On the theory of localization in disordered systems

A localization criterion is derived by using the self-consistent determination of the self-energy in the discussion of the convergence of the Green function renormalized perturbation expansion. This criterion depends on the dimensionality and the connectivity of the lattice. It yields localization for all states in one-dimension systems and tends to the Economon-Cohen criterion when the number of neighbours tends to infinity. Moreover, one can show that delocalization occurs when the width of the probability distribution of the self-energy is of the order of magnitude of the hopping integral.     

Effects of disorder on the correlation energy of rings of hydrogen atoms

The correlation energy of disordered systems has been calculated by means of second-order Rayleigh-Schrödinger perturbation theory in the M?ller-Plesset partitioning. Rings of hydrogen atoms have been chosen as model systems and the degree of disorder has been varied from complete delocalization to complete localization of the one-particle states. The correlation energy was found to have an extremum at an intermediate degree of disorder, corresponding to incomplete localization.     

Error analysis of free probability approximations to the density of States of disordered systems

Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble-averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different approximations. We identify an approximation that is accurate to the eighth moment across all noise strengths, and contrast this with perturbation theory and isotropic entanglement theory.     

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 scaling laws in the onset of dynamical delocalization

We study the destruction of dynamical localization experimentally observed in an atomic realization of the kicked rotor by a deterministic Hamiltonian perturbation, with a temporal periodicity incommensurate with the principal driving. We show that the destruction is gradual, with well-defined scaling laws for the various classical and quantum parameters, in sharp contrast to predictions based on the analogy with Anderson localization.     

The roles of extrinsic periodic information on the stability of stock price

The perturbation expansion for the nonlinear Schrödinger equation with a random potential that was developed in earlier works by some of us is extended to higher orders. As the order is increased a solution that is valid for longer time can be found. In particular it is found that Anderson localization persists in the fifth and sixth orders for times when perturbation theory is valid. The perturbation expansion is asymptotic and for the value of the nonlinearity parameter used, the fifth order is the optimal order of the perturbation theory. There are indications that for the sixth order perturbation theory may not be valid.     

一种参数摄动的混沌异结构同步方法

研究了参数摄动情形下的混沌异结构同步问题,基于Lyapunov稳定性定理并结合范数理论给出了系统参数摄动下实现混沌异结构同步的一个充分条件,为同步控制器的设计提供了一般方法.只要两混沌系统维数相等,状态变量可测,就可利用所提方法实现系统参数摄动下的异结构同步,并能够保证在同步实现后同步控制量伴随误差变量一同收敛至零.该方法鲁棒性强,适用范围广,通过对混沌系统、超混沌系统的同步仿真,证实了该方法的有效性. 关键词： 混沌 超混沌 同步 Lyapunov函数     

参数微扰激光超混沌系统模糊模型

研究了存在参数微扰的激光超混沌系统的Takagi-Sugeno (T-S) 模糊模型的逼近性及建立问题。分析了存在参数微扰的激光超混沌系统的动力学特性。基于典型T-S模糊系统的建模原理,研究了激光超混沌T-S模糊系统的通用逼近性,通过确定非线性关键变量、模糊隶属度函数及模糊规则,建立了激光超混沌系统的T-S模糊模型。仿真结果表明,所建立的模糊模型能够有效逼近存在参数微扰的激光超混沌系统。     

Reversible destruction of dynamical localization

Dynamical localization is a localization phenomenon taking place, for example, in the quantum periodically driven kicked rotor. It is due to subtle quantum destructive interferences and is thus of intrinsic quantum origin. It has been shown that deviation from strict periodicity in the driving rapidly destroys dynamical localization. We report experimental results showing that this destruction is partially reversible when the deterministic perturbation that destroyed it is slowly reversed. We also provide an explanation for the partial character of the reversibility.     

The integral quantum hall effect: Shortcomings of conventional localization theory

The localization problem in strong magnetic fields, if forced into the mold of conventional perturbation theory, leads to fundamental difficulties. These difficulties already appear on the level of mean field theory.     

Perturbation to Mei symmetry and adiabatic invariants for Hamilton systems

Based on the concept of adiabatic invariant, this paper studies the perturbation to Mei symmetry and adiabatic invariants for Hamilton systems. The exact invariants of Mei symmetry for the system without perturbation are given. The perturbation to Mei symmetry is discussed and the adiabatic invariants induced from the perturbation to Mei symmetry of the system are obtained.     

Hojman Exact Invariants and Adiabatic Invariants of Hamilton System

The perturbation to Lie symmetry and adiabatic invariants are studied. Based on the concept of higher-order adiabatic invariants of mechanical systems with action of a small perturbation, the perturbation to Lie symmetry is studied, and Hojman adiabatic invariants of Hamilton system are obtained. An example is given to illustrate the application of the results.     

Phase transitions in systems with a finite number of dominant ground states

We develop a theory of low-temperature phases of discrete lattice systems which is guided by formal perturbation theory, and which in turn yields its rigorous justification. The theory applies to many systems with an infinite number of ground states for which the perturbation theory predicts a finite number of low-temperature phases. We illustrate it on a number of examples.     

一种分布式双麦克风线阵声源定位方法

分布式麦克风阵列由于比传统的单阵列具有更大的空间孔径,可以获得更好的声源定位性能,因此基于分布式麦克风阵列的声源定位方法成为当前麦克风阵列领域研究的热点之一。本文研究了一种基于分布式双麦克风线阵的声源定位方法,并进行了系统实现,从理论上剖析了该算法的定位精度与单阵列定向误差以及声源位置之间的关系,而且还揭示了声源高度扰动对该算法定位精度的影响。最后,分别通过仿真实验和实际定位系统的测试结果,验证了本文理论分析的正确性。     

Effect of the form and localization of doping density perturbations on the current characteristics in a semiconductor superlattice

The effect doping density perturbations have on the current characteristics in a semiconductor superlattice is studied. The current characteristics are shown to depend on the localization and form of the perturbation. The effect of perturbations is strongest near the superlattice emitter. The effect grows along with the density profile integral and depends weakly on the form of the profile.     

扰动情况下基于RBF网络的混沌系统同步

基于RBF网络,在扰动存在的情况下,对混沌系统的同步和异结构同步问题进行了研究.研究表明本方法能有效地克服干扰对同步所造成的破坏,实现良好的同步效果.最后,利用Lorenz系统进行了仿真.仿真结果证明了所给方法的有效性. 关键词： 混沌系统 同步 RBF神经网络     

相空间中离散力学系统对称性的摄动与Hojman型绝热不变量

研究相空间中离散力学系统对称性的摄动与绝热不变量.列出相空间中未受扰离散力学系统的特殊Lie对称性导致的Hojman型精确不变量.基于相空间中力学系统的高阶绝热不变量的定义，研究在小扰动作用下系统Lie对称性的摄动，得到了相空间中离散力学系统的一类新的绝热不变量——Hojman型绝热不变量.举例说明结果的应用. 关键词： 相空间 Lie对称性 摄动 绝热不变量     

JMCT反应性微扰计算功能的实现

蒙特卡罗中子输运程序用于反应堆设计与安全分析计算及校验时,微小的反应性扰动容易被统计涨落所掩盖,因此一般通过微扰计算处理此类问题。基于微分算子方法在JMCT程序中实现了反应性微扰计算功能。为保证计算的精度,JMCT考虑了非源扰动的高阶效应以及一阶裂变源扰动效应。选取了具有全局扰动、局部扰动的快中子与热中子裂变系统对JMCT反应性微扰计算功能进行了测试。测试系统覆盖了正负反应性变化。     

Relaxation of finite perturbations: beyond the fluctuation-response relation

We study the response of dynamical systems to finite amplitude perturbation. A generalized fluctuation-response relation is derived, which links the average relaxation toward equilibrium to the invariant measure of the system and points out the relevance of the amplitude of the initial perturbation. Numerical computations on systems with many characteristic times show the relevance of the above-mentioned relation in realistic cases.