Lam函数和非线性演化方程的扰动方法

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.应用Jacobi椭圆函 数展开法求得了零级近似方程的准确解，并由此得到一级近似方程和二级近似方程分别满足 齐次Lam方程和非齐次Lam方程，应用Lam函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解.这样，就求得了非线性演化方程的多级准确解. 关键词： Jacobi椭圆函数 Lam函数 多级准确解 非线性演化方程 扰动方法     

特勒根方程及其应用

应用变分法的特勒根（Ｔｅｌｌｅｇｅｎ）方程，可 以很方便地解决物理学中某些复杂的问题．虽然用此 方法所求得的解是一个近似解，但只要设计合理、步 骤正确，这个近似解将有足够满意的精度．本文将用 一常见的闭合回路导出特勒根方程，并加以推广，使之具有普遍意义，再举例说明它的应用方法。     

研究碱金属原子的一个较理想的势能函数

本文对碱金属原子引入势能函数Ｖｒ）＝后解薛定谔方程求得其能量表式，解释了碱金属原子光谱的实验规律．在此基础上，将经典相对论的质量修正相应引入碱金属原子的哈密顿算符中，用近似方法求出其能量的相对论修正的一级近似．这是用量子力学方法讨论碱金属原子的一种简略方法，也是一种粗略的近似．     

Lam函数和非线性演化方程的扰动方法

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程 .应用Jacobi椭圆函数展开法求得了零级近似方程的准确解 ,并由此得到一级近似方程和二级近似方程分别满足齐次Lam 方程和非齐次Lam 方程 ,应用Lam 函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解 .这样 ,就求得了非线性演化方程的多级准确解 .     

Lamé函数和非线性演化方程的扰动方法

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.应用Jacobi椭圆函数展开法求得了零级近似方程的准确解,并由此得到一级近似方程和二级近似方程分别满足齐次Lamé方程和非齐次Lamé方程,应用Lamé函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解.这样,就求得了非线性演化方程的多级准确解.     

与一个非局域对称有关的Kaup-Kupershmidt方程新的精确解

利用Kaup-Kupershmidt（KK）方程的一个非局域对称，可在两种不同的方法上找到方程新的精确解．首先，用标准的展开近似得到KK方程有限的Lie-B?cklund变换和单孤子解．其次，把一些局域对称与这个非局域对称组合起来，给出其群不变解，进而可求得新的孤子解 关键词：     

LU(1)群的引力规范场球对称静态解

寻找引力规范理论场方程的严格解要比寻找Einstein场方程的严格解更为困难。但是,对某些物理问题来说,能够求得牛顿型近似解和后牛顿型的近似解就足够了。本文研究了一种Lorentz群和U(1)群为规范群的引力规范理论,求得了带电粒子的球对称静场的特殊有挠解,并求得了有挠的一阶近似解。     

L?(1)群的引力规范场球对称静态解

寻找引力规范理论场方程的严格解要比寻找Einstein场方程的严格解更为困难。但是,对某些物理问题来说,能够求得牛顿型近似解和后牛顿型的近似解就足够了。本文研究了一种Lorentz群和U(1)群为规范群的引力规范理论,求得了带电粒子的球对称静场的特殊有挠解,并求得了有挠的一阶近似解。 关键词：     

一个赤道太平洋西部边界潜流广义扰动机理的近似解法

研究了一类赤道太平洋西部边界潜流的摄动机理. 考虑了对应的广义控制方程. 首先引入了一个优化的同伦映射，利用相应的映射求得了原模型的近似解. 最后，通过一个例子说明了用同伦映射方法得到的近似解具有较好的精确度. 关键词： 潜流 摄动 近似解     

两自由度带电耦合振子系统的守恒量与近似解

由于两自由度带电耦合振子系统的Lagrange函数中存在耦合项,从而导致其运动微分方程是非线性耦合的.先通过坐标变换消去Lagrange函数中的耦合项,用直接积分法求得系统的守恒量,用Adomian分解法求得系统的近似解,再通过坐标反变换求得系统在原坐标下的守恒量与近似解,并对近似解作了讨论.     

S_2分子的从头算研究

采用了微机版的Ｇａｕｓｓｉａｎ９４程序以及ＣＩＳ方法和ＣＩＳ－ＭＰ２方法对Ｓ２分子的部分单重激发态和三重激发态进行了研究。计算表明：ＣＩＳ方法和ＣＩＳ－ＭＰ２方法对Ｓ２分子的２低单重激发态基本适用,可以给出较为满意的结果。但对Ｓ２分子的三重激发态和高激发态,ＣＩＳ方法还需进上步改进。     

Photon statistical properties of the cavity field in the two-atom Jaynes-Cummings model

The model that two two-level atoms interact with a singel-mode cavity is studied. The exact solution of the time evolution operator for the two-atom Jaynes-Cummings model is presented by the bare-states approach. Furthermore, we investigate the dynamical     

S_2分子的从头算研究

采用了微机版的Gaussian 94程序以及CIS方法和CIS MP2方法对S2 分子的部分单重激发态和三重激发态进行了研究。计算表明 :CIS方法和CIS MP2方法对S2 分子的低单重激发态基本适用 ,可以给出较为满意的结果。但对S2 分子的三重激发态和高激发态 ,CIS方法还需进一步改进。     

Exact Solution of the Milburn Equation for the Two—Mode Two—Photon Jaynes—Cummings Model

We adopt an algebraic method to study the two-mode two-photon Jaynes-Cummings model governed by the Milburn equation and find an exact solution of Milburn equation of the system.The influence of the intrinsic decoherence on the nonclassical effects of the system is also discussed.     

Stationary State Entanglement of Two Atoms Inside an Optical Cavity under Noise

In this paper, the entanglement properties of a system of two atoms inside an optical cavity in a stochastic interaction with field are studied by the Jaynes-Cummings Model. The phase telegraph noise is considered as a noise term and an exact solution to the model is obtained. The solution reveals the resulting decoherence effects of the noise on the entanglement properties of the system. It shows that under the noise the individual atoms do not entangle with the cavity field. However, a strong atom-atom entanglement is observed in a stationary state. It is seen that a relatively strong noise is cooperative in the construction of the steady state atom-atom entanglement.     

HIGHER-ORDER CORRECTION FOR ROTATING WAVE APPROXIMATION, RABI TRANSFORMATION, AND ITS APPLICATIONS IN THE JAYNES-CUMMINGS MODEL

Taking into account the consistence of the quantum adiabatic approximation and the rotating wave approximation in essence, we propose a method to study the interaction between atom and radiation field in a quantized cavity systematically. By using the exact solution of Jaynes-Cummings model as the lowest-order approximation, the effect of high frequency terms on the dynamics of atom-cavity field system is studied analytically.     

Effect of Intrinsic Decoherence on Nonclassical Effects of the Nondegenerate Bimodal Multiquanta JCM

We study the nondegenerate multiquanta Jaynes-Cummings model governed by Milburn equation. This models the decoherence of a quantum system as it evolves through intrinsic mechanisms beyond conventional quantum mechanics governed by the Schrödinger equation. We find an exact solution of this equation and apply it to investigate the effects of the intrinsic decoherence on nonclassical effects of the system, such as collapses and revivals of the population inversion and squeezing of the radiation field, for the resonant and the off-resonant cases when the particle (atom or trapped ion) is taken to be prepared initially in a coherent superposition state.     

Von Neumann entropy and phase distribution of two mode parametric amplifier interacting with a single atom

In the present article, we introduce a Hamiltonian model that consists of two modes of the field in a perfect cavity to interact with a single two-level atom. The interaction between the fields has been taken into account and considered to be in the parametric amplifier form. The model in one hand can be regarded as a generalization of the Jaynes-Cummings model (JCM), however, in the other hand it can be considered as a generalization of the parametric amplifier model. Under a certain condition the exact solution to the Schrödinger equation is obtained. Employing this solution and for chosen values of different parameters we discuss numerically the atomic occupation probabilities as well as the degree of entanglement through the entropy of the field. The system shows superstructure phenomenon similar to that appeared from the effect of the Kerr-like medium on the Jaynes-Cummings model. The von Neumann entropy and phase distribution for both two-mode correlated and uncorrelated coherent states cases are also considered.     

Entanglement dynamics in atom-field interaction in the presence of noise: a special application of the Burshtein equation

The entanglement dynamics in a system of the interaction of an atom with a single-mode thermal field in the presence of noise is studied by the Jaynes-Cummings model. Two-state random phase telegraph noise is considered as the noise in the interaction and an exact solution to the model under this noise is obtained by the Burshtein equation. Although the Burshtein equation is applicable for laser-atom interactions, it is shown that it can be applied to atom-thermal field system as a special case. The solution is used to investigate the entanglement dynamics of the atom-field interaction by calculating a lower bound on concurrence. It is found that the entanglement is a non monotonic function of the intensity of the noise. The degree of the entanglement decreases to a minimum value for an optimal intensity of the noise and then increases for a sufficiently large intensity. Moreover, intense noise may generate stronger entanglement compared with the absence of noise.