The algebraic Bethe ansatz for rational braid-monoid lattice models

In this paper we study isotropic integrable systems based on the braid-monoid algebra. These systems constitute a large family of rational multistate vertex models and are realized in terms of the B_n, C_nand D_n Lie algebra and by the superalgebra Osp(n||2m). We present a unified formulation of the quantum inverse scattering method for many of these lattice models. The appropriate fundamental commutation rules are found, allowing us to construct the eigenvectors and the eigenvaluesof the transfer matrix associated to the B_n, C_n, D_n, Osp(2nt-1||2), Osp(2||2nt-2), Osp(2nt-2||2) and Osp(1||2n) models. The corresponding Bethe ansatz equations can be formulated in terms of the root structure of the underlying algebra.     

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     

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.     

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.     

虚阴极产生微波的一些基本特性

用Vlasov-Poisson方程对相对论电子束在单板、双板间的传播过程进行了数值模拟,给出了单板模型空间电荷积累最大的位置,不同位置上的电流J、电子数密度n、电场E的振荡频率随入射电子数密度n₀、入射速度v₀的变化关系,双板模型空间电荷积累最大的位置,J、n、E的振荡频率随入射流J₀及两板间距离的变化关系。虚阴极位置的数值结果与稳态理论给出的结果相近,它的振荡频率符合经验公式(1~√2π)ω_peb。单板时入射电子数密度按速度服从高斯分布,能散△E_n/E_n < 10%时的数值结果给出与单能情况基本相同的结论。     

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 .     

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.     

Layer dependence of the superconducting transition temperature of HgBa2Can−1CunO2n+2+δ

High-pressure methods have been used to synthesize multiphase compositions in the Hg---12{n−1}n homologous series. The phase assemblages were examined by optical, electron diffraction and X-ray diffraction techniques, and their stoichiometries verified by electron microprobe. Transport and magnetic susceptibility measurements were combined with the results of the phase analysis to establish superconducting transition temperatures for both as-prepared and O₂- or Ar-annealed materials. It was found that the transition temperature peaks at T_c = 134 K for N = 3 and then decreases abruptly for n>4, reaching T_c<90 K for n7.     

Probing the isospin dependent in-medium nucleon–nucleon cross section by nucleon emissions

The effects of the symmetry potential and the isospin dependent in-medium nucleon–nucleon (NN) cross section on the number of proton(neutron) emissions N_p(N_n) are studied respectively within an isospin-dependent quantum molecular dynamics (IQMD) model. The isospin dependent in-medium NN cross section is found to have a strong influence on N_p(N_n) but N_p(N_n) is not sensitive to the symmetry potential for the neutron-deficient colliding system at relatively high energies. We propose to make use of the N_p(N_n) as a probe to extract information on the isospin dependent in-medium NN cross section.     

The quantum groups GLq(n) and Weyl-Heisenberg operators

It is shown that for deformation parameters q = 1, the bilinear product relations which define the quantum groups GL_q(n) can be recast as Weyl-Heisenberg relations, provided some invertibility conditions are met. Finite- and infinite-dimensional representations of GL_q(n) are then easily constructed, as shown in a few examples.     

Commutator representations of differential calculi on the quantum group SUq(2)

Let (Γ, d) be the 3D-calculus or the 4D_±-calculus on the quantum group SU_q (2). We describe all pairs (π, F) of a ^*-representation π of (SU_q(2)) and of a symmetric operator F on the representation space satisfying a technical condition concerning its domain such that there exist a homomorphism of first order differential calculi which maps dx into the commutator [iF, π(x)] for x ε (SU_q (2)). As an application commutator representations of the two-dimensional left-covariant calculus on Podles quantum 2-sphere S_qc² with c = 0 are given.     

具有Dzyaloshinskii-Moriya相互作用的XY模型的量子相干性

研究了具有Dzyaloshinskii-Moriya(DM)相互作用的一维横场XY自旋链的量子相变和量子相干性.采用约旦-维格纳变换严格求解了哈密顿量,并描绘了体系的关联函数和相图,相图包含反铁磁相、顺磁相和螺旋相.利用相对熵和Jensen-Shannon熵讨论了XY模型的量子相干性.研究发现,相对熵与Jensen-Shannon熵所表现的行为都可以很好地表征该模型的量子相变.非螺旋相中量子相干性不依赖DM相互作用,而在螺旋相DM相互作用对量子相干性有显著影响.此外,指出了在带有DM相互作用的这一类反射对称破缺体系中关联函数计算的常见问题.     

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.     

合金团簇(FeCr)n中的非共线磁序和自旋轨道耦合效应

利用密度泛函理论对合金团簇(FeCr)_n (n≤6)的几何结构、稳定性和磁性进行了系统的研究. 研究结果表明, 对n≤3的合金团簇, 其基态具有共线的反铁磁序; 而对于n≥4 的合金团簇, 其基态具有非共线磁序, 因此在n=4时体系发生了共线磁序向非共线磁序的“相变”. 此外, 虽然3d过渡金属原子中电子的自旋轨道耦合效应比较弱, 但计算结果表明对于某些小尺寸的合金团簇其轨道磁矩不能忽略. 对非共线磁性团簇的成键性质以及产生磁序“相变”的物理起源进行了详细讨论. 关键词： n合金团簇')" href="#">(FeCr)_n合金团簇 密度泛函理论 非共线磁序 自旋轨道耦合效应     

A generic intermittency model and its 1-D meta-map: Power laws, invariants and the succession of laminar sequences

Intermittent behaviour has been found in many systems able to switch between two different dynamic states, e.g. between long laminar phases and short chaotic bursts. Despite the apparently high-dimensional complexity, certain one-dimensional (1-D) maps are known to mimic properties of such dynamics. To these belongs the iterative map x_n+1,i = (x_n,i + (x_n,i)^z + ε) mod 1, giving rise to long laminar lengths. The statistics of the laminar lengths are of special interest.

Starting from this map, we are interested in the values of x_0,i which arise after passing through the modulo operation. These determine the laminar lengths uniquely. A 1-D meta-map x_0,i = f(x_0,i−1) is derived heuristically. It is used to calculate statistical properties of the laminar phases. Our results show an improvement in the behaviour of short and very long laminar phases as compared to earlier analytical results. Introducing the concept of the generic starting value, we find laminar phases not to be strictly independent of their predecessors.     

W-geometry from chiral embeddings

Recent work by Y. Matsuo and the present author is summarized. It is shown that, classically, the conformal Toda equations associated with the simple lie algebras A_n sl (n + 1) follow from the embedding of particular 2D surfaces in CPⁿ. Since these Toda theories provide Noether realizations of W-symmetries, this gives the geometrical interpretation of the corresponding two-dimensional physics.     

A complete measurement of spin-observables for intermediate-energy inclusive quasielastic polarized proton scattering from C

The complete set of Wolfenstein parameters, the polarization, the asymmetry of scattering and the unpolarized double-differential cross section are presented for inclusive quasielastic proton scattering from ¹²C at a central momentum transfer of q = 1.9 fm⁻¹ and incident energies of 290 and 420 MeV. The spin observables D₀, D_x, D_y and D_z as well as the longitudinal-to-transverse ratio of spin-flip probabilities are extracted from the data. Across the quasielastic continuum, the experimental data is compared to the variations expected from a single-scattering Fermi-gas approximation using the free NN amplitudes. Medium effects are evident in the pronounced quenching of the polarization parameter relative to the free value.     

取代基性质与饱和碳及饱和碳上质子化学位移的关系

根据多元线性回归分析,得到一个表达去屏蔽参数△_α^H与基团电负性X_G的关系式:X_G=(2.6△_α^H-n)/5+2.6.¹³C NMR去屏蔽参数△_α^C与电负性之间的关系可表达为:X_G=(△_α^C+5n)/40+2.由上述二式计算出的基团电负性与文献中提供的数据相仿,说明氢谱和碳谱化学位移主要与取代基电负性及其变形性有线性关系.不过由化学位移或去屏蔽参数计算出的基团电负住不能反映芳环等具有各向异性效应基团的诱导效应.     

Nanoparticle in a quantum crystal with a narrow vacancy band

Vacancy-assisted diffusion of a neutral probe nanoparticle with a radius R_p of a few lattice constants in a quantum crystal with a narrow vacancy band is considered. The diffusion coefficient of the probe D_p(T) in such a crystal should fall exponentially near T_melt, and it can go through a maximum at temperatures T_tr, where the transition from thermally activated hopping of localized vacancies to a proper band motion of delocalized vacancions takes place, under the condition that the mean free path of the vacancions l_v(T) at T_tr is less than R_p and increases with lowering the temperature quicker than the inverse value of the relative concentration of vacancies X_v(T). Below T_tr, where l_v is much longer than the probe diameter, the value of D_p should fall proportionally to X_v(T).