Approximate solutions of Klein-Gordon equation with improved Manning-Rosen potential in D-dimensions using SUSYQM

In this paper, we present solutions of the Klein–Gordon equation for the improved Manning–Rosen potential for arbitrary l state in d-dimensions using the supersymmetric shape invariance method. We obtained the energy levels and the corresponding wave functions expressed in terms of Jacobi polynomial in a closed form for arbitrary l state. We also calculate the oscillator strength for the potential.     

Transmission time in the reflectionless complex potential

A phase time definition directly obtained from the Schr6dinger equation is used to investigate the time delay of a particle scattered by complex reflectionless potential. The artifacts introduced by truncating in the numerical simulation are clarified. The time delay of the transmitted wave packet is found to be equal to the reflection time of the truncated potential. Both time delays are the same as the traversal time in the free space, but shorter than the time taken by a classical particle to pass the same potential.     

Bound states of the Klein－Gordon and Dirac equation for scalar and vector pseudoharmonic oscillator potentials

The exact bound state solutions of the Klein－Gordon equation and Dirac equation with scalar and vector pseudoharmonic oscillator potentials are obtained in this paper. Furthermore, we have used the supersymmetric quantum mechanics, shape invariance and alternative method to obtain the required results.     

Supersymmetric Quantum Mechanics and SUSY Dependent SU（2） Symmetry for a Spin-1/2 Charged Particle in a Magnetic Field

We find that in a supersymmetric quantum mechanics （SUSY QM） system, in addition to supersymmetric algebra, an associated SU（2） algebra can be obtained by using semiunitary （SUT） operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z-axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SUτ（2） SUσ（2） symmetry in the context of the relativistic Pauli Hamilt onian squared. We show that there exists also an SU（2） symmetry associated with the supersvmmetrv of the Dirac particle.     

N = 4 supersymmetric quantum mechanics and its large order behaviour

A model of N = 4 supersymmetric quantum mechanics is shown to have a perturbative expansion for which the large order behaviour is - (3/2)ⁿn!(9/π + 5/n + …). In the space of the coupling constants the supersymmetric case is found to be the dividing point between two different types of large order behaviour. In this way the large order behaviour of supersymmetric theories is special.     

Supersymmetric Sawada-Kotera-Ramani Equation： Bilinear Approach

In this paper, using the Hirota＇s bilineax method, we consider the N = 1 supersymmetric Sawada-Kotera- Ramani equation and obtain the Bazcklund transformation of it. Its one- and two-supersoliton solutions axe obtained and N-supersoliton solutions for N ≥ 3 are given under the condition kiξj = kjξi.     

Influence of a phonon bath in a quantum dot cavity QED system:Dependence of the shape

We present a systematic analysis on the role of the quantum dot （QD） shape in the influence of the phonon bath on the dynamics of a QD cavity QED system. The spectral functions of the phonon bath in three representative QD shapes： spherical, ellipsoidal, and disk, are calculated from the carrier wave functions subjected to the confinement potential provided by the corresponding shape. The obtained spectral functions are used to calculate three main effects brought by the phonon bath, i.e., the coupling renormalization, the off-resonance assisted feeding rate and the pure dephasing rate. It is found that the spectral function of a disk QD has the widest distribution, hence the phonon bath in a disk QD can lead to the smallest renormalization factor, the largest dephasing rate in the short time domains（≤2 ps）, and the oft-resonance assisted feeding can support the widest detuning. Except for the pure dephasing rate in the long time domains, all the influences brought by the phonon bath show serious shape dependence.     

On two-point boundary correlations of the gl（1｜1） supersymmetric vertex model

The gl（1｜1） supersymmetric vertex model with domain wall boundary conditions （DWBC） on an N ×N square lattice is considered. We obtain the reduction formulae for the two-point boundary correlation functions of the model.     

A Note on Nonclassical Symmetries of a Class of Nonlinear Partial Differential Equations and Compatibility

The nonclassical symmetries of a class of nonlinear partial differential equations obtained by the compatibility method is investigated. We show the nonclassicaJ symmetries obtained in [J. Math. Anal. Appl. 289 （2004） 55, J. Math. Anal. Appl. 311 （2005） 479] are not all the nonclassical symmetries. Based on a new assume on the form of invariant surface condition, all the nonclassical symmetries for a class of nonlinear partial differential equations can be obtained through the compatibility method. The nonlinear Klein-Gordon equation and the Cahn-Hilliard equations all serve as examples showing the compatibility method leads quickly and easily to the determining equations for their all nonclassical symmetries for two equations.     

Asymptotic Iteration Method for Energies of Inversely Linear Potential with Spatially Dependent Mass

The bound-state solution of the position dependent mass Klein-Gordon equation including inversely linear potential is obtained within the framework of the asymptotic iteration method. The relation between the scalar and vector potentials is considered to S（x） = V（x）（β - 1）. In particular, it is shown that the corresponding method exactly reproduces the spectrum of linearly inversely potentials with spatially dependent mass.     

Supersymmetry and SWKB Approach to Dirac Equation with Hyperbolic Scarf Potential

By using the supersymmetric quantum mechanics and shape invariance concept, we study the Dirac equation with the hyperbolic Scarf potential and the exact energy spectrum is obtained. Also, we calculate the bound state energy eigenvalues by using the supersymmetric WKB approximation approach so that we get the same results.     

Supersymmetry in boundary integrable models

Quantum integrable models that possess N = 2 supersymmetry are investigated on the half-space. Conformal perturbation theory is used to identify some N = 2 supersymmetric boundary integrable models, and the effective boundary Landau-Ginzburg formulations are constructed. It is found that N = 2 supersymmetry largely determines the boundary action in terms of the bulk, and in particular, the boundary bosonic potential is |W|², where W is the bulk superpotential. Supersymmetry is also investigated using the affine quantum group symmetry of exact scattering matrices, and the affine quantum group symmetry of boundary reflection matrices is analyzed both for supersymmetric and more general models. Some N = 2 supersymmetry preserving boundary reflection matrices are given, and their connection with the boundary Landau-Ginzburg actions is discussed.     

Polynomial invariants for SU(2) monopoles

We present an explicit expression for the topological invariants associated to SU(2) monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding topological quantum field theory, and it turns out that they can be expressed in terms of Seiberg-Witten invariants. In this analysis we use recent exact results on the moduli space of vacua of the untwisted N = 1 and N = 2 supersymmetric counterparts of the topological quantum field theory under consideration, as well as on electric-magnetic duality for N = 2 supersymmetric gauge theories.     

Multisymplectic Pseudospectral Discretizations for （3＋1）-Dimensional Klein-Gordon Equation

We explore the multisymplectic Fourier pseudospectral discretizations for the （3＋1）-dimensional Klein- Gordon equation in this paper. The corresponding multisymplectic conservation laws are derived. Two kinds of explicit symplectic integrators in time are also presented.     

SUSY QCD Impact on Top-Pair Production Associated with a Z^0-Boson at a Photon-Photon Collider

The top-pair production in association with a Z^0-boson at a photon-photon collider is an important process in probing the coupling between top-quarks and vector boson and discovering the signature of possible new physics. We describe the impact of the complete supersymmetric QCD （SQCD） next-to-leading order （NLO） radiative corrections on this process at a polarized or unpolarized photon collider, and make a comparison between the effects of the SQCD and the standard model （SM） QCD. We investigate the dependence of the lowest-order （LO） and QCD NLO corrected cross sections in both the SM and minimal supersymmetric standard model （MSSM） on colliding energy √s in different polarized photon collision modes. The LO, SM NLO, and SQCD NLO corrected distributions of the invariant mass of tt^--pair and the transverse momenta of final Z^0-boson are presented. Our numerical results show that the pure SQCD effects in γγ →tt^- Z^0 process can be more significant in the ＋＋ polarized photon collision mode than in other collision modes, and the relative SQCD radiative correction in unpolarized photon collision mode varies from 32.09% to -1.89% when √s goes up from 500 GeV to 1.5 TeV.     

Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry

We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the superfield approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gauge-invariant methods for constructing the low-energy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of one-loop effective actions in N = 2 supersymmetric Yang–Mills theory with hypermultiplets and in N = 4 supersymmetric Yang–Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the low-energy limit in superstring theory is discussed.     

Rosen-Morse势阱中相对论粒子的束缚态

给出了具有Rosen-Morse型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 运用超对称量子力学和形不变性得到了束缚态能谱，通过变量代换求得波函数. 把上述方法推广到相对论量子力学. 关键词： Rosen-Morse势 Klein-Gordon方程 Dirac方程 束缚态     

An Efficient Scheme for Multiparty Multi-particle State Sharing

We present an efficient scheme for sharing an arbitrary m-qubit state with n agents. In our scheme, the sender Alice first shares m Bell states with the agent Bob, who is designated to recover the original m-qubit state. Furthermore, Alice introduces n- 1 auxiliary particles in the initial state ｜0）, applies Hadamard （H） gate and Controlled-Not （CNOT） gate operations on the particles, which make them entangled with one of m particle pairs in Bell states, and then sends them to the controllers （i.e., other n - 1 agents）, where each controller only holds one particle in hand. After Alice performing m Bell-basis measurements and each controller a single-particle measurement, the recover Bob can obtain the original unknown quantum state by applying the corresponding local unitary operations on his particles. Its intrinsic efficiency for qubits approaches 100%, and the total efficiency really approaches the maximal value.     

Metric of States

Metric of quantum states plays an important role in quantum information theory. In this letter, we find the deep connection between quantum logic theory and quantum information theory. Using the method of quantum logic, we can get a famous inequality in quantum information theory, and we answer a question raised by S. Gudder.     

Multiformity of Optical Quantum Coherence Systems with Y and Inverted Y-type Schemes

Y and inverted Y-type four-level schemes for optical quantum coherence systems, which may be intuitively considered to be very simple, have not been studied intensively till now. In this paper, we present the multiformity of these two types of schemes by considering that they can be classified into nine possible level styles as the second-order sub-schemes using laser fields. Further we point out the complexity of their more than one hundred realistic configurations as the third-order four-level sub-schemes that may appear in the optical quantum coherence experiments. Throughout this paper we review which configurations have been studied in some research aspects and which ones not, according to our knowledge, in order to be propitious to next steps of theoretical and experimental investigations, especially for applications in the fields of quantum optics, quantum information science, laser spectroscopy, and so on.