Two types of quantum-confinement characters for the bound states in the InGaN/GaN quantum wells

The (Ga_1−xIn_xN)_Nw(GaN)_Nb single and multiple quantum wells (SQWs and MQWs) are investigated theoretically using the sp³s^? tight-binding (TB) method with inclusion of spin–orbit interaction. This study explores the effects of barrier thickness L_b, well width L_w, indium content x and valence-band offset (VBO) on the quantum confinement (QC) characteristics of the bound states in the well and on the electronic transitions. The calculations are based on the validity of two assumptions: the virtual crystal approximation (VCA) for the structure of the alloyed Ga_1−xIn_xN wells, and the macroscopic theory of elasticity (MTE) for the structure of the computational supercell as a whole. The results demonstrate the following main trends: (1) the existence of two types of QC characteristics for the bound states in the GaInN alloyed wells. The nitrogen p-level (, which is associated with InN TB parametrization), displays a threshold/edge that divides the bound states into two types: (i) block-like localized states (in the energy range , where is the energy gap of zinc-blende GaN) and (ii) singlet-like localized states (in the energy range , where is the energy gap of zinc-blende InN). The confinement energy versus well width L_w is found to follow an exponential rule in the former energy region and a power-law rule in the latter one. A stronger localization should be expected as the level becomes deeper in the quantum well. (2) The TB results of E_g were compared with the available photoluminescence (PL) data of 1-ML and 2-ML thick SQWs. Taking into account the error bars due to the lattice relaxation and interface specific effects, the TB results provide evidence that the high-energy emissions ( and , for 1-ML- and 2-ML-thick wells, respectively) must have originated from wells with fractional filling (i.e., low indium contents). (3) The TB results predict that the indium content would rise as the well width increases. Unfortunately, overcoming this limitation of fractional monolayers is likely to remain beyond the capability of the currently existing growth techniques. The indium content being kept low is a natural authenticity which is the compromise to make in growing ultrathin GaInN/GaN quantum wells free of misfit dislocations.     

On short and semi-short representations for four-dimensional superconformal symmetry

Possible short and semi-short representations for and superconformal symmetry in four dimensions are discussed. For the well known short supermultiplets whose lowest dimension conformal primary operators correspond to -BPS or -BPS states and are scalar fields belonging to the SU(4) R-symmetry representations [0,p,0] and [q,p,q] and having scale dimension Δ=p and Δ=2q+p, respectively, are recovered. The representation content of semi-short multiplets, which arise at the unitarity threshold for long multiplets, is discussed. It is shown how, at the unitarity threshold, a long multiplet can be decomposed into four semi-short multiplets. If the conformal primary state is spinless one of these becomes a short multiplet. For a -BPS multiplet need not have a protected dimension unless the primary state belongs to a [1,p,1] representation.     

Sapphire (0 0 0 1) surface modifications induced by long-pulse 1054 nm laser irradiation

We have investigated modifications of sapphire (0 0 0 1) surface with and without coating, induced by a single laser pulse with a 1054 nm wavelength, 2.2 s duration, 7.75 mm spot and energy of 20-110 J. A holographic optical element was used for smoothing the drive beam spatially, but it induced small hotspots which initiated damage on the uncoated and coated surfaces. The individual damage effects of hotspots became less pronounced at high fluences. Due to high temperature and elevated non-hydrostatic stresses upon laser irradiation, damage occurred as fracture, spallation, basal and rhombohedral twinning, melting, vitrification, the formation of nanocrystalline phases, and solid-solid phase transition. The extent of damage increased with laser fluences. The formation of regular linear patterns with three-fold symmetry ( directions) upon fracture was due to rhombohedral twinning. Nanocrystalline -Al₂O₃ formed possibly from vapor deposition on the coated surface and manifested linear, triangular and spiral growth patterns. Glass and minor amounts of -Al₂O₃ also formed from rapid quenching of the melt on this side. The - to -Al₂O₃ transition was observed on the uncoated surface in some partially spalled alumina, presumably caused by shearing. The nominal threshold for laser-induced damage is about 47 J cm⁻² for these laser pulses, and it is about 94 J cm⁻² at the hotspots.     

Spin in the worldline path integral in 2 + 1 dimensions

We present a constructive derivation of a worldline path integral for the effective action and the propagator of a Dirac field in 2 + 1 dimensions, in terms of spacetime and SU(2) paths. After studying some general properties of this representation, we show that the auxiliary gauge-group variable can be integrated, deriving a worldline action depending only on x(τ), the spacetime paths. We then show that the functional integral automatically imposes the constraint , while there is a spin action, which agrees with the one one should expect for a spin- field.     

Realization and field emission of CdSe nano-tetrapods with different arm lengths

The arms of CdSe nano-tetrapods can be greatly elongated with the core diameters and arm width unchanged by multiple injections. Room-temperature absorption and photoluminescence (PL) spectra of tetrapods with different arm lengths show that these tetrapods have almost the same core size, which is consistent with the high resolution TEM results. Field emission characteristics show that the onset field required drawing a current density of from CdSe nano-tetrapods with different arm lengths are , , and , respectively, and the field enhancement factors are determined to be about 218, 554, and 946, respectively. Results show that the longer is the arm of the tetrapods, the lower the turn-on field and the higher the field enhancement factor.     

Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model

This paper deals with the problem of discrete time option pricing by the fractional Black–Scholes model with transaction costs. By a mean self-financing delta-hedging argument in a discrete time setting, a European call option pricing formula is obtained. The minimal price of an option under transaction costs is obtained as timestep , which can be used as the actual price of an option. In fact, is an adjustment to the volatility in the Black–Scholes formula by using the modified volatility to replace the volatility σ, where is the Hurst exponent, and k is a proportional transaction cost parameter. In addition, we also show that timestep and long-range dependence have a significant impact on option pricing.     

Modelling of phase transitions and reaction at CO adsorption on oxygen precovered Pd(1 1 1)

Using the interaction parameters up to the third neighbors and activated form of O and CO diffusion and their reaction, the model has been proposed for Monte-Carlo simulations describing the catalytic O + CO → CO₂ reaction and occurring phase transitions on Pd(1 1 1) surface. Upon adsorption of CO the pre-adsorbed oxygen transforms from p(2 × 2)_O phase into and phases in the limit of room and moderate temperatures, respectively. We demonstrate that the kinetic effects determine both the occurrence of the p(2 × 1)_O and disappearance of the phases at moderate and low temperatures, respectively. Using reaction rate as a fit parameter, we show that at room temperature the start of the reaction can be synchronized with the occurrence of phase.     

Repulsive and bound parts of the interatomic potentials of the lowest singlet electronic energy states of the MeRg complexes (Me = Zn, Cd; Rg = He, Ne, Ar, Kr, Xe)

Laser-induced fluorescence excitation spectra of MeRg (Me = Zn, Cd; Rg = He, Ne, Ar, Kr, Xe) complexes were recorded using the D¹ ← X¹ free ← bound transition. The complexes were produced in their ground state in a free-jet expansion beam and excited with a dye-laser beam directly to the excited state. Analysis of free ← bound unstructured profiles provided a shape of the repulsive part of the D¹-state potentials. Valence ab initio calculations of the ZnRg and CdRg ground- and excited-state potentials and electronic transition dipole moments for the studied transition were performed, taking scalar relativistic and spin-orbit effects into account. Results of the calculations show regularities and correlations in the repulsive branches and bound wells of the X¹- and D¹-state potentials as well as provide information on the bonding character in both electronic energy states. The trends were compared with available experimental results for ZnRg and CdRg as well as for MgRg and HgRg.     

Comparison of |Q|=1 and |Q|=2 gauge-field configurations on the lattice four-torus

It is known that exactly self-dual gauge-field configurations with topological charge |Q|=1 cannot exist on the untwisted continuum four-torus. We explore the manifestation of this remarkable fact on the lattice four-torus for SU(3) using advanced techniques for controlling lattice discretization errors, extending earlier work of De Forcrand et al. for SU(2). We identify three distinct signals for the instability of |Q|=1 configurations, and show that these signals manifest themselves early in the cooling process, long before the would-be instanton has shrunk to a size comparable to the lattice discretization threshold. These signals do not appear for the individual instantons which make up our |Q|=2 configurations. This indicates that these signals reflect the truly global nature of the instability, rather than the local discretization effects which cause the eventual disappearance of the would-be single instanton. Monte-Carlo generated SU(3) gauge-field configurations are cooled to the self-dual limit using an -improved gauge action chosen to have small but positive errors. This choice prevents lattice discretization errors from destroying instantons provided their size exceeds the dislocation threshold of the cooling algorithm. Lattice discretization errors are evaluated by comparing the -improved gauge-field action with an -improved action constructed from the square of an -improved lattice field-strength tensor, thus having different discretization errors. The number of action-density peaks, the instanton size, and the topological charge of configurations is monitored. We observe a fluctuation in the total topological charge of |Q|=1 configurations, and demonstrate that the onset of this unusual behavior corresponds with the disappearance of multiple-peaks in the action density. At the same time discretization errors are minimal.     

Mapping from a fragile glass-forming system to a simpler one near their glass transitions

Extensive molecular-dynamics simulations on two different glass-forming systems are performed to test the prediction proposed recently by the mean-field theory (MFT) of glass transition that a fragile system can be mimicked by a simpler one near their glass transitions. One is a simulation for a hard-sphere fluid with size polydispersity where the volume fraction φ is a control parameter and the other is for a Lennard-Jones binary mixture where the inverse temperature 1/T is a control parameter. Then, their mean-square displacements are fully analyzed by MFT. Thus, we show that both results are collapsed on a master curve given by MFT when , where is a long-time self-diffusion coefficient. We also investigate the non-singular behavior of consistently from a unified standpoint based on MFT. Thus, we show that macroscopic physical quantities in a fragile system can be transformed into those in a simpler one through a universal parameter .     

Effect of a periodic magnetic field on phase matching condition in second harmonic generation at interactions of laser-plasma

In this paper, the process of second harmonic generation (SHG) is studied in underdense plasma in the presence of a periodic magnetic field. It is shown that the difference of momentums of photon of second harmonic and two photons of main wave can be provided by momentum of everyone of Fourier components of periodic magnetic field so that momentum of nth Fourier component can be chosen by . It is also proven that the highest efficiency of second harmonic generation will be provided by the first Fourier component of periodic magnetic field . It is revealed that periodic magnetic field can produce longitudinal waves at and as well.