N = 4 Supersymmetric Morse Oscillator and Its Spectrum-Generating Algebra

In this paper N = 4 supersymmetry of generalized Morse oscillators in one dimension is studied. Both bound states and scattering states of its four superpartner Hamiltonians are analyzed by using unitary irreducible representations of the noncompact Lie algebra su(1,1). The spectrum-generating algebra governing the Hamiltonian of the N = 4 supersymmetric Morse oscillator is shown to be connected with the realization of Lie superalgebra osp(1,2)or B(0,1) in terms of the variables of a supersymmetric two-dimensional harmonic oscillator.     

AN IDEA OF IMPROVING INNER WHEEL DIFFERENCE PROBLEM OF SEMI-TRAILER TRUCK

基于降低货车内轮差安全隐患的考虑,根据已有的研究成果对半挂车内轮差问题改善方向提出设想,基于刚体运动学原理提出具体改进方案,导出转弯时半挂车运动轨迹方程,运用Matlab软件从理论上进行了验证。     

Beltrami—McKeon—Schubert Realizations of osp(1|4) Algebra and Possible Supersymmetric Kinematics

The possible supersymmetric kinematics are presented by the contraction method in different limits from Beltrami—McKeon—Schubert realizations of osp(1|4). The connections among the superalgebras are established. The comparison with the superalgebras contracted from Beltrami—Ivanov—Sorini realization is made.     

Eigenfunction statistics on quantum graphs

We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.     

Large bending behavior of creased paperboard. II. Structural analysis

The mechanics of a paradigmatic typical carton corner with five creases is analyzed theoretically, in closed form. A general kinematical analysis of the mechanism (in finite rotation) is presented, assuming the versor of the intermediate crease, s, as a 2-degree-of-freedom Lagrangian parameter. The rotation θ_c of the cth crease is derived, together with the existence domain and a discussion of the singular configurations.The actions, driving the carton during a prescribed quasi-static erection program, are derived in a very efficient manner using the Virtual Works Equation, taking into account a non-linear anholonomic bending constitutive law of the creased paperboard. In particular, the active and reactive components of the moment ?, driving s along its path, are identified. No resort to the tangent stiffness computation is required. Some numerical examples illustrate the rotation and the driving forces obtained for both monotone-loading and complex loading–unloading erection paths.The presented results, “exact” within the scope of the restrictive hypotheses assumed, may be used in a preliminary design approach as well as a benchmark for more realistic FEM or CAE simulators.     

Study on the Effects of the Light CP-odd Higgs via the Leptonic Decays of Pseudoscalar Mesons

To explain the anomalously large decay rate of Σ⁺→p+μ⁺μ^-, it was proposed that a new mechanism where a light CP-odd pseudoscalar boson of m_A1⁰=214.3 MeV makes a crucial contribution. Later, some authors have studied the transition π⁰→ e⁺e^- and r → γA₁⁰ in terms of the same mechanism and their result indicates that with the suggested mass one cannot fit the data. This discrepancy might be caused by experimental error of Σ⁺→ p+μ⁺μ^- because there were only a few events. Whether the mechanism is a reasonable one motivates us to investigate the transitions π⁰→ e⁺e^-;η(η')→ μ⁺μ^-; η_c→ μ⁺μ^-; η_b→τ⁺τ^- within the same framework. It is noted that for π⁰→ e⁺e^-, the standard model (SM) prediction is smaller than the data, whereas the experimental central value of η→μ⁺μ^- is also above the SM prediction. It means that there should be extra contributions from other mechanisms and the contribution of A₁⁰ may be a possible one. Theoretically calculating the branching ratios of the concerned modes, we would check if we can obtain a universal mass for A₁⁰ which reconcile the theoretical predictions and data for all the modes. Unfortunately, we find that it is impossible to have such a mass with the same coupling |gl|. Therefore we conclude that the phenomenology does not favor such a light A₁⁰, even though a small window is still open.     

Finite deformation analysis of slip-induced crystalline rotations during tensile and compressive tests on bcc iron crystals

This work compares slip-induced lattice rotations calculated from double-slip, finite-deformation analytical solutions to electron-back-scattering-diffraction (EBSD) rotation measurements from SEM in situ, room temperature straining of bcc iron crystals. The finite-deformation modelling assumes slip proportionality between the two dominant active systems. Four experimental cases from a recently published work (2015) are examined, two in axial tension and two in axial compression. They correspond to mixed double-slip on {110} and {112} planes, with slip on the latter in both ‘easy’ and ‘hard’ orientations. In the experiments, EBSD rotation measurements were made on three faces of the iron samples and the dominant active systems were identified from slip traces. Here the relative contributions of the two systems for the best match with available rotation data are determined for each case, and the results discussed in relation to initial shear stress and (probable) critical shear-strength ratios. The analyses provide insight into achievable accuracy in crystal-slip quantification, based on slip-trace observations and rotation measurements of a sample’s load and lateral axes, and some assessment of the relative hardening of active slip systems.     

Gravitational Waves,baryon asymmetry of the universe and electric dipole moment in the CP-violating NMSSM

In this work, we make the first study of electroweak baryogenesis(EWBG) based on the LHC data in the CP-violating next-to-minimal supersymmetric model(NMSSM) where a strongly first order electroweak phase transition(EWPT) is obtained in the general complex Higgs potential. With representative benchmark points which pass the current LEP and LHC constraints, we demonstrate the structure of EWPT for those points and how a strongly first order EWPT is obtained in the complex NMSSM where the resulting gravitational wave production properties are found to be within the reaches of future space-based interferometers like BBO and Ultimate-DECIGO. We further calculate the generated baryon asymmetries where the CP violating sources are(1): higgsino-singlino dominated,(2): higgsino-gaugino dominated or(3): from both sources. It is shown that all three representing scenarios could evade the strong constraints set by various electric dipole moments(EDM) searches where cancellations among the EDM contributions occur at the tree level(higgsino-singlino dominated) or loop level(higgsino-gaugino dominated).The 125 GeV SM like Higgs can be either the second lightest neutral Higgs H_2 or the third lightest neutral Higgs H_3. Finally, we comment on the future direct and indirect probe of CPV in the Higgs sector from the collider and EDM experiments.     

Verification of the spin-weighted spheroidal equation in the case of s=1

The spin-weighted spheroidal equation in the case of s = 1 is studied. By transforming the independent variables, we make it take the Schrdinger-like form. This Schrdinger-like equation is very interesting in itself. We investigate it by using super-symmetric quantum mechanics and obtain the ground eigenvalue and eigenfunction, which are consistent with the results previously obtained.     

Exploring sequential quantum adiabatic switching across supersymmetric partners for finding the eigenstates of a system

We demonstrate that one can exhaustively determine the n‐bound eigenstates of a Hamiltonian H by constructing a sequence of supersymmetric (SUSY) partner Hamiltonians and invoking a time‐dependent quantum adiabatic switching algorithm for passage from the ground state of one to the other. The ground states of the initial pair H⁽⁰⁾ and H⁽¹⁾ are constructed by solving the Riccati equation for the superpotential ?⁽⁰⁾ for H⁽⁰⁾ and adiabatically switching from the ground state Ψ of H⁽⁰⁾ to the ground state Ψ of H⁽¹⁾. The charge operator Q is then used to recover the first excited state Ψ of H⁽⁰⁾. The procedure is repeated for the ground states of SUSY pairs H^{(n + 1)} and H^{(n + 2)}, and appropriate charge operators lead to the excited states Ψ of H⁽⁰⁾ with , thereby exhausting the full eigenspectrum of H⁽⁰⁾. The workability of the proposed method is shown with several well‐known examples. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011