无序度对一维长程关联无序系统中局域化-退局域化转变的影响

对长程幂律关联能量序列进行了修正,使其能体现出无序度在一维长程关联无序系统中的影响,并利用重正化群方法,计算了能反映该系统局域化-退局域化转变的Lyapunov指数.结果表明,在由于关联指数p的影响而在系统中出现的局域化向退局域化的转变中,无序度起着相反的作用.当关联指数p一定而无序度W增大时,系统中心能区范围内由于长程关联而引起的扩展态逐渐向局域态转变.当无序度W增大到某一临界值W_c时,系统中所有本征态均转变为局关键词：长程关联Lyapunov指数无序度局域化-退局域化转变     

一维长程关联无序系统中的电子态

利用傅里叶滤波法在一维Anderson无序系统中产生了具有幂律谱密度公式s(q)∝q^-p形式的长程关联随机能量序列,并利用传输矩阵方法计算了系统中引入了长程关联后的局域长度,同时应用负本征值理论对系统中的电子态密度进行了分析,并分别把计算结果与系统中不具有长程关联时的局域长度与电子态密度进行了比较.结果表明,长程幂律关联的引入对电子态的性质产生了很大的影响,当关联指数p≥2.0时,在系统能带中心范围内发生了部分局域态向退局域态的转变,而同时电子态密度也发生了很大的变化,出现了六个范霍夫奇点,系统的能带范围也相应地得到展宽.关键词：无序系统长程关联局域长度电子态密度     

一维Anderson无序模型电子局域态

本文应用一种新方法,得到了包括次近邻相互作用,且无序点阵从五百到一万的一维安德逊无序模型电子本征态。结果表明此模型的本征态随着无序点阵的增加均从扩展态变为局域态,且变化的快慢受系统无序度的影响。     

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：     

一维准周期晶格的性质及应用

准周期晶格在冷原子领域被广泛研究,它使得人们可以在一维或者二维系统里研究扩展到安德森局域的转变. 2008年, Inguscio研究组在冷原子系统里制备了一维准周期晶格,并观测到了安德森局域化现象,这极大地推动了准周期系统的理论和实验研究.后来, Bloch研究组在制备的一维和二维准周期晶格中都观测到了多体局域的现象.最近,他们还在准周期晶格中成功观测到迁移率边以及存在迁移率边的系统的多体局域现象.这些冷原子实验推动了多体局域以及迁移率边等方向的研究.准周期晶格已经成为一个平台,它对很多物理现象的影响正在被广泛研究,并可以尝试在冷原子实验中观测到这种影响.本文结合作者的一些相关工作,对一维准周期晶格一些近期的研究进行了简要综述,介绍了一些相关的重要的冷原子实验,讨论了准周期晶格的一些重要性质,以及它对一些物理现象(比如拓扑态)的影响.     

两维局域互联神经网络的关联存储

本文将局域互联神经网络的新概念推广到两维情形,并对两维局域互联关联存储进行了理论分析和大量的计算机模拟.结果表明,两维局域互联神经网络的优点是,在满足存储容量限制的前提下,它与全局互联神经网络具有相同的关联存储能力,而其互联权重矩阵要比全局互联网络小得多.因而,有利于使用现有的空间光调制器实现两维大规模的人工神经网络.     

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     

量子能谱中的长程关联

从可积系统求迹公式出发,运用Einstein-Brillouin-Keller(EBK)量子化条件,导出了二维无关联振子系统周期轨道作用量量子化条件,由此发现了量子能级与周期轨道之间的对应关系.这种对应关系表明,如果两条能级对应的周期轨道的拓扑相同,这两条能级对回归函数的贡献相干.回归谱中的一个峰是量子能谱中一组与具有相同拓扑的周期轨道相对应的能级之间相干的结果,这一组能级间存在着长程关联.     

高阶局域互联神经网络的关联存储

给出了高阶局域互联神经网络的数学模型。在计算机上对其关联存储能力进行了模拟计算。结果表明，这种局域互联神经网络的互联权重数大大减少，同时依然具有良好的关联存储能力；另一方面，如果限定了互联权重矩阵的大小，利用本文给出的高阶局域互联神经网络模型可构造较大的人工神经网络。     

一维准周期晶格中玻色子对的迁移率边

研究了一维非公度的准周期晶格中的玻色子对的迁移率边.通过微扰方法,解析推导出强相互作用极限下准周期晶格中玻色子对迁移率边的解析表达式,通过数值证明在系统参数b较小时,迁移率边的解析结果符合得较好,而当b→1时,解析结果将发生偏离.     

State vector evolution localized over the edges of a square tight-binding lattice

We study the time evolution of a state vector in a square tight-binding lattice, focusing on its evolution localized over the system surfaces. In this tight-binding lattice, the energy of atomic orbital centred at surface site is different from that at the interior (bulky) site by an energy shift U. It is shown that for the state vector initially localized on a surface, there exists an exponential law (y=a\e^x/b+y₀) determined by the absolute value of the energy shift, |U|, which describes the transition of the state evolving on the square tight-binding lattice, from delocalized over the whole lattice to localized over the surfaces.     

Anderson localization and the space-time characteristic of continuum states

A proof of Anderson localization is obtained by ruling out any continuous spectrum on the basis of the space-time characteristic of its states.     

Electronic properties of one-dimensional systems with long-range correlated binary potentials

We study numerically the electronic properties of one-dimensional systems with long-range correlated binary potentials.The potentials are mapped from binary sequences with a power-law power spectrum over the entire frequency range,which is characterized by correlation exponent β.We find the localization length ξ increases with β.At system sizes N →∞,there are no extended states.However,there exists a transition at a threshold β c.When β > β c,we obtain ξ > 0.On the other hand,at finite system sizes,ξ≥ N may happen at certain β,which makes the system "metallic",and the upper-bound system size N (β) is given.     

二维合金系统的有序动力学研究

采用主方程方法在对概率近似下对三元fcc结构晶体在(001)方向的一个层面的有序无序动力学过程进行了研究.计算了长程序参量(LRO)和短程序参量(SRO)随时间的演化过程.在系统从完全无序态弛豫到平衡态的过程中存在各种瞬态有序相.瞬态相有着不同的特点,如序参量(LRO,SRO)瞬态相曲线形状不同等.产生它们的原因有不同的原子特征迁移时间、原子间最近邻和次近邻相互作用差异、短程相关性和长程相关性的差异对弛豫过程的影响.关键词：对概率近似瞬态有序相长程序参量(LRO)长程相关性     

The Repulsion Between Localization Centers in the Anderson Model

In this note we show that, a simple combination of deep results in the theory of random Schrödinger operators yields a quantitative estimate of the fact that the localization centers become far apart, as corresponding energies are close together.     

Zero Energy Anomaly in One-Dimensional Anderson Lattice with Exponentially Correlated Weak Diagonal Disorder

We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the correlation of the disorder increases. We found that higher order terms of the correlation must be included into the current perturbation result in order to give the correct localization length, and to connect smoothly the anomaly at zero correlation with the perturbation result for large correlation.     

Zero Energy Anomaly in One-Dimensional Anderson Lattice with Exponentially Correlated Weak Diagonal Disorder

We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the correlation of the disorder increases. We found that higher order terms of the correlation must be included into the current perturbation result in order to give the correct localization length, and to connect smoothly the anomaly at zero correlation with the perturbation result for large correlation.     

Quantum phase transitions in matrix product states of one-dimensional spin-1 chains

We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equM coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement.     

Properties of Parity Non-conserved and Parity Conserved States in MatrixProduct Systems

In terms of reflection transformation of a matrix product state (MPS), the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state |Ψ_e> and the odd-parity state |Ψ_o>. It is interesting to find that the parity non-conserved reflective MPSpair have no long-range correlations; instead the even-parity state|Ψ_e> and the odd-parity state |Ψ_o> constructed from them have the same long-range correlations for the parity non-conserved block operators. Moreover, the entanglement between a block of n contiguous spins and the rest of the spin chain for the states |Ψ_e> and |Ψ_o > is larger than that for the reflective MPS pair except for n=1, and the difference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1. Thesecharacteristics indicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode, and that the parity conserved MPSs contain more correlation, coherence, and entanglement than the parity non-conserved ones.