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.     

非线性系统的非对角Berry相

研究了非线性系统中非对角情况的Berry相位, 给出了非线性非对角Berry相位的计算公式. 结果表明, 在非线性非对角情况下, 总相位包含有动力学相位, 通常意义的Berry相位, 以及非线性引起的附加相位. 此外, 还包含有非对角情况时所特有的新的附加项. 这新的一项表示, 当系统哈密顿慢变时产生的Bogoliubov涨落, 与另一个瞬时本征态之间的交叉效应, 进而对总的Berry相位产生影响. 作为应用, 对二能级玻色爱因斯坦凝聚体系, 具体计算了非线性非对角的Berry相位. 关键词： Berry 相位 非对角 绝热演化 玻色爱因斯坦凝聚     

绝热演化中一般量子态的几何相位

在绝热演化中的几何相位（即Berry相位）被推广到包括非本征态的一般量子态.这个新的几何相位同时适用于线性量子系统和非线性量子系统.它对于后者尤其重要因为非线性量子系统的绝热演化不能通过本征态的线性叠加来描述.在线性量子系统中,新定义的几何相位是各个本征态Berry相位的权重平均.     

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.     

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     

介观电容耦合LC电路在有限温度下的能量及热效应

由正则量子化方法导出了介观电容耦合LC电路体系的哈密顿算符, 利用幺正变换使哈密顿算符对角化. 用系综理论给出了体系的平均能量及其涨落, 在此基础上, 借助于广义Hellmann-Feynman定理, 讨论了有限温度下电路体系中电荷与自感磁通的量子涨落. 结果表明, 体系中电荷与自感磁通的量子涨落不仅与电路元件参数有关, 而且还与温度有关. 关键词： 介观电路 量子涨落 广义Hellmann-Feynman定理 有限温度     

介观电容耦合LC电路在有限温度下的能量及热效应

由正则量子化方法导出了介观电容耦合LC电路体系的哈密顿算符, 利用幺正变换使哈密顿算符对角化. 用系综理论给出了体系的平均能量及其涨落, 在此基础上, 借助于广义Hellmann-Feynman定理, 讨论了有限温度下电路体系中电荷与自感磁通的量子涨落. 结果表明, 体系中电荷与自感磁通的量子涨落不仅与电路元件参数有关, 而且还与温度有关.     

量子体系缓变过程的准绝热近似和Berry相因子

本文首先基于群论的方法,通过分析量子体系哈密顿的对称性,给出一种求解波动方程的近似方法——准绝热近似,以用来解决体系的哈密顿量作缓慢有限改变的量子跃迁问题.作为零级近似,严格地证明了具有简并情况的量子绝热定理,它的推论给出具有明显拓朴性质的Berry相因子.我们还给出了绝热条件破坏的几何解释,并说明了Berry相因子普遍存在于以哈密顿量确定的变化所需时间T所标度的量子过程中.最后我们指出了对应于绝热条件破坏的缓变过程的可观察效应.     

教学研究:介绍量子力学几个基本概念——兼答《关于量子几何相位的评注》中的几个主要问题

介绍了量子绝热定理的物理含义及成立的条件，认为有关主要献（Aharonov-Anandan,Bohm，孙昌璞等）的表述是正确的，而《关于量子几何相位的评注》^[1]（以下简称《评注》）相应的表述不完全正确。在此基础上，认为这些献和教材（R.Shankar)得出的涉及Berry绝热相位的一些论述（不含Berry绝热相因子的瞬时能量本征态不满足含时Schroedinger方程等）也是正确的，而《评注》的论述与此相反。《评注》认为只有γn(C)才是Berry相位。本作则倾向于把γn（t）叫做Berry绝热相位，而把γn（C）=γn（T）-γn（0）叫做几何相位（geometric phase)^[2]。     

绝热定理表述的改进以及Berry相位和Wilczek-Zee算符导出的简化

用Hamiltouian随时间的变化率来定量地界定量子系统的“缓慢变化”,从而对绝热定理的表述做了改进,使它更精确其证明过程变得更简单,绝热近似的误差估计也被做得更直捷,并得到了(?)/(?)(?)相对于能量本征函数的非对角元的估计式.据此,对Berry相位和Wilczek-Zee算符的导出做了简化.而Berry相因于作为wilczek-Zee算符的特例这一点,也被表述得更加严格和清楚. 关键词：     

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.     

Weak localization in mesoscopic hole transport: berry phases and classical correlations

We consider phase-coherent transport through ballistic and diffusive two-dimensional hole systems based on the Kohn-Luttinger Hamiltonian. We show that intrinsic heavy-hole-light-hole coupling gives rise to clear-cut signatures of an associated Berry phase in the weak localization which renders the magnetoconductance profile distinctly different from electron transport. Nonuniversal classical correlations determine the strength of these Berry phase effects and the effective symmetry class, leading even to antilocalization-type features for circular quantum dots and Aharonov-Bohm rings in the absence of additional spin-orbit interaction. Our semiclassical predictions are confirmed by numerical calculations.     

Holonomy structure of parameter manifolds

The Berry holonomy phase is usually attributed to homotopically nontrivial maps induced by the Hamiltonian in the space of orthonormal eigenstates constructed over a parameter manifold. We show that the issues of mappings and eigenstates should be addressed separately and that equivalence between them implies a trivial Berry phase.     

Semiclassical diagonalization of quantum Hamiltonian and equations of motion with Berry phase corrections

It has been recently found that the equations of motion of several semiclassical systems must take into account terms arising from Berry phases contributions. Those terms are responsible for the spin Hall effect in semiconductor as well as the Magnus effect of light propagating in inhomogeneous media. Intensive ongoing research on this subject seems to indicate that a broad class of quantum systems may be affected by Berry phase terms. It is therefore important to find a general procedure allowing for the determination of semiclassical Hamiltonian with Berry Phase corrections. This article presents a general diagonalization method at order ħ for a large class of quantum Hamiltonians directly inducing Berry phase corrections. As a consequence, Berry phase terms on both coordinates and momentum operators naturally arise during the diagonalization procedure. This leads to new equations of motion for a wide class of semiclassical system. As physical applications we consider here a Dirac particle in an electromagnetic or static gravitational field, and the propagation of a Bloch electrons in an external electromagnetic field.     

Interference of instanton trajectories during quantum tunneling in small particles of real antiferromagnets

For a two-sublattice antiferromagnet, the Lagrangian is constructed taking into account Berry’s phase whose form is matched with the quantum-mechanical Heisenberg Hamiltonian. Tunnel effects are analyzed taking into account the crystallographic symmetry and possible types of Dzyaloshinski interaction. It is shown that, when the real magnetic symmetry and the Dzyaloshinski interaction are taken into consideration, the effects of destructive instanton interference and the suppression of macroscopic quantum tunneling may come into play. This may lead to a periodic dependence of the ground-state level splitting on the Dzyaloshinski interaction constant; the magnitude of this splitting is calculated.     

SU(3) spin-orbit coupled fermions in an optical lattice

We propose a scheme to realize the SU(3)spin-orbit coupled three-component fermions in an one-dimensional optical lattice.The topological properties of the single-particle Hamiltonian are studied by calculating the Berry phase,winding number and edge state.We also investigate the effects of the interaction on the ground-state topology of the system,and characterize the interaction-induced topological phase transitions,using a state-of-the-art density-matrix renormalization-group numerical method.Finally,we show the typical features of the emerging quantum phases,and map out the many-body phase diagram between the interaction and the Zeeman field.Our results establish a way for exploring novel quantum physics induced by the SOC with SU(N)symmetry.     

A New First-Order Phase Transition for an Extended Jaynes–Cummings–Dicke Model with a High-Finesse Optical Cavity in the BEC System<Superscript>†</Superscript>

We present a two-level atomic Bose–Einstein condensate (BEC) with dispersion, which is coupled to a high-finesse optical cavity. We call this model the extended Jaynes–Cummings–Dicke (JC-Dicke) model and introduce an effective Hamiltonian for this system. From the direct product of Heisenberg–Weyl (HW) coherent states for the field and U(2) coherent states for the matter, we obtain the potential energy surface of the system. Within the framework of the mean-field approach, we evaluate the variational energy as the expectation value of the Hamiltonian for the considered state. We investigate numerically the quantum phase transition and the Berry phase for this system. We find the influence of the atom–atom interactions on the quantum phase transition point and obtain a new phase transition occurring when the microwave amplitude changes. Furthermore, we observe that the coherent atoms not only shift the phase transition point but also affect the macroscopic excitations in the superradiant phase.     

Berry phase in open quantum systems: a quantum Langevin equation approach

The evolution of a two level system with a slowly varying Hamiltonian, modeled as a spin 1/2 in a slowly varying magnetic field, and interacting with a quantum environment, modeled as a bath of harmonic oscillators is analyzed using a quantum Langevin approach. This allows to easily obtain the dissipation time and the correction to the Berry phase in the case of an adiabatic cyclic evolution.     

Observable Berry Phase for Charge Qubit in a Dissipative Environment

A geometric phase of open system is directly obtained from Schrödinger equation with a hermitian Hamiltonian of a two-level atomic system interacting with its reservoirs. We find that the dynamical phases are proportional to the geometric phases in terms of Weisskopf-Wigner theory in the rotational frame. Thus an effective scheme to measure the Berry phase in a charge qubit dissipative system is proposed by coherently controlling the macroscopic quantum states formed in superconducting circuits. Our approach does not need any operations to cancel the dynamical phases so as to reduce the experimental errors. Furthermore, we find that the dissipative effects can be overcome by choosing adapted parameters of the superconducting circuit.