Localisation in disordered systems—I: The disordered spectrum

Starting from a definition of the localisation-delocalisation of electronic, wavefunctions in disordered systems based on the nature of the disordered spectrum, a delocalisation criterion identical to that of Abou-Chacraet al is recovered. The new derivation on provides a very clear picture of the mechanism of delocalisation and brings out its incompatibility with the normalisability of wavefunctions at the transition.     

Generalization of the Foldy-Lax formula for the self-energy of a wave propagating in a disordered system of scatterers

We presesent an exact generalization of the Foldy-Lax formula for the self-energy of a wave propagating in a disordered system of identical spherical scatterers. The Foldy-Lax formula yields an expression for the self-energy valid to first order in the density of scatterers. Our exact formula allows a systematic calculation of corrections to this low-density approximation. The formula is based on a renormalized cluster expansion which was presented earlier.     

Full counting statistics of phonon transport in disordered systems

The coherent potential approximation (CPA) within full counting statistics (FCS) formalism is shown to be a suitable method to investigate average electric conductance, shot noise as well as higher order cumulants in disordered systems. We develop a similar FCS-CPA formalism for phonon transport through disordered systems. As a byproduct, we derive relations among coefficients of different phonon current cumulants. We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders. For binary disorders as well as Anderson disorders, we calculate up to the 8-th phonon transmission moments and demonstrate that the numerical results of the FCS-CPA method agree very well with that of the brute force method. The benchmark shows that the FCS-CPA method achieves 20 times more speedup ratio. Collective features of phonon current cumulants are also revealed.     

一种基于多重散射的光学Hash函数

本文提出了一种基于光与多重散射介质相互作用的光学Hash函数构造方法.该方法创新性地利用多重散射介质对相干调制光的天然随机散射作用,实现了对调制光的"混淆"和"扩散",从而满足了Hash函数的核心功能要求:高安全强度的单向编码/加密.所设计的光电混合系统能有效地模拟Hash函数中的"压缩函数",结合具有特征提取功能的S...     

Localization in disordered,nonlinear dynamical systems

We study localization and wave trapping in disordered, nonlinear dynamical systems. For some models of classical, disordered anharmonic crystal lattices, we prove that, with large probability, there are quasiperiodic lattice vibrations of finite total energy which lie on some infinite-dimensional, compact invariant tori in phase space. Such vibrations remain localized, for all times, and there is no transport of energy through the lattice. Our general concepts and techniques extend to other systems, such as disordered, nonlinear Schrödinger equations, or randomly coupled rotors.     

On a cluster expansion for lattice spin systems: A finite-size condition for the convergence

A study is made of the statistical mechanics of classical lattice spin systems with finite-range interactions in two dimensions. By means of a decimation procedure, a finite-size condition is given for the convergence of a cluster expansion that is believed to be useful for treating the range of temperature between the critical oneT _c and the estimated thresholdT ₀ of convergence of the usual high-temperature expansion.     

The cluster expansion for classical and quantum lattice systems

We develop a high-temperature expansion for general lattice systems which can be applied to classical as well as quantum systems. Applying the expansion we prove analyticity of correlation functions, uniqueness of equilibrium states, and cluster properties for classical and quantum lattice systems in the high-temperature region.     

光学厚度对颗粒媒质的多重散射的影响

基于辐射传播方程及多重散射基础理论,利用Fraunhofer近似,对颗粒媒质的多重散射光强进行了计算。研究了光学厚度对多重散射的影响,揭示了多重光散射的角分布特征,光强大小随光学厚度的变化,以及单散射引起的误差等方面的规律。为实际的颗粒媒质的光学测量等提供了理论根据。     

Fourier acceleration of iterative processes in disordered systems

Technical details are given on how to use Fourier acceleration with iterative processes such as relaxation and conjugate gradient methods. These methods are often used to solve large linear systems of equations, but become hopelessly slow very rapidly as the size of the set of equations to be solved increases. Fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm. The method is explained for the Jacobi relaxation and conjugate gradient methods and is applied to two models: the random resistor network and the random central-force network. In the first model, acceleration works very well; in the second, little is gained. We discuss reasons for this. We also include a discussion of stopping criteria.     

Direct current hopping conductance in one-dimensional diagonal disordered systems

Based on a tight-binding disordered model describing a single electron band, we establish a direct current (dc) electronic hopping transport conductance model of one-dimensional diagonal disordered systems, and also derive a dc conductance formula. By calculating the dc conductivity, the relationships between electric field and conductivity and between temperature and conductivity are analysed, and the role played by the degree of disorder in electronic transport is studied. The results indicate the conductivity of systems decreasing with the increase of the degree of disorder, characteristics of negative differential dependence of resistance on temperature at low temperatures in diagonal disordered systems, and the conductivity of systems decreasing with the increase of electric field, featuring the non-Ohm's law conductivity.     

On multiple small-angle scattering

An analytical approach has been taken for analyzing the multiple scattering effects in small angle scattering (SAS) from both monodisperse and polydisperse systems. Two limiting regions, viz the Guinier region and the Porod region have been studied. A modified form of Guinier law has been deduced for the scattered intensity distribution in the region of small wave vector transfer, q. In the regionq(=|q|)→∞, it is shown that the effect of multiple scattering does not alter the Porod (q ⁻⁴) law. In the case of polydisperse systems, a correlation has been established between the size distribution of the inhomogeneities and the experimentally extractable parameters. The validity of the formalism has been examined by reinterpretation of the multiple SANS data (Hardman-Rhyne and Berk 1985) on polydisperse Al₂O₃ samples. This formalism is useful in characterizing the inhomogeneities from SAS measurements, particularly when thick samples are used.     

多次散射的分级计算及数值模拟

本文改进了多次散射的计算方法并提出了一个引理,经简化的数值模拟其结果与巳发表的实验数据相吻合.     

Stimulated raman scattering in fiber optic systems

The effect of stimulated Raman scattering (SRS) in fiber optic communications is considered. On one hand, SRS limits the launch power in a multiple-channel communication system; while on the other hand, SRS can provide optical amplification in the 1.3-μm and 1.55-μm windows. In most of the previous work these issues have been treated separately by using different assumptions. A solution is usually obtained by solving differential equations. We present a numerical method that involves the simultaneous solution of integral equations describing SRS in optical fiber. The method is general enough to be applicable for wavelength division multiplexing (WDM), optic frequency division multiplexing (OFDM), and optical amplification. However, it is efficient and simple to program and uses just a few realistic assumptions. A WDM communication system with 10 optical channels in the 1.55-μm window is studied by using this method, The data rate is above 1 Gbps. The system parameters are such that the other nonlinear effects, such as stimulated Brillouin scattering and four-wave mixing, are less significant for the system. Launch power limitations imposed by SRS are investigated for IM / DD and coherent systems. The receiver dynamic range over the wavelengths of interest is an important factor in determining the launch power limitations. An optical amplifier in the 1.3-μm window is also analyzed. The two-pump technique is investigated. With pump power levels of about 500 mw 0-dB gain can be achieved for a 30-km repeaterless link. Finally, the calculated results agree with the experiments.     

准一维多链无序体系跳跃电导特性

在单电子紧束缚近似下,建立了准一维多链无序体系直流、交流电子跳跃输运模型,通过计算探讨了无序模式、维度效应、温度及外场对其直流、交流电导率的影响.计算结果表明:准一维多链无序体系的直流、交流电导率随着格点能量无序度的增大而减小,非对角无序具有增强体系电子输运能力的作用.随着链数的增加,体系的直流、交流电导率增大,但格点能量无序度较小时,维度效应的影响不明显.在对角无序情况下准一维多链无序体系的交流电导率随温度的升高而增大,而在非对角无序模式下却随温度的升高而减小,但对于直流情况,体系的直流电导率随温度的升     

Multiple scattering in random media. III. Coherent potential propagators and fluctuations

An earlier microscopic approach to the theory of the averaged resolvent operator for an electron interacting with impurities is formulated in terms of coherent propagators. We study the corrections to the coherent potential approximation arising from fluctuations. For uncorrelated positions of the impurities, the linear, restricted, and general two-body additive approximations to the treatments of fluctuations are studied. For general correlations, the linear and restricted two-body additive approximations are studied. For both coherent and bare propagators, corresponding treatments of fluctuations involve the same correlation functions for impurities.Work supported in part by the National Science Foundation under Contract No. NSF DMR 79-23213.     

Numerical study on Anderson transitions in three-dimensional disordered systems in random magnetic fields

The Anderson transitions in a random magnetic field in three dimensions are investigated numerically. The critical behavior near the transition point is analyzed in detail by means of the transfer matrix method with high accuracy for systems both with and without an additional random scalar potential. We find the critical exponent ν for the localization length to be 1.45 ± 0.09 with a strong random scalar potential. Without it, the exponent is smaller but increases with the system sizes and extrapolates to the above value within the error bars. These results support the conventional classification of universality classes due to symmetry. Fractal dimensionality of the wave function at the critical point is also estimated by the equation-of-motion method.     

Lidar model with parameterized multiple scattering for retrieving cloud optical properties

Cirrus clouds play an important role in the climate through their optical and microphysical properties. The problem with measuring optical properties of these clouds can be partially addressed by using lidar systems. This paper presents a new model for describing the multiple scattering contribution to the backscatter signal measured by the lidar system. The new lidar equation introduced this way, expresses the backscatter signal in terms of a polynomial function of the cloud scattering coefficient. Cloud optical properties such as the extinction coefficient and lidar ratio can be deduced from the new proposed lidar equation. Moreover, some cloud microphysical properties can also be inferred from these optical properties. The method is applied to lidar data collected by the micropulsed lidar operating at Nauru under the auspices of the US Department of Energy ARM program.     

紫外光非视距多次散射信道模型研究

利用蒙特卡罗方法对紫外光非视距传输过程进行了模拟,讨论了传输过程中固体角的确定,仿真分析了系统的角度设置对传输损耗的影响.结果表明,增大收发仰角可以降低系统的传输损耗,并且小角度集中发射与大视场角接收可以降低系统的传输损耗.     

Deterministic quantum dense coding with cluster state in optical systems

We propose two optical schemes for implementing the deterministic single-particle and two-particle quantum dense coding using four-qubit cluster states. In the protocols, the photon is neuter particle, so it has longer decoherence time with the environment than other particles. It is easy to implement single-bit gate using the linear optical elements under certain conditions, so the transformations performed on the photons by Alice can be easily achieved. Here the cluster states can be exactly discriminated using the parity detector, PBS and FS-PBS. In addition, the success probabilities of the dense coding are both equal to 1.     

Semiclassical expansion of quantum characteristics for many‐body potential scattering problem

In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star‐product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical coordinates and momenta, can be used to solve the evolution equations for symbols of other operators acting in the Hilbert space. To any fixed order in the Planck's constant, many‐body potential scattering problem simplifies to a statistical‐mechanical problem of computing an ensemble of quantum characteristics and their derivatives with respect to the initial canonical coordinates and momenta. The reduction to a system of ordinary differential equations pertains rigorously at any fixed order in ?. We present semiclassical expansion of quantum characteristics for many‐body scattering problem and provide tools for calculation of average values of time‐dependent physical observables and cross sections. The method of quantum characteristics admits the consistent incorporation of specific quantum effects, such as non‐locality and coherence in propagation of particles, into the semiclassical transport models. We formulate the principle of stationary action for quantum Hamilton's equations and give quantum‐mechanical extensions of the Liouville theorem on conservation of the phase‐space volume and the Poincaré theorem on conservation of 2p‐forms. The lowest order quantum corrections to the Kepler periodic orbits are constructed. These corrections show the resonance behavior.