Invariant tensors for simple groups

The forms of the invariant primitive tensors for the simple Lie algebras A_l, B_l, C_l, and D_l are investigated. A new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology. For the A_l algebra it is explicitly shown that the generic forms of these tensors become zero except for the l primitive ones and that they give rise to the l primitive Casimir operators. Some recurrence and duality relations are given for the Lie algebra cocycles. Tables for the 3- and 5-cocycles for su(3) are su(4) are also provided. Finally, new relations involving the d and f su(n) tensors are given.     

Orbitally excited D and B mesons in the approach of the QCD string with quarks at the ends

In this Letter we discuss the masses and the splittings of 1^2S+1P_J states in the spectrum of D and B mesons, as they appear in the approach of the QCD string with quarks at the ends. We find good agreement of our predictions with those of other QCD-motivated models as well as with the lattice and experimental data, including recent experimental results. We discuss the ordering pattern for P levels in D- and B-mesonic spectrum.     

Scaling properties of resonant electron transfer in ion—metal-surface interactions

Scaling properties of resonant electron transfer in the interaction of atoms and positive ions with metal surfaces are revealed by examining the dependence of numerically calculated transition matrix elements and (first-order) transition rates upon the scaled ion-surface distance D = D/D_n, where D_n is the classical threshold distance for electron transfer involving ionic stat principal quantum number n. For zero orbital angular momentum and fixed energy of the ionic states, the n-dependence of the rates at D = 1 is found to approach, in the large-n limit, a simple power law. A scaling law is established that connects, in the range D 1, transition rates for arbitrary (large) principal quantum numbers.     

1/f-type fluctuation of electron transmission in one-dimensional disordered systems

A universal feature of 1/f-type fluctuation is numerically observed in the system-size n dependence of the transmission amplitude t_n in various one-dimensional disordered systems. The power spectrum P(f) of the transmission coefficient T(n)=|t_n|² exhibits the power law of 1/f², irrespective to the type of disorder of the system whether it is of short-range or of long-range correlation. That of the phase θ_t(n) of t_n also does the universal power law of 1/f^1.4.     

The Arnol''d cat: Failure of the correspondence principle

The classical Hamiltonian H = p²/2m + ε(q²/2)Σδ[s-(t/T)] has an integrable mapping of the plane, [q_n+1, p_n+1]= [q_n+1+p_n, q_n+2p_n], as its equations of motion. But then by introducing periodic boundary conditions via (mod 1) applied to both q and p variables, the equations of motion become the Arnol'd cat map, [q_n+1, p_n+1] = [q_n + p_n, q_n + 2p_n], (mod 1), revealing it to be one of the simplest fully chaotic systems which can be derived from a Hamiltonian and analyzed. Consequently, we here quantize the Arnol'd cat and examine its quantum motion for signs of chaos using algorithmic complexity as the litmus. Our analysis reveals that the quantum cat is not chaotic in the deep quantum domain nor does it become chaotic in the classical limit as required by the correspondence principle. We therefore conclude that the correspondence principle, as defined herein, fails for the quantum Arnol'd cat.     

Precision flavour physics and supersymmetry

We review the salient features of a comparative study of the profile of the CKM unitarity triangle, and the resulting CP-violating phases , β and γ in B decays, in the standard model and in several variants of the minimal supersymmetric standard model (MSSM), reported recently by us. These theories are characterized by a single phase in the quark flavour mixing matrix and give rise to well-defined contributions in the flavour-changing-neutral-current transitions in K and B decays. We analyse the supersymmetric contributions to the mass differences in the B_d⁰– and B_s⁰– systems, ΔM_d and ΔM_s, respectively, and to the CP-violating quantity || in K decays. Our analysis shows that the predicted ranges of β in the standard model and in MSSM models are very similar. However, precise measurements at B-factories and hadron machines may be able to distinguish these theories in terms of the other two CP-violating phases and γ.     

Synthesis and characterization of HgBa2Can−1CunO2n+2+δ (n = 1, 2, and 3)

We have successfully prepared the first three members of the mercury-based superconducting compounds Hg--- Ba₂Ca_n−1Cu_nO_2n+2+δ, namely Hg---1201, Hg---1212 and Hg---1223 with high purity and very good quality. T he influence of the synthesis parameters is studied in detail. Using the sealed quartz tube method, very simple procedures are found to ensure a 100% reproducibility of nearly 100% pure Hg---1201 and 85–90% Hg---1212 and Hg---1223. Oxygen annealing of the sample Hg---1201 at 300°C for 18 h results in an enhancement of its critical temperature up to 97 K. The symmetry of the first and second members is tetragonal with lattice parameters a = 3.8831 (1) Å, C = 9.5357 (2) Å, and A = 3.8624 (1) Å, C = 12.7045 (2) Å, respectively. X-ray diffraction lines of Hg---1223 can be indexed in a tetragonal cell with a = 3.8564 (1) Å and C = 15.8564 (9) Å as well as in an orthorhombic cell with lattice parameters a = 5.4537 (1) Å, B = 5.4247 (1) Å, and C = 15.8505 (7) Å.     

Projective and affine connections on S and integrable systems

It is known that the Korteweg–de Vries (KdV) equation is a geodesic flow of an L² metric on the Bott–Virasoro group. This can also be interpreted as a flow on the space of projective connections on S¹. The space of differential operators Δ⁽ⁿ⁾=∂ⁿ+u₂∂ⁿ⁻²++u_n form the space of extended or generalized projective connections. If a projective connection is factorizable Δ⁽ⁿ⁾=(∂−((n+1)/2−1)p₁)(∂+(n−1)/2p_n) with respect to quasi primary fields p_i’s, then these fields satisfy ∑_i=1ⁿ((n+1)/2−i)p_i=0. In this paper we discuss the factorization of projective connection in terms of affine connections. It is shown that the Burgers equation and derivative non-linear Schrödinger (DNLS) equation or the Kaup–Newell equation is the Euler–Arnold flow on the space of affine connections.     

A new upper bound formula for the ground state energies of N-boson systems

The energy E_N of an N-body system of pairwise interacting bosons is shown to satisfy the inequality, E_N < [N(N − 1)/n(n − 1)] E_n, where N > n 2. This inequality generalizes the Bruch-Sawada result, E₃ < 3E₂, and is superior in its predictive ability to Lim et al.'s .     

Existence and stability of propagating fronts for an autocatalytic reaction-diffusion system

We study a one-dimensional reaction-diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic (A + B → 2B) and a cubic (A + 2B → 3B) autocatalysis. The parameters of this system are in the ratio D = D_B/D_A of the diffusion constants of the reactant A and the autocatalyst B, and the relative activity k of the cubic reaction. First, for all values of D > 0 and k ≥ 0, we prove the existence of a family of propagating fronts (or travelling waves) describing the advance of the reaction. In particular, in the quadratic case k = 0, we recover the results of Billingham and Needham [Phil. Trans. R. Soc. London A 334 (1991) 1–24]. Then, if D is close to 1 and k is sufficiently small, we prove using energy functionals that these propagating fronts are stable against small perturbations in exponentially weighted Sobolev spaces. This extends part of the results that are known for the scalar equation to which our system reduces when D = 1.     

Crystal structures of stage-n iodine-intercalated compounds IBi2nSr2nCanCu2nOx

The crystal structure of stage-3 iodine-intercalated superconducting IBi₆Sr₆Ca₃Cu₆O_x has been determined by transmission electron microscopy to belong to the space group Pma2 with lattice parameters a=5.4Å, B=5.4Å and C=49.4Å. Ioidine atoms intercalated between every three Bi---O bilayers expand the distance between the Bi---O layers by 3.6Å and alter the atomic stacking across Bi---O layers from the staggered configuration characteristic of host superconducting Bi₂Sr₂CaCu₂O_x to an aligned configuration characteristic of stage-1 iodine-intercalated superconducting IBi₂Sr₂CaCu₂O_x. Higher-stage intercalation has also been observed as stacking faults which predominantly contain both stage-2 and stage-3 phases. The space groups and c-axis dimensions of the higher-stage phases have been deduced to be Pma2 with c=3.6+15.3n Å when stage number n is odd, and Bbmb with c=2(3.6+15.3n) Å when n is even.     

MC与$lt;i$gt;M$lt;/i$gt;$lt;sub$gt;$lt;i$gt;n$lt;/i$gt;+1$lt;/sub$gt;$lt;i$gt;AC$lt;/i$gt;$lt;sub$gt;$lt;i$gt;n$lt;/i$gt;$lt;/sub$gt;稳定性与电子特征的第一性原理研究

研究MC与M_n+1AC_n(M=Sc, Ti, V, Cr, Mn; A=Al, Si, P, S; n=1, 2, 3)结构的稳定性与电子特征有利于探究三元层状结构M_n+1AC_n稳定性的内在原因和设计新型M_n+1AC_n结构. 第一性原理计算研究表明, M-3d与C-2p轨道间的电子转移对MC与M_n+1AC_n 的形成焓有较大影响. 供电子能力较强的前过渡金属可以形成稳定的MC结构. 计算结果显示, MC结构是缺电子体系, 其趋向于与具有一定供电子能力的MA结构结合形成M_n+1AC_n. 与M₂PC和M₂SC 相比, M₂AlC和M₂SiC可以更为容易地被分离成二维 M₂C结构. 关键词： MAX相结构 第一性原理 电子结构 过渡金属碳化物     

Semileptonic decay of B-meson into D and the Bjorken sum rule

We study the semileptonic branching fraction of the B-meson into the higher resonance of the charmed meson D^** by using the Bjorken sum rule and the heavy quark effective theory (HQET). This sum rule and the current experiment of the B-meson semileptonic decay into D and D^* predict that the branching ratio D^**lν_l is about 1.7%. This predicted value is larger than the value obtained by various models.     

Entropy of planar random surfaces on the lattice

We study planar random surfaces on a hypercubic lattice in two and three dimensions by Monte Carlo techniques. Our data are consistent with the formula n₀(A;C) A^b₀A, where n₀(A;C) is the number of planar random surfaces with area A and boundary C. We find b₀ = −1.4 ± 0.2, = 5.31 ± 0.03 (for d = 2) and b₀ = −1.5 ± 0.2, = 7.13 ± 0.05 (for d = 3). The values of b₀ disagree with those obtained from the Polyakov string model.     

What can we learn from B→DsKπ, Bd→DsKπ and Bd→DsK decays?

We study the nonresonant three-body decays of B⁺→D^(*)−_sK⁺π⁺ and B_d→D_s^(*)−K⁰π⁺. We find that these decays can provide the information on the time-like form factors of D^(*)_sK. We also explicitly investigate B_d→D_s^(*)−K^*+ decays by discriminating the nonresonant contributions with the unknown D^(*)_s wave functions being fixed by the measured mode of B_d→D_s⁻K⁺.     

Mo-SiO2-C3H6催化反应体系的ESR动态表征

文章考察了Mo-SiO₂催化剂体系在丙烯歧化反应过程中的动态ESR波谱,发现在催化歧化反应过程中有两种Mo⁵⁺顺磁中心,一种为扰动八面体配位,g_||=1.89,g_⊥=1.94;另一种为扰动四棱锥配位,g_||=1.86,g_⊥=1.95。测得同位素^95,97Mo⁵⁺的各向异性超精细耦合常数A_||=90.3×10^-4cm^-1,A_⊥=44.8×10^-4cm^-1;观测到反应产生的积炭信号,g≈2.0O₂;氧阴离子自由基信号g₁=2.018,g₂=2.011,g₃=2.005。用LCAO-MO理论对上述Mo⁵⁺的ESR波谱进行计算,求得分子轨道系数,发现并总结出△g_||/△g_⊥与△g成直线关系,并建议用△g_||/△g_⊥=4(△E(B₂→E))/(△E(B₂→B₁)(β₁/ε)²之比值作为衡量C_4v扰动程度的尺度。     

Study of the magnetic properties of single-crystal Ba0.6K0.4BiO3

The magnetic properties of single-crystal Ba_0.6K_0.4BiO₃ were studied. The results show that this isotropic superconductor (cubic structure with T_c ≈ 32 K) exhibits irreversibility and relaxation properties similar to those observed in the layered, high temperature superconductors. For fields above 0.1 T, an irreversibility line B_irr = B_irr (0) (1 − t)ⁿ with n = 3/2 and B_irr (0) = 20 T is observed. The comparison among several superconducting systems with different anisotropies suggests that the irreversibility line is unlikely to be the melting line for the YBa₂Cu₃O_7−δ.     

Nonergodicity and dynamical approach to the anharmonic oscillator

General lower bounds for the time average C^AA(∞)≡lim_T→∞(1/T)∝^T₀ C^AA(t) dt of the correlation C^AA(t)≡A(t)A(0)−A² of an arbitrary variable A are derived, which depend only on the temperature derivatives of the canonical averages of A and the Hamiltonian of the system. The bounds may be used to give good estimations for C^AA(∞) which is different from zero when A is nonergodic. It is important to take care of these terms when dynamical theories made for interacting systems are applied to isolated systems. We show explicitely that our recently developed dynamical approach to phonon systems with quartic anharmonicity yields excellent results for the corresponding isolated system, the anharmonic single well oscillator, when nonvanishing time averages are taken into account.     

Mn(SiO2)3(M=Fe,Co,Ni;n=1-3)团簇的几何结构、光电性质及磁性

基于密度泛函理论中的广义梯度近似系统研究M_n(SiO₂)₃(M=Fe,Co,Ni;n=1-3)团簇的几何结构、光电性质和磁学性质.结果表明:Fe,Co原子相对于Ni原子更易于在(SiO₂)₃团簇上聚集;通过分析团簇的分裂途径及其产物,发现稳定性较好的氧化硅是一种很好的用于负载过渡金属"岛膜"的载体材料;M_n(SiO₂)₃团簇的能隙恰好位于近红外光谱范围内.通过磁性分析发现,该复合团簇的磁矩主要局域在过渡金属原子周围,而且,Fe₂(SiO₂)₃和Co₃(SiO₂)₃具有相对较大的磁矩,这主要源于过渡金属原子的d轨道间相互耦合.能隙和磁性两方面性质进一步肯定了二氧化硅磁性复合材料在医学界被用作光动力靶向治疗的可观前景.     

Deformed traces and covariant quantum algebras for quantum groups GLqp(2) and GLqp (1¦1)

The q-deformed traces and orbits for the two parametric quantum groups GL_qp(2) and GL_qp(1¦1) are defined, they are subsequently used in the construction of q-orbit invariants for these groups. General qp-(super)oscillator commutation relations are obtained, which remain invariant under the coactions of groups GL_qp(2) and GL_qp(1¦1). The GL_qp(2)-covariant deformed algebra is deduced in terms of the bilinears of bosonic qp-oscillators, which turns out to be a central extension of the Witten-type deformation of sl(2) algebra. In the case of the supergroup GL_qp(1¦1), the corresponding covariant algebras contain the N = 2 supersymmetric quantum mechanical subalgebras.