Differential cohomology of C (a)

Let be a finite dimensional real Lie algebra and ^* its dual. ^* is a Poisson manifold. Thus the space C^∞( ^*) of C^∞ functions on ^* has an associative and a Lie algebra structure. The problem of formal deformations of such a structure needs the determination of some cohomology groups of C^∞( ^*), considered as a module on itself for left multiplication or adjoint representation. We determine here these groups. The result is very similar to the case of C^∞(W), where W is a symplectic manifold except for the Lie algebras h_r × ^m, direct products of Heisenberg and abelian Lie algebras.     

Double quantization of CP type orbits by generalized Verma modules

It is known that symmetric orbits in g^* for any simple Lie algebra g are equipped with a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the reduced Sklyanin bracket associated to the “canonical” R-matrix. We realize quantization of the Poisson pencil CPⁿ type orbits (i.e. orbits in sl(n + 1)^* whose real compact form is CPⁿ) by means of q-deformed Verma modules.     

Calogero-Moser and Toda systems for twisted and untwisted affine Lie algebras

The elliptic Calogero-Moser Hamiltonian and Lax pair associated with a general simple Lie algebra G are shown to scale to the (affine) Toda Hamiltonian and Lax pair. The limit consists in taking the elliptic modulus τ and the Calogero-Moser couplings m to infinity, while keeping fixed the combination M = m e^iδθτ for some exponent δ. Critical scaling limits arise when 1/δ equals the Coxeter number or the dual Coxeter number for the untwisted and twisted Calogero-Moser systems respectively; the limit consists then of the Toda system for the affine Lie algebras G⁽¹⁾ and (G⁽¹⁾)^V. The limits of the untwisted or twisted Calogero-Moser system, for δ less than these critical values, but non-zero, consists of the ordinary Toda system, while for δ = 0, it consists of the trigonometric Calogero-Moser systems for the algebras G and G^V respectively.     

Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

Using the bosonic numerical renormalization group method, we studied the equilibrium dynamical correlation function C(ω) of the spin operator σ_z for the biased sub-Ohmic spin-boson model. The small-ω behavior C(ω) ∝ω~s is found to be universal and independent of the bias ε and the coupling strength α(except at the quantum critical point α = αc and ε = 0). Our NRG data also show C(ω) ∝χ~2ω~s for a wide range of parameters, including the biased strong coupling regime(ε = 0 and α α_c), supporting the general validity of the Shiba relation. Close to the quantum critical point αc,the dependence of C(ω) on α and ε is understood in terms of the competition between ε and the crossover energy scale ω_0~*of the unbiased case. C(ω) is stable with respect to ε for ε《ε~*. For ε》ε~*, it is suppressed by ε in the low frequency regime. We establish that ε~*∝(ω_0~*)~(1/θ)holds for all sub-Ohmic regime 0≤s 1, with θ = 2/(3s) for 0 s≤1/2 and θ = 2/(1 + s) for 1/2 s 1. The variation of C(ω) with α and ε is summarized into a crossover phase diagram on the α–ε plane.     

Exact Solutions of the Morse-like Potential,Step-Up and Step-Down Operators via Laplace Transform Approach

We intend to realize the step-up and step-down operators of the potential V (x) = V₁ e ^2βx + V₂ e ^βx. It is found that these operators satisfy the commutation relations for the SU(2) group. We find the eigenfunctions and the eigenvalues of the potential by using the Laplace transform approach to study the Lie algebra satisfied the ladder operators of the potential under consideration. Our results are similar to the ones obtained for the Morse potential (β → -β).     

Decay Analysis of Ge Isotopes Formed in Reactions Induced by Tightly and Loosely Bound Projectiles

The dynamical cluster-decay model (DCM) is employed to investigate the decay of ^68,70Ge^* compound nuclei formed respectively via tightly (⁴He) and loosely (⁶He) bound projectiles, using ⁶⁴Zn target. The study is carried out over a wide energy range (E_c.m.~5 MeV to 16 MeV) by including the quadrupole deformations (β2i) and optimum orientations (θ_i^opt) of the decaying fragments. The fusion cross-sections, obtained by adding various evaporation channels show nice agreement with the experimental data for ⁴He+⁶⁴Zn reaction. The contribution from competing compound inelastic scattering channel is also analyzed particularly for ⁶⁸Ge^* nucleus at above barrier energies. On the other hand, the decrement in the fusion cross-sections of ⁷⁰Ge^* nuclear system is addressed by presuming that ⁶⁵Zn ER is formed via two different modes:(i) the αn evaporation of ⁷⁰Ge^* nucleus, and (ii) 1n-evaporation of ⁶⁶Zn^* nuclear system, formed via breakup and 2n-transfer channels due to halo structure of the ⁶He projectile. Besides this, the suppression in 2np evaporation cross-sections suggests the contribution of another breakup and transfer process of ⁶He i.e. ⁴He+⁶⁴Zn. The contribution of breakup+transfer channels for ⁶He+⁶⁴Zn reaction is duly addressed by applying relevant energy corrections due to the breakup of " ⁶He" projectile into 2n and ⁴He. In addition to this, the barrier lowering, angular momentum and energy dependence effects are also explored in view of the dynamics of chosen reactions.     

层流圆管潜射流生成蘑菇形涡结构特性数值研究

基于不可压Navier-Stokes方程, 采用计算流体力学方法, 数值模拟与分析了层流圆管潜射流在密度均匀黏性流体中的演化机理及其表现特征, 定量研究了蘑菇形涡结构无量纲射流长度L^*、螺旋型涡环半径R^*及其包络外形长度d^*等几 何特征参数随无量纲时间t^*的变化规律. 数值结果表明, 蘑菇形涡结构的形成与演化过程可分为三个不同的阶段: 启动阶段、发展阶段和衰退阶段. 在启动阶段, L^*和d^*随t^* 线性变化, 而R^*则近似为一个常数; 在发展阶段, 蘑菇形涡结构的演化具有自相似性, L^*, R^*和d^*与t^*1/2均为同一正比关系, 而且雷诺数和无量纲射流时间不影响该正比关系; 在衰退阶段, L^* 和R^* 正比于t^*1/5, 而d^*则近似为一个常数. 此外, 还对蘑菇形涡结构二次回流点、 动量源作用中心及其几何中心的速度变化规律、垂向涡量分布特征和 涡量-流函数关系进行了分析. 关键词： 圆管潜射流 蘑菇形涡结构 演化机理     

Symplectic Geometry,Hopf Algebraic Structures of Classical and Quantum q-Deformations of SU(2) Algebra

By deforming the symplectic structure on S², we get the q-deformation of SU(2) algebra at classical level, SU_q,h→0(2), in a Hamiltonian approach. Furthermore, we construct a set of operators on the line bundle over the deformed symplectic manifo1d.S_q² such that they form SU_q,h→0(2) in Lie brackets and set up a nontrivial Hopf algebra with a parameter q only in such a classical Hamiltonian system. We also show that the deformations from S_q² to S_q² are a set of quasiconformal transformations. The quantization via geometric approach of the system gives rise to the quantum q-deformed algebra SU_q,h(2), wnich has a Hopf algebraic structure with two independent parameters q and h.     

The Three-Pion Decays of the a1(1260)

We investigate the decay of a₁⁺ (1260)→π⁺π⁺π^- with the assumption that the a₁(1260) is dynamically generated from the coupled channel ρπ and KK^* interactions. In addition to the tree level diagrams that proceed via a₁⁺ (1260)→ρ⁰π⁺→π⁺π⁺π^-, we take into account also the final state interactions of ππ→ππ and KK→ππ. We calculate the invariant π⁺π^- mass distribution and also the total decay width of a₁⁺ (1260)→π⁺π⁺π^- as a function of the mass of a₁(1260). The calculated total decay width of a₁(1260) is significantly different from other model calculations and tied to the dynamical nature of the a₁(1260) resonance. The future experimental observations could test of model calculations and would provide vary valuable information on the relevance of the ρπ component in the a₁(1260) wave function.     

Center for Elliptic Quantum Group Eτ,η(sln)

We give the center of the elliptic quantum group in general cases. Based on the dynamical Yang-Baxter relation and the fusion method, we prove that the center commutes with all generators of the elliptic quantum group. Then for a kind of assumed form of these generators, we find that the coefficients of these generators form a new type of closed algebra. We also give the center for the algebra.     

Strong Decays of Charm Mesons D1*(2680), D3*(2760), D2*(3000)

In this article, we assign the higher charm mesons D₁^*(2680), D₃^*(2760) and D₂^*(3000) to be the 2S 1^-, 1D 3^- and 1F 2⁺ states, respectively, and study the two-body strong decays to the ground state charm mesons and light pseudoscalar mesons with the heavy meson effective theory. We obtain the ratios among the strong decays, which can be confronted to the experimental data in the future and shed light on the nature of those higher charm mesons.     

Structure Evolution in the Even-Even 124-134Xe with IBM2

We have investigated the structure evolution of the ^124-134Xe isotopic chain in the framework of the proton-neutron interacting model IBM2. The positive parity spectra of the ground state, quasi-β and quasi-γ bands are reproduced well. The staggering in ^124-130Xe are almost completely removed and the γ band agree well with the experiment data, even for the high-spin quasi-γ states. The key quantities of the collective structure evolution, including level energies, the B(E2) transition branching ratios, and the M1 excitations to 1₁⁺ mixer-symmetry states are analyzed by comparing with the experimental data. The parameters for representation of the O_πν(6) and SU_πν^*(3) features in isotopes are examined. Both experimental data and theoretical results show that the shape phase transition of ^124-134Xe isotopic chain is from the SU_πν^*(3) (triaxial rotation) to the U_πν(5) (vibration motion) with a considerable constituent of the O_πν(6) symmetry (γ-unstable rotation), where the shape phase transition rapidly takes place between the neutron number N = 76 and N = 78.     

A Method for Obtaining Integrable Couplings

By making use of the vector product in R³, a commuting operation is introduced so that R³ becomes a Lie algebra. The resulting loop algebra \tilde R³ is presented, from which the well-known AKNS hierarchy is produced. Again via applying the superposition of the commuting operations of the Lie algebra, a commuting operation in R⁶ is constructed so that R⁶ becomes a Lie algebra. Thanks to the corresponding loop algebra \tilde R³ of the Lie algebra R³, the integrable coupling of the AKNS system is obtained. The method presented in this paper is rather simple and can be used to work out integrable coupling systems of the other known integrable hierarchies of soliton equations.     

Gauge Theory of the Generalized Symmetry on the Torus Membrane

The SDIFF(T²)_local-generalized Kac-Moody \hat G(T²) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the SDIFF(T²)_local algebra and the generalized Kac-Moody algebra \hat g(T²). In this paper, we construct the linearly realized gauge theory of the SDIFF(T²)_local-generalized Kac-Moody \hat G(T²) symmetry.     

Anomalous action in gauge invariant, nonlocal, dynamical quark model

Anomalous sector of chiral Lagrangian is calculated in a gauge invariant, nonlocal, dynamical quark model. The Wess–Zumino term is proved coming from two kinds of sources, one is independent of and another dependent on dynamical quark self energy Σ(k²). p⁶ and more higher order anomalous sectors come only from Σ(k²) dependent source. After some cancellation, standard Wess–Zumino action is obtained.     

The ΔNγ electromagnetic transition form factors GM(q) and GE(q)

A parameter-free, nonperturbative calculation of the ΔNγ electromagnetic transition amplitudes GM*(q2), GE*(q2), and the resonant multipole ratio REM(q2)≡E1+3/2(q2)/M1+3/2(q2) is performed in terms of the well-known nucleon isovector Sachs form factor GMV. Our methods are fully relativistic with conservation of the electromagnetic current guaranteed. We find that GM*(q2) decreases more rapidly than the nucleon dipole form factor when −q21 GeV2/c2 and that REM(q2) remains small even for very high four-momentum transfer implying that the perturbative QCD prediction REM(q2)→1 is purely asymptotic and is valid only for extremely high |q2|.     

矢量介子及其激发态的讨论

在Regge唯象下, 首先研究自旋-宇称多重态中六个介子质量间的关系式. 运用验证后的关系式, 重点计算基态矢量介子多重态(1³S₁)中尚未观测到的双重粲-底介子 B_c^*的质量. 还计算了径向激发态2³S₁多重态的介子质量和轨道激发态1³G₅介子九重态的质量. 根据计算结果结合实验数据和其他理论进行讨论, 建议在6355 MeV附近寻找和研究 B_c^*介子, 将 D(2600)和 D_s1(2700)分别作为主要成分为 nc(2³S₁)和 sc(2³S₁)的态进行研究; 分别在5812, 5917, 6896 MeV附近寻找矢量介子第一径向激发态 B^*(2S), B_s^*(2S)和 B_c^*(2S). 建议将 ω₅(2250)安排在1³G₅介子九重态的同位旋标量态, 实验上在2259 MeV附近进一步研究 ρ₅(2350)的性质, 在2438 MeV附近寻找和研究 φ₅(1³G₅). 研究结果对于相关介子的自旋-宇称安排和通过实 验寻找新的介子激发态具有重要的参考价值. 关键词： Regge唯象 矢量介子 质量谱     

Remarks on stochastic non-linear birth and death models

The first part of this paper is an attempt to formulate and motivate additional work on the important problem of obtaining global bounds applicable to the controlled truncation of the paper relates specifically to the linear birth, quadratic death model. Asymptotic results are given for the first finite difference ΔT_m where T_m is the exactly known mean time to extinction starting from state m (m= 0,1,…). These results are in terms of the environmental carrying capacity n^* taken to be large. For m near zero ΔT_me^n*/(n^*)²; whereas, for m near n^*ΔT_m ≈ (π/2)^1/2/(n^*)^3/2. This indicates the vastly different time scales in those two regions of state space - with considerably slower action near extinction than near n^*.     

CHClF2在强红外激光作用下C2*d3Пg态的形成机制

用TEACO₂激光辐照CHCIF₂分子生成电子激发态C₂^*自由基,观察到斯旺带系的六个谱带。本文根据C₂分子态位能曲线的特点,提出C₂^*d³Π_g态的形成机制。C₂是少数较特殊的分子之一,其激发态b³Σ_g^-与第一激发态a关键词：