边界条件对无序体系本征态的影响

本文仔细地分析了当无序体系被嵌放在一个无限有序体系之中时,边界条件对体系本征态的影响。结果表明,在离边界距离大于局域长度的区域内,这种本征态能够重现无序体系的性质。这就提出了研究无序体系本征态的一种方便的方法。 关键词：     

一维无序系统本征矢的解法

本文提出了一种直接求解五对角厄米特矩阵本征矢的方法,即通过代数运算求出本征矢,而不是用三对角块矩阵来解。该方法对计算一维无序系统的本征矢特别适用。计算结果表明,此方法的存储量小,计算精度高,速度快,并可计算上十万个点阵的无序系统本征矢。     

一维无序二元固体中电子局域性质的研究

从单电子紧束缚模型的哈密顿量出发，格点能量随机取ε_A和ε_B，只计及格点之间的近程跳跃积分，建立了一维无序二元固体模型. 利用负本征值理论及无限阶微扰理论，对系统电子的本征值和本征态进行了数值计算. 结果表明与一定能量本征值对应的电子波函数只分布在系统的一定范围内，显示了其局域性. 借助传输矩阵方法，计算出电子的局域长度，讨论了局域长度随本征能量和无序度的变化关系，并研究了计入不同范围跳跃积分下，局域长度的变化特征. 关键词： 无序 二元固体 电子态 局域长度     

无序系统中电子局域态分布

本文应用一种计算无序系统中电子本征态的方法,求得了含有2000个粒子的无序系统中电子局域态的分布,并结合态密度、计算误差进行了分析讨论。所得结果表明,在不同的能量范围内局域态的分布不同,分布可遍及整个系统,且与无序度有关。 关键词：     

一种发光二极管模型中无序光子晶体对光输出影响的研究

摘要利用Order-N算法及超晶格技术讨论了位置无序及尺寸无序对石墨点阵柱状光子晶体光子带隙的影响.计算结果表明,对于电场偏振模,光子带隙对尺寸无序更加敏感.在此基础上,利用三维时域有限差分方法进一步讨论了无序光子晶体对石墨点阵柱状中心柱光子晶体GaN发光二极管模型光输出效率的影响.计算结果表明,无序对这种光子晶体发光二极管模型光输出效率的影响较小,且这种影响也是随机的.     

非完整超晶格中电子透射问题的计算机模拟

采用转移矩阵方法,模拟研究了垒高无序和阱宽无序非完整超晶格的电子态问题.计算了垒高无序有限超晶格的透射谱和其局域态波函数以及阱宽无序有限超晶格的透射谱和本征值,直观地给出了垒高无序和阱宽无序非完整有限超晶格其电子态行为的物理图像.模拟结果表明:垒高无序和阱宽无序这两种常见非完整一维有限超晶格的子带带隙间均存在强烈的电子运动定域化,且电子波的布喇格散射对周期性势场更敏感;这两种非完整性引起的局域,通过计算电子局域态波函数和有限系统的本征值得到了证实;对本文讨论的这种类型和周期的超晶格,如果控制阱宽在9.1～10.9nm间随机变化,即阱宽的值最大相差1.8岫时,计算机模拟的结果是,阱宽的这种非周期性开始使子带的带隙消失.     

准一维无序系统的电子结构

利用负本征值理论的态密度计算方法，研究了准一维双链无序系统的电子结构。并针对系统大小，对角和非对角无序程等各种参数，探讨了电子的局域化，系统能量分布范围等问题。在引进无序参量后，对角无序主要引起电子局域态的增多，而非对角无序则使系统的能量分布范围发生变化。     

考虑晶体应力情况下的单块非平面环形腔分析

简要分析了单块非平面环形腔单频激光器的基本原理,并采用琼斯矩阵计算了单块单向行波非平面环形腔内的本征偏振态。深入分析了磁场强度、输出面偏振反射系数、入射角、非平面角及腔内其它参量对各本征偏振态的损耗及两本征偏振态间损耗差的影响,并且指出如何选择各参量以降低本征偏振态的损耗且增大两本征偏振态间的损耗差。最后还通过计算晶体应力在两个本征偏振态方向引起的相位差,讨论了应力作用方向以及应力双折射系数对腔内本征偏振态的损耗和两本征偏振态间损耗差的影响。     

相位Landau态

引入Landau系统(带电粒子在垂直于均匀磁场平面内的运动)的相位本征态，利用这些本征态可方便地描述带电粒子圆周运动，且所得结果与规范的选择无关. 关键词： Landau系统 相位本征态     

外磁场中海森伯反铁磁模型的代数结构和压缩态解

外磁场中的XYZ海森伯反铁磁模型，其哈密顿量在自旋波近似下具有so(3,2)李代数结构. 利用代数对角化方法，可得到压缩态形式的能量本征态和相应的能量本征值. 用此方法进一步讨论本征态的基本性质，并建立反铁磁模型与特定类型的双模耦合谐振子的联系. 关键词： 海森伯反铁磁模型 代数对角化 压缩态     

Geometric phase for degenerate states of spin-1 and spin-1/2 pair

The geometric phase of a bi-particle model is discussed. One can drive the system to evolve by applying an external magnetic field, thereby controlling the geometric phase. The model has degenerate lowest-energy eigenvectors. The initial state is assumed to be the linear superposition or mixture of the eigenvectors. The relationship between the geometric phase and the structures of the initial state is considered, and the results are extended to a more general model.      

Entanglement of a Five-Qubit Heisenberg XX Chain in a Magnetic Field

We calculate the eigenvalues and eigenvectors of a five-qubit isotropic Heisenberg model in an external magnetic field, and give analytical results for the concurrence of two nearest-neighbor qubits. A magnetic field can eliminate degeneration and change the ground state of the system. Therefore increasing the value of the magnetic field can induce entanglement in a certain range both for the antiferromagnetic and ferromagnetic case.     

Solving Laguerre-Gauss Mode Eigenvectors and Eigenfunctions in Entangled State Representation

We solve the Laguerre-Gauss mode eigenvectors and eigenfunctions in the entangled state representation by searching for common eigenvectors of the 2-dimensional harmonic oscillator's total energy operator and the angular momentum operator. We find that in the entangled state representation the eigen-solution satisfies the Hukuhara equation, and its solution is confluent hypergeometric function.     

In—Phase Resonances with Generic Transmission Zeros and Eigenvectors of Hamiltonian in Models of Single Channel Transport

We investigate the phase coherent transport in a single channel system.The theory that the tranmission zeros lead to abrupt phase change and in-phase resonances in confirmed numerically in two tight-binding models.After calculating the eigenvalues and eigenvectors of the Hamiltonians we also confirmed that the same symmetry of the eigenvectors also leads to the abrupt phase change and in-phase resonances that equal the transmission zero.     

The six-vertex model eigenvectors as critical limit of the eight-vertex model bethe ansatz

The critical limit of the eight-vertex model eigenvectors obtained by means of the generalized Bethe Ansatz is shown to give the six-vertex eigenvectors as constructed in a previous paper by two of the authors. Furthermore, an explicit mapping is established between these eigenvectors and the usual Bethe Ansatz eigenvectors of the six-vertex model. This allows one to show that the indexv labeling the eight-vertex eigenstates becomes exactly the third component of the total spin in the critical limit.     

Boson bound states in the β-Fermi–Pasta–Ulam model

The bound states of four bosons in the quantum β-Fermi–Pasta–Ulam model are investigated and some interesting results are presented using the number conserving approximation combined with the number state method. We find that the relative magnitude of anharmonic coefficient has a significant effect on forming localized energy in the model, and the wave number plays an important role in forming different bound states. The signature of the quantum breather is also set up by the square of the amplitudes of the corresponding eigenvectors in real space.     

Experimental observation of the topological structure of exceptional points

We report on a microwave cavity experiment where exceptional points (EPs), which are square root singularities of the eigenvalues as function of a complex interaction parameter, are encircled in the laboratory. The real and imaginary parts of an eigenvalue are given by the frequency and width of a resonance and the eigenvectors by the field distributions. Repulsion of eigenvalues--always associated with EPs--implies frequency anticrossing (crossing) whenever width crossing (anticrossing) is present. The eigenvalues and eigenvectors are interchanged while encircling an EP, but one of the eigenvectors undergoes a sign change which can be discerned in the field patterns.     

新纠缠态表象对耦合2谐振子系统的应用

我们研究一个耦合2谐振子系统的本征态问题。我们构造了由算子（x1+p2）和（x2+p1）的共同本征态组成的新纠缠态表象︱γ>。在︱γ>表象得到了系统哈密顿的本征值和本征态。同样的问题用二次量子化表象进行了研究。我们发现在Fock空间，二次量子化表象可以被用来推得本征态的正规积表示。特别是发现了系统基态为广义2模压缩态     

An improved quantum principal component analysis algorithm based on the quantum singular threshold method

Quantum principal component analysis (qPCA) is a dimensionality reduction algorithm for getting the eigenvectors corresponding to top several eigenvalues of the data matrix and then reconstructing. However, qPCA can only construct the quantum state contains all the eigenvectors and eigenvalues. In this paper, we present an improved quantum principal component analysis (Improved qPCA) algorithm with a fixed threshold. We can reduce the singular value less than the threshold to 0 and obtain a target quantum state which can be used to get an output similar to qPCA after phase estimation. Compared with qPCA, our algorithm has only the target eigenvalues and the probability that we get each target eigenvalue is greater. Furthermore, our algorithm can serve as an additional regularization method and a subroutine for subsequent data processing.