一类积分—微分方程离散谱的存在性

本文讨论在迁移理论中出现的一类较广泛的积——微分方程,研究方程所确定的算子的离散谱存在的充分必要条件,并给出了离散谱存在的一个充分条件。     

“数学物理方法”中关于希尔伯特空间的教学改革实践

目前国内物理专业为期一学期的“数学物理方法”课程多缺乏对于希尔伯特空间及相关概念的讲解,然而此部分内容对于物理专业的后续学习非常重要.为了进一步提高“数学物理方法”课程的教学效果,针对希尔伯特空间部分进行了教学改革实践.本文阐述了本次教学改革的教学安排和授课内容,展示了收集到的效果反馈,并对其进行了讨论和分析,从而得出一些具有建设性的改革方向,为大家进一步教学改革提供参考.     

A Hierarchy of Integrable Nonlinear Lattice Equations and New Integrable Symplectic Map

A discretespectral problem is discussed.and a hierarchy of integrable nonlinear lattice equations related to this spectral problem is devised.The new integrable symplectic map and finite-dimensional integrable systems are given by nonlinearization method.The binary Bargmann constraint gives rise to a Baecklund transformation for the resulting integrable lattice equations.     

Solutions to Generalized mKdV Equation

A transformation is introduced for generalized mKdV (GmKdV for short) equation and Jacobi elliptic function expansion method is applied to solve it. It is shown that GmKdV equation with a real number parameter can be solved directly by using Jacobi elliptic function expansion method when this transformation is introduced, and periodic solution and solitary wave solution are obtained. Then the generalized solution to GmKdV equation deduces to some special solutions to some well~known nonlinear equations, such as KdV equation, mKdV equation, when the real parameter is set specific values.     

XYZ自旋开链的Lax及其边界K矩阵

明显构造了开边界条件下ＸＹＺ模型的Ｌａｘ对，进而得到了其一般边界Ｋ矩阵。     

浅谈工科积分变换课程教学

分析了工科院校的积分变换课程的内容特点和授课对象的特点,指出了工科积分变换课程教学中遇到的问题,给出了课程教学中问题解决的一些见解.     

High-order perturbed corrections with scaling transformation

The performance of the so-called superconvergent quantum perturbation theory （Wenhua Hal et al2000 Phys. Rev. A 61 052105） is investigated for the case of the ground-state energy of the helium-like ions. The scaling transformation τ → τ/Z applied to the Hamiltonian of a two-electron atomic ion with a nuclear charge Z （in atomic units）. Using the improved Rayleigh-SchrSdinger perturbation theory based on the integral equation to helium-like ions in the ground states and treating the electron correlations as perturbations, we have performed a third-order perturbation calculation and obtained the second-order corrected wavefunctions consisting of a few terms and third-order energy corrections. We find that third-order and higher-order energy corrections are improved with decreasing nuclear charge. This result means that the former is quadratically integrable and the latter is physically meaningful. The improved quantum perturbation theory fits the higher-order perturbation case. This work shows that it is a development on the quantum perturbation problem of helium-like systems.     

Nonlocal Symmetries to Systems of Nonlinear Diffusion Equations

In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Thosesystems have physical applications in soil science, mathematical biology, and invariant curve flows in R^3. Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded.     

Integrable Coupling of （2＋1）-Dimensional Multi-component DLW Integrable Hierarchy and Its Hamiltonian Structure

A new multi-component Lie algebra is constructed, and a type of new loop algebra is presented. A （2＋1）-dimensional multi-component DLW integrable hierarchy is obtained by using a （2＋1）-dimensional zero curvature equation. Furthermore, the loop algebra is expanded into a larger one and a type of integrable coupling system and its corresponding Hamiltonian structure are worked out.     

One-Step Implementation of Mulitqubit Quantum Phase Gate in a Cavity QED System

An alternative protocol is proposed to implement three-qubit phase gate between photon and atoms in a high-Q bimodel optical cavity. The idea can be extended to directly implement N-qubit phase gate, and the gating time that is required to implement the protocol does not rise with increasing number of qubits. The influence of cavity decay and atomic spontaneous emission on the gate fidelity is also discussed.