DNA分子链的电子局域性质及电导的研究

将一维随机二元固体模型应用于DNA分子链，利用传输矩阵方法来研究系统电子态的局域性质并进而讨论系统的导电性质.对一个链长为50000个碱基对的DNA序列，数值分析了局域长度和电导随碱基对的摩尔百分数、本征能量和无序度的变化关系.结果表明，系统的局域长度和电导强烈地依赖于能量，在能带中心部分局域长度大于边沿部分.无序度也在一定程度上影响着局域长度，双方成反向变化的关系.对有限长度的DNA分子链，局域长度体现出明显的对碱基对摩尔百分数的依赖关系，对正常成分比例的随机DNA序列，在所有能量范围内系统的态都是局域的，系统的电导很小，系统呈现绝缘体行为.仅当一种碱基对在序列中所占比例很小时，系统中可以发现与特定分立能量值相对应的“扩展态”存在，处在这些态下的系统有较大的电导，但这些扩展态是不稳定的，在热力学极限之下会消失. 关键词： DNA分子链 电子局域 局域长度 电导     

AN EFFECTIVE TWO-LEVEL CHANNEL FOR AN IMPURITY IN A SUPERLATTICE

The eigenstates and eigenspectrum of a charged particle in a one-dimensional semiconductor superlattice with an impurity under the action of a dc electric field are investigated employing the single-band tight-binding model. We find that the system undergoes a series of avoided crossings, at which resonant oscillations between the impurity and its nearest neighbour occur if appropriate conditions are met, suggesting an effective two-level approximation. This phenomenon shows that introducing an impurity in a perfect lattice provides a promising structure for the observation of terahertz radiation.     

DNA分子链电子结构特性研究

在单电子紧束缚近似下，建立了一维无序二元DNA分子链模型，计算了链长为2×10⁴个碱基对的DNA分子链的电子态密度、局域化特性，并探讨了碱基对的不同组分、格点能量无序度对电子局域态的影响.结果表明：由于DNA分子链中格点能量无序及碱基对的不同组分的存在，其电子波函数呈现出局域化的特性，而局域长度作为衡量电子局域化程度的一个尺度，受碱基对的组分及格点能量无序度的影响. 关键词： DNA分子链 电子结构 电子局域态 局域长度     

A General Framework for Localization of Classical Waves: II. Random Media

We study localization of classical waves in random media in the general framework introduced in Part I of this work. This framework allows for two random coefficients, encompasses acoustic waves with random position dependent compressibility and mass density, elastic waves with random position dependent Lamé moduli and mass density, electromagnetic waves with random position dependent magnetic permeability and dielectric constant, and allows for anisotropy. We show exponential localization (Anderson localization) and strong Hilbert–Schmidt dynamical localization for random perturbations of periodic media with a spectral gap. This revised version was published online in July 2006 with corrections to the Cover Date.     

Chaos‐related Localization in Modulated Lattice Array

This paper will discuss the chaos‐related localization in a lattice array with an external periodical field acted on a boundary site that allows us to realize the controllable chaotic dynamics with a tunable driving frequency. Two types of chaos‐related localization, short‐term and long‐term localization, which are closely related to the degree of chaos are reported and may provide a way to realize switching from chaos‐related localization to chaos‐assisted tunneling. Interestingly, with the increase of nonlinearity, driving frequency or even second‐order coupling, there always exists a parameter window with sharp edges for long‐term localization which facilitates us to find the thresholds to control the system into or out of localization region. In addition, the numerical results further demonstrate that the initial phase of the driving field may greatly influence the degree of the chaos. These results can be extended to finite driven N‐site system and may deepen our understanding of chaos‐related localization in nonlinear driving system.     

The nature of the spectrum for a Landau Hamiltonian with delta impurities

We consider a single-band approximation to the random Schrödinger operator in an external magnetic field. The random potential consists of delta functions of random strengths situated on the sites of a regular two-dimensional lattice. We characterize the entire spectrum of this Hamiltonian when the magnetic field is sufficiently high. We show that the whole spectrum is pure point, the energy coinciding with the first Landau level in the absence of a random potential being infinitely degenerate, while the eigenfunctions corresponding to energies in the rest of the spectrum are localized.     

劈尖干涉条纹定域的解析研究

得到了劈尖干涉定域中心参量方程和定域深度的解析解,解析地讨论了定域中心和定域深度与入射角、劈尖角、相对折射率、光源位置等物理量的依赖关系.研究的结果对确定清晰的劈尖干涉条纹位置具有指导意义.     

一种水下三维被动定位技术

本文给出了一种三维被动定位方法。该方法利用三元水平阵和二元垂直阵实现对目标的三维定位。由三元水平阵首先求得目标斜距和目标方位,在此基础上利用垂直阵估计目标深度坐标,最后综合已有测量结果来求解目标水平坐标。本文还通过仿真分析了该方法的定位性能。     

Theory of many-body localization in periodically driven systems

We present a theory of periodically driven, many-body localized (MBL) systems. We argue that MBL persists under periodic driving at high enough driving frequency: The Floquet operator (evolution operator over one driving period) can be represented as an exponential of an effective time-independent Hamiltonian, which is a sum of quasi-local terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the time-dependence from the original Hamiltonian. When the driving evolves smoothly in time, the theory can be sharpened by estimating the probability of adiabatic Landau–Zener transitions at many-body level crossings. In all cases, we argue that there is delocalization at sufficiently low frequency. We propose a phase diagram of driven MBL systems.     

Localization of Non-Relativistic Particles

This paper is a contribution to the problem of particle localization in non-relativistic Quantum Mechanics. Our main results will be (1) to formulate the problem of localization in terms of invariant subspaces of the Hilbert space, and (2) to show that the rigged Hilbert space incorporates particle localization in a natural manner.     

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.     

电声子相互作用对半导体超晶格动力学局域化的影响

本文用单带模型分别研究了直流外场和交流外场作用下，电声子相互作用对半导体超晶格的动力学局域化性质的影响。结果表明：电声子相互作用会破坏电子的动力学局域化。对同一声子频率，电声子相互作用的强度越大，电子越快被散射；当声子频率等于直流场的布洛赫频率或交流场频率时，初始局域在某一格点的电子被迅速地散射到其他格点上去，亦即光声子共振场会严重破坏电子的动力学局域化性质。     

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在文献[1]中,通过分析实验上观察到的测地声模的小密度-电位比与测地声模谐波定级的自洽性,论证了测地声模是在转向点附近一种“蝌蚪状”的定域结构,但没有给出导致这种结构的物理机制.从随机媒质对波传播产生定域化的角度进行了探讨,采用测地声模由漂移波湍流参量激发的产生模型,计算了随机定域化导致的也是文献[1]所关注的相干长度.讨论了与实验观测比较的有关问题.     

High-precision two-dimensional atom localization via probe absorption in an M-scheme atomic system

In the present paper, we investigate the behavior of two-dimensional atom localization in a five-level M-scheme atomic system driven by two orthogonal standing-wave fields. We find that the precision and resolution of the atom localization depends on the probe field detuning significantly. And because of the effect of the microwave field, an atom can be located at a particular position via adjusting the system parameters.     

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.     

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.     

Nonergodic Brownian Motion

The long-time behavior of a system is suggested to confirm nonergodicity of non-Markovian Brownian dynamics, namely, whether the stationary probability density function （PDF） of the system characterized mainly by low moments of variables depends on the initial preparation. Thus we classify nonergodic Brownian motion into two classes： the class-I is that the PDF of a force-free particle depends on the initial velocity and the equilibration can be recovered through a bounded potential; while the PDF in the class-H depends on the initial coordinate and the equilibration can not be approached by introducing any potential. We also compare our result with the conditions of three kinds for ergodicity.     

Dynamical localization and nondispersion of energy spectrum

Within a finite band model, we present a proof of the theorem that dynamical localization happens if and only if the energy spectrum is dispersionless for an electron in a semiconductor superlattice under the influence of time-periodic electric fields. The electron may display several localization patterns.     

The localization properties of a random steady flow on a lattice

We consider a random stationary vector field on a multidimensional lattice and investigate flow-connected subsets of the lattice invariant under the action of the associated flow. The subsets of primary interest are cycles, and vortices each of which is the set of orbits terminating in the same cycle. We prove that with probability 1 each vortex only involves a finite number of sites of the lattice. Under the assumption of independence of the vector field in different sites, we find that with probability 1 the vortices exhaust all possible maximal flowconnected invariant subsets of the lattice if and only if the probability of existence of a cycle is positive. Thus, if cycles exist, a particle under the action of the flow only moves within a bounded region, i.e., it is completely localized.     

频率对环绕声声像定位的影响

本文考虑双耳相位差的高级近似，导出了中频情况下适用的具有更普遍意义的平面环绕声声像定位公式。在低频时该式将化为通常的环绕声声像定位公式，而随着声音频率的增加，声像位置将与频率有关。将新的公式用到方型排列和棱型排列的４－４－４环绕声系统，得到了同实验相一致的结果。文中着重指出，声像随频率而变化是导致环绕声重发中侧向声像不稳定的重要在而为今后改进环绕声系统提供了理论基础。