表面张力-重力短峰波作用的海底边界层速度二阶解

依据最近提出的三阶表面张力-重力短峰波理论,通过求解经典的Prandtl边界层方程,给出海底边界层速度的二阶解析解,为确定海底边界层的质量输运提供了一个必备的先行理论基础.     

修正高阶非线性薛定锷方程的解析孤波解

解析求解了考虑喇曼自频移效应后的修正高阶非线性薛定锷方程.为了获得精确解,引入了非线性增益和失谐效应.结果给出精确亮孤波解和暗孤波解的表达式,同时给出了两种解存在的参量条件,并且指出亮孤波解存在于负三阶色散区,而暗孤波解存在于正三阶色散区.     

半导体激光器输出功率的线性特性研究

本文从理论上研究了半导体激光器输出功率的线性特性.通过求出半导体激光器多模速率方程组的隐式解析解,我们获得了半导体激光器输出功率对电流的一阶至三阶导数的解析表达式.在此基础上,我们模拟了半导体激光器的输出功率和输出功率对电流的一阶至三阶导数随电流的变化曲线.     

一维非自治经典谐振子的精确解析解

一维时间相关的经典谐振子是一个SU(1,1) 非自治经典系统,物理上十分有用,而数学上难于得到其精确解析解. 首次把新颖的代数动力学方法用于经典动力学系统,得到了这个模型的一般精确解;当时间相关的弹性系数为某些初等函数时,给出了精确解的解析形式. 这是关于这一问题的重要结果. 从精确解出发,推导出最近文献中提出的"解析近似解",并指出该近似解的适用条件.     

基于格林函数法的奇型Mathieu-Gaussian光束

根据光束传播的独立性和叠加性原理,引入了一组能够产生第一类(2n+2阶)奇型Mathieu-Gaussian光束的虚光源点.利用虚源点技术和格林函数法,计算得到第一类奇型Mathieu-Gaussian光束的严格解析积分表达式.利用该表达式得到了轴上光场分布的积分解析解.以三阶非旁轴修正为例,得到了第一类奇型Mathieu-Gaussian光束保留到三阶非旁轴修正项的轴上光场分布精确解.     

一般反射短峰波的普适法则——倍频率通向短峰波

考虑环境均匀流效应,给出从垂直防波堤发生一般部分反射短峰波的三阶解析解.据此推断出一项普适法则:倍频率通向短峰波.     

一般反射短峰波的普适法则——倍频率通向短峰波

考虑环境均匀流效应,给出从垂直防波堤发生一般部分反射短峰波的三阶解析解.据此推断出一项普适法则：倍频率通向短峰波.     

经典三阶驻波、短峰波的有效匹配解

发现经典非线性三阶驻波、短峰波解并不满足其所必须的波幅方程,这势必要影响与这些经典理论密切相关的现代短峰波理论的发展.基于此,提出了一套消除这种解与方程不相匹配的理论判据,从而可充分保证最终所得之解的内在和谐性和正确性. 关键词： 匹配解 理论判据 驻波 短峰波     

微环辅助Mach-Zehnder光调制器的线性特性

分析了有损耗的多环辅助Mach-Zehnder(MZ)光调制器,获得了在偏置点处令二阶和三阶高次项同时为零的方程,并在此基础上解得单环和双环辅助下的设计参量的解析表达式.利用解析式可方便地得到在偏置点处二阶和三阶高次项同时为零的高线性MZ光调制器的设计方案.同时对微环辅助MZ光调制器的特性进行了分析.     

高阶色散效应常系数Ginzburg-Landau方程自相似脉冲演化的解析分析

采用自相似分析方法,基于常系数高阶色散的Ginzburg-Landau方程,通过分离变量法得出了高阶色散效应自相似脉冲演化的解析解,给出了自相似脉冲的振幅、相位、啁啾以及脉冲宽度的一般表达式.研究表明,在增益光纤的二阶正常色散区域,同时考虑高阶色散和增益色散双重效应影响下演化的自相似孤子脉冲仍然保持线性啁啾;振幅解析解的三阶色散效应显著.这与数值计算的结果非常一致. 关键词： 三阶色散 Ginzburg-Landau方程 自相似脉冲 二阶正常色散     

Quantum and Classical Exact Solutions of Harmonic Oscillator in a Time-Dependent Magnetic Field

In cylindrical coordinate, exact wave functions of the two-dimensional time-dependent harmonic oscillator in a time-dependent magnetic field are derived by using the trial function method. Meanwhile, the exact classical solution as well as the classical phase is obtained too. Through the Heisenberg correspondence principle, the quantum solution and the classical solution are connected together.     

Classical and quantum oscillators of quartic anharmonicities: second-order solution

An analytical solution up to the second order in the coupling constant λ is obtained for a classical quartic anharmonic oscillator by using Taylor series method. Our solution yields, as a special instance, the corresponding results obtained by using Laplace transform. With the help of correspondence principle, the classical solution is used to obtain the solution corresponding to a quantum quartic anharmonic oscillator. In the weak coupling regime (i.e., anharmonic constant λ⪡1), the so-called secular terms in classical and quantum solutions are tucked in (summed up) to avoid the nonconvergence. Both the classical and quantum solutions are used to obtain the frequency shifts of the quartic oscillators. It is found that these frequency shifts coincide exactly with those of the earlier results obtained by other methods. From the quantum field theoretic point of view, our solution exhibits the so-called Lamb shift. As an application of the solution for the quantum oscillator, we examine the possibility of getting squeezed states out of the input coherent light interacting with a nonlinear medium of inversion symmetry.     

The rotating two-electron atom in an external electric field

Three rigid-body solutions for a rotating two-electron atom under the influence of an electric field along the rotation axis have been obtained within a classical approach. One exact solution gives in the zero-field case a previous result known as a rotor, another exact solution in the zero-field case gives the Wannier unbound solution, and a numerical solution in the zero-field case gives the asymmetric top or Langmuir solution. The stability analysis of the linearized motions around each of the equilibrium configurations was made for different values of the electric field. We find critical values of the electric field beyond which no equilibrium exists. Values for the classical polarizability of rotating H^– and He are reported.     

Conformal Fluctuations of the Interior Schwarzschild Solution

The basic formalism for conformal fluctuations of the gravitational field is presented. After developing a master propagator for the interior Schwarzschild solution, the time development of the gravitational wave function is considered. The effect of the two classical singularities (resp. pseudo-singularities) of the Schwarzschild solution on the quantum wave function for the gravitational field is studied using a wave function initially localized on the classical solution. While the true singularity at r = 0 imparts consequences on the wave function that cannot be ignored, the pseudo-singularity at the event horizon does not seem to cause any divergences on the interior fluctuations of the Schwarzschild solution.     

Korteweg-de Vries方程的准孤立子解及其在离子声波中的应用

应用推广的tanh函数展开法,给出了Korteweg-de Vries方程具有准孤立子行为的两组孤子-椭圆周期波解,其中一组为新解.推导了均匀磁化等离子体中描述离子声波动力学行为的Korteweg-de Vries方程,发现电子分布、离子电子温度比、磁场大小、磁场方向对离子声准孤立子的波形具有显著影响.     

Extending Newton's law from nonlocal-in-time kinetic energy

We study a new equation of motion derived from a context of classical Newtonian mechanics by replacing the kinetic energy with a form of nonlocal-in-time kinetic energy. It leads to a hypothetical extension of Newton's second law of motion. In a first stage the obtainable solution form is studied by considering an unknown value for the nonlocality time extent. This is done in relation to higher-order Euler-Lagrange equations and a Hamiltonian framework. In a second stage the free particle case and harmonic oscillator case are studied and compared with quantum mechanical results. For a free particle it is shown that the solution form is a superposition of the classical straight line motion and a Fourier series. We discuss the link with quanta interpretations made in Pais-Uhlenbeck oscillators. The discrete nature emerges from the continuous time setting through application of the least action principle. The harmonic oscillator case leads to energy levels that approximately correspond to the quantum harmonic oscillator levels. The solution to the extended Newton equation also admits a quantization of the nonlocality time extent, which is determined by the classical oscillator frequency. The extended equation suggests a new possible way for understanding the relationship between classical and quantum mechanics.     

Numerical evaluation of the one-loop effective action in static backgrounds with spherical symmetry

The problem of evaluating the one-loop quantum corrections to the energy of classical solution is ubiquitous in elementary particle physics. In many cases already the classical solution is known only numerically so that methods based on exact wave functions for the quantum excitations cannot be applied. We propose here a numerical method based on the use of Euclidean Green's functions which allows to extract the finite parts after Lorentz covariant regularization and renormalization.     

Diffusion in fluids with large mean free paths: Non-classical behavior between Knudsen and Fickian limits

Diffusion in fluids is analyzed at non-classical conditions, intermediate between the Knudsen and Fickian limits. The fluid is considered in the framework of the Einstein’s diffusion evolution equation involving expansions of the density distribution in powers of displacement and time. The standard truncation of these expansions results in the classical model of diffusion; however, higher-order terms lead to a departure from classical behavior. This has not been studied or discussed adequately in the literature previously.Here, we present an exact solution of the Einstein’s diffusion evolution equation without truncation of the density expansions. This solution illustrates limitations in the classical truncations and demonstrates non-classical effects due to large mean free paths, λ. In particular, this new solution shows that, at large λ, there are significant quantitative deviations from classical diffusion profiles. In addition, this solution demonstrates a dramatic change in the diffusion mechanism from the state where the molecular motions are predominantly ballistic to one of molecular chaos. This has implications for fundamentals of fluids between the Knudsen and Fickian limits, and for a variety of fields where evolution of a system includes random, multi-scale displacement of particles, such as nanotechnology, vacuum techniques, turbulence, and astrophysics.     

Is Classical Reality Completely Deterministic?

We interpret the concept of determinism for a classical system as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally believed to hold for all autonomous classical systems. Our analysis of classical electrodynamics in a world with one temporal and one spatial dimension provides counterexamples of this belief. Given the initial conditions of a particular type, the Cauchy problem may have an infinite set of solutions. Therefore, random behavior of closed classical systems is indeed possible. With this finding, we give a qualitative explanation of how classical strings can split. We propose a modified path integral formulation of classical mechanics to include indeterministic systems.     

Classical Liouville action on the sphere with three hyperbolic singularities

The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy–momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.