Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices

The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie transformations acting on the lattice, as well as the equations and the determining equations of the Lie symmetries are obtained for the nonholonomic Hamiltonian systems. The discrete analogue of the Noether conserved quantity is constructed by using the Lie point symmetries. An example is discussed to illustrate the results.     

Integrable Couplings of Classical-Boussinesq Hierarchy and Its Hamiltonian Structure＊

By using a Lie algebra, an integrable couplings of the classicai-Boussinesq hierarchy is obtained. Then, the Hamiltonian structure of the integrable couplings of the classical-Boussinesq is obtained by the quadratic-form identity.     

Algebraic Hamiltonian for Vibrational Spectra of Stibine

An algebraic Hamiltonian, which in a limit can be reduced to an extended local mode model by Law and Duncan, is proposed to describe both stretching and bending vibrational energy levels of polyatomic molecules, where Fermi resonances between the stretches and the bends are considered. The Hamiltonian is used to study the vibrational spectra of stibine (SbH3). A comparison with the extended local mode model is made. Results of fitting the experimental data show that the algebraic Hamiltonian reproduces the observed values better than the extended local mode model.     

Two Integrable Couplings of Modified Tu Hierarchy

Two different integrable couplings of the modified Tu hierarchy are obtained under the zero curvature equation by using two higher dimension Lie algebras. Furthermore, a complex Hamiltonian structures of the second integrable couplings is presented by taking use of the variational identity.     

Si2O2 molecule: structure of ground state and the excited properties under different external electric fields

Geometry and vibrational frequencies of the ground state of Si 2 O 2 molecule are studied using density function theory (DFT) at the level of cc-pvtz and 6-311++G.It is found that the optimizing value by B3lyp/cc-pvtz is closer to the experimental data.The excited properties under different external electric fields are also investigated by the time-dependent-DFT method.Transitions from the ground state of Si 2 O 2 molecule to the first singlet state under different external electric fields can take place more easily.The corresponding absorption spectral line is about 360 nm in wavelength and the excitation energy is about 3.4 eV.     

Hamiltonian Tri-Integrable Couplings of the AKNS Hierarchy

We propose a systematic approach for generating Hamiltonian tri-integrable couplings of soliton hierarchies. The resulting approach is based on semi-direct sums of matrix Lie algebras consisting of 4 × 4 block matrix Lie algebras. We apply the approach to the AKNS soliton hierarchy, and Hamiltonian structures of the obtained tri-integrable couplings are constructed by the variational identity.     

Studies on Nematic Liquid Crystal Using Spin Wave Theory

A spin wave theory is proposed to study nematic liquid crystals. Since the orientation of the molecular long axis and the angular momentum of the molecule rotating around its long axis have the same direction, operators can be introduced to research the nematic liquid crystal. By transforming the intermolecular interaction potential,the Hamiltonian of the system has the same form as that of the ferromagnetic substance. The relation of the order parameters to the reduced temperature can be obtained. It is in good agreement with the experimental results in the low temperature region. In the high temperature region close to the transition point, by using the Hamiltonian, the transition point can be obtained, which is near to the Maier-Saupe‘s result.     

Studies on Nematic Liquid Crystal Using Spin Wave Theory

A spin wave theory is proposed to study nematic liquid crystals. Since the orientation of the molecularlong axis and the angular momentum of the molecule rotating around its long axis have the same direction, operatorscan be introduced to research the nematic liquid crystal. By transforming the intermolecular interaction potential,the Hamiltonian of the system has the same form as that of the ferromagnetic substance. The relation of the orderparameters to the reduced temperature can be obtained. It is in good agreement with the experimental results in thelow temperature region. In the high temperature region close to the transition point, by using the Hamiltonian, thetransition point can be obtained, which is near to the Maier-Saupe‘s result.     

BCS Ground State and XXZ Antiferromagnetic Model as SU（2）,SU（1,1） Coherent States：AN Algebraic Diagonalization Method

An algebraic diagonalization method is proposed.As two examples,the Hamiltonians of BCS ground state under mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized by using SU(2),SU(1,1) Lie algebraic method,respectively.Meanwhile,the eignenstates of the above two models are revealed to be SU(2),SU(1,1) coherent states,respectively,The relation between the usual Bogoliubov-Valatin transformation and the algebraic method in a special case is also discussed.     

（2＋2）-Dimensional Discrete Soliton Equations and Integrable Coupling System

In this paper, we extend a （2＋2）-dimensional continuous zero curvature equation to （2＋2）-dimensional discrete zero curvature equation, then a new （2＋2）-dimensional cubic Volterra lattice hierarchy is obtained. Fhrthermore, the integrable coupling systems of the （2＋2）-dimensional cubic Volterra lattice hierarchy and the generalized Toda lattice soliton equations are presented by using a Lie algebraic system sl（4）.     

用代数模型研究非刚性HCP分子的振动谱

提出一种研究非刚性HCP分子的高激发非线性振动的代数哈米顿量,它在极限条件下退化为传统的用谐振子算子表示的模型,拟合观测的实验数据表明,代数模型比传统模型较好地描述了这些数据．     

Saddle points of the potential energy surface for HCCF determined by an algebraic approach

The potential energy surface of the tetratomic molecule HCCF is determined by the U(4) algebraic method. The combination coefficients in the Hamiltonian are gotten from fitting the spectroscopic data. The molecular properties, such as, force constants and dissociation energies, are obtained in terms of the potential energy surface. A saddle point is also derived.Received: 17 November 2003, Published online: 9 March 2004PACS: 02.20.Sv Lie algebras of Lie groups - 34.20.Cf Interatomic potentials and forces     

Energy transfer to an anharmonic diatomic system

We model an anharmonic diatomic molecule using deformed creation and annihilation operators such that the energy spectrum generated by a Hamiltonian of the harmonic oscillator's form written in terms of deformed operators is similar to that of a Morse potential. We construct an approximate time evolution operator and evaluate transition probabilities which are compared with those obtained by an expansion in a basis of Morse eigenfunctions. The algebraic results compare favorably with the numerical results.     

On the determination of the intramolecular potential energy surface of polyatomic molecules: Hydrogen sulfide and formaldehyde as an illustration

We present here an approach for determining the Hamiltonian of polyatomic molecules that allows one to successfully solve the problem of potential energy surface (PES) determination via construction and diagonalization of a Hamiltonian matrix of large dimension. In the suggested approach, the Hamiltonian is very simple and can be used both for any “normal” polyatomic molecule and for any isotopic species of a molecule. Molecules with two to four equivalent X-Y bonds are considered, and for illustration of the efficiency of the suggested approach, numerical calculations are made for the three-atomic (hydrogen sulfide) and four-atomic (formaldehyde) molecules.     

用代数哈米顿量研究CH3C1分子的振动谱

我们提出一种描述XH3分子的伸缩和弯曲振动的U(2)代数哈米顿量,其中包括了伸缩和弯曲振动的费米共振耦合;用它来拟合CH3Cl分子的实验数据,结果表明有较少参数的代数模型算得的偏差比其它模型算得的偏差要小.     

用代数哈米顿量研究CH_3Cl分子的振动谱(英文)

我们提出一种描述XH3分子的伸缩和弯曲振动的U(2)代数哈米顿量,其中包括了伸缩和弯曲振动的费米共振耦合,用它来拟合CH3Cl分子的实验数据,结果表明有较少参数的代数模型算得的偏差比其它模型算得的偏差要小.     

线型三原子分子在强激光场中多光子激发的李代数方法

使用二次非谐振子模型和Magnus近似方法构造了在强激光场下线型三原子分子的振动哈密顿并推导出时间演化算符的代数形式,在此基础上研究了线型DCN分子的跃迁几率随外场的频率和强度的变化关系,表明了多光子跃迁谱的特点.     

Potential energy surfaces in algebraic molecular models using coherent states

The potential energy surfaces provided by the coherent states formalism for the case of interacting one-dimensional oscillators is investigated. The case of two interacting oscillators modelled with Morse potentials are considered in detail. First the traditional treatment is presented in order to identify the need to establish a new transformation between the parameters and the classical variables that allow the full Hamiltonian to be recovered. To this end the connection between the su(2) algebraic model and the usual treatment in configuration space was taken into account. It is shown that the coherent state approach when applied to recover the potential energy surface (PES) from a polyad preserving Hamiltonian is viable only in systems with a local mode behaviour. For molecules with a normal mode behaviour the approach is still valid, but the polyad must be broken in order to recover the PES. Our approach is evaluated through the calculation of the force constants for H₂O and CO₂, representative examples of local and normal behaviours.     

核类似铜酸盐超导模型的su_s(1,1)su_d(1,1)代数结构

由Iachello提出的核类似铜酸盐超导模型具有su(3)代数结构,其平均场近似下的Hamilton量可以写成su(3)生成元的线性组合.通过代数生成元的实现,该模型约化的Hamilton量具有Su_s(1,1)SU_d(1,1)代数结构,利用相干算子U(θ,φ)的幺正变换,可得到系统约化Hamilton量的能隙方程及本征值,发现应用不同代数结构求解会得到不同侧重点的分析结果.