Superintegrability on sl(2)-coalgebra spaces

A recently introduced set of N-dimensional quasi-maximally superintegrable Hamiltonian systems describing geodesic motions that can be used to generate “dynamically” a large family of curved spaces is revisited. From an algebraic viewpoint, such spaces are obtained through kinetic energy Hamiltonians defined on either the sl(2) Poisson coalgebra or a quantum deformation of it. Certain potentials on these spaces and endowed with the same underlying coalgebra symmetry have also been introduced in such a way that the superintegrability properties of the full system are preserved. Several new N = 2 examples of this construction are explicitly given, and specific Hamiltonians leading to spaces of nonconstant curvature are emphasized. The text was submitted by the authors in English.     

Superintegrable systems on spaces of constant curvature

Construction and classification of two-dimensional (2D) superintegrable systems (i.e. systems admitting, in addition to two global integrals of motion guaranteeing the Liouville integrability, the third global and independent one) defined on 2D spaces of constant curvature and separable in the so-called geodesic polar coordinates are presented. The method proposed is applicable to any value of curvature including the case of Euclidean plane, sphere and hyperbolic plane. The main result is a generalization of Bertrand’s theorem on 2D spaces of constant curvature and covers most of the known separable and superintegrable models on such spaces (in particular, the so-called Tremblay–Turbiner–Winternitz (TTW) and Post–Winternitz (PW) models which have recently attracted some interest).     

Proof of a decomposition theorem for symmetric tensors on spaces with constant curvature

In cosmological perturbation theory a first major step consists in the decomposition of the various perturbation amplitudes into scalar, vector and tensor perturbations, which mutually decouple. In performing this decomposition one uses – beside the Hodge decomposition for one‐forms – an analogous decomposition of symmetric tensor fields of second rank on Riemannian manifolds with constant curvature. While the uniqueness of such a decomposition follows from Gauss' theorem, a rigorous existence proof is not obvious. In this note we establish this for smooth tensor fields, by making use of some important results for linear elliptic differential equations.     

Finite-dimensional representations of U q (osp(1/2n)) and its connection with quantum so(2n+1)

It is shown that the quantum supergroup U _q (osp(1/2_n)) is essentially isomorphic to the quantum group U _-q (so(2n+1)) restricted to tensorial representations. This renders it straightforward to classify all the finite-dimensional irreducible representations of U _q (osp(1/2n)) at generic q. In particular, it is proved that at generic q, every-dimensional irrep of this quantum supergroup is a deformation of an osp(1/2n) irrep, and all the finite-dimensional representations are completely reducible.     

New integrable (2+1)- and (3+1)-dimensional sinh-Gordon equations with constant and time-dependent coefficients

In this work, we mainly address two new integrable (2+1)- and (3+1)-dimensional sinh-Gordon equations, which naturally appear in surface theory and fluid dynamics. The first equation includes constant coefficients, while the other is characterized with time-dependent coefficients. It is of further value to investigate the integrability of each model. This study puts forward a Painlevé test to reveal the Painlevé integrability. We show that the first equation passes the Painlevé test to confirm its integrability. However, the compatibility conditions of the second model with time-dependent coefficients provides the relation between these coefficients to ensure its integrability. We show that the dispersion relations of the two equations are distinct, whereas the phase shifts are identical. We apply the simplified Hirota's method where four sets of multiple soliton are derived for these equations.     

Two-dimensional observation of N2+ and N+ scattering patterns from Cu(001)

Low-energy (<1 keV) N₂⁺ and N⁺ ion scattering from the Cu(001) surface was directly observed by using a two-dimensional detection system. The two-dimensional pattern of the scattered ions changed when the primary ion energy was increased from 200 to 600 eV. The scattering peak shifted toward the [110] azimuth, to which the incident plane was not parallel, above 600 eV. The difference of ion-survival probabilities between N₂⁺ and N⁺ was discussed from the full width at half maximum of the angular distribution of scattered ions.     

5 kW泵浦增益一体化复合功能激光光纤

5 kW泵浦增益一体化复合功能激光光纤林傲祥, 湛 欢 , 黄志华, 王瑜英, 王小龙, 倪 力, 唐 选, 梁小宝, 彭 昆, 高 聪 , 王 祯 , 贾兆年, 向小雨, 尤阿妮, 林宏奂, 赵 磊, 王建军, 景 峰     

5 kW泵浦增益一体化复合功能激光光纤

5 kW泵浦增益一体化复合功能激光光纤 林傲祥, 湛 欢 , 黄志华, 王瑜英, 王小龙, 倪 力, 唐 选, 梁小宝, 彭 昆, 高 聪 , 王 祯 , 贾兆年, 向小雨, 尤阿妮, 林宏奂, 赵 磊, 王建军, 景 峰     

Distribution of energy of solutions of the wave equation on singular spaces of constant curvature and on a homogeneous tree

In the paper, the Cauchy problem for the wave equation on singular spaces of constant curvature and on an infinite homogeneous tree is studied. Two singular spaces are considered: the first one consists of a three-dimensional Euclidean space to which a ray is glued, and the other is formed by two three-dimensional Euclidean spaces joined by a segment. The solution of the Cauchy problem for the wave equation on these objects is described and the behavior of the energy of a wave as time tends to infinity is studied.The Cauchy problem for the wave equation on an infinite homogeneous tree is also considered, where the matching conditions for the Laplace operator at the vertices are chosen in the form generalizing the Kirchhoff conditions. The spectrum of such an operator is found, and the solution of the Cauchy problem for the wave equation is described. The behavior of wave energy as time tends to infinity is also studied.     

Folded localized excitations of the (2+1)-dimensional (M+N)-component AKNS system

Starting from the standard truncated Painlevé expansion and a multilinear variable separation approach, a quite general variable separation solution of the (2+1)-dimensional (M+N)-component AKNS (Ablowitz–Kaup–Newell–Segur) system is derived. In addition to the single-valued localized coherent soliton excitations like dromions, breathers, instantons, peakons, and a previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is obtained by introducing some appropriate lower-dimensional multiple valued functions. The folded phenomenon is quite universal in the real natural world and possesses quite rich structures and abundant interaction properties.     

New Exact Solution of (N+1)-Dimensional Burgers System

In this letter, using a Bäcklund transformation and the new variable separation approach, we find a new general solution of the (N+1)-dimensional Burgers system. The form of the universal formula obtained from many (2+1)-dimensional system is extended.     

Thermal desorption of N2 from (N2 + O2) coadsorbed on polycrystalline rhenium surfaces

The coadsorption of ¹⁵N₂ and O₂ on polycrystalline rhenium filament has been studied by thermal desorption mass spectroscopy. The sample was exposed to a mixture of ¹⁵N₂ and O₂ with various concentrations of ¹⁵N₂ at room temperature. It is suggested that NO on Re at low coverage is dissociative and the bonding strength of nitrogen on Re is weakened by the coadsorption with oxygen atoms.     

Letter: Constraint Propagation in (N + 1)-Dimensional Space-Time

Higher dimensional space-time models provide us an alternative interpretation of nature, and give us different dynamical aspects than the traditional four-dimensional space-time models. Motivated by such recent interests, especially for future numerical research of higher-dimensional space-time, we study the dimensional dependence of constraint propagation behavior. The N+1 Arnowitt-Deser-Misner evolution equation has matter terms which depend on N, but the constraints and constraint propagation equations remain the same. This indicates that there would be problems with accuracy and stability when we directly apply the N+1 ADM formulation to numerical simulations as we have experienced in four-dimensional cases. However, we also conclude that previous efforts in re-formulating the Einstein equations can be applied if they are based on constraint propagation analysis.     

Baryons in chiral SU(N)—QCD on the light-cone in 1 + 1-dimensions

We demonstrate that using bosonization techniques in 1+1-dimensional QCD in the chiral limit a unique definition of baryons is possible for finiteN _c despite the fact that mesons, baryons and anti-baryons are massless. The definition which is based on the construction of an SU(2)-algebra provides the basis for a new approach to investigate hadronic properties in the strong coupling limit. It is used to study the Fock-state decomposition and structure functions of baryons for various finite values ofN _c . The results are discussed in comparison to similar calculations based on discretized lightcone quantization.     

Theoretical Study of the Collision-Induced Double Transition CO(2) (nu(3) = 1) + N(2) (nu(1) = 1) <-- CO(2) (nu(3) = 0) + N(2) (nu(1) = 0) at 296 K

A procedure is presented for the calculation of the double vibrational collision-induced absorption CO(2) (nu(3) = 1) + N(2) (nu(1) = 1) <-- CO(2) (nu(3) = 0) + N(2) (nu(1) = 0) on the basis of quantum lineshapes computed using an isotropic potential and dipole-induced dipole functions. The linestrengths and energies of the vibration-rotation transitions are treated explicitly for N(2), utilizing the HITRAN database for CO(2). The theoretical absorption profile is compared to recent experimental results. By narrowing the width of the individual lines contributing to the overall absorption profile relative to their values determined for N(2)-N(2) collision-induced absorption, excellent agreement between theory and experiment is obtained. Copyright 2000 Academic Press.     

Interaction between compacton and anticompacton,peakon and antipeakon in （2 ＋ 1）-dimensional spaces

Starting from the variable separation solution obtained by using the extended homogenous balance method, a class of novel localized coherent structures such as the multi-peakon－antipeakons solution and the multi-compacton－anticompactons solution of the (2+1)-dimensional dispersive long wave equation are found by selecting appropriate functions. These new structures exhibit some novel interaction features that are different from one of the known results. Their interaction behaviour is very similar to the completely elastic collisions between two classical particles.     

Quantization of a nonlinear oscillator as a model of the harmonic oscillator on spaces of constant curvature: One- and two-dimensional systems

The quantum version of a nonlinear oscillator, previously analyzed at the classical level, is studied first in one dimension and then in two dimensions. This is a problem of quantization of a system with position-dependent mass of the form m = (1 + λx ²)⁻¹ and with a λ-dependent nonpolynomial rational potential. The quantization procedure analyzes the existence of Killing vectors and makes use of an invariant measure. It is proved that this system can be considered as a model of the quantum harmonic oscillator on two-dimensional spaces of constant curvature. The text was submitted by the authors in English.