Berry相与AB相的关系

Ｂｅｒｒｙ曾论证，Ａｈａｒｏｎｏｖ－Ｂｏｈｍ相可以看成是Ｂｅｒｒｙ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Ｂｅｒｒｙ的结论是正确的，但在该论证过程中需要作绝热近热似。     

强磁场中碱金属原子的演化和Aharonov－Anandan相因子

利用量子不变量理论研究了任意随时间变化的强磁场中碱金属原子系统的演化问题，得到了此系统精确的演化态，并利用此精确的演化态求出了相应的Ａｎａｒｏｎｏｖ－Ａｎａｎｄａｎ相因子和绝热极限下的Ｂｅｒｒｙ相因子。将此系统精确的演化态按哈密顿量的瞬时本征态展开，可以得到绝热近似的任意阶修正。     

强磁场中碱金属原子原演化和Aharonov—Anandan相因子

利用量子不变量理论研究了任意随变化的强磁场中碱金属原子系统的演化问题，得到了此精确的演化态，并利用此精确的演化态求出了相应的Ａｈａｒｏｎｏｖ－Ａｎａｎｄａｎ相因子和绝热极限下的Ｂｅｒｒｙ相因子。将此系统精确的演化按哈密顿量的瞬音本征态展开，可以得到绝热近似似的任意阶修正。     

飞秒激光脉宽对非绝热耦合分子波包运动的影响研究

利用含时波包法研究了强飞秒泵浦-探测激光场中激光脉宽对非绝热耦合NaI分子波包运动的影响.发现波包的振荡周期随脉宽增长而增大,而振荡幅度随脉宽增长而减小.非绝热效应引起的波包在交叉区域的分裂情况影响各态布居.脉宽增长,NaI分子的激发概率增大,而解离概率减小.研究表明调节激光场脉宽可实现对波包运动的控制从而控制态布居的选择性分布.研究结果可以为实验上实现分子的光控制以及量子调控过程提供一定的参考.     

动力参照系中的Berry相因子及其可观测物理效应

本文在非相对论情况下,讨论了运动参照系中Schrodinger方程绝热近似解的性质和Berry相因子大坐标变换下的行为,对转动和平动参照系两种具体情况作了较为详尽的分析.这些讨论表明了Berry相因子的出现与参照系的选择有关.对于涉及到平动参照系的Bitter和Dubbers的中子极化问题.我们不仅在零级近似下给出理论和实验相符合的结果,而且还进一步分析了绝热条件破坏时可能出现的高阶效应.     

飞秒激光参数对非绝热耦合分子态布居的影响

利用含时波包法研究强飞秒泵浦-探测激光场中激光脉宽、波长和场强对非绝热耦合NaI分子各态布居的影响.波包在势能面上做周期性运动,周期约为1 000 fs.延时为200 fs时,波包第一次到达交叉区域分裂成两部分.波包在交叉区域的分裂情况影响各态布居.脉宽增长,NaI分子的激发概率增大,而解离概率减小.泵浦波长为共振波长318 nm时,激发概率最大.泵浦波长增长,NaI分子的解离概率减小.泵浦场强增大,激发概率增大,但解离概率不变.探测激光波长和场强不影响NaI分子各态布居分布.调节激光场参数可实现对波包运动的控制从而控制态布居的选择性分布.研究结果为实验上实现分子的光控制过程提供参考.     

NaI分子的非绝热效应

利用含时波包法研究了NaI分子在飞秒脉冲激光作用下的动力学演化情况.由于受非绝热效应的影响,波包运动到势能面的交叉区域时发生分裂.研究表明:非绝热效应引起的波包分裂是分子解离的根源,而且随着演化时间的增加非绝热效应变得越来越明显.同时,分别采用量子力学和经典力学理论探讨了NaI分子在非绝热过程中的演化规律以及解离概率随脉冲波长的变化关系. 关键词： 非绝热效应 NaI分子 飞秒脉冲 含时波包     

原子质心运动与暗态原子

本文利用高阶量子绝热近似方法讨论了量子微腔驻波场中三能级暗态原子与光场相互作用中原子质心运动对电子,光场系统动力学的影响。文章分析了绝热近似成立的条件以及非绝热因子对动力学演化的影响。文中还计算了原子在腔中的非绝热跃迁几率及各部分能量分布的平均值。     

耦合振子系统的多稳态同步分析

本文讨论了一维闭合环上Kuramoto相振子在非对称耦合作用下同步区域出现的多定态现象. 研究发现在振子数N≤3情形下系统不会出现多态现象, 而N≥4多振子系统则呈现规律的多同步定态. 我们进一步对耦合振子系统中出现的多定态规律及定态稳定性进行了理论分析, 得到了定态渐近稳定解. 数值模拟多体系统发现同步区特征和理论描述相一致. 研究结果显示在绝热条件下随着耦合强度的减小, 系统从不同分支的同步态出发最终会回到同一非同步态. 这说明, 耦合振子系统在非同步区由于运动的遍历性而只具有单一的非同步态, 在发生同步时由于遍历性破缺会产生多个同步定态的共存现象.     

原子双阱势中电子波包的非绝热操控

交叉电场和磁场中的氢原子具有双阱势能结构。本文基于量子力学模拟,采用半周期脉冲（HCP）序列开展电子波包的非绝热操控。详细研究了HCP的电场幅度、数量和时间间隔对电子波包的空间和能量分布的影响,实现了将初始电子波包非绝热转移到远离库伦中心的外势阱中的低能态,这些低能态较为稳定且显示出很大的电偶极矩。相比光激发和绝热操控,本文的方法更为快速、高效,可以应用于更为复杂的外场或分子体系。     

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.     

Wave-packet dynamics of Bloch electrons—Role of Berry phase

Motivated by a recent proposal on the possibility of observing a monopole in the band structure, and by an increasing interest in the role of Berry phase in spintronics, we reconsidered the problem of adiabatic motion of a wave packet of Bloch functions, under a perturbation varying slowly and incommensurately to the lattice structure. We showed, using only the fundamental principles of quantum mechanics, that the effective wave-packet dynamics of Bloch electrons is conveniently described by a set of equations of motion (EOM) in which a non-Abelian Berry phase associated with the internal degree of freedom appears.     

Aharonov-Anandan Phase and Superadiabatic Approximaton

In this paper, the exact evolving state for a two-level quantum system is found by making use of the Lewis-Riesenfeld invariant theory. In principle, the correction to an arbitrary order in the adiabatic approximation parameter c can be obtained from this exact evolving state. To the n-th order in ∈, it is shown that the exact evolving state reduces to the superadiabatic basis introduced by Berry recently. The Aharonov-Anandan phase and its adiabatic limit (Berry phase for the system) are also calculated. e for the system) are also calculated.     

Berry phase of coupled two arbitrary spins in a time-varying magnetic field

In this paper, we investigate the Berry phase of two coupled arbitrary spins driven by a time-varying magnetic field where the Hamiltonian is explicitly time-dependent. Using a technique of time-dependent gauge transform the Berry phase and time-evolution operator are found explicitly in the adiabatic approximation. The general solutions for arbitrary spins are applied to the spin-1/2\ system as an example of explanation.     

Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

Motivated by a recent proposal on the possibility of observing a monopole in the band structure, and by an increasing interest in the role of Berry phase in spintronics, we studied the adiabatic motion of a wave packet of Bloch functions, under a perturbation varying slowly and incommensurately to the lattice structure. We show, using only the fundamental principles of quantum mechanics, that the effective wave-packet dynamics is conveniently described by a set of equations of motion (EOM) for a semiclassical particle coupled to a non-Abelian gauge field associated with a geometric Berry phase.

Our EOM can be viewed as a generalization of the standard Ehrenfest's theorem, and their derivation was asymptotically exact in the framework of linear response theory. Our analysis is entirely based on the concept of local Bloch bands, a good starting point for describing the adiabatic motion of a wave packet. One of the advantages of our approach is that the various types of gauge fields were classified into two categories by their different physical origin: (i) projection onto specific bands, (ii) time-dependent local Bloch basis. Using those gauge fields, we write our EOM in a covariant form, whereas the gauge-invariant field strength stems from the noncommutativity of covariant derivatives along different axes of the reciprocal parameter space. On the other hand, the degeneracy of Bloch bands makes the gauge fields non-Abelian.

For the purpose of applying our wave-packet dynamics to the analyses on transport phenomena in the context of Berry phase engineering, we focused on the Hall-type and polarization currents. Our formulation turned out to be useful for investigating and classifying various types of topological current on the same footing. We highlighted their symmetries, in particular, their behavior under time reversal (T) and space inversion (I). The result of these analyses was summarized as a set of cancellation rules. We also introduced the concept of parity polarization current, which may embody the physics of orbital current. Together with charge/spin Hall/polarization currents, this type of orbital current is expected to be a potential probe for detecting and controlling Berry phase.     

自旋为1粒子在旋转磁场中的几何相位和动力学相位(英文)

文章研究了自旋为1的粒子在旋转磁场中的几何相位和动力学相位.推导出如何计算自旋为1的粒子在绝热和非绝热演化中的几何相位和动力学相位公式,并利用这些公式计算其相位.最后我们讨论了三种情况下的Berry相位,当考虑ω1<<ω时,系统处于绝热近似,此时,几何相位就是Berry相位.     

含时边界条件和Berry相位

对一具有含时边界条件的量子体系,有效哈密顿算符可用一种简单的方式去构造而不涉及任何几何处理。用这种方法构造了一个在半径随时间变化的球形盒子内的量子粒子的有效哈密顿算符,并用它来计算波函数的Berry相位。发现有效哈密顿算符与原哈密顿算符在形式上由一静态规范变换相关联。这两个哈密顿算符的量子态差Berry相位。 关键词：     

BERRY'S PHASE FACTORS IN MOVING FRAMES OF REFERENCE AND THEIR OBSERVABLE EFFECTS

Under non-relativistic conditions,the properties of adiabatic solutions of the Schrodinger equation in moving frame of reference and the behaviours of the corresponding Berry's Phase are analysed.Two cases of translation and rotation are discussed in detail,which show that the existence of Berry's phase depends on the choice of frame of reference.While Bitter and Dubbers's experiment is explained by the first-order approximation in our discussion,the nonadiabatic effects in this experiment are predicted by the second-order approximation when the adiabatic condition is broken.     

First-principle calculations of the Berry curvature of Bloch states for charge and spin transport of electrons

Recent progress in wave packet dynamics based on the insight of Berry pertaining to adiabatic evolution of quantum systems has led to the need for a new property of a Bloch state, the Berry curvature, to be calculated from first principles. We report here on the response to this challenge by the ab initio community during the past decade. First we give a tutorial introduction of the conceptual developments we mentioned above. Then we describe four methodologies which have been developed for first-principle calculations of the Berry curvature. Finally, to illustrate the significance of the new developments, we report some results of calculations of interesting physical properties such as the anomalous and spin Hall conductivity as well as the anomalous Nernst conductivity and discuss the influence of the Berry curvature on the de Haas-van Alphen oscillation.     

Berry phase in Tavis-Cummings model

In this paper we investigate the Berry phase in Tavis-Cummings model in the rotating wave approximation. The dipole-dipole interaction between the atoms is considered. The eigenfunctions of the system are obtained and thus the Berry phase is evaluated explicitly in terms of the introduction of the phase shift. It is shown that the Berry phase can be easily controlled by the atom-cavity coupling strength, the cavity frequency detuning, which can be important in applications in geometric quantum computing.