一族离散的可积Hamilton方程与可积的辛映射

该文讨论一个新的离散特征值问题，导出了相应的离散的Hamilton系统的保谱族，并且证明了它们是Liouville可积系。通过谱问题的双非线性化，导出一个新的可积的辛映射 。      

半无限晶体中慢速运动的表面极化子

本文研究电子与体纵光学声子耦合弱、与表面光学声子耦合强的半无限晶体中的表面极化子的性质.采用改进了的线性组合算符法和微扰法导出了半无限晶体中的慢速运动极化子的有效哈密顿量.在计及电子在反冲效应中发射和吸收的不同波矢的声子之间的相互作用时,讨论了对有效哈密顿量,诱生势和有效质量的影响.对AgBr晶体进行了数值计算,结果表明反冲效应中发射和吸收的不同波矢的声子之间的相互作用对有效质量和诱生势的影响随耦合常数αt的增加而增加,对有效质量的影响随坐标z的增加而减小的更多,对诱生势的影响随z的增加而增加的更多.     

Translations and Associated Dirichlet Polyhedra in Complex Hyperbolic Space

We study a nonidentity transvection (i.e. (strictly) hyperbolic isometry) or nonidentity Heisenberg translation f of complex hyperbolic space H ⁿ and a Dirichlet polyhedron P of the cyclic group f. We have four main results: (a) If z & in H ⁿ and the axis of a nonidentity transvection are not complex collinear, then, roughly speaking, any two distinct 'naturally arising' geodesics passing through z are not complex collinear. (b) If g is also a transvection or Heisenberg translation of H ⁿ and z & in H ⁿ such that f(z)=g(z) and f ^–1(z)=g ^–1(z), then f=g. (c) We classify all this kind of polyhedra up to congruence in H ⁿ. (d) We obtain an equivalent condition for P to be cospinal (which means that the complex spines of the two sides of P coincide) in terms of the distance of the spines of the two sides of P.     

Nonintegrability of a Fifth-Order Equation with Integrable Two-Body Dynamics

We consider a fifth-order partial differential equation (PDE) that is a generalization of the integrable Camassa–Holm equation. This fifth-order PDE has exact solutions in terms of an arbitrary number of superposed pulsons with a geodesic Hamiltonian dynamics that is known to be integrable in the two-body case N==2. Numerical simulations show that the pulsons are stable, dominate the initial value problem, and scatter elastically. These characteristics are reminiscent of solitons in integrable systems. But after demonstrating the nonexistence of a suitable Lagrangian or bi-Hamiltonian structure and obtaining negative results from Painlevé analysis and the Wahlquist–Estabrook method, we assert that this fifth-order PDE is not integrable.     

General Solution for Hamiltonians with Extended Cubic and Quartic Potentials

In terms of hyperelliptic functions, we integrate a two-particle Hamiltonian with quartic potential and additional linear and nonpolynomial terms in the Liouville integrable cases 1:6:1 and 1:6:8.     

Two-Step High Order Starting Values for Implicit Runge–Kutta Methods

In this article a simple form of expressing and studying the order conditions to be satisfied by starting algorithms for Runge–Kutta methods, which use information from the two previous steps is presented. In particular, starting algorithms of highest order for Runge–Kutta–Gauss methods up to seven stages are derived. Some numerical experiments with Hamiltonian systems to compare the behaviour of the new starting algorithms with other existing ones are presented.     

Spectral Properties of Hamiltonians of Charged Systems in a Homogeneous Magnetic Field: II. The Structure of the Pure Point Spectrum

We study the pure point spectrum of the energy operator H(P ) of a many-particle charged quantum system in a homogeneous magnetic field based on the results in our previous work under fixation of the sum P of the pseudomomentum components of the system. We prove that the discrete spectrum H(P ) of a short-range system is infinite under some conditions (which, for example, hold for a system of two oppositely charged particles) even in the case of a finitely supported potential. For a long-range system of the type of a (+)-ion of an atom (including the ion), the discrete spectrum is infinite.     

基于哈密顿体系的平面无限解析元

在有限元法中,无限域的问题不便于处理求解。但无限域往往可以由规则的无限外域再加上有限的局部域组成。将无限域问题中的有限局部域用有限元法处理,在规则的无限外域中建立极坐标系,将规则无限域问题导向哈密顿体系,利用本征向量展开的方法,推导出一种新的半解析无限解析元,其刚度阵是精确的。该单元可用常规方法作为一个超级有限单元与有限的局部域连接。数值计算结果表明,该单元具有精度高,应用方便,数据处理非常简单的特点。对无限域问题的数值求解有重要意义。该方法可推广到三维无限域问题中。     

The one-dimensional Hubbard model for large or infiniteU

The magnetic properties of the one-dimensional Hubbard model with a hardcore interaction on a ring (periodic boundary conditions) are investigated. At finite temperatures it is shown to behave up to exponentially small corrections as a pure paramagnet. An explicit expression for the ground-state degeneracies is derived. The eigenstates of this model are used to perform a perlurbational treatment for large but finite interactions. In first order inU ¹ an effective Hamiltonian for the one-dimensional Hubbard model is derived. It is the Hamiltonian of the one-dimensional Hcisenberg model with antiferromagnetic couplings between nearest neighbor spins. An asymptotic expansion for the ground-state energy is given. The results are valid for arbitrary densities of electrons.