Measures of chaos and equipartition in integrable and nonintegrable lattices

We have simulated numerically the behavior of the one-dimensional, periodic FPU-alpha and Toda lattices to optical and acoustic initial excitations of small--but finite and large amplitudes. For the small-through-intermediate amplitudes (small initial energy per particle) we find nearly recurrent solutions, where the acoustic result is due to the appearance of solitons and where the optical result is due to the appearance of localized breather-like packets. For large amplitudes, we find complex-but-regular behavior for the Toda lattice and "stochastic" or chaotic behaviors for the alpha lattice. We have used the well-known diagnostics: Localization parameter; Lyapounov exponent, and slope of a linear fit to linear normal mode energy spectra. Space-time diagrams of local particle energy and a wave-related quantity, a discretized Riemann invariant are also shown. The discretized Riemann invariants of the alpha lattice reveal soliton and near-soliton properties for acoustic excitations. Except for the localization parameter, there is a clear separation in behaviors at long-time between integrable and nonintegrable systems.     

Disordered quantum walks in two-dimensional lattices

The properties of the two-dimensional quantum walk with point,line,and circle disorders in phase are reported.Localization is observed in the two-dimensional quantum walk with certain phase disorder and specific initial coin states.We give an explanation of the localization behavior via the localized stationary states of the unitary operator of the walker+coin system and the overlap between the initial state of the whole system and the localized stationary states.     

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.     

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.     

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.     

Weak chaos in the disordered nonlinear Schrödinger chain: Destruction of Anderson localization by Arnold diffusion

The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is shown that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of equilibration at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids. The corresponding macroscopic transport equations are obtained.     

Epidemic spreading in a scale-free network of regular lattices

The susceptible-infected-susceptible (SIS) epidemics in a scale-free network in which each node is a square lattice itself is investigated through large-scale computer simulations. The model combines a local contact process among individuals in a node (or city) with stochastic long-range infections due to people traveling between cities interconnected by the national transportation scale-free network. A nonzero epidemic threshold is found and it is approached with a power-law behavior by the density of infected individuals, as observed in the small-world network of Watts and Strogatz. Also, the epidemic propagation follows a 1/f$1/f$, hierarchical dynamics from the highly connected square lattices to the smaller degree nodes in outbreaks with sizes distributed accordingly a Gaussian function.     

用推广的Maxwell速度分布律证明转动、振动方式能均分定理

将描述分子平动速度分布的Maxwell速度分布律推广到转动和振动方式,并用推广的Maxwell分布律成功地证明了转动、振动方式的能均分定理．     

Critical quantum chaos in 2D disordered systems with spin-orbit coupling

We examine the validity of the recently proposed semi-Poisson level spacing distribution function P(S), which characterizes “critical quantum chaos”, in 2D disordered systems with spin-orbit coupling. At the Anderson transition we show that the semi-Poisson P(S) can describe closely the critical distribution obtained with averaged boundary conditions, over Dirichlet in one direction with periodic in the other and Dirichlet in both directions. We also obtain a sub-Poisson linear number variance , with asymptotic value . The obtained critical statistics, intermediate between Wigner and Poisson, is discussed for disordered systems and chaotic models. Received 1 September 1999     

也谈转动和振动的概率分布与能均分定理的证明

严格推导出分子转动角速度、振动位移概率分布,指明三种概率分布并不局限于近独立子系,它们适用于有相互作用的很多系统。     

耦合映像格子中时空混沌的状态反馈控制

利用状态反馈的方法，实现了耦合映像格子中时空混沌的稳定控制.反馈方式可以是没有延迟的，也可以是有延迟的；控制方式可以是连续的，也可以是脉冲的.数值模拟结果证明了状态反馈方法的有效性. 关键词： 耦合映像格子 时空混沌 状态反馈控制     

基于元胞自动机考虑传播延迟的复杂网络病毒传播研究

基于元胞自动机,研究传播延迟对复杂网络病毒传播动力学行为的影响,提出一种新的易染状态-感染状态-易染状态(SIS)传播模型.研究表明,传播延迟的存在显著降低了网络的传播临界值,增强了网络中病毒爆发的危险性.研究还发现,随着传播延迟的增大,病毒的感染程度以及传播速率都明显增大.此外,SIS传播模型不仅能够反映病毒的平均传播趋势,而且可以描述病毒随时间的动态演化过程以及病毒的爆发和消亡等概率事件,从而有效地克服了利用平均场方法构建的微分方程模型只能反映病毒平均传播趋势的局限性.同时,还给出有效控制网络中病毒传 关键词： 复杂网络 病毒传播 元胞自动机 传播延迟     

Energy level statistics in disordered metals with an anderson transition

We present numerical scaling results for the energy level statistics in orthogonal and symplectic tight-binding Hamiltonian random matrix ensembles defined on disordered two and three-dimensional electronic systems with and without spinorbit coupling (SOC), respectively. In the metallic phase for weak disorder the nearest level spacing distribution functionP(S), the number variance <(N)²>, and the two-point correlation functionK ₂(), are shown to be described by the Gaussian random matrix theories. In the insulating phase, for strong disorder, the correlations vanish for large scales and the ordinary Poisson statistics is asymptotically recovered, which is consistent with localization of the corrosponding eigenstates. At the Anderson metal-insulator transition we obtain new universal scale-invariant distribution functions describing the critical spectral density fluctuations.     

Non-Abelian gauge potentials driven localization transition in quasiperiodic optical lattices

Derived from quantum waves immersed in an Abelian gauge potential, the quasiperiodic Aubry-André-Harper (AAH) model is a simple yet powerful Hamiltonian to study the Anderson localization of ultracold atoms. Here, we investigate the localization properties of ultracold atoms in quasiperiodic optical lattices subject to a non-Abelian gauge potential, which are depicted by non-Abelian AAH models. We identify that the non-Abelian AAH models can bear the self-duality. We analyze the localization of such non-Abelian self-dual optical lattices, revealing a rich phase diagram driven by the non-Abelian gauge potential involved: a transition from a pure delocalization phase, then to coexistence phases, and finally to a pure localization phase. This is in stark contrast to the Abelian counterpart that does not support the coexistence phases. Our results establish the connection between localization and gauge symmetry, and thus comprise a new insight on the fundamental aspects of localization in quasiperiodic systems, from the perspective of non-Abelian gauge potential.     

Energy equipartition and unidirectional emission in a spaser nanolaser

A spaser is a nanoplasmonic counterpart of a laser, with photons replaced by surface plasmon polaritons and a resonant cavity replaced by a metallic nanostructure supporting localized plasmonic modes. By combining analytical results and first‐principle numerical simulations, we provide a comprehensive study of the ultrafast dynamics of a spaser. Due to its highly‐nonlinear nature, the spaser is characterized by a large number of interacting degrees of freedom, which sustain a rich manifold of different phases we discover, describe and analyze here. In the regime of strong interaction, the system manifests an irreversible ergodic evolution towards the configuration where energy is equally shared among all the available degrees of freedom. Under this condition, the spaser generates ultrafast vortex‐like lasing modes that are spinning on the femtosecond scale and whose direction of rotation is dictated by quantum noise. In this regime, the spaser acquires the character of a nanoparticle with an effective spin. This opens up a range of interesting possibilities for achieving unidirectional emission from a symmetric nanostructure, stimulating a broad range of applications for nanoplasmonic lasers as unidirectional couplers and random information sources.

     

Kosterlitz-Thouless-like transition in two-dimensional lattices with long-range correlated hopping terms

We study the Anderson localization in two-dimensional lattices with long-range correlated hopping terms. The hopping energies along one lattice direction will be generated by a superposition of uncorrelated and long-range correlated contributions. Our numerical results strongly suggest the presence of a Kosterlitz-Thouless-like transition above a critical correlation degree.     

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.     

一维长程关联无序系统的局域性

研究了在紧束缚近似下,由de Moura和Lyra提出的一维长程关联无序模型的局域性. 分布在［-W/2,W/2］区间的格点位能,其关联函数〈ε_iεj〉的傅里叶变换满足S(k)∝k^-α,其中关联强度α>0. 利用participation ratio不仅证实了在α>2和W<4 关键词： 安德森局域化 长程关联 扩展态     

Bifurcation,chaotic phenomena and control of chaos in a one—dimensional discrete Josephson lattice

We have investigated the fluxon dynamical behaviour in a one-dimensional parallel array of small Josephson junctions in the presence of an externally applied magnetic field. In the case of high damping,the system is in stable state. On the contrary, in the case of low damping, bifurcation and chaotic phenomena have been observed. Control of chaos is achieved by a delayed feedback mechanism, which drives the chaotic system into a selected unstable periodic orbit embadded within the associated strange attractor. It is attractive to control chaos to a periodic state, rather than operating always outside the device parameter space where chaos dominates.