1 lump moving on S^2 does not generically travel on a great circle.Comment: 29 pages, 1 figure; typos corrected, references added, expanded discussion of the main function spac

Nitrogen pair-induced temperature insensitivity of the band gap of GaNSb alloys

The temperature dependence of the band gap of GaN x Sb1−x films with x ≤ 1.3% has been studied in the 1.1–3.3 m (0.35–1.1 eV) range using infrared absorption spectroscopy between 4.2 and 300 K. As with other dilute nitride semiconductors, the temperature dependence of the band gap is reduced by alloying with nitrogen when compared to the host binary compound. However, for GaNSb, the smallest variation of the band gap with temperature is observed for samples with the lowest N content for which the band gap is almost totally insensitive to temperature changes. This contrasts with the more widely studied GaN x As1−x alloys in which the band gap variation with temperature decreases with increasing N content. The temperature-dependent absorption spectra are simulated within the so-called band anticrossing model of the interaction between the extended conduction band states of the GaSb and the localized states associated with the N atoms. The N next-nearest neighbor pair states are found to be responsible for the temperature insensitivity of the band gap of the GaNSb alloys as a result of their proximity to the conduction band edge giving them a more pronounced role than in GaNAs alloys

Growth and properties of GaSbBi alloys

Molecular-beam epitaxy has been used to grow GaSb 1− x Bi x alloys with x up to 0.05. The Bi content, lattice expansion, and film thickness were determined by Rutherford backscattering and x-ray diffraction, which also indicate high crystallinity and that >98% of the Bi atoms are substitutional. The observed Bi-induced lattice dilation is consistent with density functional theory calculations. Optical absorption measurements and valence band anticrossing modeling indicate that the room temperature band gap varies from 720 meV for GaSb to 540 meV for GaSb 0.95Bi0.05, corresponding to a reduction of 36 meV/%Bi or 210 meV per 0.01 Å change in lattice constant

Band gap reduction in InNxSb1-x alloys: Optical absorption, k . P modeling, and density functional theory

Using infrared absorption, the room temperature band gap of InSb is found to reduce from 174 (7.1 μm) to 85 meV (14.6 μm) upon incorporation of up to 1.13% N, a reduction of ∼79 meV/%N. The experimentally observed band gap reduction in molecular-beam epitaxial InNSb thin films is reproduced by a five band k ⋅· P band anticrossing model incorporating a nitrogen level, EN, 0.75 eV above the valence band maximum of the host InSb and an interaction coupling matrix element between the host conduction band and the N level of β = 1.80 eV. This observation is consistent with the presented results from hybrid density functional theory

Aortic remodelling in Fabry disease

Aims To evaluate thoracic aortic dilation in patients with Fabry disease (FD). Methods and results A cohort of 106 patients with FD (52 males; 54 females) from three European centres were studied. The diameter of the thoracic aorta was assessed at three levels (sinus of Valsalva, ascending aorta, and descending aorta) using echocardiograms and cardiovascular magnetic resonance imaging. Aortic dilation at the sinus of Valsalva was found in 32.7% of males and 5.6% of females; aneurysms were present in 9.6% of males and 1.9% of females. No aortic dilation was observed in the descending aorta. There was no correlation between aortic diameter at the sinus of Valsalva and cardiovascular risk factors. Conclusion Fabry disease should be considered as a cardiovascular disease that affects the heart and arterial vasculature, including the thoracic aorta. Thus, patients with FD should be closely monitored for the presence, and possible progression and complications of aortic dilation. Clinical Trial Registration: Protocol 101/01. Ethics committee, Faculty of Medicine, Lausann

High Bi content GaSbBi alloys

The epitaxial growth, structural, and optical properties of GaSb 1– x Bi x alloys have been investigated. The Bi incorporation into GaSb is varied in the range 0 < x ≤ 9.6% by varying the growth rate (0.31–1.33 μm h−1) at two growth temperatures (250 and 275 °C). The Bi content is inversely proportional to the growth rate, but with higher Bi contents achieved at 250 than at 275 °C. A maximum Bi content of x = 9.6% is achieved with the Bi greater than 99% substitutional. Extrapolating the linear variation of lattice parameter with Bi content in the GaSbBi films enabled a zinc blende GaBi lattice parameter to be estimated of 6.272 Å. The band gap at 300 K of the GaSbBi epitaxial layers decreases linearly with increasing Bi content down to 410 ± 40 meV (3 μm) for x = 9.6%, corresponding to a reduction of ∼35 meV/%Bi. Photoluminescence indicates a band gap of 490 ± 5 meV at 15 K for x = 9.6%

Collapse of an Instanton

We construct a two parameter family of collapsing solutions to the 4+1 Yang-Mills equations and derive the dynamical law of the collapse. Our arguments indicate that this family of solutions is stable. The latter fact is also supported by numerical simulations.Comment: 17 pages, 1 figur

Ge interface engineering using ultra-thin La2O3 and Y2O3 films: A study into the effect of deposition temperature

A study into the optimal deposition temperature for ultra-thin La2O3/Ge and Y2O3/Ge gate stacks has been conducted in this paper with the aim to tailor the interfacial layer for effective passivation of the Ge interface. A detailed comparison between the two lanthanide oxides (La2O3 and Y2O3) in terms of band line-up, interfacial features, and reactivity to Ge using medium energy ion scattering, vacuum ultra-violet variable angle spectroscopic ellipsometry (VUV-VASE), X-ray photoelectron spectroscopy, and X-ray diffraction is shown. La2O3 has been found to be more reactive to Ge than Y2O3, forming LaGeOx and a Ge sub-oxide at the interface for all deposition temperature studied, in the range from 44 °C to 400 °C. In contrast, Y2O3/Ge deposited at 400 °C allows for an ultra-thin GeO2 layer at the interface, which can be eliminated during annealing at temperatures higher than 525 °C leaving a pristine YGeOx/Ge interface. The Y2O3/Ge gate stack deposited at lower temperature shows a sub-band gap absorption feature fitted to an Urbach tail of energy 1.1 eV. The latter correlates to a sub-stoichiometric germanium oxide layer at the interface. The optical band gap for the Y2O3/Ge stacks has been estimated to be 5.7 ± 0.1 eV from Tauc-Lorentz modelling of VUV-VASE experimental data. For the optimal deposition temperature (400 °C), the Y2O3/Ge stack exhibits a higher conduction band offset (>2.3 eV) than the La2O3/Ge (∼2 eV), has a larger band gap (by about 0.3 eV), a germanium sub-oxide free interface, and leakage current (∼10−7 A/cm2 at 1 V) five orders of magnitude lower than the respective La2O3/Ge stack. Our study strongly points to the superiority of the Y2O3/Ge system for germanium interface engineering to achieve high performance Ge Complementary Metal Oxide Semiconductor technology

Quantum lump dynamics on the two-sphere

It is well known that the low-energy classical dynamics of solitons of Bogomol'nyi type is well approximated by geodesic motion in M_n, the moduli space of static n-solitons. There is an obvious quantization of this dynamics wherein the wavefunction evolves according to the Hamiltonian H_0 equal to (half) the Laplacian on M_n. Born-Oppenheimer reduction of analogous mechanical systems suggests, however, that this simple Hamiltonian should receive corrections including k, the scalar curvature of M_n, and C, the n-soliton Casimir energy, which are usually difficult to compute, and whose effect on the energy spectrum is unknown. This paper analyzes the spectra of H_0 and two corrections to it suggested by work of Moss and Shiiki, namely H_1=H_0+k/4 and H_2=H_1+C, in the simple but nontrivial case of a single CP^1 lump moving on the two-sphere. Here M_1=TSO(3), a noncompact kaehler 6-manifold invariant under an SO(3)xSO(3) action, whose geometry is well understood. The symmetry gives rise to two conserved angular momenta, spin and isospin. A hidden isometry of M_1 is found which implies that all three energy spectra are symmetric under spin-isospin interchange. The Casimir energy is found exactly on the zero section of TSO(3), and approximated numerically on the rest of M_1. The lowest 19 eigenvalues of H_i are found for i=0,1,2, and their spin-isospin and parity compared. The curvature corrections in H_1 lead to a qualitatively unchanged low-level spectrum while the Casimir energy in H_2 leads to significant changes. The scaling behaviour of the spectra under changes in the radii of the domain and target spheres is analyzed, and it is found that the disparity between the spectra of H_1 and H_2 is reduced when the target sphere is made smaller.Comment: 35 pages, 3 figure