By using the bosonization and renormalization group methods, we have studied the low energy physical properties in one-dimensional extended Hubbard model. The formation of charge and spin gaps is investigated at the half-filled electron band. An analytical expression for the charge gap in terms of the Coulomb repulsive interaction strength U and the nearest-neighbour interaction parameter V is obtained.

Using relativistic spin-flavor wave functions of a Lorentz-covariant light cone quark model, we calculate the electromagnetic form factors of two S₁₁ resonances, N(1535) and N(1650), and the helicity amplitudes A_1/2 and S_1/2 for electroexcitation of the S₁₁ resonances from the nucleon. The electromagnetic form factors of these S₁₁ resonances are found to be similar to those of the nucleon in shape, while the charge form factor of neutral N(1650) is nearly zero. The relative peak height of the S₁₁ charge form factors is controlled by the mixing angle common to both resonance wave functions. As in most quark models, there is a systematic overestimate of A^p_1/2 in both N(1535) and N(1650) cases at the photon point. A sizeable S_1/2 for all cases is produced as suggested by experiments.

In this paper, we consider a system of (2+1)-dimensional nonlinear models by using CK direct method and Hereman-Nuseir method generated by the Jaulent-Miodek Hierarchy. We construct some new multiple kink and singular kink solutions of (2+1)-Dimensional Nonlinear Models with the aid of symbolic computation.

In this study, the analytical solutions of the radial Schrödinger equation for the central Woods-Saxon potential together with spin-orbit interaction and centrifugal terms have been derived by using Nikiforov-Uvarov method. The energy eigenvalues and corresponding eigenfunctions of nucleons have been obtained for various values of n, l, and j quantum numbers. The obtained results using this method are in satisfactory agreement with available data in the special case.

We calculate the lowest-order quantum-interference correction to the density of states (DOS) of weakly-disordered two-dimensional (2D) tight-binding square lattices around half filling. The impurities are assumed to be randomly distributed on small fractions of the sites, and have a strong potential yielding a unitary-limit scattering. In addition to the usual diffusive modes in the retarded-advanced channel, there appear diffusive π modes in the retarded-retarded (or advanced-advanced) channel due to the existence of particle-hole symmetry. It is found that the π-mode diffuson gives rise to a logarithmic suppression to the DOS near the band center, which prevails over the positive correction contributed by π-mode cooperon. As a result, the DOS is subject to a negative total correction. This result is qualitatively different from the divergent behavior of the DOS at the band center predicted previously for disordered 2D two-sublattice models with the particle-hole symmetry.

The time evolution of an initially localized mode in a one-dimensional lattice with off-diagonal nonlinearity disorder is studied by solving a modified nonlinear Schrodinger equation. Absence of localization is found when the nonlinearity parameter is beyond the selftrapping region for corresponding periodic httice. The propagation of electrons shows ballistic behavior even in the presence of disorder. When self-trapping occurs, the untrapped portion still escapes ballistically.

Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4,R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4,R)\supset U(2).

We present a simple, general method for calculating the binding energies of excitons in semiconductor quantum wires. The binding energy is given by an integral (over the electron and hole two-dimensional coordinates perpendicular to the wire) of a prescribed function weighted by the squares of the electron and hole subband envelope functions. Taking as an example, we calculate the binding energy of exciton in quantum wires assuming an infinite confining potential. This method should be applicable to a variety of more complex systems.

We have proposed a quantum system with equally-distant partially-entangled alphabet states which has the minimal mutual overlap and the highly distinguishability, these quantum states are used as the “signal states” of the quantum communication. We have also constructed the positive operator-valued measure for these “signal states” and discussed their entanglement properties and measurement of entanglement. We calculate the accessible information for these alphabet states and show that the accessible information is closely related to the entanglement of the “signal states”: the higher the entanglement of the “signal states”, the better the accessible information of the quantum system, and the accessible information reaches its maximal value when the alphabet states have their maximal entanglement.

In this paper, based on the adjacency matrix of the network and its powers, the formulas are derived for the shortest path and the average path length, and an effective algorithm is presented. Furthermore, an example is provided to demonstrate the proposed method.

The time evolution of the time-dependent harmonic oscillator is studied by a sequence of unitary transformations and the exact evolving state for the system is obtained. A specific model of frequency variation for the time-dependent harmonic oscillator is discussed as an illustrative example.

The way of handling boundary conditions with simple bounce-back rule in the lattice gas and lattice Boltzmann method had been considered as one of the advantage compared with other numerical schemes. The half-way bounce-back rule inherits the advantage of the bounce-back rule and improves the accuracy to the second-order on flat boundaries. In this paper, we test the possible application of the half-way bounce-back rule to the system with complex geometry. Our simulation results show that the half-way bounce-back rule is a good boundary condition in the problems without emphasis on accuracy.

In this paper, the Adomian's decomposition method (ADM) is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided.

The solutions of the Laplace equation in n-dimensional space are studied. The angular eigenfunctions have the form of associated Jacobi polynomials. The radial solution of the Helmholtz equation is derived.

Hamiltonian of a one-dimensional Bose-Hubbard model is re-formulated by using differential realization of the boson algebra. Energy matrices can then be generated systematically by using a Mathematica package. The output can be taken as the input of other diagonalization codes. As examples, exact energy eigenvalues and the corresponding wavefunctions for some cases are obtained with a Fortran diagonalization code. Phase transition of the model is analyzed.

In this paper, a classical system of ordinary differential equations is built
to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-imensional equations by using the generating function method. Besides the Birkhoffian structure-preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f. Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.

With the help of the effective refractive index method we have numerically analyzed a multilayer planar waveguide structure and calculated the propagation constants, confinement factors, and transverse electric (TE) modes. A five-layer waveguide model has been provided to analyze the electro-magnetic wave propagation process. The analysis method has been applied to the 980 nm laser with active layer of GaInAs/GaInAsP strained quantum wells, GaInAsP confinement layers and GaInP cap layers. By changing the thickness of confinement layers, we obtained confinement factor as high as 95% with higher TE modes TE1 and TE2. The results are in good agreement with the experiment by A. Al-Muhanna et al. and give the new idea to enhance output power of semiconductor lasers. The analysis method can also be extended to any other slab multilayer waveguide structures, and the results are useful to the fabrication of optic-electronic devices.

We review the problem of dark energy, including a survey of theoretical models and some aspects of numerical studies.

The linear-muffin-tin orbital method is used to study the electronic-energy-band structure of zinc-blende CdS. Incorporating the 4d states of Cd into the valence band gives substantially the main-valenceband width, and yields valenceband features in agreement with the experiment. The calculated equilibrium lattice constant is in accord with the measured result. The fundamental band gap is found to be direct at T point and the value is about 1.21 eV. The band structure calculation shows that the present results are in good agreement with experiments and other calculations.

Surface properties of SiC power devices mostly depend on the passivation layer (PL).This layer has direct influence on electrical characteristics of devices.2D numerical simulation of forward and reverse characteristics with and without different (PLs) (SiO₂,HfO₂ and Si₃N₄) has been performed.Simulation results show that the breakdown voltage increases with increasing PL thickness,and there is a lesser significant effect on forward characteristics.The maximum breakdown voltage with and without SiO₂ PL is 1240 V and 276 V,respectively.SiO₂ PL has compatibility with SiC surface providing high breakdown voltage,6 and 8% higher than that of HfO₂ and Si₃N₄ respectively.Low leakage current is observed which then further decreases on reducing the thickness of PL.Furthermore,variation of forward current with dielectric constant and thickness of PLs was observed.Finally,it is suggested that matches of our results with published experimental results indicate that the Sentaurus TCAD simulator is a predictive tool for the SiC Schottky barrier diode simulation.

The recurrence relations are presented for the calculation of basic overlap integrals, by making use of which other overlap integrals are calculated analytically. These recurrence relations are especially useful for the calculation of any overlap integral for large quantum numbers. For the arbitrary values of screening constants of atomic orbitals and internuclear distances an accuracy of the computer results is satisfactory for the values of principal quantum numbers of Slater functions up to 50.

It is pointed out that the assertion that the eigenfunction of the creation operator a⁺ is identically zero is not rigorous.On the contrary, the eigenfunction of a⁺ may be discussed by using the contour integral representation of δ function, the property of which and the relation with the eigenstate of the annihilation operator are discussed. Its applications, especially the application in thoroughly studying the inverse operator's properties, are presented. It is shown that the phase operator can also be represented by the inverse operator.

A general solution of sun tracking for an arbitrarily oriented heliostat towards an arbitrarily located target on the earth is published. With the most general form of solar tracking formulae, it is seen that the used azimuth-elevation, spinning-elevation tracking formulae etc. are the special cases of it. The possibilities of utilizing the general solution and its significance in solar energy engineering are discussed.

The linear variable separation approach is successfully extended to (1+1)-dimensional Korteweg-de Vries (KdV) type models related to Schrödinger system. Some significant types of solitons such as compacton, peakon, and loop solutions with periodic behavior are simultaneously derived from the (1+1)-dimensional soliton system by entrancing appropriate piecewise smooth functions and multivalued functions.

An exact analogy is approached between systems in thermal equilibrium and those far from equilibrium which can be the cases without detailed balance. The analogy is based on the requirement that a given drift in the Fokker-Planck equation can be decomposed into two parts, one of which is divergence-free and the other can be derived from a potential which is invariant along the direction of the first part. If the conditions are fulfilled the Fokker-Planck equation changes in to a standard Poisson equation. The relations of this requirement to other conditions are diecussed. As a concrete example, the stationary Fokker-Planck equation for optical bistability is solved by using"this method.

Spin-wave expansion is used to evaluate the staggered magnetization of frustrated antiferromagnetic (AF) Heisenberg model with next-nearest-neighbor exchange couplings on a square lattice to the order O(1/S) at zero temperature. It is shown that the O(1/S) order correction increases the staggered magnetization and its presence invalidates the conventional spin- wave conclusions at large frustrations. We apply the mean-field approximation to deal with the quartic terms in the Hamiltonian of the Holstein-Primakoff transformation. A phaqe diagtam is obtained, suggesting that the NCel order is not destroyed for S≥1 at any frustration, while for S = 1/2 there may exist a disordered phase for strong frustrations.

The amorphous silicon nanoparticles (Si NPs) embedded in silicon nitride (SiN_x) films prepared by helicon wave plasma-enhanced chemical vapor deposition (HWP-CVD) technique are studied. From Raman scattering investigation, we determine that the deposited film has the structure of silicon nanocrystals embedded in silicon nitride (nc-Si/SiNx) thin film at a certain hydrogen dilution amount. The analysis of optical absorption spectra implies that the Si NPs is affected by quantum size effects and has the nature of an indirect-band-gap semiconductor. Further, considering the effects of the mean Si NP size and their dispersion on oscillator strength, and quantum-confinement, we obtain an analytical expression for the spectral absorbance of ensemble samples. Gaussian as well as lognormal size-distributions of the Si NPs are considered for optical absorption coefficient calculations. The influence of the particle
size-distribution on the optical absorption spectra was systematically studied. We present the fitting of the optical absorption experimental data with our model and discuss the results.

The explicit forms of the quantum Clebsch-Gordan coefficients and the first-type quantum Racah coefficients for the quantum sl(2) enveloping algebra are computed in detail. Exact values of some coefficients are listed. An important relation, quantum Racah sum rule, is proved.

In the present paper, we study effect of the long-range Coulomb interaction on the thermodynamic properties of graphene by renormalization group methods. Our calculations show that both the specific heat and the magnetic susceptibility of the material behave differently from the Landau Fermi liquid. More precisely, we find that these quantities are logarithmically suppressed with respect to its noninteracting counterpart when temperature is low.

Simple arguments are used to construct a model to explain the extreme ultraviolet radiation conversion efficiency (EUV-CE) of a tin-based droplet target laser produced plasmas by calculating the laser absorption efficiency, radiation efficiency, and spectral efficiency. The dependence of drive laser pulse duration and laser intensity on EUV-CE is investigated. The results show that at some appropriate laser intensity, where the sum energy of the thermal conduction, out-off band radiation and plasma plume kinetic losses is at a minimum, the EUV-CE should reach a maximum. The EUV-CE predicted by the present simple model is also compared with the available experimental and simulation data and a fair agreement between them is found.

A comprehensive first principles study of III-Antimonide binary compounds is
hardly found in literature. We report a broad study of structural and electronic
properties of boron antimonide (BSb), aluminium antimonide (AlSb), gallium
antimonide (GaSb) and indium antimonide (InSb) in zincblende phase based on density functional theory (DFT). Our calculations are based on
Full-Potential Linearized Augmented Plane wave plus local orbitals
(FP-L(APW+lo)) method. Different forms of exchange-correlation energy
functional and corresponding potential are employed for structural and
electronic properties. Our computed results for lattice parameters, bulk
moduli, their pressure derivatives, and cohesive energy are consistent with
the available experimental data. Boron antimonide is found to be the hardest
compound of this group. For band structure calculations, in addition to LDA
and GGA, we used GGA-EV, an approximation employed by Engel and Vosko. The band gap results with GGA-EV are of significant improvement over the earlier work.

In this article, we discuss the mean first-passage time for non-Markovian processes driven by continuous noise. Applying the iterative method to the Volterra integral equation, we obtain for the first time the series solution to the mean first-passage time problem and present the exact expression for the mean first-passage time in both the cases of rectangular distribution and long-tail distribution.

The lattice parameters, bulk modulus, phase transition pressure, and temperature dependencies of the elastic constants c_ij of CdSe are investigated by using the Cambridge Serial Total Energy Package (CASTEP) program in the frame of Density Functional Theory (DFT). It is found that the phase transitions from the ZB structure to the RS structure and from WZ structure to RS structure are 2.2 GPa and 2.8 GPa, respectively. Our results agree well with the available experimental data and other theoretical results. The aggregate elastic modulus (B, G, E, A), the Poisson's ratio (υ), the Grüneisen parameter (γ), the Debye temperature Θ_D on pressure and temperature are also successfully obtained.

An explicit derivation of the renormalization group equations of the fermion-Higgs Yukawa coupling constants and the Higgs-quartic coupling constant in the standard model with n generations of fermions is given in the Feynman gauge.

The notes here presented are of the modifications introduced in the application of WKB method. The problems of two- and three-dimensional harmonic oscillator potential are revisited by WKB and the new formulation of quantization rule respectively. It is found that the energy spectrum of the radial harmonic oscillator, which is reproduced exactly by the standard WKB method with the Langer modification, is also reproduced exactly without the Langer modification via the new quantization rule approach. An alternative way to obtain the non-integral Maslov index for three-dimensional harmonic oscillator is proposed.

Using an expression of optical conductivity, based on the linear response theory, the Green's function technique and within the Holstein Hamiltonian model, the effect of electron-phonon interaction on the optical conductivity of graphene plane is studied. It is found that the electron-phonon coupling increases the optical conductivity of graphene sheet in the low frequency region due to decreasing quasiparticle weight of electron excitation while the optical conductivity reduces in the high frequency region. The latter is due to role of electrical field's frequency.

In this paper, we proved that the null geodesic equations in general isotropic metric are rigorously equivalent to the differential equations bf light rays in a medium of flat 3-dimension.,31 space, which are the fundamental equations of geometrical optics, when the effect bf gravitational field tb light ray is taken as that of a variable "refractive index"。Our results provide the basic way to strictly describe the characteristics of some gravitational fields in terms of the Euclidean framework. It may be useful in the computation of modern astrometry and gravitational Lens effects. Finally, as a special example，the deflection of Iight by gravitational field is discussed by means of the formula of pure classical geometrical optics.

We report the electronic band structure and optical parameters of X-Phosphides (X=B, Al, Ga, In) by first-principles technique based on a new approximation known as modified Becke-Johnson (mBJ). This potential is considered more accurate in elaborating excited states properties of insulators and semiconductors as compared to LDA and GGA. The present calculated band gaps values of BP, AlP, GaP, and InP are 1.867 eV, 2.268 eV, 2.090 eV, and 1.377 eV respectively, which are in close agreement to the experimental results. The band gap values trend in this study is as: E_g(mBJ-GGA/LDA) > E_g(GGA) > E_g(LDA). Optical parametric quantities (dielectric constant, refractive index, reflectivity and optical conductivity) which based on the band structure are also presented and discussed. BP, AlP, GaP, and InP have strong absorption in between the energy range 4-9 eV, 4-7 eV, 3-7 eV, and 2-7 eV respectively. Static dielectric constant, static refractive index and coefficient of reflectivity at zero frequency, within mBJ-GGA, are also calculated. BP, AlP, GaP, and InP show significant optical conductivity in the range 5.2-10 eV, 4.3-8 eV, 3.5-7.2 eV, and 3.2-8 eV respectively. The present study endorses that the said compounds can be used in opto-electronic applications, for different energy ranges.

In this paper, we present the coordinate and the matrix representation of the icosahedron by using a direct and simple method of vector analysis.

The aim of this paper is to generate exact travelling wave solutions of the Harry-Dym equation through the methods of Adomian decomposition, He's variational iteration, direct integration, and power series. We show that the two later methods are more successful than the two former to obtain more solutions of the equation.