Hubbard model,conserved quantities,and computer algebra

The constants of motion of the half-filled four-point Hubbard model with cyclic boundary conditions are given in Wannier and Bloch representation. The total number operator and total spin operator are conserved and spin-reversal symmetry exists. In Wannier representation we have additionally the C_4v symmetry and in Bloch representation we have the total momentum operator which is conserved. The anticommutation relations for Fermi operators with spin are implemented using computer algebra. Using computer algebra, all the constants of motion are given. The one-dimensional Hubbard model admits a Lax representation. From the Lax pair we find a new constant of motion.     

Two types of loop algebras and their expanding Lax integrable models

Though various integrable hierarchies of evolution equations were obtained by choosing proper U in zero-curvature equation U_t-V_x+[U,V]=0, but in this paper, a new integrable hierarchy possessing bi-Hamiltonian structure is worked out by selecting V with spectral potentials. Then its expanding Lax integrable model of the hierarchy possessing a simple Hamiltonian operator \widetilde{J} is presented by constructing a subalgebra \widetilde{G } of the loop algebra \widetilde A₂. As linear expansions of the above-mentioned integrable hierarchy and its expanding Lax integrable model with respect to their dimensional numbers, their (2+1)-dimensional forms are derived from a (2+1)-dimensional zero-curvature equation.     

On generalized Lax equation of the Lax triple of KP Hierarchy

In terms of the operator Nambu 3-bracket and the Lax pair (L, B_n) of the KP hierarchy, we propose the generalized Lax equation with respect to the Lax triple (L, B_n, B_m). The intriguing results are that we derive the KP equation and another integrable equation in the KP hierarchy from the generalized Lax equation with the different Lax triples (L, B_n, B_m). Furthermore we derive some no integrable evolution equations and present their single soliton solutions.     

Potential models and local mode vibrational eigenvalue calculations for acetylene

Two potential models for acetylene are developed and tested by comparison between variational calculations for the stretching vibrational term values and available spectroscopic data. The first model based on local bond potentials with harmonic interbond coupling gives root mean square deviations of 6 cm^?1 for C₂H₂ and 3 cm^?1 for C₂D₂. The second model is more ambitious, being designed to reproduce the dissociation characteristics of the molecules, and the calculated root mean square deviations from the experimental vibrational term values are larger, 32 cm^?1 for C₂H₂ and 24 cm^?1 for C₂D₂. The eigenvalue spectrum of C₂H₂ is shown to differ from that of C₂D₂ in showingmarked local mode features and this difference in behaviour is underlined by means of a correlation diagram. Finally it is shown how the known normal mode frequencies and anharmonic constants may be introduced into a simple model in order to predict the excited term values of C₂H₂, again with a root mean square deviation of 6 cm^?1.     

A new integrable case of the motion of the 4-dimensional rigid body

A Lax pair for a new family of integrable systems on SO(4) is presented. The construction makes use of a twisted loop algebra of theG ₂ Lie algebra. We also describe a general scheme producing integrable cases of the generalized rigid body motion in an external field which have a Lax representation with spectral parameter. Several other examples of multi-dimensional tops are discussed.     

C (2) N+1 Ruijsenaars–Schneider Models

We define the notion of C ⁽²⁾ _N+1Ruijsenaars–Schneider models and construct their Lax formulation. They are obtained by a particular folding of the A _2N+1 systems. Their commuting Hamiltonians are linear combinations of Koornwinder–van Diejen external fields Ruijsenaars–Schneider models, for specific values of the exponential one-body couplings but with the most general two double-poles structure as opposed to the formerly studied BC _N case. Extensions to the elliptic potentials are briefly discussed.     

Elliptic Linear Problem for the Calogero—Inozemtsev Model and Painlevé VI Equation

We introduce a 3N × 3N Lax pair with spectral parameter for the Calogero—Inozemtsev model. The case of one degree freedom appears to have 2 × 2 Lax representation. We derive it from the elliptic Gaudin model via some reduction procedure and prove algebraic integrability. This Lax pair provides an elliptic linear problem for the Painlevé VI equation in elliptic form.     

On the integrable hierarchies associated with the N = 2 super Wn algebra

A new Lax operator is proposed from the viewpoint of constructing the integrable hierarchies related with the N = 2 super W_n algebra. It is shown that the Poisson algebra associated to the second Hamiltonian structure for the resulting hierarchy contains the N = 2 super Virasoro algebra as a proper subalgebra. The simplest cases are discussed in detail. In particular, it is proved that the supersymmetric two-boson hierarchy is one of the N = 2 supersymmetric KdV hierarchies. Also, a Lax operator is supplied for one of the N = 2 supersymmetric Boussinesq hierarchies.     

Towards an understanding of the helium–acetylene van der Waals complex

The weakly bound complex He–C₂D₂ is studied in the ν ₃ fundamental band of C₂D₂ (≈2440?cm^?1) using a tuneable infrared diode laser to probe a pulsed supersonic slit jet expansion. This is the first published spectrum for helium–acetylene. Transitions observed in the region of the C₂D₂ R(0) line are assigned with the help of theoretical results based on an ab initio intermolecular potential, and fitted using a simple Coriolis model. The results indicate that the complex is rather close to the free rotor limit, helping to explain the absence of previous data. Scaled parameters from the model are used to predict a spectrum for He–C₂H₂.     

Generalized Landau-Lifshitz models on the interval

We study the classical generalized gln Landau-Lifshitz (L-L) model with special boundary conditions that preserve integrability. We explicitly derive the first non-trivial local integral of motion, which corresponds to the boundary Hamiltonian for the sl₂ L-L model. Novel expressions of the modified Lax pairs associated to the integrals of motion are also extracted. The relevant equations of motion with the corresponding boundary conditions are determined. Dynamical integrable boundary conditions are also examined within this spirit. Then the generalized isotropic and anisotropic gln Landau-Lifshitz models are considered, and novel expressions of the boundary Hamiltonians and the relevant equations of motion and boundary conditions are derived.     

On generalized Lax equations of the Lax triple of the BKP and CKP hierarchies

Based on the Lax triple (B_m, B_n, L) of the BKP and CKP hierarchies, we derive the nonlinear evolution equations from the generalized Lax equation. The solutions of some evolution equations are presented, such as soliton and rational solutions.     

Geometric shielding corrections for total cross section calculations of electron scattering by CH4, C2H6, C2H3F3, C2H4, C2F4, C2Cl4 and C2Cl2F2 from 30–5000?eV

To quantify the changes in the geometric shielding effect in a molecule as the incident electron energy varies, an empirical fraction, which represents the total cross section contributions of shielded atoms in a molecule at different energies, is presented. Using this empirical fraction, the total cross sections for electron scattering by CH₄, C₂H₆, C₂H₃F₃, C₂H₄, C₂F₄, C₂Cl₄ and C₂Cl₂F₂ are calculated over a wide energy range from 30 to 5000 eV by the additivity rule model at the Hartree-Fock level. The quantitative total cross sections are compared with those obtained by experiment and other theories where available. Good agreement is attained above 100 eV.     

Towards the construction of N = 2 supersymmetric integrable hierarchies

We formulate a conjecture for the three different Lax operators that describe the bosonic sectors of the three possible N = 2 supersymmetric integrable hierarchies with N = 2 super-W_n second Hamiltonian structure. We check this conjecture in the simplest cases, then we verify it in general in one of the three possible supersymmetric extensions. To this end we construct the N = 2 supersymmetric extensions of the Generalized Non-Linear Schrödinger hierarchy by exhibiting the corresponding super Lax operator. To find the correct Hamiltonians we are led to a new definition of super-residues for degenerate N = 2 supersymmetric pseudo-differential operators. We have found a new non-polynomials Miura-like realization for N = 2 superconformal algebra in terms of two bosonic chiral-anti-chiral free superfields.     

Model for Estimating the Atmosphere Structure Constant at Millimeter-Wave on Earth-Space Paths

A atmosphere structure constant C_n ² model, which varies with height, is presented based on Karasawa's amplitude scintillation model, existing ITU-R C_n ² model for optical and Xi'an area meteorologic measured relative humidity data in cloud cover, at 3050GHz. In this C_n ² model it is considered that relative humidity u varies with height. The log-amplitude scintillation deviation calculated in terms of the C_n ² model compare with values predicted by means of STNV2 model applied to Italsat channels. It is emerged that the calculation results based on the C_n ² model are distinctly smaller then the values predicted by STNV2 model. Their differences increase with decrease of u, because the water vapor content in the atmosphere at continental climate Xi'an area is smaller then the one at Italy, which is oceanic cilmate. When the water vapor in atmosphere approach saturation, the calculation results agree almost with prediction results. Therefore, it is shown that the C_n ² model is usable and is applied at the continental climate area as Xi'an area.     

Formation of soot particles in pyrolysis and oxidation of aliphatic and aromatic hydrocarbons: Experiments and detailed kinetic modeling

Experiments on pyrolysis and oxidation of rich mixtures of various aliphatic and simple aromatic hydrocarbons in reflected shock waves have been performed. The mixtures C₂H₂/Ar, C₂H₆/Ar, C₂H₄/Ar, C₂H₄/O₂/Ar, CH₄/Ar, CH₄/O₂/Ar, C₃H₈/Ar, C₃H₆/Ar, toluene/Ar, and benzene/Ar were studied. The yield of soot and the temperature of soot particles were determined experimentally by the double-beam absorption emission method. The kinetic model of soot formation during the pyrolysis and oxidation of rich mixtures of aliphatic and aromatic hydrocarbons complemented with a set of nucleations of soot particles from both polyaromatic fragments and unsaturated aliphatic hydrocarbons was suggested. This kinetic model of soot formation was successfully tested. It describes the experimental literature data on the yield of the products of pyrolysis and oxidation of acetylene and diacetylene in a shock tube. The results of our experiments and kinetic calculations of the time, temperature, and concentration dependences are in good agreement for all hydrocarbons under study. All the kinetic parameters of the model remained strictly constant.     

Calculated Vibrational Frequencies of PMo12O40 3- and its Fragments

Calculated vibrational frequencies are reported for the PMo₁₂O₄₀ ^3– ion according to a 53-atomic tetrahedral model (T_d). The results are compared with calculated frequencies for fragments of this structure, viz. PO₄ (T_d), Mo₃O₁₃ (C_3v), Mo₃O₇ (C_3v, Mo₂O₁₁ (C_s) and Mo₂O₁₀ (C_s).

A complete vibrational analysis of the PMo₁₂O₄₀ ^3– ion has been performed. The adopted model of T_d symmetry is an idealization of x-ray structure data. 1 The normal modes of vibration according to this model are distributed as:     

Branching ratios of successive emission (up to three) of C2n + (n = 1–5) fragments in asymmetrical fission processes of C60 r+ ions (r = 4–6)

Highly charged C₆₀ molecules are produced in collisions between neutral C₆₀ and multiply charged ions within a large range of temperatures. Successive emission of one, two or three light monocharged fragments referred as one-, two- and three-step processes have been observed. The experimental mass branching ratios for the emission of one C_2n⁺ fragment from C₆₀⁶⁺, C₆₀⁵⁺ and C₆₀⁴⁺ ions are compared with the theoretical values using a statistical model. From hotter C₆₀⁶⁺ ions, branching ratios for three-step processes have been measured and the data are in good agreement with an estimation using the branching ratios in one-step process.     

带有Dzyaloshinski-Mariya相互作用的两比特XXZ模型的纠缠量子热机

以带有Dzyaloshinski-Mariya 相互作用的两比特XXZ模型为工作物质构建纠缠量子热机. 在量子热力学平衡态下, 采用Kieu的形式描述了做功与热传递.对于不同的各向异性参数, 分析了热机循环中量子纠缠与热传递、做功以及机械效率等热力学量之间的关系. 结果表明: 在这个纠缠体系中, 热力学第二定律依然成立; 机械效率的等值线图是环状曲线; 当各向异性参数Δ较小时, 热机在C₁ > C₂ 和C₁ < C₂ 两区域运行, 当增大Δ值时, 热机只在C₁ > C₂ 区域运行. 关键词： 量子热机 并发度 机械效率     

Theoretical and experimental studies on the adsorption behavior of thiophenol on gold nanoparticles

FT‐Raman spectra were obtained for thiophenol (TP) and TP on gold nanoparticles. All vibrational fundamentals for the TP molecule are assigned on the basis of the scaled quantum force field procedure. Three model systems are studied and compared for the interactions of TP with the Au atom: (1) TP with a Au atom, C₆H₅SH Au; (2) TP anion with a Au atom, C₆H₅S⁻ Au; and (3) TP with a Au atom and subsequent formation of thiophenylate, C₆H₅SAu. The equilibrium structures and Raman spectra were calculated for the model systems using density functional theory (DFT) with the B3LYP functionals and the mixed basis set 6‐311 + G** (for C, S, H) and LANL2DZ (for Au), and theoretical Raman wavenumbers of C₆H₅SAu and C₆H₅S⁻ Au were assigned according to potential energy distributions. The third model system is shown to be preferred over the other two. The calculated binding energies are also shown to support the third model system. It is suggested that a simple model, such as the one used in the present study, is reasonable to describe surface‐enhanced Raman spectroscopy of thiophenol adsorbed on gold nanoparticles. Copyright © 2007 John Wiley & Sons, Ltd.     

Hf8C12金属碳多面体电子结构的从头计算研究

用赝势从头计算方法研究Hf₈C₁₂多面体．先对T和Td分子构型作几何优化，发现Td对称构型比T构型稳定．利用非限制的Hartre Fock方法及自然键轨道分析研究Td构型的Hf₈C₁₂基团，结果表明：Hf₈C₁₂存在三种自旋不同的基态，这种基态的多样性与成键机制、电子组态和电子能谱分布密切相关．其中S=0时，Hf₈C₁₂主要是由外四面体Hf原子与类乙烯C₂单元形成极性共价键构成．S=1时，6个类乙炔C₂单元吸附在Hf₈金属框架．S=2时，部分C₂中的ｐπ键断裂与Hf原子形成ｄ←ｐπ键．进一步分析发现，Td对称性的结构模型为(Hf₈)^+4.5(C^-0.75₂)₆，在高自旋态下具有铁磁性，电子能级分布及其能隙随自旋态而变化． 关键词：