Narrow Results

The one-dimensional problem of N particles with contact interaction in the presence of a tunable transmitting and reflecting impurity is investigated along the lines of the coordinate Bethe ansatz. As a result, the system is shown to be exactly solvable by determining the eigenfunctions and the energy spectrum. The latter is given by the solutions of the Bethe ansatz equations which we establish for different boundary conditions in the presence of the impurity. These impurity Bethe equations contain as special cases well-known Bethe equations for systems on the half-line. We briefly study them on their own through the toy-examples of one and two particles. It turns out that the impurity can be tuned to lift degeneracies in the energies and can create bound states when it is sufficiently attractive. The example of an impurity sitting at the center of a box and breaking parity invariance shows that such an impurity can be used to confine a stationary state asymmetrically. This could have interesting applications in condensed matter physics.

CaB₆ single crystals were synthesized by the Al flux method and the Fe-impurity concentration in the crystal was measured using the PIXE method. As a result, we found that the amount of the Fe impurity, included in a CaB₆ powder sample used as a starting material, is drastically reduced after the synthesis process. Lightly La doped CaB₆ single crystals were also synthesized and the La concentration was determined by PIXE.

In the present work, genetic algorithm method (GA) is applied to the problem of impurity at the center of a spherical quantum dot for infinite confining potential case. For this purpose, any trial variational wave function is considered for the ground state and energy values are calculated. In applying the GA to the problem under investigation, two different approaches were followed. Furthermore, a standard variational procedure is also performed to determine the energy eigenvalues. The results obtained by all methods are found in satisfactory agreement with each other and also with the exact values in literature. But, it is found that the values obtained by genetic algorithm based upon wavefunction optimization are closer to the exact values than standard variational and also than genetic algorithm based on parameter optimization methods.

We investigate boron and nitrogen substitutional doping single wall carbon nanotubes (SWCNTs) by first-principles calculations. The optimized geometres of boron and nitrogen substituted SWCNTs exhibit bamboo-like structures. Boron and nitrogen impurities form acceptor and donor states in semiconductor SWCNTs. The highest occupied molecular orbital (HOMO) indicates the trend of forming inter-tube bonds in doping SWCNTs. It may start a new way to form inter-tube bonds by doping in SWCNTs.

The effects of spin-orbit coupling (SOC) and relativistic correction (RC) on the energy levels of a hydrogenic impurity in a GaAs/Ga_1-xAl_xAs quantum wire are studied. The quantum wire has a V-shaped cross-section and the impurity located in its center. Our numerical calculations have done using a variational procedure within the effective mass approximation. Our results show that (i) the splitting due to the SOC decreases with increasing the wire width, (ii) the SOC and RC increase when the concentration increases, (iii) the SOC is zero for l = 0 (l is angular momentum) and nonzero for l ≠ 0, (iv) for a given wire width, the RC is different for l = 0 and l = 1 due to expectation values of and (r is distance between the electron and impurity). We also computed the conductance of the quantum wire with and without impurity.

We investigate the variant regularly diluted situations of in S=1 isotropic antiferromagnetic chains by the quantum Monte Carlo loop cluster algorithm. Our results manifest significant different magnetic properties in the ground state with respect to the odd (even) host S=1 spins in one unit cell with an impurity S=1/2, and the doped system gradually transits to the pure Haldane chain in two different tendencies with the decreasing of the impurity concentrations.

The large variety of the measured magnetic penetration depth is interpreted by using two microscopic gap models. We calculate the penetration depth of superconductor MgB₂ in low temperatures by using two gap and an anisotropic s-wave gap models. In the two gap model we consider that the total penetration depth is a weighted sum of the contribution from σ- and π-bands and the interaction between these two bands is ignored. The effect of impurities on the σ-band is less than that π-band and there are tremendous modifications of the temperature dependence of the penetration depth for π-band.

We use the effective mass model to describe spinless electrons near the Fermi level in metallic, single-wall carbon nanotubes. Taking into account two nonequivalent valleys (K-points) produces a four component Dirac equation for massless fermions, with the role of spin assumed by pseudospin due to the relative amplitude of the wavefunction on the two nonequivalent sublattice atoms. We show that the position of a short-ranged impurity within the hexagonal graphite unit cell produces a particular 4×4 matrix structure of the corresponding effective Hamiltonian. The symmetry of this Hamiltonian with respect to pseudospin flip is related to degeneracy breaking and, for an armchair tube, symmetry with respect to mirror reflection in the nanotube axis is related to pseudospin mixing. In a nanotube of finite length, we predict a sinusoidal oscillation of energy level shift as a function of energy with a period determined by the position of the impurity along the tube axis.

The Davydov's soliton propagation in the linear polymer chain is analyzed numerically by solving the discrete equations of motion for exciton and phonon amplitudes. The main difference with respect to the results of continual approximation is that two exciton–phonon coupling constants influence separately the soliton behavior. Their influence is studied both in the ideal chain and the chain with single impurity.

Binding energies of negative and positive trions in high magnetic fields are compared. Simultaneous inclusion of several Landau levels and quantum well subbands in exact numerical diagonalization allowed quantitative description of the coupling between in-plane dynamics (governed by interplay of cyclotron quantization and Coulomb interactions) and single-particle excitations in the normal direction. Symmetric and asymmetric GaAs quantum wells of different widths were considered, as well as the effect of a possible binding of trions by sparse ionized impurities nearby the quantum well.

The effects of impurities on the generation of voids in composites fabricated by vacuum-assisted resin transfer molding was investigated to help reduce mechanical weakening in large structures. Impurities were intentionally inserted into laminates, which were then observed optically. Internal voids were generated in specimens with impurities of 2 – 3mm thickness. The voids grew as the impurities' thicknesses increased to 4 – 5 mm. The voids' diameters were proportional to the thickness of the impurity. Void generation was shown to depend on the thickness of impurities. Environmental control during vacuum-assisted resin transfer molding was shown to be important for ensuring the quality of the resulting composites.

Scattering of a discrete soliton by a single impurity in dipolar Bose–Einstein condensate is investigated numerically. The results show that the increase of the strength of dipolar interactions leads to repeated reflection, transmission and trapping regions due to energy exchange between the center of mass motion and the internal modes of the impurity. However, increasing the strength of the attractive nonlocal dipole–dipole interaction will result in different scattering windows. While the dipole–dipole interaction can significantly expand the trapping region of the system, nevertheless transmission resonances through the impurity are still observed.

In this paper, the effect of dilute charged impurity and external magnetic field on orbital-resolved density of states (DOS) and electronic heat capacity (EHC) of a monolayer hydrogenated graphene which is called chair-like graphane is investigated within the Harrison model and Green’s function technique. The self-consistent Born approximation has been implemented to describe the effect of scattering between electrons and dilute charged impurities. Our results show that the graphane is a semiconductor and its band gap decreases with impurity and magnetic field. EHC reaches almost linearly to Schottky anomaly and does not change at low temperatures in the presence of impurity and magnetic field. Generally, EHC increases with the mentioned parameters. Surprisingly, impurity doping only affects the salient behavior of $p_y$ orbital contribution of carbon atoms due to the symmetry breaking.

In this work, the influence of boron atom impurity is investigated on the electronic properties of a single-wall carbon nanotube superlattice which is connected by pentagon–heptagon topological defects along the circumference of the heterojunction of these superlattices. Our calculation is based on tight-binding $\pi$-electron method in nearest-neighbor approximation. The density of states (DOS) and electronic band structure in presence of boron impurity has been calculated. Results show that when boron atom impurity and nanotube atomic layers have increased, electronic band structure and the DOS have significant changes around the Fermi level.

We have investigated the effect of impurity X (X = C and O) atoms on the behavior of hydrogen in vanadium, which is an ideal structural material for nuclear fusion reactors, by first-principles calculations. We found that (1) in bulk V, the interaction between an interstitial H atom and an X atom is repulsive, and the interaction with O is much stronger than that with C. (2) The X–vacancy (vac) cluster can act as a center for capturing H in V. The C-vac cluster can trap as many as two H atoms, while the O–vac cluster can capture up to four H atoms. (3) C and O impurities can effectively decrease the trapping energy of a single H atom in a vacancy. The H-trapping energies in the C–vac and O–vac complexes are 0.88 eV and 0.46 eV, respectively, both of which are lower than those in the X-free vacancy. (4) Both H–X and X-metal interactions affect the H solubility in V. The above results provide important information for application of vanadium as a structural material for nuclear fusion tokamaks.

The influences of the dispersion, the impurity and the electron–phonon coupling (EPC) on the properties of the Gaussian confining (GC) potential qubit with magnetic field were studied by Pekar-type variation method. Results show that the decoherence time will increase with increasing the dielectric constant (DC) ratio, the dispersion coefficient and the EPC strength, respectively. The phase rotation quality factor increases with increasing the dielectric constant ratio, the dispersion coefficient and EPC strength, respectively. The magnetic field has a regulatory effect on the decoherence time and the phase rotation quality factor.

We examine some new DNLS-like equations that arise when considering strongly-coupled electron-vibration systems, where the local oscillator potential is anharmonic. In particular, we focus on a single, rather general nonlinear vibrational impurity and determine its bound state(s) and its dynamical selftrapping properties.

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

By using the concept of concurrence, we study pairwise entanglement between the two end spins in the open-ended Heisenberg XXX and XY chains up to ten spins. The results show that by introducing two boundary impurities, one can obtain maximum entanglement at the limit of the impurity parameter |J₁| ≪ J for the even-number qubits. When |J₁/J| > 0, the entanglement always decreases with the increase in the absolute value of J₁/J, and for the Heisenberg XXX chain, C disappears when J₁/J exceeds a certain critical point J_ic, and attains an asymptotic value C₀ when |J₁| ≫ J(J₁ < 0), while for the Heisenberg XY chain, C always disappears when |J₁/J| exceeds a certain critical point J_ic. Both C₀ and J_ic decrease with the increase of the length of the chain.

The ground-state exciton binding energy and interband emission wavelength in the direct-gap Ge/SiGe quantum dot (QD) are investigated by means of a variational approach, within the framework of effective-mass approximation. Numerical results show that the ground-state exciton binding energy has a maximum value with increasing quantum size of the direct-gap Ge/SiGe QD. The interband emission wavelength is increased when the QD size is increased. Our results indicate the direct-gap Ge/SiGe QD can be applied for long wavelength optoelectronic devices.