秋千非线性参变共振解的简单推导

用另一种方法导出了秋千非线性动力学微分方程的近似解,很适合课堂讨论.     

A simple solution to the strong CP problem with a harmless axion

We describe a simple generalization of the Peccei-Quinn mechanism which eliminates the strong CP problem at the cost of a very light, very weakly coupled axion. The mechanism requires no new fermions and is easily implemented in grand unified theories.     

动态电路冲激响应初始值的一种简易求法

给出了求解动态电路冲激响应初始值和动态奇异电路响应初始值的一种简易方法.在电路换路后,其电容电压或电感电流的初始状态一般不产生跃变,但有时也可能产生跃变,当一时难于确定时,可先将电路化为其s域模型,并将0-值带进换路后的电路模型,再应用拉氏变换的初值定理,即可在s域解决t域响应的初始状态0 值的问题.该方法广泛适用于各种电路.     

A simple proof of the perturbative uniqueness of the Kerr solution

We present a mathematically simple and coordinate-free proof, based on the GHP spin-coefficient formalism, that a small stationary perturbation of a Kerr solution results in a new Kerr solution. Thus, under physically reasonable assumptions, we give a new and simple proof that a stationary black hole is given by a Kerr solution.     

A simple and direct periodic solution of the Korteweg-de vries equations

The solutionq(x, t) of one of the KdV hierarchy is assumed to be a potential in the Schrödinger equation as usual. We differentiate this equation with respect to the time variable and solve it with the aid of the Green function. The obtained equation relatesw _t (x, t, λ)=φ _t (x + c, x, t, λ) withq _t (x, t). The functionφ(x, x ₀,t, λ) obeys the Schrödinger equation and the boundary conditionsφ(x ₀,x ₀,t, λ)=0,φ _x (x ₀,x ₀;t, λ)=1. The shiftingc is equal to the period. We differentiatew _t (x, t, λ) three times with respect to thex coordinate and obtain the time derivative of the Milne equation. The integration of this equation with respect tox allows to solve simply the inverse problem. The reconstructed periodic potential is given by means of the well known formula for the root functions ofw(x, t, λ). The time behaviour of this function, i.e. the solution of the KdV equation, is obtained when one replacesq _t (x, t) by an expression of the KdV hiearchy in the relation betweenq _t (x, t) andw _t (x, t, λ) and transforms it. We estimated also the limit, whenc → ∞, i.e. the possible relation of the periodic solutions with the soliton ones.     

非线性单摆的格林函数解法

应用格林函数方法,给出了非线性单摆运动的较好近似解．     

A simple analytic solution of the dirac equation with a scalar linear potential

We give a simple, approximate analytic solution of the massless Dirac equation with a scalar linear potential. Its accuracy is better than 99% for the energy eigenvalues. We also discuss the effect of the centre-of-mass correction as well as the spin-orbit splitting with the help of the analytic solution.     

A simple,analytic solution of the semiclassical Rabi model in the red-detuned regime

We consider the semiclassical Rabi model in the large, red-detuned regime. Using the method of multiple-scales we obtain a simple, analytic, and approximate solution that describes the evolution of the system accurately for long times and for arbitrary values of the qubit-field coupling. It is used to characterize the probability to find the qubit in the excited state and the trajectory of the associated Bloch vector. Finally, we present physical situations where the results can be applied.     

一种简单的基于蔡氏电路的数字加密通信实验

介绍一种简单的基于蔡氏电路的对数字信号进行加密传输以及解密的实验方法,以及该实验作为一个新的与前沿科学相结合的普通物理实验的优点.     

非线性单摆的Jacobi椭圆函数解

对非线性单摆运动进行了数值分析,用Matlab绘出其运动相图,并求出了它在一定条件下的Jacobi椭圆函数解.     

A simple approach to the nuclear dynamics

We propose an approach to the nuclear dynamics which enables us to understand the relations between the time-dependent Hartree-Fock method and the quantumstatistical approach to the heavy ion reactions. The same formalism allows us to generalize the random phase approximation in order to include the spreading width of collective states.     

A simple analytic solution for transient simultaneous four-wave mixing in photorefractive crystals

Very simple solution of the coupled partial differential equations that leads to analytic formula for diffraction efficiency which describes the time dependence of four-wave mixing in photorefractive crystals is presented. The obtained results were used for analysis of simultaneous read–write dynamics in Bi₁₂SiO₂₀ crystal.     

有阻尼单摆的冲击波解

研究和分析有阻尼单摆的运动方程,应用近似法方程时发现存在冲击波解并精确求解.同时结合有阻尼单摆的相图分析冲击波解存在的物理意义.     

A solution to the non-Abelian duality problem

Dualities uniquely excel at resolving non-perturbative aspects of complex phase diagrams of interacting, Landau or topologically ordered, systems. However, traditional duality transformations fail for systems like the Heisenberg model and non-Abelian gauge theories. The bond-algebraic theory of quantum and classical dualities provides a solution to this long-standing conundrum, the so-called non-Abelian duality problem, by embedding traditional dualities into a more general transformation scheme that always preserves locality in any number of dimensions. Remarkably, it turns out to be unimportant whether a model?s group of symmetries is Abelian or non-Abelian. The capability of the bond-algebraic approach to handle finite and infinite systems with arbitrary boundary conditions has recently led to the discovery of holographic symmetries  , relating topological order, edge states, and generalized order parameters. We discuss the interplay between these distinguished boundary symmetries and our solution to the non-Abelian duality problem. To illustrate our technique we present, among others, novel dualities for the SU(2)$\mathit{SU}(2)$ principal chiral field and both U(1)$U(1)$ and SU(2)$\mathit{SU}(2)$ generalizations of the planar quantum compass model of orbital ordering.     

A simple approach to nonlinear oscillators

A very simple and effective approach to nonlinear oscillators is suggested. Anyone with basic knowledge of advanced calculus can apply the method to finding approximately the amplitude-frequency relationship of a nonlinear oscillator. Some examples are given to illustrate its extremely simple solution procedure and an acceptable accuracy of the obtained solutions.     

"广义芝诺悖论"的探讨

两辆相向匀速运动的车之间有一只小鸟,在两车间来回飞行.小鸟运动速率比车的要大,其初始位置是x0.当两车最终相遇时,相遇位置就是小鸟的最终位置.现在逆向演示(回放)该过程,即小鸟从两辆车相遇位置出发而两车作相背运动.当两车回到它们的初始位置时,小鸟将回到x0点.然而,在正过程中,由于两车相遇位置(即小鸟的最终位置)实际上和小鸟的初始位置无关,因此在逆过程中,小鸟最终可以处在任意位置而未必回到x0点.由此产生悖论,称做“广义芝诺悖论”.通过建立适当的物理模型,利用运动定律,分析并最终解决了这个悖论问题.     

A possible solution to the main cosmological problems

A model of the universe with an additional term Λ(x)g_μν in the energy-momentum tensor is motivated and presented. The model is completely determined by the assumption that the energy density ofthe universe equals its critical value. It has k = 1 geometry, is free of the initial singularity and does not possess a horizon, entropy or monopole problem.     

A gut solution to the solar neutrino problem

Within the supersymmetric flipped SU(5)×U(1) model, we propose a mechanism for realization of the Voloshin-Vysotsky-Okun solution to the solar neutrino problem by attributing a large magnetic moment to the electron neutrino, as required to explain the solar neutrino data.