The n = 0 replica limit of U(n) and models

Recently the replica limit n = 0 of the U(n) and models have attracted interest since they describe the Anderson localization behaviour in the band-centre of a two-sublattice model. For n ≠ 0 the theories can be decomposed into one with symmetry U(1) and one for SU(n) and . This does not no longer hold for n = 0. We show how the beta-functions and zeta-functions for operators without derivatives can be obtained in this limit from those of SU(n) and and draw consequences for these functions in this limit.     

Matrix elements for the representations of SO(n) and SO0(n, 1)

Matrix elements of the unitary irreducible representations of the group SO(n) of class higher then 1 (with respect to SO(n−1)) in Gel'fand-Zetlin basis are obtained in explicit form. They are represented as polynomials in cosθ and sinθ of the order equal to the first coordinate of the highest weight. Making use of them the representation matrix elements for the group SO₀(n, 1) in SO(n) basis are calculated.     

The characteristics of O＋HD （v = 0, j = 0） reaction dynamics

The analytical potential energy function of HDO is constructed at first using the many-body expansion method.The reaction dynamics of O+HD(v = 0,j = 0) in five product channels are all studied by quasi-classical trajectory(QCT) method.The results show that the long-lived complex compound HDO is the dominant product at low collision energy.With increasing collision energy,O+HD → OH+D and O+HD → OD+H exchange reactions will occur with remarkable characteristics,such as near threshold energies,different reaction probabilities,and different reaction cross sections,implying the isotopic effect between H and D.With further increasing collision energy(e.g.,up to 502.08 kJ/mol),O+HD → O+H+D will occur and induce the complete dissociation into single O,H,and D atoms.     

Integrable string models with constant torsion in terms of chiral invariants of SU(n), SO(n), SP(n groups

We used the invariant local chiral currents of principal chiral models for SU(n), SO(n), SP(n) groups to construct new integrable string equations of hydrodynamic type on the Riemann space of the chiral primitive invariant currents and on the chiral nonprimitive Casimir operators as Hamiltonians.     

The structural,electronic, and magnetic properties of SrFeOn（n=2 and 2.5）： a GGA＋U study

Using density-functional calculations within the generalized gradient approximation (GGA)+U framework,we investigate the structural,electronic,and magnetic properties of the ground states of SrFeOn (n = 2 and 2.5).The magnetism calculations show that the ground states of both SrFeO2 and SrFeO2.5 have G type antiferromagnetic ordering,with indirect band gaps of 0.89 and 0.79 eV,respectively.The electronic structure calculations demonstrate that Fe cations are in the high-spin state of (dz2 )2(dxz,dyz)2(dxy)1(dx2 y2 )1(S = 2),unlike the previous prediction of (dxz,dyz)3(dxy)1(dz2 )1(dx2 y2 )1(S = 2) for SrFeO2,and in the high-spin state of (dxy,dxz,dyz,dx2 y2 ,dz2 )5(S = 5/2) for SrFeO2.5.     

宽带非均匀半径渐变TE0n-TE0(n+1)模式转换器的设计研究

基于耦合波理论,对两类半径渐变圆波导TE_0n-TE_0(n+1)模式转换器进行理论分析、数值计算和仿真模拟.均匀半径渐变波导高功率模式转换器,采用中心频率为17.14GHz、六周期TE₀₂-TE₀₃模式和中心频率为34.30GHz、六周期TE₀₁-TE₀₂模式两种设计参数.非均匀半径渐变波导高功率模式转换器,采用中心频率为34.30GHz、六周期TE 关键词： 模式转换器 耦合波理论 非均匀半径渐变 转换带宽     

Scaling contributions to the free energy in the 1/n expansion of O(n) nonlinear sigma models in d-dimensions

Within the 1/N expansion of O(N) nonlinear σ models for d≤4 it is possible to separate consistently the spin-wave and the massive-mode contributions to the scaling part of the free energy near criticality, and to evaluate them to O(1/N). For critical dimensions d=2+2/n the Abe-Hikami anomaly is recovered, while for d=2 the removal of the spin-wave term is justified.     

Study of n=2,Δn=0 transition of Be-, B-, C-, N- and O-like sequence in the beam--foil spectrum of titanium

The foil-excited the spectrum of highly stripped titanium ions between 12-40 nm has been studied. Titanium ions of 80 and 120 MeV were provided by the HI-13 tandem accelerator at the China Institute of Atomic Energy. GIM-957 XUV-VUV monochromator was refocused to get highly-resolved spectra. Our experimental results and the published spectral data of laser-produced plasma show agreement in nearly all cases within ±0.03 nm. The spectra contained some weak or strong lines previously unclassified. These spectral lines mainly belong to 2s2p^2 for TiXVⅢ, 2p^3 for TiXVIII, 2s2p^3 for TiXVII, 2p^6 4p for Ti XII and 2p^6 3d for Ti XII transitions.     

Orbital responses to methyl sites in CnH2n+2 (n=1-6)

Orbital responses to methyl sites in C_nH_2n+2 (n=1-6) are studied by B3LYP/TZVP based on the most stable geometries using the B3LYP/aug-cc-pVTZ method. Vertical ionization energies are produced using the SAOP/et-pVQZ model for the complete valence space. The highest occupied molecular orbital (HOMO) investigations indicate the p-electron profiles in methane, ethane, propane, and n-butane. By increasing the number of carbon-carbon bonds in lower momentum regions, the s, p-hybridized orbitals are built and display strong exchange and correlation interactions in lower momentum space (P≤0.50 a.u.). Meanwhile, the relative intensities of the isomers in lower momentum space show the strong bonding number dependence of the carbon-carbon bonds, meaning that more electrons have contributed to orbital construction. The study of representative valence orbital momentum distribution further confirms that the structural changes lead to evident electronic rearrangement over the whole valence space. An analysis based on the isomers reveals that the valence orbitals are isomer-dependent and the valence ionization energy experiences an apparent shift in the inner valence space. However, such shifts are greatly reduced in the outer valence space. Meanwhile, the opposite energy shift trend is found in the intermediate valence space.     

Density functional study of AunCu (n=1-7) clusters

The possible stable geometrical configurations and the relative stabilities of the lowest-lying isomers of copper-doped gold clusters,Au n Cu (n=1-7),are investigated using the density functional theory.Several low-lying isomers are determined.The results indicate that the ground-state Au n Cu clusters have planar structures for n=1-7.The stability trend of the Au n Cu clusters (n=1-7),shows that odd-numbered Au n Cu clusters are more stable than the neighbouring even-numbered ones,thereby indicating the Au 5 Cu clusters are magic cluster with high chemical stability.     

多参考组态相互作用方法计算研究XOn(X=S,Cl；n=0,±1)的解析势能函数和光谱常数

采用从头计算的多参考组态相互作用方法和含扩散基的3个基组aug-cc-PVXZ (X=D,T,Q) 计算了SO和ClO分子及其分子离子的势能曲线，确定了平衡几何结构、离解能，并采用Feller拟合递推方法得到了基函数为无穷大计算水平值. 确定了SO^－，ClO⁺，ClO^-分子离子的基态. 通过Murrell-Sorbie势能函数和最小二乘法拟合得到了解析势能函数. 基于所得的势能函数，通过解核运动的薛定谔方程得到振 关键词： 多参考组态相互作用 势能曲线 解析势能函数 光谱常数     

Spatial distribution of SiCln （n=O-2） in SICl4 plasma measured by mass spectroscopy

For a better understanding of the deposition mechanism of thin films in SiCl4 source gas, we have measured the spatial distributions of SiCln （n=0-2） radicals in SICl4 radio frequency glow discharge plasma utilizing a mass spectrometer equipped with a movable gas sampling apparatus. The experimental results demonstrate that the relative densities of SiCln （n=0-2） radicals have peak values at the position of 10 mm above the powered electrode along the axial direction; the relative densities of the Si and SiCIn （n=1, 2） radicals have peak values at the positions of 27mm and 7 mm away from the axis along the radial direction, respectively. Generally speaking, in the whole SICl4 plasma bulk region, the relative density of Si is one order of magnitude higher than that of SICl, and the relative density of SiCl is several times higher than that of SICl2. This reveals that Si and SiCl may be the primary growth precursors in forming thin films.     

Structures and electronic properties of Mo2nNn（n=1-5）:a density functional study

The lowest-energy structures and the electronic properties of Mo2nNn(n=1-5) clusters have been studied by using the density functional theory(DFT) simulating package DMol 3 in the generalized gradient approximation(GGA).The resulting equilibrium geometries show that the lowest-energy structures are dominated by central cores which correspond to the ground states of Mo n(n = 2,4,6,8,10) clusters and nitrogen atoms which surround these cores.The average binding energy,the adiabatic electron affinity(AEA),the vertical electron affinity(VEA),the adiabatic ionization potential(AIP) and the vertical ionization potential(VIP) of Mo2nNn(n=1-5) clusters have been estimated.The HOMO-LUMO gaps reveal that the clusters have strong chemical activities.An analysis of Mulliken charge distribution shows that charge-transfer moves from Mo atoms to N atoms and increases with cluster size.     

Cross-section measurements of (n, 2n) and (n, p) reactions on 124,126,128,130,131,132Xe in the 14 MeV region and theoretical calculations of their excitation functions

The reaction cross-sections of ¹²⁴Xe(n, 2n)¹²³Xe, ¹²⁶Xe(n, 2n)¹²⁵Xe, ¹²⁸Xe(n, 2n)¹²⁷Xe, ¹³⁰Xe(n, 2n)^129mXe, ¹³²Xe(n, 2n)^131mXe, ¹³⁰Xe(n, p)¹³⁰I, ¹³¹Xe(n, p)¹³¹I, and ¹³²Xe(n, p)¹³²I were measured at the 13.5, 13.8, 14.1, 14.4, and 14.8 MeV neutron energies. The monoenergetic neutrons were generated via the ³H(d,n)⁴He reaction at the China Academy of Engineering Physics using the K-400 Neutron Generator with a solid ³H-Ti target. A high-purity germanium detector was employed to measure the activities of the product. The reactions ⁹³Nb(n, 2n)^92mNb and ²⁷Al(n, α)²⁴Na were adopted for neutron flux calibration. The cross sections of the (n, 2n) and (n, p) reactions of the xenon isotopes were obtained within the 13–15 MeV neutron energy range. These cross-sections were then compared with the IAEA-exchange format (EXFOR) database-derived experimental data, together with the evaluation results of the CENDL-3, ENDF/B-VIII.0, JENDL-4.0, RUSFOND, and JEFF-3.3 data libraries, as well as the theoretical excitation function obtained using the TALYS-1.95 code. The cross-sections of the reactions (except for the ¹²⁴Xe(n, 2n)¹²³Xe and ¹³²Xe(n, p)¹³²I) at 13.5, 13.8, and 14.1 MeV are reported for the first time in this study. The obtained results are beneficial in providing better cross-section constraints for the reactions in the 13–15 MeV region, thus improving the quality of the corresponding database. Meanwhile, these data can also be used for the verification of relevant nuclear reaction model parameters.     

Structural and spectroscopic properties of small Pun （n= 2-5） molecules

The equilibrium structures and the electronic, spectroscopic and thermodynamic properties of small Pu_n (n=2-5) molecules are systematically investigated using the methods of general gradient approximation (GGA) of density functional theory (DFT). The results show that the bond length of the lowest-energy structure of Pu₂ is 2.578 AA. The ground state structure of Pu₃ is a triangle with D_3h symmetry, whereas for Pu₄, the ground state structure is a square (D_4h) and the spin polarization of 16 for molecule Pu₅ with square geometry (D_4h) is the most stable structure. For the ground state structures, the vibrational spectra as well as thermodynamic parameters are worked out. In addition, the values for the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) along with the energy gap of all the Pu_2-5 structures are presented. The relevant structural and chemical stabilities are predicted.     

B$lt;sub$gt;$lt;i$gt;n$lt;/i$gt;$lt;/sub$gt;Y($lt;i$gt;n$lt;/i$gt;=1–11)团簇的结构和电子性质

利用密度泛函理论TPSSh方法对B采用6-311+G(d), 对Y采用Lanl2dz相对论有效势基组, 研究了B_nY (n=1–11)团簇的平均结合能、二阶能量差分、最高分子占据轨道和最低空轨道之间的能级间隙、极化率和第一静态超极化率等物理化学性质. 结果表明, 随着尺寸的增大, B_nY (n=1–11)团簇的最低能量结构从平面逐步演变为立体结构. 随硼原子数n的增加, 团簇的平均结合能表明了较好的热力学稳定性, 有利于Y掺杂B团簇形成较大的块体材料.二阶能量差分表明基态B₃Y, B₅Y和B₇Y团簇较相邻团簇稳定. 能隙表明了基态B₃Y, B₅Y, B₇Y和B₉Y的化学稳定性较高. 综合说明B_nY (n=1–11)硼团簇中, 基态B₃Y, B₅Y和B₇Y具有较好的稳定性. 极化率表明基态B_nY团簇的电子结构随B原子的增加趋于紧凑, 第一静态超极化率表明基态B₅Y, B₄Y, B₃Y和B₆Y平面结构的团簇具有明显的非线性光学性质, 为寻找性能优异的非线性光学材料提供了一定的参考. 关键词： 密度泛函TPSSh方法 nY (n=1–')" href="#">B_nY (n=1– 11)团簇 几何结构 电子性质     

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.     

Lower bounds for eigenvalues of the Dirac operator on n-spheres with SO(n)-symmetry

In this paper we derive estimates for the eigenvalues of the Dirac operator and their multiplicity on manifolds diffeomorphic to Sⁿ with an isometric SO(n)-action. Especially we prove a new lower bound for the first eigenvalue and show an example, where this new bound coincides in the limit with the known upper bounds.     

An ab initio study of niobium (n = 2--11) clusters: structure, stability and magnetism

The ground-state configurations of the Nbn (n = 2-11) clusters are studied through the first-principles calculations. It is found that niobium clusters (n = 2-11) tend to form compact structures with low symmetry. The clusters with 4, 8 and 10 atoms are found to be magic and have relatively large highest occupied-lowest unoccupied molecular orbital (HOMO-LUMO) gaps. The Nbn clusters possess low magnetic moments, which exhibit an odd-even oscillational character. The analyses of calculated electronic density and population of the lowest-energy niobium clusters for n = 2, 3, 5, 7, 9, 11 show that the total magnetic moments of Nbn originate mainly from a few Nb atoms with longer spacings between them in most cases, while they are located on two Nb atoms for n = 2, 3, 5. The total magnetic moments come mainly from the 4d local moments but with the exception of the Nb5 cluster.     

Density functional theory study on Ni-doped MgnNi (n=1-7) clusters

The possible geometrical and the electronic structures of small MgnNi(n = 1-7) clusters are optimised by the density functional theory with a LANL2DZ basis set.The binding energy,the energy gap,the electron affinity,the dissociation energy and the second difference in energy are calculated and discussed.The properties of Mg n Ni clusters are also discussed when the number of Mg atom increases.