Dynamical algebras for Pöschl-Teller Hamiltonian hierarchies

The dynamical algebras of the trigonometric and hyperbolic symmetric Pöschl-Teller Hamiltonian hierarchies are obtained. A kind of discrete-differential realizations of these algebras are found which are isomorphic to so(3, 2) Lie algebras. In order to get them, first the relation between ladder and factor operators is investigated. In particular, the action of the ladder operators on normalized eigenfunctions is found explicitly. Then, the whole dynamical algebras are generated in a straightforward way.     

Nonlinear dynamical systems,first integrals,Bose operators,and Lie algebras

A connection between nonlinear autonomous systems of ordinary differential equations, first integrals, Bose operators and Lie algebras is described. An extension to nonlinear partial differential equations is given.     

Integrable systems on so(n)-valued Lie algebras on higher genus curves

We consider special quasi-graded so(n)-valued Lie algebras on higher genus curves. Using them we find new Lie theoretical interpretation of the integrability of generalized Manakov tops and generalized Clebsch systems and explicitly construct their isomorphism on trajectories.     

Noncommutative *-product continual Lie algebras and solvable models

Noncommutative counterparts of exactly solvable models are proposed on the basis of *-product continual Lie algebras. Examples of noncommutative Liouville and sine/sh-Gordon equations are discussed.     

机电动力系统的动量依赖对称性和非Noether守恒量

研究了Lagrange-Maxwell机电动力系统的Hamilton正则方程及动量依赖对称性的定义、判据、结构方程和守恒量的形式.研究表明，结构方程中的函数ψ只需是对称群的不变量.得到求解机电动力系统守恒量的新方法，并给出了应用实例. 关键词： 机电动力系统 Lie群分析 对称性 守恒量     

黑克、布劳、及伯曼-温采尔代数的诱导及分导系数和量子经典李代数的耦合与重新耦合系数

本文总结了计算黑克、布劳、及伯曼 温采尔代数在各种工数链下诱导及分导系数的线性方程方法(LEM)。特别强调了关于A,B,C,D型李代数及其量子情形与其中心代数之间的舒尔 魏尔 布劳双关性关系。这一关系使我们能够利用相应中心代数的诱导及分导系数计算出经典李代数及其量子情形的耦合与重新耦合系数。讨论了从该方法得到B,C,D型李代数不可约表示克罗内克积分解的应用。基于LEM还得到了处理对应于置换群CG系列问题的黑克代数张量积的方法。     

Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration

The Lie symmetries and conserved quantities of a two-dimensional nonlinear diffusion equation of concentration are considered. Based on the invariance of the two-dimensional nonlinear diffusion equation of concentration under the infinitesimal transformation with respect to the generalized coordinates and time, the determining equations of Lie symmetries are presented. The Lie groups of transformation and infinitesimal generators of this equation are obtained. The conserved quantities associated with the nonlinear diffusion equation of concentration are derived by integrating the characteristic equations. Also, the solutions of the two-dimensional nonlinear diffusion equation of concentration can be obtained.     

Invariant functions and contractions of certain types of Lie algebras of lower dimensions

In this paper, we deal with contractions of Lie algebras. We use two invariant functions of Lie algebras as a tool, named ψ and ? function, respectively, which have a great application in Physics due to their remarkable properties. We focus the study of these functions in the frame of the filiform Lie algebras, trying to extend to these algebras some of the properties of such functions over semi-simple Lie algebras.     

Graded differential lie algebras and model building

We develop a mathematical concept towards gauge field theories based upon a Hilbert space endowed with a representation of a skew-adjoint Lie algebra and an action of a generalized Dirac operator. This concept shares common features with the non-commutative geometry à la Connes/Lott, differs from that, however, by the implementation of skew-adjoint Lie algebras instead of unital associative *-algebras. We present the physical motivation for our approach and sketch its mathematical strategy. Moreover, we comment on the application of our method to the standard model and the flipped SU(5)×U(1)-grand unification model.     

有限自由度系统的定域Lie对称性和守恒量

研究有限自由度系统定域Lie对称性的正问题和逆问题。给出了定域Lie对称性的定义、确定方程、结构方程和守恒量。进一步从定域Lie对称性导出在有限连续群无限小变换下的Lie对称性。最后给出一个例子去说明这些结果。     

Lie symmetries and invariants of constrained Hamiltonian systems

According to the theory of the invariance of ordinary differential equations under the infinitesimal transformations of group, the relations between Lie symmetries and invariants of the mechanical system with a singular Lagrangian are investigated in phase space. New dynamical equations of the system are given in canonical form and the determining equations of Lie symmetry transformations are derived. The proposition about the Lie symmetries and invariants are presented. An example is given to illustrate the application of the result in this paper.     

The mermin-wagner phenomenon and cluster properties of one- and two-dimensional systems

We give optimal conditions concerning the range of interactions for the absence of spontaneous breakdown of continuous symmetries for one- and two-dimensional quantum and classical lattice and continuum systems. For a class of models verifying infrared bounds our conditions are necessary and sufficient. Using the same techniques we obtain a priori bounds on clustering for systems with continuous symmetry, improving results of Jasnow and Fisher.Partially supported by CAPES-PICD.Partially supported by the CNP_q.Partially supported by N.S.F. under grant MCS 7801433.     

Polynomial poisson algebras for two-dimensional classical superintegrable systems and polynomial associative algebras for quantum superintegrable systems

The integrals of motion of the classical two-dimensional superintegrable systems close in a restrained polynomial Poisson algebra, whose general form is discussed. Each classical superintegrable problem has a quantum counterpart, a quantum superintegrable system. The polynomial Poisson algebra is deformed to a polynomial associative algebra, the finite-dimensional representations of this algebra are calculated by using a deformed parafermion oscillator technique. It is conjectured that the finite-dimensional representations of the polynomial algebra are determined by the energy eigenvalues of the superintegrable system. The calculation of energy eigenvalues is reduced to the solution of algebraic equations, which are universal for a large number of two-dimensional superintegrable systems. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

单面完整约束系统的速度依赖对称性与Lutzky守恒量

研究单面完整约束系统的对称性与守恒量.给出单面完整约束系统Lie对称性的定义，得到了由依赖于速度的一般Lie对称性直接导致的Lutzky守恒量，并给出了它的若干特例：有多余坐标的完整约束系统、非保守力学系统、Lagrange系统的Lutzky守恒量.并举例说明结果的应用. 关键词： 分析力学 单面约束 Lie对称性 Lutzky守恒量     

Investigation of dodecylammonium adsorption on mica,albite and quartz surfaces by QM/MM simulation

The absorption mechanisms of collector and mineral surface structures play important roles in studies of lepidolite flotation. In this work, quantum mechanics (QM) and hybrid quantum mechanics/molecular mechanics (MM) methods were implemented to investigate the flotation mechanisms of lepidolite from muscovite, quartz and albite. The crystal structures, electron density distributions, bonds and the densities of states of lepidolite were calculated and compared with those of muscovite. The adsorption structures and energies of monomer dodecylammonium (DDA) on the three different minerals were also calculated. The headgroup of the DDA cation was found to adsorb on the surface of minerals, with its hydrophobic tail stretching into the vacuum slab, approximately perpendicular to the surface. Simulation results indicate that the purity of fine lepidolite is limited by the existence of muscovite, due to their similarities in surficial structure and properties. Other gangues were found to be removed efficiently with the use of acidic conditions. The results are in good agreement with other experiments. Compared with simple MM simulations, the use of the QM/MM methods to investigate the adsorption on minerals without specific forcefield parameters was concluded to be a more accurate method to attain monomer surfactant–mineral adsorption energies.     

Momentum-dependent symmetries and non-Noether conserved quantities for nonholonomic nonconservative Hamilton canonical systems

This paper investigates the momentum-dependent symmetries for nonholonomic nonconservative Hamilton canonical systems. The definition and determining equations of the momentum-dependent symmetries are presented, based on the invariance of differential equations under infinitesimal transformations with respect to the generalized coordinates and generalized momentums. The structure equation and the non-Noether conserved quantities of the systems are obtained. The inverse issues associated with the momentum-dependent symmetries are discussed. Finally, an example is discussed to further illustrate the applications.     

Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems

This paper concentrates on studying the Lie symmetries and conserved quantities of controllable nonholonomicdynamicM systems. Based on the infinitesimal transformation, we establish the Lie symmetric determining equationsand restrictive equations and give three definitions of Lie symmetries before the structure equations and conservedquantities of tile Lie symmetries are obtained. Then we make a study of the inverse problems. Finally, an example ispresented for illustrating the results.