RLC电路非线性现象的演示

非线性现象的研究在电子线路、化学反应及非 平衡热力学等各个领域都有重要的理论和实际意义． 本文介绍用普通的白炽灯泡、变压器线圈和电容组成的 ＲＬＣ非线性电路，可以演示单稳、双稳、无稳等各种 现象．     

RLC串联谐振教学实验的研究

ＲＬＣ串联谐振教学实验的研究陆申龙，曹正东（复旦大学上海２００４３３）（同济大学上海２０００９２）在物理实验教材中，ＲＬＣ串联谐振实验的教学重点是通过做ＲＬＣ串联谐振实验，使学生学习该谐振电路的电流随频率变化的特性，并掌握测量电路谐振曲线的方法．由谐...     

RLC并联电路暂态过程实验

介绍笔者的设计ＲＬＣ并联电路暂态过程实验装置，利用电子开关，可方便地在通示波器上观察ＲＬＣ并联电路的暂态过程，有关参数的测量结果与理论结果得到较好符合。     

关于RL-C并联谐振特性曲线的讨论

从理论上导出了ＲＬ－Ｃ并联谐振电路的阻抗公式，由此分析谐振特性曲线的性质，并得出献中引用的ＲＬ－Ｃ谐振特性曲线成立的充分条件。     

介观电路的量子效应

本用涨落耗散定理证明了一个有源ＲＬＣ电路，在温度接近绝对零度时，存在量子效应；而当温度升高时，这一量子效应被热力学涨落淹没，并给出了绝对零度时，该电路的量子噪声的大小，以及电荷，电流的测不准点系。     

关于有源RLC电路的量子化

提出一种将有源ＲＬＣ电路量子化的方法,修正了有关文献中的错误。     

RLC串联电路暂态过程的演示

介绍一种能显示ＲＬＣ串联电路暂态过程中三种不同情况下Ｒ和Ｃ上的电压波形的演示实验．     

RLC串联电路暂态过程中的几个问题

本文讨论了以周期性方波为电源的ＲＬＣ串联电路暂态过程中的几个问题．主要是给出了ＲＣ电路时间常数大于、小于或等于方波半周期的几种情况下电路微分方程的解和相应的实验结果，还讨论了ＲＬＣ串联电路临界电阻的测量方法和影响测量准确度的原因．     

二阶非自治电路中的混沌振荡

本文研究在正弦电源激励下的二阶电路中的非线性动力学性质。在该电路中，唯一的非线性元件是具有负阻特性的单结管，电路实验的结果表明，当改变电源频率时，振荡制式呈现周期递增模式。     

非线性模拟电路可测试性度量研究

模拟电路的可测试性度量是指导其进行可测试性设计的基础,针对目前非线性模拟电路可测试性分析过程复杂,无法量化的问题,在深入研究模拟电路可测试性度量和非线性模拟电路特性的基础上,利用分段线性方法将非线性模拟电路近似等效为线性模拟电路,并给出了非线性模拟电路可测试性度量的计算方法,极大拓宽了可测试性度量的应用范围;最后通过实例详细讲解了计算过程,并利用模拟电路可测试性度量的定义验证了该结果的有效性,该方法计算量小,不受容差影响,对非线性模拟电路可测试性研究具有一定的指导意义。     

SUPERPOSITION OF COHERENT STATES IN KERR MEDIUM

The evolution of the input coherent state in the Kerr medium is studied. Upon the derivation we know that the output state at time t which corresponds to a rational number is Schr?dinger's cat state. Using Fourier integral of the evolution operator, we obtain the integral expression of the output state at time t which corresponds to an irrational number. It is a kind of one-dimensional continuous superposition of coherent states, not an ordinary Schr?dinger's cat state.     

An approach to dark energy problem through linear invariants

The time evolution of vacuum energy density is investigated in the coherent states of inflationary universe using a linear invariant approach. The linear invariants we derived are represented in terms of annihilation operators. On account of the fact that the coherent state is an eigenstate of an annihilation operator, the wave function in the coherent state is easily evaluated by solving the eigenvalue equation of the linear invariants. The expectation value of the vacuum energy density is derived using this wave function. Fluctuations of the scalar field and its conjugate momentum are also investigated. Our theory based on the linear invariant shows that the vacuum energy density of the universe in a coherent state is decreased continuously with time due to nonconservative force acting on the coherent oscillations of the scalar field, which is provided by the expansion of the universe. In effect, our analysis reveals that the vacuum energy density decreases in proportion to t_β where β is 3/2 for radiation-dominated era and 2 for matter-dominated era. In the case where the duration term of radiation-dominated era is short enough to be negligible, the estimation of the relic vacuum energy density agrees well with the current observational data.     

三种方法求解外场驱动含时谐振子系统的异同

讨论了外场驱动含量谐振子系统的三种解法的异同，发现利用相干态平均方法与量子不变量理论所得结果一致，而利用海森伯运动方程所求结果与上述两种结果相关一个相位因子。     

Dynamic Evolution of Squeezing Maintenance

By virtue of the coherent state representation and solving Riccati equation we derive dynamic evolution operator for maintaining squeezing, i.e., we demonstrate that the final state keeps squeezing when the initial state is a squeezed vacuum state. The number-phase squeezing maintenance mechanism is also studied.     

SORE APPLICATIONS OF THE COHERENT STATE FORMULATION OF THE WIGNER OPERATOR

On the basis of the preceding paper^[1]we present some new applications of both the normal rroduct form and the coherent state form of the Wigner operator,which involve deriving some new quantum operator formulas, giving the coherent state generalization of the Moyal theorem, evaluating some quantum operators which correspond to the given classical functions in the weyl manner and vice versa. Were it not for the Wigner operator's coherent state formulation given by us the above-mentioned calculations would be hard to perform.     

COHERENT STATE FORMULATION OF THE WEYL CORRESPONDENCE AND THE WIGNER FUNCTION

We point out that there is a close connection between the Weyl correspondence and coherent state correspondence. Bu virtue of differential and integral method within normal ordered products we demonstrate that the essence of the Gleyl correspondence is just coherent state correspondence in both boson and fermion cases. Furthermore, coherent state form and explicit operator form for the Wigner function are given. With these forms we can derive some important operator formulas from the Wey1 correspondence. The Wigner function's zero-point value is also discussed.     

SOME APPLICATIONS OF COHERENT STATE FORMULATION OF THE WIGNER OPERATOR

In this paper both the normal product form and the coherent state form of the Wigner operator are derived. Furthermore, the applications of the new forms of the Wigner operator are also presented, which are involved in deriving some new quantum operator formulas, in the coherent state generalization of the Moyal theorem, and in evaluating some quantum operators which corresponds to the given classical functions in the Weyl manner and vice versa.     

Normally-Ordered Time Evolution Operator for Mass-Varying Harmonic Oscillator and Wigner Function of Squeezed Number State

For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integration operator in coherent state representation and then perform this integral by virtue of the technique ofintegration within an ordered product of operators. The normally orderedtime evolution operator is thus obtained. We then derive the Wigner functionof$u(t)| n>, where | n> is a Fock state, which exhibits a generalized squeezing, the squeezing effect is related to the varying mass with time.     

哈密顿算符是SU(1,1)和SU(2)算子含时线性组合量子系统的时间演变及厄密不变量

研究了哈密顿算符是SU(1,1)和SU(2)算子线性组合且系数显含时间量子系统的时间演化,我们发现适当选取厄密不变量,不仅可得到统一的量子态时间演化封闭解,而且可得到时间演化幺正算符。用时间演化算符我们讨论了含时双光子压缩态和SU(1,1)相干态以及SU(2)压缩态的压缩性质。     

SOME NEW QUANTUM OPERATOR FORMULAS --NEW APPLICATIONS OF THE COHERENT STATE

We present a novel method for deriving some new quantum operator formulas by carrying out,the integrations within a normal product symbol. The idea underlying this method is com- bining the properties of normal product and of coherent state together. For example, we can deduce operator ordering theorems, the Fujiwara formula, and some disentangling theorems simply and directly. Bymeans of this method we also get the explicit operator form and coherent state form for the Wigner function with these new forms, the wigner function's eigen-state is found and its zero point value property is discussed. Furthermore some famous quantum unitary transformations and the transformed matrix element for functional obtained conveniently. integral may be also