Random walk in dynamically disordered chains: Poisson white noise disorder

Exact solutions are given for a variety of models of random walks in a chain with time-dependent disorder. Dynamic disorder is modeled by white Poisson noise. Models with site-independent (global) and site-dependent (local) disorder are considered. Results are described in terms of an affective random walk in a nondisordered medium. In the cases of global disorder the effective random walk contains multistep transitions, so that the continuous limit is not a diffusion process. In the cases of local disorder the effective process is equivalent to usual random walk in the absence of disorder but with slower diffusion. Difficulties associated with the continuous-limit representation of random walk in a disordered chain are discussed. In particular, we consider explicit cases in which taking the continuous limit and averaging over disorder sources do not commute.     

Quasi-ballistic evolution of a quantum particle in a random potential with arbitrary correlation time

The evolution of the mean kinetic energy and of the mean square displacement of a quantum particle in a time-dependent random potential is studied by perturbation theory in the near ballistic regime. Convenient general formulas are derived for an arbitrary correlation time, τ, of the disorder. These formulas are studied analytically near the limit of perfect dynamic disorder (τ=0) and for static disorder (τ=∞), where detailed comparison is made with earlier results. This work is the first to relate the limits of perfect dynamic disorder and of static disorder via a unified treatment for finite τ.     

Strong disorder fixed point in absorbing-state phase transitions

The effect of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class is studied by a strong disorder renormalization group approach and by density matrix renormalization group calculations. We show that for sufficiently strong disorder the critical behavior is controlled by a strong disorder fixed point and in one dimension the critical exponents are conjectured to be exact: beta=(3-sqrt[5])/2 and nu( perpendicular )=2. For disorder strengths outside the attractive region of this fixed point, disorder dependent critical exponents are detected. Existing numerical results in two dimensions can be interpreted within a similar scenario.     

共轭聚合物中链内无序效应对极化子输运的影响

基于扩展的Su-Schrieffer-Heeger紧束缚模型, 利用非绝热动力学方法研究了链内无序效应对共轭聚合物中极化子输运机制的影响. 研究发现, 极化子的输运由外加电场和链内无序效应共同作用的结果所决定. 在一般情况下, 链内无序效应不利于极化子的输运, 但随着电场强度的增大, 无序对极化子输运的影响减小. 关键词： 共轭聚合物 极化子输运 链内无序     

二维介观环中持续电流的梯度无序效应

基于紧束缚模型,考虑无序的梯度衰减,研究了无序-有序二维介观环体系中无序梯度及结构尺寸等因素对持续电流的影响.在表面无序区无梯度衰减时,持续电流随无序度的变化先减小后增大,观察到类弹道和局域性的转变.当存在梯度衰减时,无序区部分区域无序度相应减小,对有序区产生较强散射,典型电流比没有无序衰减时偏小.有趣的是,当无序度指数衰减时,上述类弹道和局域性的转变却消失了,揭示了介观实验中能否观察到该转变与无序的梯度分布密切相关.此外,计算表明表面无序渗透的深度和环的宽度对持续电流也有重要影响,呈现奇异的量子尺寸效应.这不同于以前的理论预言. 关键词： 介观环 梯度无序 持续电流     

New multiple histogram method for studying phase transitions

For temperature zero the effects of disorder for interacting bosons are considered. The disorder induced superfluid-insulator transition in thed-dimensional disordered Bogoliubov model is discussed. Results for a short-range and a long-range random potential are given. For short-range disorder we argue that ford<4 arbitrarily small disorder localizes the Bose condensate for vanishing interaction potential. Ford>4 a certain strength of the disorder potential is necessary in order to localize the condensate. For the three-dimensional Bogoliubov model our results are in agreement with a recent calculation. We compare our theoretical predictions with numerical experiments for a disordered boson Hubbard model.     

Engineering disorder in three-dimensional photonic crystals

We demonstrate the effect of introducing controlled disorder in self-assembled three-dimensional photonic crystals. Disorders are induced through controlling the self-assembling process using an electrolyte of specific concentrations. Structural characterization reveals increase in disorder with increase in concentrations of the electrolyte. Reflectivity and transmittance spectra are measured to probe the photonic stop gap at different levels of controlled disorder. With increase in disorder the stop gap is vanished and that results in a fully random photonic nanostructure where the diffuse scattered intensity reaches up to 100%. The estimated scattering mean free path shows significant reduction for photonic crystals with 100% controlled disorder as compared to those with 0% controlled disorder. Our random photonic nanostructure is unique in which all scatters have the same size and shape. Therefore, we observe the resonant characteristics in the multiple scattering of light.     

Precursor phenomena in frustrated systems

To understand the origin of the dynamical transition, between high-temperature exponential relaxation and low-temperature nonexponential relaxation, that occurs well above the static transition in glassy systems, a frustrated spin model, with and without disorder, is considered. The model has two phase transitions, the lower being a standard spin glass transition (in the presence of disorder) or fully frustrated Ising (in the absence of disorder), and the higher being a Potts transition. Monte Carlo results clarify that in the model with (or without) disorder the precursor phenomena are related to the Griffiths (or Potts) transition. The Griffiths transition is a vanishing transition which occurs above the Potts transition and is present only when disorder is present, while the Potts transition which signals the effect due to frustration is always present. These results suggest that precursor phenomena in frustrated systems are due either to disorder and/or to frustration, giving a consistent interpretation also for the limiting cases of Ising spin glass and of Ising fully frustrated model, where also the Potts transition is vanishing. This interpretation could play a relevant role in glassy systems beyond the spin systems case.     

Critical Phenomena in Systems with Pseudo-Long-Range is Disorder

Critical phenomena in systems with long(bu t finite)-range-correlated disorder of "random temperature" are studied. The disorder with correlation function g (k)~v + w/(p + k^d-a) (d is the spatial dimension) is considered. The critical behavior in an m-vector spin system with such a disorder is investigated by using renormalization-group expansion in ε = 4 - d and δ = 4 - a. The recursion relations of coupling constants for (T > T_c) are obtained. It is shown that critical phenomena in systems with such a pseudo-long-range disorder will exhibit crossover from tricritical to critical behavior for a < d. In the crossover regime the scaling relations are expected to break down.     

Partially Annealed Disorder and Collapse of Like-Charged Macroions

Charged systems with partially annealed charge disorder are investigated using field-theoretic and replica methods. Charge disorder is assumed to be confined to macroion surfaces surrounded by a cloud of mobile neutralizing counterions in an aqueous solvent. A general formalism is developed by assuming that the disorder is partially annealed (with purely annealed and purely quenched disorder included as special cases), i.e., we assume in general that the disorder undergoes a slow dynamics relative to fast-relaxing counterions making it possible thus to study the stationary-state properties of the system using methods similar to those available in equilibrium statistical mechanics. By focusing on the specific case of two planar surfaces of equal mean surface charge and disorder variance, it is shown that partial annealing of the quenched disorder leads to renormalization of the mean surface charge density and thus a reduction of the inter-plate repulsion on the mean-field or weak-coupling level. In the strong-coupling limit, charge disorder induces a long-range attraction resulting in a continuous disorder-driven collapse transition for the two surfaces as the disorder variance exceeds a threshold value. Disorder annealing further enhances the attraction and, in the limit of low screening, leads to a global attractive instability in the system.     

Strong disorder renormalization group primer and the superfluid–insulator transition

This brief review introduces the method and application of real-space renormalization group to strongly disordered quantum systems. The focus is on recent applications of the strong disorder renormalization group to the physics of disordered-boson systems and the superfluid–insulator transition in one dimension. The fact that there is also a well-understood weak disorder theory for this problem allows us to illustrate what aspects of the physics change at strong disorder. In particular, the strong disorder RG analysis suggests that the transitions at weak disorder and strong disorder belong to distinct universality classes, but this question remains under debate and is not fully resolved to date. Further applications of the strong disorder renormalization group to higher-dimensional Bose systems and to bosons coupled to dissipation are also briefly reviewed.     

Non-locally correlated disorder and delocalization in one dimension (I): Density of states

We study delocalization transition in a one-dimensional electron system with quenched disorder by using supersymmetric (SUSY) methods. Especially we focus on effects of non-local correlation of disorder, for most of studies given so far considered δ-function type white noise disorder. We obtain wave function of the “lowest-energy” state which dominates partition function in the limit of large system size. Density of states is calculated in the scaling region. The result shows that delocalization transition is stable against non-local short-ranged correlation of disorder. Especially states near the band center are enhanced by the correlation of disorder which partially suppresses random fluctuation of disorder. Physical picture of the localization and the delocalization transition is discussed.     

Models of plastic depinning of driven disordered systems

Two classes of models of driven disordered systems that exhibit historydependent dynamics are discussed. The first class incorporates local inertia in the dynamics via nonmonotonic stress transfer between adjacent degrees of freedom. The second class allows for proliferation of topological defects due to the interplay of strong disorder and drive. In mean field theory both models exhibit a tricritical point as a function of disorder strength. At weak disorder depinning is continuous and the sliding state is unique. At strong disorder depinning is discontinuous and hysteretic.     

Transport properties of mesoscopic graphene rings

Based on a recursive Green's function method, we investigate the conductance of mesoscopic graphene rings in the presence of disorder, in the limit of phase coherent transport. Two models of disorder are considered: edge disorder and surface disorder. Our simulations show that the conductance decreases exponentially with the edge disorder and the surface disorder. In the presence of flux, a clear Aharonov-Bohm conductance oscillation with the period Φ₀ (Φ₀=h/e) is observed. The edge disorder and the surface disorder have no effect on the period of AB oscillation. The amplitudes of AB oscillations vary with gate voltage and flux, which is consistent with the previous results. Additionally, ballistic rectification and negative differential resistance are observed in I-V curves, with on/off characteristic.     

成分无序颗粒体系中切向力的分布

采用离散元模拟研究成分无序颗粒体系中切向力的几率分布.将切向力分为主切向力和次切向力分别进行统计,结果表明主切向力与次切向力服从不同的分布.随着缺陷率的增加,主切向力由近似的正态分布变为双峰状的分布,最后变为单峰状的分布;而次切向力总是指数型分布.通过理论计算和模拟讨论了切向力分布,说明缺陷率较大的成分无序体系与结构无序体系有类似的力分布规律.     

Localisation of elastic waves in two-dimensional randomly disordered solid phononic crystals

Combined with the supercell technique, the plane wave expansion method is used to calculate the band structures of the two-dimensional solid–solid phononic crystals with the random disorders in either radius or location of the scatterers. Phononic systems with plumbum scatterers embedded in an epoxy matrix are calculated in detail. The influences of the disorder degree on the band structures for both anti-plane and in-plane wave modes are investigated. It is found that, with increase of the disorder degree, the band gaps become narrower with more flat bands appearing in the gaps. Both displacement distribution and response spectra show that at the flat bands, elastic waves are localised due to the presence of the disorder. Wave localisation is more pronounced at the flat bands near the lower/upper edge for the radius/location disorder. Wave propagation and localisation in a randomly disordered system with a point defect is also studied. The influence of the disorder on the point-defect state is discussed. The results show that the disorder can tune the frequencies of the defect states. It is particularly noticed that the double degenerate mode appearing within the gap of the mixed in-plane waves is split up into two separated ones when the random disorder is introduced into the system. Generally, the influence of the disorder is more pronounced for the mixed in-plane modes than the anti-plane modes. The analysis of this paper is relevant to the assessment of the influences of manufacture errors on wave behaviours in phononic crystals as well as the possible control of wave propagation by intentionally introducing disorders into periodic systems.     

Multi-Synchronization Caused by Uniform Disorder for Globally Coupled Maps

We investigate the motion of the globally coupled maps （logistic map） driven by uniform disorder. It is shown that this disorder can produce multi-synchronization for the globally coupled chaotic maps studied by us. The disorder determines the synchronized dynamics, leading to the emergence of a wide range of new collective behaviour in which the individual units in isolation are incapable of producing in the absence of the disorder. Our results imply that the disorder can tame the collective motion of the coupled chaotic maps.     

Driven diffusive systems with disorder

We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn, random disorder in the properties of particles; disorder in the spatial distribution of transition rates, both with a single easy direction and with random reversals of the easy direction; dynamical disorder, where particles move in a disordered landscape which itself evolves in time. In every case, the system exhibits phase separation; in some cases, it is of an unusual sort. The time-dependent properties of density fluctuations are in accord with the kinematic wave criterion that the dynamical universality class is unaffected by disorder if the kinematic wave velocity is nonzero.     

A high-efficiency spin polarizer based on edge and surface disordered silicene nanoribbons

Using the tight-binding formalism, we explore the effect of weak disorder upon the conductance of zigzag edge silicene nanoribbons (SiNRs), in the limit of phase-coherent transport. We find that the fashion of the conductance varies with disorder, and depends strongly on the type of disorder. Conductance dips are observed at the Van Hove singularities, owing to quasilocalized states existing in surface disordered SiNRs. A conductance gap is observed around the Fermi energy for both edge and surface disordered SiNRs, because edge states are localized. The average conductance of the disordered SiNRs decreases exponentially with the increase of disorder, and finally tends to disappear. The near-perfect spin polarization can be realized in SiNRs with a weak edge or surface disorder, and also can be attained by both the local electric field and the exchange field.