Relationships between lattice energy and electronic polarizability of AB crystals

The correlations between the electronic polarizability, determined from Clausius-Mosotti equation based on dielectric constant ε, and the lattice energy density u have been established for A^NB^8-N crystals, such as the systems of rock salt crystals (group I-VII, II-VI) and tetrahedral coordinated crystals (group II-VI, III-V). For the A^NB^8-N crystals systems, our present conclusions suggest that lattice energy density u decreases exponentially with increasing electronic polarizability, and the normal mathematical expression between lattice energy density u and electronic polarizability is u = pα^q, p and q depend on the type of crystals. For the same cation binary A^NB^8-N crystals systems, curve fitting equations have been obtained, and the relevant squares of the correlation coefficient R² are larger than 0.99, which show all lattice energy density u are in good exponential relation with electronic polarizability. These empirical equations will give more information on calculating lattice energy or electronic polarizability. New data of lattice energy have been calculated on the above equation u = pα^q, and a good linear trend in the calculating values along with the Zhang’s values has been obtained.     

From the Dirac operator to Wess-Zumino models on spatial lattices

We investigate two-dimensional Wess-Zumino models in the continuum and on spatial lattices in detail. We show that a non-antisymmetric lattice derivative not only excludes chiral fermions but in addition introduces supersymmetry breaking lattice artifacts. We study the non-local and antisymmetric SLAC derivative which allows for chiral fermions without doublers and minimizes those artifacts. The supercharges of the lattice Wess-Zumino models are obtained by dimensional reduction of Dirac operators in high-dimensional spaces. The normalizable zero modes of the models with N=1 and N=2 supersymmetry are counted and constructed in the weak- and strong-coupling limits. Together with known methods from operator theory this gives us complete control of the zero mode sector of these theories for arbitrary coupling.     

Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges

In this paper, we consider two-dimensional N=(4,4) supersymmetric Yang-Mills (SYM) theory and deform it by a mass parameter M with keeping all supercharges. We further add another mass parameter m in a manner to respect two of the eight supercharges and put the deformed theory on a two-dimensional square lattice, on which the two supercharges are exactly preserved. The flat directions of scalar fields are stabilized due to the mass deformations, which gives discrete minima representing fuzzy spheres. We show in the perturbation theory that the lattice continuum limit can be taken without any fine tuning. Around the trivial minimum, this lattice theory serves as a non-perturbative definition of two-dimensional N=(4,4) SYM theory. We also discuss that the same lattice theory realizes four-dimensional N=2U(k) SYM on R²×(Fuzzy R²) around the minimum of k-coincident fuzzy spheres.     

Interface property of silicon nitride films grown by inductively coupled plasma chemical vapor deposition and plasma enhanced chemical vapor deposition on In0.82Al0.18As

Au/silicon nitride/In_0.82Al_0.18As metal insulating semiconductor (MIS) capacitors were fabricated and then investigated by capacitance voltage (C–V) test at variable frequencies and temperatures. Two different technologies silicon nitride (SiN_x) films deposited by inductively coupled plasma chemical vapor deposition (“ICPCVD”) and plasma enhanced chemical vapor deposition (“PECVD”) were applied to the MIS capacitors. Fixed charges (N_f), fast (D_it) and slow (N_si) interface states were calculated and analyzed for the different films deposition MIS capacitors. The D_it was calculated to be 4.16 × 10¹³ cm⁻² eV⁻¹ for “ICPCVD” SiN_x MIS capacitors, which was almost the same to that of “PECVD” SiN_x MIS capacitors. The D_it value is obviously higher for the extended wavelength In_xGa_1−xAs (x > 0.53) epitaxial material as a result of lattice mismatch with substrate. Compared to the results of “PECVD” SiN_x MIS capacitors, the N_si was significantly lower and the N_f was slightly lower for “ICPCVD” SiN_x MIS capacitors. X-ray photoelectron spectroscopy (XPS) analysis shows good quality of the “ICPCVD” grown SiN_x. The low temperature deposited SiN_x films grown by “ICPCVD” show better effect on decreasing the dark current of In_xGa_1−xAs photodiodes.     

Lattice Dynamical Simulation of Guest-Host Interaction in N2 Clathrate Hydrate

We perform the lattice dynamical simulation studies of hydrate host lattice interacting with Xe, Ar, and N2 atoms/molecules. The calculated results show that the well-defined peaks （2.0meV and 3.8meV） and another peak （6.2 me V） are assigned to the vibrations of N2 molecules in large and small cages, respectively. It is confirmed that the double N2 molecule occupancies of large cage lead to filling of the mode gap between the small cage and the large cage.     

Electronic structure and ferromagnetism of polycrystalline Zn1−xCoxO (0≤x≤0.15)

The electronic structure of polycrystalline ferromagnetic Zn_1−xCo_xO (0.05≤x≤0.15) and the oxidation state of Co in it, have been investigated. The Co-doped polycrystalline samples are synthesized by a combustion method and are ferromagnetic at room temperature. XPS and optical absorption studies show evidence for Co²⁺ ions in the tetrahedral symmetry, indicating substitution of Co²⁺ in the ZnO lattice. However, powder XRD and electron diffraction data show the presence of Co metal in the samples. This give evidence to the fact that some Co²⁺ ion are incorporated in the ZnO lattice which gives changes in the electronic structure whereas ferromagnetism comes from the Co metal impurities present in the samples.     

Raman spectroscopic study of carbon substitution in MgB2

We study the effect of carbon doping on the Raman spectrum of the MgB₂ superconductor. Out data show that significant changes in the Raman spectra of the MgB_2−xC_x compounds occur for carbon concentrations x>0.04. The E_2g mode at ∼580 cm⁻¹ hardens only moderately upon increased doping despite direct carbon substitution in the boron layers, while the dependence of its full width at half maximum (FWHM) on x reveals the competing effects of reduced electron-phonon coupling and increased disorder. The results are discussed in the framework of anisotropic lattice contraction and the position of the σ sub-bands with respect to the Fermi energy level. The relative intensity of the phonon peak at ∼770 cm⁻¹, associated with a peak in the phonon density of states, increases considerably and dominates for x=0.08. Additionally, it hardens and broadens with increasing x in the range 0.04-0.08. These changes can be associated with carbon substitution-induced disorder in the investigated samples.     

Finite-size corrections in the Ising model with special boundary conditions

The Ising model in two dimensions with the special boundary conditions of Brascamp and Kunz (BK) is analyzed. We derive exact finite-size corrections for the free energy F   of the critical ferromagnetic Ising model on the M×N$M\times N$ square lattice with Brascamp–Kunz boundary conditions [H.J. Brascamp, H. Kunz, J. Math. Phys. 15 (1974) 66]. We show that finite-size corrections strongly depend not only on the boundary conditions but also on the shape and pattern of the lattice. In the limit N→∞$N\to \infty$ we obtain the expansion of the free energy and the inverse correlation lengths for infinitely long strip with BK boundary conditions. Our results are consistent with the conformal field theory prediction for the mixed boundary conditions.     

Boson-like quantum dynamics of association in ultracold Fermi gases

We study the collective association dynamics of a cold Fermi gas of 2N atoms in M atomic modes into a single molecular bosonic mode. When the atomic translational motion is slow compared to the atom-molecule conversion rate, the many-body fermionic problem for 2^M amplitudes is effectively reduced to a dynamical system of min{N, M} + 1 amplitudes, making the solution no more complex than the solution of a two-mode Bose-Einstein condensate and allowing realistic calculations with up to 10⁴ particles. The many-body dynamics is shown to be formally similar to the dynamics of the bosonic system under the mapping of boson particles to fermion holes, producing collective enhancement effects due to many-particle constructive interference.     

On bound states in the continuum of N-body systems and the virial theorem

We prove generalized versions of the quantum mechanical virial theorem and apply them to the investigation of the spectrum of N body Hamiltonians. We show, in particular, that for N particles interacting through 2-body potentials which may have singularities but “don't wiggle too much,” no positive energy bound state can exist. We also prove results on the absence of bound states with energy bigger than some value E⁰ ? − ∞ and extend them to the case of N particles interacting through ν-body forces (ν = 1, 2,…, N) and with an external electromagnetic field. Also some remarks for the case of a Dirac electron in an external potential are given as well as for some problems with boundary conditions. A by-product of this investigation is the unitarity of the S matrix and the strong asymptotic completeness for systems of N particles interacting by 2-body forces which are not restricted to be purely repulsive.     

ZN Gauge theories on a lattice and quantum memory

In the present paper we shall study (2+1)-dimensional Z_N gauge theories on a lattice. It is shown that the gauge theories have two phases, one is a Higgs phase and the other is a confinement phase. We investigate low-energy excitation modes in the Higgs phase and clarify relationship between the Z_N gauge theories and Kitaev’s model for quantum memory and quantum computations. Then we study effects of random gauge couplings (RGC) which are identified with noise and errors in quantum computations by Kitaev’s model. By using a duality transformation, it is shown that time-independent RGC give no significant effects on the phase structure and the stability of quantum memory and computations. Then by using the replica methods, we study Z_N gauge theories with time-dependent RGC and show that nontrivial phase transitions occur by the RGC.     

BML model on non-orientable surfaces

Two-dimensional Biham-Middleton-Levine traffic model on a N×N square lattice embedded on a Klein bottle and a projective plane is investigated by computer simulations. The behavior of the model with these boundary conditions is compared with the model under toroidal boundary conditions. Our numerical results show that the phase diagram depends strongly on the underlying topology. We also investigate the influence of the ratio between the number of red and blue particles has over the speed of the system and conclude that the projective plane case differs considerably from the other cases reviewed here.     

Improved performance and stability by an Al/Ni bilayer cathode in organic light-emitting diodes

Al/Ni bilayer cathode was used to improve the electroluminescent (EL) efficiency and stability in N,N′-bis(1-naphthyl)-N,N′-diphenyl-1,1′ biphenyl 4,4′-dimaine (NPB)/tris-(8-hydroxyquinoline) aluminum (Alq₃)-based organic light-emitting diodes. The device with LiF/Al/Ni cathode achieved a maximum power efficiency of 2.8 lm/W at current density of 1.2 mA/cm², which is 1.4 times the efficiency of device with the state-of-the-art LiF/Al cathode. Importantly, the device stability was significantly enhanced due to the utilization of LiF/Al/Ni cathode. The lifetime at 30% decay in luminance for LiF/Al/Ni cathode was extrapolated to 400 h at an initial luminance of 100 cd/m², which is 10 times better than the LiF/Al cathode.     

A path-functional field theory of lattice gauge models and the large-N limit

We transform lattice gauge models to a theory of functional fields defined on a set of closed paths. Some relevant properties of the formalism are discussed in detail, with emphasis on symmetry and topological structure. We then investigate the large-N limit of the U(N) lattice gauge model in arbitrary dimensions using this formalism. Assuming the existence of the limit, we show, to arbitrary order of the strong coupling expansion parameter (g²N)^?, which is kept fixed, that for the leading contribution in the limit: (i) the flow of indices in color space can be represented by planar diagrams; (ii) when the diagrams are immersed in space-time they are random surfaces without handles; (iii) there are interactions of the surfaces which can be depicted as the formation of multisheet bubblesw in the surfaces. This formalism also makes it possible to set up a gauge-invariant mean-field approximation.     

Discrete solitons in nonlinear Schrödinger lattices with a power-law nonlinearity

We study the discrete nonlinear Schrödinger lattice model with the onsite nonlinearity of the general form, |u|^2σu. We systematically verify the conditions for the existence and stability of discrete solitons in the one-dimensional version of the model predicted by means of the variational approximation (VA), and demonstrate the following: monostability of fundamental solitons (FSs) in the case of the weak nonlinearity, 2σ+1<3.68; bistability, in a finite range of values of the soliton’s power, for 3.68<2σ+1<5; and the presence of a threshold (minimum norm of the FS), for 2σ+1≥5. We also perform systematic numerical simulations to study higher-order solitons in the same general model, i.e., bound states of the FSs. While all in-phase bound states are unstable, stability regions are identified for antisymmetric double solitons and their triple counterparts. These numerical findings are supplemented by an analytical treatment of the stability problem, which allows quantitively accurate predictions for the stability features of such multipulses. When these waveforms are found to be unstable, we show, by means of direct simulations, that they self-trap into a persistent lattice breather, or relax into a stable FS, or sometimes decay completely.     

First-principles calculations on ferroelectricity and lattice dynamics of Type-II multiferroic SmMn2O5

In this work, we report on the structural, electronic, and ferroelectric properties of SmMn₂O₅ by using first-principles density functional theory plus on-site Coulomb interaction (DFT + U) calculations. A thorough analysis was preformed to reveal the competing characteristics of different high-temperature (T) phases and the polarization mechanism in the low-T multiferroic phase. We show that the structural characteristics of the high-T phases have a strong influence on the low-T multiferroicity. In addition to the spin-induced lattice distortion that reduces substantially the purely electronic ferroelectricity, the dominant polarization mechanism in low-T SmMn₂O₅ still originates from the electronic polarization. By performing mode decomposition of the Hellmann–Feynman forces and the lattice distortion induced by the q = (0.5, 0, 0) magnetic order, we find that the Raman-active A_g mode characterized by the Mn⁴⁺O₆ octahedron distortion and synergistic displacement of Mn³⁺ and Sm ions is of primary importance, while the infrared (IR)-active B_2u mode plays a secondary role. These findings provide a theoretical foundation for future studies concerning the enhanced magnetoelectric effects of SmMn₂O₅ due to its pure exchange–striction mechanism.     

Hot twists for the single-point model of large-N QCD

We construct two types of twists for the SU(N→∞) twisted-Eguchi-Kawai model, which mimic a periodic boundary condition in the temporal direction only and over an arbitrary extent N₀. In this way we introduce finite temperature (T=N₀^?1 in lattice units) in the single-point model. In weak coupling one gets the correct planar expansion.     

Eigenvalues, eigenfunctions, and surface states in finite periodic systems

Using a simple approach that requires neither the Bloch functions nor the reciprocal lattice, new, compact, and rigorous analytical formulas are derived for an accurate evaluation of resonant energies, resonant states, energy eigenvalues and eigenfunctions of open and bounded n-cell periodic systems with arbitrary 1D potential shapes, provided the single cell transfer matrix is given. These formulas are applied to obtain the energy spectra and wave functions of a number of simple but representative open and bounded superlattices. We solve the fine structure in bands and exhibit unambiguously that the true eigenfunctions do no not fulfill the periodicity property |Ψ_μ,ν (z + l_c)|² = |Ψ_μ,ν (z)|², with l_c the single cell length. We show that the well known surface states and surface energy levels come out naturally. We analyze the surface repulsion effect and calculate exactly the surface energy levels for different potential discontinuities an the ends.