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.     

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.     

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     

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.     

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.     

Anomalous localization in low-dimensional systems with correlated disorder

This review presents a unified view on the problem of Anderson localization in one-dimensional weakly disordered systems with short-range and long-range statistical correlations in random potentials. The following models are analyzed: the models with continuous potentials, the tight-binding models of the Anderson type, and various Kronig–Penney models with different types of perturbations. Main attention is paid to the methods of obtaining the localization length in dependence on the controlling parameters of the models. Specific interest is in an emergence of effective mobility edges due to certain long-range correlations in a disorder. The predictions of the theoretical and numerical analysis are compared to recent experiments on microwave transmission through randomly filled waveguides.     

Metal-insulator transition in two-dimensional systems with long-range correlated disorder

We study the localization properties of electrons in a two-dimensional model with on-site energies exhibiting long-range correlated disorder. The localization length and conductance of the system are calculated by using the finite size scaling method combined with transfer matrix technique. In the presence of long-range correlations, we find that there is a continuous line of fixed points indicating that the system undergoes a disorder driven Kosterlitz-Thouless-type metal-insulator transition. Received 6 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: wsliu@sjtu.edu.cn     

Localization properties of driven disordered one-dimensional systems

We generalize the definition of localization length to disordered systems driven by a time-periodic potential using a Floquet-Green function formalism. We study its dependence on the amplitude and frequency of the driving field in a one-dimensional tight-binding model with different amounts of disorder in the lattice. As compared to the autonomous system, the localization length for the driven system can increase or decrease depending on the frequency of the driving. We investigate the dependence of the localization length with the particle's energy and prove that it is always periodic. Its maximum is not necessarily at the band center as in the non-driven case. We study the adiabatic limit by introducing a phenomenological inelastic scattering rate which limits the delocalizing effect of low-frequency fields.     

Coherent electronic dynamics and absorption spectra in an one-dimensional model with long-range correlated off-diagonal disorder

In this work we study an one-dimensional Anderson model with long-range correlated off-diagonal disorder. We numerically demonstrate the presence of extended states and an anomalous optical absorption spectrum for high degrees of correlation. We also show that the electric field biased electronic wave packet dynamics shows Bloch-like oscillations.     

Bloch-like oscillations in a one-dimensional lattice with long-range correlated disorder

We study the dynamics of an electron subjected to a uniform electric field within a tight-binding model with long-range-correlated diagonal disorder. The random distribution of site energies is assumed to have a power spectrum S(k) approximately 1/k(alpha) with alpha>0. de Moura and Lyra [Phys. Rev. Lett. 81, 3735 (1998)]] predicted that this model supports a phase of delocalized states at the band center, separated from localized states by two mobility edges, provided alpha>2. We find clear signatures of Bloch-like oscillations of an initial Gaussian wave packet between the two mobility edges and determine the bandwidth of extended states, in perfect agreement with the zero-field prediction.     

Localization-delocalization transition in one-dimensional system with long-range correlated diagonal disorder

We show that the electronic states in a one-dimensional (1D) Anderson model of diagonal disorder with long-range correlation proposed by de Moura and Lyra exhibit localization-delocalization phase transition in varying the energy of electrons. Using transfer matrix method, we calculate the average resistivity and investigate how it changes with the size of the system N. For given value of α (> 2) we find critical energies E_c1 and E_c2 such that the resistivity decreases with N as a power law ∝ N ^{- γ} for electron energies within the range of [E _c1, E _c2], and exponentially grows with N outside this range. Such behaviors persist in approaching the transition points and the exponent γ is in the range from 0.92 to 0.96. The origin of the delocalization in this 1D model is discussed. Received 18 December 2001 / Received in final form 2 May 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: sjxiong@nju.edu.cn     

von Neumann entropy signatures of a transition in one-dimensional electron systems with long-range correlated disorder

We study the von Neumann entropy and related quantities in one-dimensional electron systems with on-site long-range correlated potentials. The potentials are characterized by a power-law power spectrum S(k) μ\propto 1/k ^α, where α is the correlation exponent. We find that the first-order derivative of spectrum-averaged von Neumann entropy is maximal at a certain correlation exponent α _m for a finite system, and has perfect finite-size scaling behaviors around α _m . It indicates that the first-order derivative of the spectrum-averaged von Neumann entropy has singular behavior, and α _m can be used as a signature for transition points. For the infinite system, the threshold value α _c = 1.465 is obtained by extrapolating α _m .