查询词典 Hamiltonian

The hamiltonian problem named for Sir William Rowan Hamilton can trace its origins to the 1850s. In 1971 Bondy [11] posed that the graph was hamiltonian also implies that it was pancyclic (except for maybe a simple family of exceptional graphs).

哈密尔顿问题在十八世纪五十年代由William Rowan Hamilton提出，在1971年，Bondy 在[11]中提出除了一部分特殊的图类外，如果一个图是哈密尔顿的蕴涵了这个图也是泛圈图。

Further, with the help of Riccati equations, an infinite number of conservation laws for the solton hierarchy are deduced. For the sake of simplicity, taking the general TD hierarchy as an illustrative example, we prove that its 2×2 Lenard pair of operators forms a Hamiltonian pair. Thus the isospectral evolution TD hierarchy is the general Hamiltonian system and possesses the Bi-Hamiltonian structures and Multi-Hamiltonian structures. By using the method of derivation of functional under some constraint condition, a complete one-to-one correspondence between the Hamiltonian functions of the hierarchy and its conservation density functions can be built. These results can also be applied to the isospectral evolution soliton hierarchy of this paper. Finally, there's a gauge transformation between the spectral problem of this paper and the AKNS system. Moreover, the potentials in these spectral problems satisfy the general Miura transformation, the corresponding relationship between the two soliton hierarchies is also given.

进一步本文还通过特征函数的组合关系所满足的Riccati方程，得到了该等谱方程族的无穷多个守恒律；为简便起见，本文以广义TD族为例，由它的2×2 Lenard算子对的性质证明了此算子对为Hamilton算子对，这说明广义TD族是广义Hamilton系统且具有Bi-Hamilton结构和Multi-Hamilton结构；进而利用它的依赖于谱参数的一般守恒密度的积分在约束条件下求泛函导数的方法，得到了广义TD族的Hamilton函数与守恒密度之间的对应关系，这些性质对于由本文提出的2×2谱问题所导出的等谱孤子族仍成立；另外此谱问题与AKNS系统存在着规范变换，位势之间有广义Miura变换，而孤子方程之间也满足一定的等价关系。

In this thesis the process of constructing the non-perturbative Hamiltonian theory is de-scribed and is applied to estimate the vacuum condensate. It contains the following contents:At the very beginning, by using the path integral method and eliminating the gluon freedom, aGCM action 〓 of current quarks including lower order current-current coupling was derivedfrom the QCD Lagrangian and the effective Hamiltonian operator that could hardly be doneby the normal methods was derived. After doing this, the broken vacuum is introduced whichincludes quark-antiquark condensate through the generalized Bogoliubov-Valatin transformation,the effective Hamiltonian of constituent quark was derived. The detailed formulas containingthe spatial current-current coupling term for the effective Hamiltonian and gap equations wasworked out by parameterizing the correlation kernel as a quadratic potential. And then, the gapequation was solved and the quark-antiquark condensate of vacuum was studied both in the casesof instantaneous interaction and retarded interaction. In the end, the effective Hamiltionian withtwo-body quark-quark interaction was derived with one-body approximation, and with the helpof the functional integral method the coupling non-linear dynamic equations for systems withnuclear matter was derived. Finally, these equations were solved by selfconsistent method andthe effect of nuclear matter on vacuum condensate was studied. The spatial current-current coupling term is too difficult to handle, hence the correlationkernel is assumed to be not important and usually omitted in the pure vacuum condensate, andthe instantaneous interaction generally is adopted. Retaining the spatial current-current termand partial retardation effect, the quark pairs condensate in pure vacuum was studied, and theeffect of quark mass was also studied. At present, little study is focused in the case with nuclearmatter and spatial current-current term also omitted. Under the approximation with partialspatial current-current term, the effect of nuclear matter on vacuum condensate was studied.

本论文描述了量子色动力学整体色对称模型哈密顿量方法的构建过程，得到了反映正反夸克对凝聚真空结构的关于组分夸克的有效哈密顿量算符，它隐含了胶子作用，并且准确至流-流耦合项；接着，通过参数化哈密顿量中的夸克作用关联核，导出平方禁闭势参数化选择的哈密顿量的具体公式和能隙方程；随后，应用公式，编程求解，考察了瞬时作用下和部分延迟作用下真空的正反夸克对凝聚，在计算中保留了空间流-流耦合作用；之后，导出瞬时势和延迟势下包含二体作用项的哈密顿量公式，并采用单体化近似，通过泛函变分方法得到核物质存在时耦合的非线性动力学方程；在保留部分空间双流耦合作用的近似下，求解核物质的动力学方程，考察核物质密度对真空凝聚的影响，以往考察真空凝聚，对关联核的选用，由于空间流-流耦合项不易处理，也认为作用不大，常忽略该项，并且常采用瞬时作用；本文保留空间双流项和部分延迟作用，考察了真空情形的夸克对凝聚，还考察了夸克质量对纯真空凝聚的影响，以往对核物质存在情形的真空凝聚考察很少，也都忽略空间流-流项，本文在考虑部分空间流-流项近似下，考察了核物质存在对真空凝聚的影响。

The abstract result contains several concrete results in the literature and can also be used to deal with some new cases for resonant differential equations.In the introduction, we briefly introduce the development process of the variational methods. In Chapter 2, we list some basic knowledges refering to the variational methods, including the Sobobev space,—△ operator, the weak solution and the minimizing sequence methods and some minimax theorems. In Chapter 3, we introduce the research process of Hamiltonian system of second order and the semilinear elliptic problems, using the methods introduced previously. In Chapter 4, we prove the main theorem of the thesis, and apply it to the problems in the previous Chapter, and can also be applied to some new resonant cases.

在前言中，简要介绍了变分法的产生、发展过程，在第二章中我们介绍了有关变分法的一些基本知识，包括Sobolev空间，—△算子，弱解，极小化序列方法和一些极小极大定理，在第三章中我们介绍了非线性项有界或满足次线性条件，以及它满足推广的Ahmad-Lazer-Paul条件时，二阶Hamiltonian系统和半线性椭圆问题的研究历程，最后在第四章中我们证明了本论文的主要定理，并把它应用到第三章的问题中，使得前面的几种共振的情形都可以统一到这个抽象的结果中。

Contents: A Brief Review of Elementary Quantum Chemistry; An Introduction to Electronic Structure Theory; The Born-Oppenheimer Approximation; Time Evolution of Wavefunctions; Angular Momentum Summary; The Unitary Group Form of the Hamiltonian; Introduction to Hartree-Fock Theory; Permutational Symmetries of Integrals; Notes on Excited Electronic States; The Quantum Harmonic Oscillator; Assigning Symmetries of Vibrational Modes; Notes on Elementary Linear Algebra

内容： 初等量子化学的简评；电子结构理论的介绍；天生奥本海默的接近； Wavefunctions的时间演化；角动量摘要； Hamiltonian的单位的组形式；哈特里-Fock 理论的介绍；积分的Permutational对称性；在令人激动的电子国家上注明；这台量谐波振荡器；分配振动的方式的对称性；在初等线性代数上注明

SERID has following features:(1) The laser pulse is characterized by the vector potential A that is coupled to the Hamiltonian through the time-dependent Peierls substitution.

该方法有以下主要特点：(1)在电子Hamiltonian中通过时间有关的Peierls替代引入了辐射场与分子的相互作用。

The purpose of this paper is to give the way of solving the noncommutative KP hierarchy and noncommutative constraint KP hierarchy and their bi-Hamiltonian structures.

本文试图解决一般情形下的非交换KP系列及其对应约束下的cKP系列的求解问题和它们的双Hamiltonian结构。

Using the Hamiltonian constructed above, in theMajorana operator describing the vibrational interactions, we separate in the matrixelements the local mode couplings from the Fermi couplings, in order toinvestigate the Fermi resonance for linear triatomic molecules solely.

利用上一章建立的Hamiltonian，将描写振动相互作用的Majorana算子中的Darling-Dennison耦合项与Fermi耦合项分开，从而可以单独研究线形分子的Fermi共振现象。

In a quark model description of the nucleon, however, such time-derivative term might contribute because it is hard to construct a true Hamiltonian eigenstate of relativistic interacting quarks.

我们同样也注意到在一个复合粒子的现象模型中这一项可能是非零的，因为这个模型中的波函数可能不是真实的Hamiltonian本征态。

In this paper we turn the problem of sub-Riemannian geodesics into an optimal control problem, express the constraint to, and sub-Riemannian Hamiltonian H=1/2g^(-1)pl(subscript D, pl in detail.

该文从最优控制论的角度，将次黎曼刚地线问题转化为一个最优控制问题，将约束条件γ'∈D转化为，进而得到了次黎曼Hamiltonian H=1/2g^(-1)pl(下标 D， pl的具体形式。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了