高离化Kr33+离子22P -n2S(2≤n≤9)的耦极跃迁行为

本文构造了高离化Kr33+离子 1s2ns (2≤n≤9)和1s22p 态的波函数并利用其计算了体系的非相对论能量。为了得到高精度的理论计算结果,将相对论修正和质量极化效应作为一级微扰计算了体系的总能量和22P -n2S(2≤n≤9)跃迁能,本文的结果与有限的实验数据符合的较好。在此基础上完成了22P -n2S(2≤n≤9)偶极跃迁三种规范下振子强度的理论计算,三者的一致性进一步证明所构造的波函数在整个空间的准确性和可靠性。     

高功率高增益大直径相对论返波管

对大直径同轴相对论返波管采用双板波纹波导模型结合电子运动的罗伦兹力方程、电荷连续性方程和电磁波麦克斯韦方程建立了系统的线性流体理论.使用该理论详细地研究了器件的各系统参数对束波相互作用,特别是对微波指数增长率的影响.给出了3cm波段的大直径同轴相对论返波管实验装置的系统参数.     

非谐振腔型KTP光参变振荡器

研究了双晶体走离补偿、非谐振腔型KTP光参变振荡器，利用一套膜片实现了KTP相位匹配所允许的全波段调谐，信号光调谐范围0.698μm-1.026μm，闲频光调谐范围1.105μm-2.237μm。5倍阈值处，信号光840nm最高输出能量53mJ，能量转换效率25.8%，量子转换效率40％，闲频光的量子郊率也达到32％。     

An open plus nonlinear closed loop control of chaotic oscillators

An open plus nonlinear closed loop control law is presented for chaotic oscillations described by a set of nonautonomous second-order ordinary differential equations.It is proven that the basins of entrainment are global when the right-hand sides of the equations are given by arbitrary polynomical functions.The forece Duffing oscillator and the forced van der Pol oscillator are treated as numerical examples to demonstrate the applications of the method.     

A priori tests of a stochastic mode reduction strategy

Several a priori tests of a systematic stochastic mode reduction procedure recently devised by the authors [Proc. Natl. Acad. Sci. 96 (1999) 14687; Commun. Pure Appl. Math. 54 (2001) 891] are developed here. In this procedure, reduced stochastic equations for a smaller collections of resolved variables are derived systematically for complex nonlinear systems with many degrees of freedom and a large collection of unresolved variables. While the above approach is mathematically rigorous in the limit when the ratio of correlation times between the resolved and the unresolved variables is arbitrary small, it is shown here on a systematic hierarchy of models that this ratio can be surprisingly big. Typically, the systematic reduced stochastic modeling yields quantitatively realistic dynamics for ratios as large as 1/2. The examples studied here vary from instructive stochastic triad models to prototype complex systems with many degrees of freedom utilizing the truncated Burgers–Hopf equations as a nonlinear heat bath. Systematic quantitative tests for the stochastic modeling procedure are developed here which involve the stationary distribution and the two-time correlations for the second and fourth moments including the resolved variables and the energy in the resolved variables. In an important illustrative example presented here, the nonlinear original system involves 102 degrees of freedom and the reduced stochastic model predicted by the theory for two resolved variables involves both nonlinear interaction and multiplicative noises. Even for large value of the correlation time ratio of the order of 1/2, the reduced stochastic model with two degrees of freedom captures the essentially nonlinear and non-Gaussian statistics of the original nonlinear systems with 102 modes extremely well. Furthermore, it is shown here that the standard regression fitting of the second-order correlations alone fails to reproduce the nonlinear stochastic dynamics in this example.     

Heisenberg方程的保结构计算

出了Heishenberg方程的保等时交换关系-辛格式,为Heishenberg图景下计算量子系统(特别是时间相关外场中的原子)的时间演化提供了保结构的算法,用这种算法计算了一个非线性谐振子,结果显示保等时交换关系-辛格式对求解Heishenberg方程是精确和有效的.     

相位差与q变形广义相干叠加态的压缩特性

对于q变形的非简谐振子广义相干态的叠加态β〉+eiφβeiδ〉,其量子涨落的可能高阶压缩阶数可以表示为k≠2πn/δ,这里n是整数.当δ=π时,压缩阶数不能是偶数即只能是奇数,这正是q变形非简谐振子广义奇偶相干态的结果.由此表明参数相位差δ对决定q变形的非简谐振子广义相干态叠加态的高阶压缩阶数起决定性作用.     

有界随机噪声激励下软弹簧Duffing振子的安全盆分叉

研究了软弹簧Duffing振子在有界随机噪声激励下，系统安全盆的侵蚀现象，并提出了随机安全盆分叉的概念. 计算表明，由于随机扰动的影响，系统的随机安全盆分叉点发生了偏移. 关键词： Duffing振子 有界随机噪声 安全盆 分叉     

On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point

We consider the two-dimensional stochastic Ising model in finite square with free boundary conditions, at inverse temperature >₀ and zero external field. Using duality and recent results of Ioffe on the Wulff construction close to the critical temperature, we extend some of the results obtained by Martinelli in the low-temperature regime to any temperature below the critical one. In particular we show that the gap in the spectrum of the generator of the dynamics goes to zero in the thermodynamic limit as an exponential of the side length of , with a rate constant determined by the surface tension along one of the coordinate axes. We also extend to the same range of temperatures the result due to Shlosman on the equilibrium large deviations of the magnetization with free boundary conditions.