具有含时频率和边界条件的谐振子量子态的Berry相位

对具有一运动边界的一维无限深势阱内频率随时间变化的谐振子的含时Schrdinger方程连续进行两次规范变换，可以得到精确解和Lewis不变量算符.基于该精确解利用几何距离和曲线的几何长度概念计算了体系量子态的Berry相位. 关键词：     

动边界量子含时谐振子系统的Lewis-Riesenfeld相位与Berry相位

根据Lewis-Riesenfeld的量子不变量理论,计算了一维动壁无限深势阱内频率随时间变化的谐振子的Lewis-Riesenfeld相位,发现刘登云文中“非绝热Berry相位”与Lewis-Riesenfeld相位中的几何部分完全一致.也许更为重要的是,证明了至少对于做正弦振动的边界,在绝热近似下,该系统不存在非零的Berry相位. 关键词： Berry相位 Lewis-Riesenfeld相位 量子不变量 动边界     

应用于量子含时波包方法的高精度透明边界条件

本文提出了一种适用于量子含时波包方法的透明边界条件. 该量子含时波包方法结合分离变量表象方法使用的时候,本质上是具有谱收敛性质的. 相对于以往的复数吸收势,该透明边界条件的突出优点是其对于波函数的能谱分布并不敏感. 采用具有共振态的一维势垒散射模型,本文对该方法的特点做了阐述.     

等离子体波背景下的光子Berry相位

利用光学度规将强激光脉冲激发的电子等离子体波描述为有效几何背景.借助于广义相对论中弯曲时空下的Maxwell方程组得到了探针光子在等离子体中电子等离子体波背景下(被处理为有效度规)所满足的运动方程及光子的Hamilton表达式.导出了电子等离子体波对光子Berry相位贡献的解析表达式并且对光子在真空中Berry相位的修正做了数值估算. 关键词： 电子等离子体波 等离子体 Berry相位     

有限维希尔伯特空间含时谐振子的时间演化及Berry相位

研究了有限维希尔伯特空间含时谐振子的时间演化．通过适当的含时规范变换得到有限维含时谐振子量子态时间演化的封闭解,并给出量子态的Ｂｅｒｒｙ相位．最后讨论了驱动项对相干态压缩特性的影响 关键词：     

转动核对转移矩阵元与Berry相位

采用粒子数守恒方法,对推转壳模型(j=11/2)进行了精确计算,详细分析了转动原子核中对转移矩阵元随转动频率的变化.与粒子数投影的Hatree-Fock-Bogoliubov方法导出的结论相反,“diabolic对转移”现象仅出现在高激发带,而晕带到晕带的对转移矩阵元则变化较为缓慢,并不出现振荡现象.     

量子Berry相因子与相位教学

回顾了经典物理和量子力学中的相位问题,着重讨论了量子几何Berry相位及在量子力学中如何进行量子相位教学的问题.     

含时调制的Jaynes-Cummings模型的Pancharatnam相位

基于含时调制的Jaynes-Cummings模型的SU(2)群结构,求得它的Pancharatnam相位,并分析 了该模型从绝热开启直到关闭原子与场的相互作用的整个过程的相位变化.讨论了该模型在 半经典近似条件下的情况. 关键词： 含时调制的Jaynes-Cummings模型 Pancharatnam相位 SU(2)群     

THE FORCED VIBRATION AND BOUNDARY CONTROL OF PRETWISTED TIMOSHENKO BEAMS WITH GENERAL TIME DEPENDENT ELASTIC BOUNDARY CONDITIONS

The governing differential equations and the general time-dependent elastic boundary conditions for the coupled bending-bending forced vibration of a pretwisted non-uniform Timoshenko beam are derived by Hamilton's principle. By introducing a general change of dependent variable with shifting functions, the original system is transformed into a system composed of four non-homogeneous governing differential equations and eight homogeneous boundary conditions. The transformed system is proved to be self-adjoint. Consequently, the method of separation of variables can be used to solve the transformed problem. The physical meanings of these shifting functions are explored. The orthogonality condition for the eigenfunctions of a pretwisted non-uniform beam with elastic boundary conditions is also derived. The relation between the shifting functions and the stiffness matrix is derived. The boundary control of a pretwist Timoshenko beam is studied. The effects of the total pretwist angle, the position of loading and the boundary spring constants on the energy required to control the performance of a pretwisted beam are investigated.     

Bery相与AB相的关系

Ｂｅｒｒｙ曾经论证，Ａｈａｒｏｎｏｖ-Ｂｏｈｍ相可以看成是Ｂｅｒｙ相．在论证中放弃了绝热近似，也未涉及量子态的非定态性．重新探讨了此论证，表明Ｂｅｒｙ的结论是正确的，但在该论证过程中需要作绝热近似．ＡＢ效应中运动电子是用一个运动波包（非定态）来描述的，ＡＢ相的出现，是要求波包的演化必须满足Ｓｃｈｒ?ｄｉｎｇｅｒ方程的结果，但ＡＢ相的出现不受绝热条件的限制 关键词：     

量子Hall效应与Berry相因数

本文将绝热过程中的Berry相因数的概念推广到简并系统,并且研究了量子Hall效应与Berry相因数之间的关系,证明了不论是整数还是分数量子Hall电导率都对应于特殊的Berry相因数。 关键词：     

THE MECHANICAL BERRY PHASE AND CORRESPONDING CLASSICAL TOPOLOGICAL PHASE ANGLE

Recently,a new effect,which nay be called the mechanical Aharonov-Bohm effect,was suggested and verified experimentally.In this paper,we proceed to study and calculate the mechanical Berry's phase and corresponding topological phase angle.     

BERRY PHASES IN THE QUANTUM STATE OF THE ISOTROPIC HARMONIC OSCILLATOR WITH TIME-DEPENDENT FREQUENCY AND BOUNDARY CONDITIONS

The problem of the isotopic harmonic oscillator of time-dependent frequency confined in a spherical box with time-dependent radius is studied. We show that the exact solution and the Lewis invariant operator can be obtained by performing two consecutive gauge transformations on the time-dependent Schr?dinger equation. On the basis of the exact solution the non-adiabatic Berry phases for the system are calculated.     

TIME-DEPENDENT LANDAU SYSTEM AND NON-ADIABATIC BERRY PHASE IN TWO DIMENSIONS

By applying the time-independent unitary transformation, the time-dependent Landau system is transformed into a product of a time-independent Landau system's Hamiltonian and a factor only depending on time, which can be solved exactly. Both the invariant operator and the eigenstate are obtained. In the periodical time-dependent case, the non-adiabatic Berry's phase is also presented.     

由含时边界条件的两种有限深量子势阱构造的哈密顿算符和它们的复BERRY相位

在量子基础理论的框架下分别从一维含时边界条件的半壁无限高量子势阱和三维含时边界条件的有限深球方势阱构造了两种描述带电粒子在电磁场作用下的新哈密顿算符.在绝热近似下，计算了这两种新量子体系的复Berry相位.     

QUASI-ADIABATIC APPROXIMATION FOR THE SLOWLY-CHANGING QUANTUM PROCCESS AND BERRY PHASE FACTOR

By using group representation theory,the quasi-adiabatic approximation solution of the schrodinger equation of a quantum system with slowly-changing Hamiltonian are presented in this paper.We not only obtained the Berry phase factor and strictly proved the quantum adiabatic theorem as the zeroth-order approximation,but also studied the universal Berry phase factor and its geometrical interpretation when the adiabatic condition is violated.It is pointed out that this universal Berry phase factor has observable effects.