介观并联RLC电路的量子涨落

将介观并联RLC电路量子化，并利用幺正变换给出其波函数及能谱的精确解.在此基础上获得各支路中电流和电压的量子涨落. 关键词： 并联RLC电路 幺正变换 量子涨落     

非对易空间R2N的转动及其实现

给出非对易R^2N中坐标辛变换对应的幺正变换的实现;给出这种幺正变换引起的波函数的变化,也就是在Hilbert空间的幺正变换的矩阵元     

幺正极限附近费米气体反常激发模式的涡旋

在幺正极限附近研究了处于旋转外势中费米气体的量子化涡旋动力学. 选取适当的试探波函数并利用含时变分法, 得到了小振幅涡旋运动方程及描述其反常激发模式的解. 详细讨论了在幺正极限附近的反常模式产生的条件. 结果显示系统囚禁外势的临界转动频率在幺正极限附近随粒子间相互作用参数的增加而变大, 而涡旋进动的周期则随着粒子间相互作用参数的增加而减小. 关键词： 费米气体 涡旋 幺正极限     

介观RLC电路的精确波函数和压缩态

利用一系列幺正变换求出了介观RLC电路的精确波函数和基本不变量,并发现此系统基本不变量的本征态是压缩态,它可用介观RLC电路的精确波函数来构造。     

从幺正变换的角度理解半波损失

机械波或者光波在介质的分界面处反射可能会发生半波损失的现象.半波损失与能量守恒都体现在波函数的求解结果中.本文以机械波为例,从幺正变换的角度理解半波损失发生的条件及其与能量守恒之间的必然关系.     

双模积分型投影算符及其应用

引进了幺正的双模积分型投影算符,利用有序算符内的积分(IWOP)技术分析了其变换特性;然后利用该积分型投影算符对角化了双模耦合量子谐振子体系的哈密顿量,从而求出了体系的本征能级与本征波函数;最后讨论了特例情形.     

单模光子在光纤中运动的极化及几何相因子

研究在光纤中运动的单模光子在固定系中的自旋算符表式,在将螺旋度当作不变量的基础上构造使光纤中光子极化面转动的有效哈密顿量,运用与不变量有关的幺正变换方法,获得了光纤中运动光子演化方程(含时薛定谔方程)的精确解,并研究光子在光纤中运动的极化问题,包括几何相因子、总哈密顿量和波函数演化算符的显式. 关键词： 几何相因子 光纤 不变量 幺正变换     

求解H=αa~+a+βb~+b+γ(a~+b~++ab)的波函数的简单方法

本文用能生成玻戈留玻夫变换的幺正变换的坐标表象简捷地给出哈密顿量Ｈ＝αａ~＋ａ＋βｂ~＋ｂ＋γ（ａ~＋ｂ~＋＋ａｂ）的波函数．     

双模坐标-动量积分型投影算符及其在量子光学中的应用

引进了幺正的双模坐标-动量积分型投影算符,利用有序算符内的积分（IWOP）技术分析了其变换特性,并导出了其正规乘积展开式.然后利用该积分型投影算符对角化了双模耦合量子谐振子体系的哈密顿量,从而求出了体系的本征能级与本征波函数.最后讨论了特例情形. 关键词： 积分型投影算符 有序算符内的积分技术 坐标-动量耦合     

一种应用于量子数据压缩的幺正变换生成方法

提出了一种两类正交基矢按照特定要求相互转换的幺正变换生成方法. 特定要求为第一类基矢中特定的四种典型基矢经幺正变换后, 第三个量子比特特定为|0>, 而四种非典型基矢经幺正变换后, 第三个量子比特为|1>. 将该幺正变换应用于量子数据压缩, 准确度达到0.942. 该方法的提出为量子压缩和解压缩的实现提供了基础, 对于其他要求特定对应关系的幺正变换的生成具有借鉴意义. 关键词： 幺正变换 正交基矢 特定要求 量子压缩     

Basic Neutron Interference Experiments and the Information Interpretation of the Wavefunction

No Heading Two fundamental neutron interference experiments are discussed, the measurement of an unknown phase-shift and the simultaneous measurement of which-way and visibility duality. The experiments have been realized solely with unitary phase transformations in the spirit of minimal interaction between the neutron and its environment. The scope of the quantum measurements is to strengthen the information interpretation of quantum mechanics. As result the interpretation of the wavefunction, describing the information about potential measurements on single quantum systems, is confirmed, and the search for realistic scenarios tor the wavefunction and the measurement process is weakened by such basic quantum experiments.     

The Quantum Fluctuations of Two Coupled Josephson Junctions with the Discreteness of Electric Charge

The quantization of two Josephson junctions coupled via inductor with the discreteness of electric charges is proposed. The finite-difference Schrodinger equation of the circuit system has been obtained in charge representation, and the Schrodinger equation is turned to be Mathieu equation in flux representation. The wavefunction and energy spectrum can be solved by adopting the canonical transformation and unitary transformation method. The results indicate that the quantum fluctuations of the flux in the ground states of each mesh exist and are interrelated.     

Discreteness and the origin of probability in quantum mechanics

Attempts to derive the Born rule, either in the Many Worlds or Copenhagen interpretation, are unsatisfactory for systems with only a finite number of degrees of freedom. In the case of Many Worlds this is a serious problem, since its goal is to account for apparent collapse phenomena, including the Born rule for probabilities, assuming only unitary evolution of the wavefunction. For finite number of degrees of freedom, observers on the vast majority of branches would not deduce the Born rule. However, discreteness of the quantum state space, even if extremely tiny, may restore the validity of the usual arguments.     

外周期驱动场作用下介观铁磁畴的共振运动

从铁磁畴的能量方程出发，利用正则量子化方法和么正变换技术，解析地求得了磁畴量子化运动的波函数。结果表明，即令磁畴的本征频率与外加周期驱动场频率不一致，磁畴的运动仍能表现出精确共振行为。另外，磁畴量子化运动的涨落只受阻尼力的影响，而完全与外加周期驱动场无关。     

Dual wavefunction of the Felderhof model

We study the Felderhof free-fermion six-vertex model, whose wavefunction recently turned out to possess rich combinatorial structure of the Schur polynomials. We investigate the dual version of the wavefunction in this paper, which seems to be a harder object to analyze. We evaluate the dual wavefunction in two ways. First, we give the exact correspondence between the dual wavefunction and the Schur polynomials, for which two proofs are given. Next, we make a microscopic analysis and express the dual wavefunction in terms of strict Gelfand–Tsetlin pattern. As a consequence of these two ways of evaluation of the dual wavefunction, we obtain a dual version of the Tokuyama combinatorial formula for the Schur polynomials. We also give a generalization of the correspondence between the dual wavefunction of the Felderhof model and the factorial Schur polynomials.     

Magnetic properties and spin waves of bilayer magnets in a uniform field

The two-layer square lattice quantum antiferromagnet with spins 12 shows a zero-field magnetic order-disorder transition at a critical ratio of the inter-plane to intra-plane couplings. Adding a uniform magnetic field tunes the system to canted antiferromagnetism and eventually to a fully polarized state; similar behavior occurs for ferromagnetic intra-plane coupling. Based on a bond operator spin representation, we propose an approximate ground state wavefunction which consistently covers all phases by means of a unitary transformation. The excitations can be efficiently described as independent bosons; in the antiferromagnetic phase these reduce to the well-known spin waves, whereas they describe gapped spin-1 excitations in the singlet phase. We compute the spectra of these excitations as well as the magnetizations throughout the whole phase diagram. Received 23 April 2001     

Upper Bounds to the Overlap of Approximate and Exact Wavefunctions

One measure of how accurately an approximate wavefunction approximatesthe true wavefunction is the overlap of the two functions. In general the truewavefunction is not known so this overlap cannot be directly calculated. Wederive two methods from the t expansion of Horn and Weinstein to bound fromabove the magnitude of the overlap of an approximate wavefunction with theground state. The first method relies on the ability to divide the Hamiltonian intoa base problem and a perturbation. The second method is more general and seemsmuch more promising.     

Higher order JWKB expressions for the energy levels and the wavefunction at the origin

We derive an exact quantization condition for the energy levels of a particle in a radial potential assumed finite at the origin. This is used to derive corrections to the semiclassical JWKB quantization condition. We further relate the normalization integral of the wavefunction to the energy derivative of wavefunction at origin and use this expression to derive the corrections to the semiclassical JWKB expressions for the wavefunction at origin. An application to upsilon leptonic decay width is also given.