自旋相干态变换和自旋-玻色模型的基于变分法的基态解析解

提出一种基于自旋相干态变换求解自旋-玻色模型基态的变分法, 并将其用于单原子模型, 得到旋波近似和非旋波近似情形下的解析基态能量和波函数, 特别是在光场与原子的弱、强耦合区域都与数值对角化结果符合得很好. 另外, 该方法也可以直接用于求解任意原子数的Dicke模型基态和相应的量子相变研究, 而通常基于Holstein-Primakoff变换的变分法, 原则上只适用于原子数趋于无穷的热力学极限情形. 关键词： 自旋相干态 变分法 J-C模型     

DNA模型的有限格点系的严格对角化解

讨论了DNA一维Holstein模型的严格对角化求解方法,在此基础上比较它与相干态变分法的结果,从而对后者的可靠性及精确程度进行检验,得到的结果表明两者确有明显的差异,严格对角化解方法得到的基态能量更低,达到饱和情形的格点数更少,本方法不仅可以讨论系统的基态,而且还能给出其能谱及激发态.严格对角化解方法对DNA的研究较之变分法的讨论有显著的改进. 关键词： Holstein模型 严格对角化解 基态能量 能谱     

氢分子离子H_2~+键长和基态能量的计算与模拟

利用里兹 (Ritz)变分法求解氢分子离子H+ 2 的键长和基态能量E ,并通过计算机来完成理论公式的推导与数值模拟     

四参数法计算氦原子基态能级研究

在求解氦原子径向Schr dinger方程时,设计了含有四参数的基态波函数,推导出含有四参数的氦原子基态能级表达式,分别采用Matlab 7.0最优化运算和Monte-Carlo法,计算了氦原子的基态能量,得到了相应的波函数.将计算结果与其它文献采用变分法所得计算值及实验值进行了比较,结果表明:这种方法不仅计算简便有效,准确性较高,而且所得氦原子基态空间波函数自动满足空间对称性的要求.     

Rashba效应对抛物量子阱中极化子基态能的影响

采用LLP变分法研究了抛物量子阱中极化子的Rashba效应,得到了极化子基态能量的表达式,并讨论了半阱宽及波矢与基态能量之间的关系.结果显示,基态能量是半阱宽和电子-声子耦合强度的减函数,而是波矢的增函数.由于Rashba效应基态能量零自旋轨道分裂成两支.     

用玻尔的量子论计算氢分子的基态能量

利用玻尔处理氢原子基态的方法,在假定了氢分子基态的半经典模型后,给出了氢分子基态能量与电子轨道半径.该结果可以与实验结果和量子变分法的计算结果相比较,对理解共价键的物理本质有一定意义.     

抛物量子点中极化子的温度依赖性

根据Pekar类型变分法在电子与声子强耦合的条件下计算了抛物量子点中强耦合极化子的基态能量.讨论了电子-声子耦合强度,量子点受限长度对基态能量的影响,同时引进温度参数并讨论了其对基态能量的影响,结果得出在低温的条件下,耦合强度和受限长度对基态的能量影响起主要作用;在高温的条件下,温度对基态的能量影响起主要作用,而耦合强度与受限长度的影响很小.     

透镜型量子点中类氢杂质基态能的计算

通过有效质量近似和变分法，研究了垂直磁场下透镜型量子点中类氢杂质基态能量，并与球型量子点进行了比较.研究表明：对于球型量子点，基态能仅与杂质的偏离距离有关，与垂直和水平偏离无关；而对于透镜型量子点，由于水平方向和垂直方向束缚势的非对称性，电子基态能不仅与杂质的偏离距离有关，还与杂质偏离方向有关. 关键词： 透镜型量子点 基态能 变分法     

双电子平面量子点基态能量的计算

由于库仑作用,目前的研究还得不到双电子平面量子点基态波函数和基态能量的精确解析解.分别利用微扰法、精确对角化方法和变分法,计算双电子平面量子点的基态能量,与早期的无约束哈特利-福克研究结果比较,发现三参量的变分波函数是基态的极好表征.且能对多电子平面量子点的基态描述提供参考.     

原子-原子相互作用影响下Dicke模型的量子相变

原子与光腔相互作用的动力学特性的研究一直是量子光学研究的热点,本文利用自旋相干态变换和基态变分法从理论上求解光腔中冷原子系统的基态能量表达式,并且给出丰富的基态相图。在正常相时给出基态能量稳定值的解析解;而超辐射相时,我们可以利用迭代的方法近似得到原子布居数、平均光子数和基态能量随原子-场耦合强度的变化。本文主要呈现出原子-原子相互作用强度改变正常相到超辐射相的量子相变点,且是一阶相变,但未出现新的量子相和量子相变。     

Real-Code Genetic Algorithm for Ground State Energies of Hydrogenic Donors in GaAs-(Ga,Al)As Quantum Dots

We present a global optimization method, called the real-code genetic algorithm (RGA), to the ground state energies. The proposed method does not require partial derivatives with respect to each variational parameter or solving an eigenequation, so the present method overcomes the major difficulties of the variational method. RGAs also do not require coding and encoding procedures, so the computation time and complexity are reduced. The ground state energies of hydrogenic donors in GaAs-(Ga,Al)As quantum dots have been calculated for a range of the radius of the quantum dot radii of practical interest. They are compared with those obtained by the variational method. The results obtained demonstrate the proposed method is simple, accurate, and easy implement.     

Structure optimization by heuristic algorithm in a coarse-grained off-lattice model

A heuristic algorithm is presented for a three-dimensional off-lattice AB model consisting of hydrophobic (A) and hydrophilic (B) residues in Fibonacci sequences. By incorporating extra energy contributions into the original potential function, we convert the constrained optimization problem of AB model into an unconstrained optimization problem which can be solved by the gradient method. After the gradient minimization leads to the basins of the local energy minima, the heuristic off-trap strategy and subsequent neighborhood search mechanism are then proposed to get out of local minima and search for the lower-energy configurations. Furthermore, in order to improve the efficiency of the proposed algorithm, we apply the improved version called the new PERM with importance sampling (nPERMis) of the chain-growth algorithm, pruned-enriched-Rosenbluth method (PERM), to face-centered-cubic (FCC)-lattice to produce the initial configurations. The numerical results show that the proposed methods are very promising for finding the ground states of proteins. In several cases, we found the ground state energies are lower than the best values reported in the present literature.     

无限深量子阱中强耦合极化子的基态结合能

研究了无限深量子阱中极化子的基态性质,采用线性组合算符和变分相结合的方法导出了强耦合极化子的振动频率λ、基态能量E₀和基态结合能E_b,讨论了阱宽L和电子-LO声子耦合强度α对强耦合极化子的振动频率λ、基态能量E₀和基态结合能E_b的影响。通过数值计算,结果表明:强耦合极化子的振动频率和基态结合能随阱宽L的增大而减小,随电子-LO声子耦合强度α的增强而增大;基态能量随阱宽L的增大而减小,其绝对值随电子-LO声子耦合强度α的增强而增大;当量子阱阱宽L趋近于无限大和无限小两种极限情况下,分别与三维和二维极化子的结果相一致。     

Variational quantum eigensolvers by variance minimization

The original variational quantum eigensolver (VQE) typically minimizes energy with hybrid quantum-classical optimization that aims to find the ground state. Here, we propose a VQE based on minimizing energy variance and call it the variance-VQE, which treats the ground state and excited states on the same footing, since an arbitrary eigenstate for a Hamiltonian should have zero energy variance. We demonstrate the properties of the variance-VQE for solving a set of excited states in quantum chemistry problems. Remarkably, we show that optimization of a combination of energy and variance may be more efficient to find low-energy excited states than those of minimizing energy or variance alone. We further reveal that the optimization can be boosted with stochastic gradient descent by Hamiltonian sampling, which uses only a few terms of the Hamiltonian and thus significantly reduces the quantum resource for evaluating variance and its gradients.     

The quantum adiabatic algorithm applied to random optimization problems: The quantum spin glass perspective

Among various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal value of an arbitrary cost function (ground state energy). Random optimization problems provide a natural testbed to compare its efficiency with that of classical algorithms. These problems correspond to mean field spin glasses that have been extensively studied in the classical case. This paper reviews recent analytical works that extended these studies to incorporate the effect of quantum fluctuations, and presents also some original results in this direction.     

数字图像散斑相关技术的蚁群优化方法

基于蚁群优化方法提出新的数字图像散斑相关算法。该方法模仿了真实蚂蚁从其巢到食物找到最短路径的方式,通过对蚁群优化方法改进,减少迭代次数并改善解的质量。将新的数字图像散斑相关算法应用到计算机模拟的散斑图像和实验获得的散斑图像中,并与广泛使用的Newton-Raphson算法进行了比较。实验结果展示了新算法的精度、可行性和有效性。当数量级为0.01像素,误差离散均方根小于0.002像素。     

Bound polaron in a quantum pseudodot under Rashba effect

In the present work, the influence of Rashba effect on bound polaron in a quantum pseudodot is studied. Using the Lee–Low–Pines unitary transformation method and the Pekar type variational procedure, we have derived an expression for the bound polaron ground state energy. The ground state energy as functions of the wave vector, the electron–phonon coupling strength, and quantum confinement size is obtained by considering different Coulomb bound potentials. It is found that (i) the ground state energy is decreased with raising the Coulomb bound potential, the electron–phonon coupling strength, and quantum confinement size. (ii) The ground state energy increases when the wave vector is increasing. (iii) The ground state energy splits into two branches (spin-up and spin-down) due to the Rashba effect.     

声子和磁场对量子环中极化子性质的影响

采用求解能量本征方程、幺正变换和变分相结合的方法,研究声子和磁场对量子环中极化子性质的影响. 对KBr量子环的数值计算表明,电子或极化子的基态能量随量子环频率(或平均半径)的增大而增大,极化子基态能移随量子环频率的增大(或平均半径的减小)而减小,极化子中的平均声子数随量子环频率的增大(或平均半径的减小)而增大. 当有垂直磁场时,极化子基态能量和基态能移与外磁场及电子转动状态有关. 随着磁场强度的增大,基态能量出现简并且呈现非周期性振荡;能移随磁场强度的增大(或转动量子数绝对值的减小)而减小.     

遗传-蚁群混合算法在高温超导匀场磁体优化设计中的应用

遗传算法具有很强的自适应性、鲁棒性和全局搜索能力,但其局部搜索能力相对较弱,计算后期易出现进化缓慢、过早收敛等问题,蚁群算法是近几年迅速发展起来的一种新的全局优化算法,具有正反馈机制,但是计算初期由于信息素差别小,初始收敛速度较慢.本文将这两种优化方法结合起来,充分发挥各自的优势,形成了遗传-蚁群混合算法,并选用测试函数对算法的优化性能作了对比计算,最后以高温超导匀场磁体为实际应用目标,以绕制磁体所用超导带长度为目标函数对磁体结构进行优化设计,优化方案比原始方案节省7.32%的超导带材用量.     

An adiabatic quantum optimization for exact cover 3 problem

A perturbation method is applied to study the structure of the ground state of the adiabatic quantum optimization for the exact cover 3 problem. It is found that the instantaneous ground state near the end of the evolution is mainly composed of the eigenstates of the problem Hamiltonian, which are Hamming close to the solution state. And the instantaneous ground state immediately after the starting is mainly formed of low energy eigenstates of the problem Hamiltonian. These results are then applied to estimate the minimum gap for a special case.