Non-locally correlated disorder and delocalization in one dimension (II). Localization length

We study the delocalization transition in a one-dimensional Dirac fermion system with randomly varying mass by using supersymmetric (SUSY) methods. In a previous paper, we calculated density of states and found that (quasi-) extended states near the band center are enhanced by non-local correlation of the random Dirac mass. Numerical studies support this conclusion. In this paper, we calculate the localization length as a function of the correlation length of the disorder. The result shows that the localization length is an increasing function of the correlation of the random mass.     

Domain wall delocalization,dynamics and fluctuations in an exclusion process with two internal states

We investigate the delocalization transition appearing in an exclusion process with two internal states, respectively on two parallel lanes. At the transition, delocalized domain walls form in the density profiles of both internal states, in agreement with a mean-field approach. Remarkably, the topology of the system’s phase diagram allows for the delocalization of a (localized) domain wall when approaching the transition. We quantify the domain wall’s delocalization close to the transition by analytic results obtained within the framework of the domain wall picture. Power law dependences of the domain wall width on the distance to the delocalization transition as well as on the system size are uncovered, they agree with numerical results.     

Delocalization transition of two-dimensional disordered systems in a strong magnetic field

The delocalization transition in two-dimensional systems and a strong magnetic field is investigated with respect to its dependence on the Landau band indexj and on the type of disorder. The generation of random potentials according to a given correlation functionf and for a chosen correlation lengthd is described. The spectral properties of random eigenvalue sequences are examined as measures for the extension of wavefunctions and indicate a nonuniversal delocalization behaviour in higher Landau bands for short ranged correlated potentials. The critical exponents of the localization length of wavefunctions are determined for rapidly varying potentials in the second lowest Landau band (j=1) and depend on the correlation lengthd of the disorder. This different critical behaviour compared to that in the lowest band is confirmed by calculations for the density-density correlations of wavefunctions at the centers of the Landau levels. Calculations in different geometries also show that the critical systems of delocalized states are conformal invariant in the case of the nonuniversal delocalization transition (dl ₀), whereas such local rescaling properties cannot be expected for slowly varying potentials.     

Disorder induced transition into a one-dimensional wigner glass

The destruction of quasi-long-range crystalline order as a consequence of strong disorder effects is shown to accompany the strict localization of all classical plasma modes of one-dimensional Wigner crystals at T=0. We construct a phase diagram that relates the structural phase properties of Wigner crystals to a plasmon delocalization transition recently reported. Deep inside the strictly localized phase of the strong disorder regime, we observe glasslike behavior. However, well into the critical phase with a plasmon mobility edge, the system retains its crystalline composition. We predict that a transition between the two phases occurs at a critical value of the relative disorder strength. This transition has an experimental signature in the ac conductivity as a local maximum of the largest spectral amplitude as a function of the relative disorder strength.     

Inverse Anderson transition caused by flatbands

We propose a new disorder-induced insulator-metal transition of one-electron states, which may be called the "inverse Anderson transition." We first make a highly degenerated localized states by constructing a three-dimensional periodic system possessing only flat dispersion relations. When we introduce a disorder into it, a finite-size scaling of the level statistics shows two clear (localization-delocalization and delocalization-localization) transitions for a wide range of the energy, with increasing the degree of disorder. These transitions are confirmed also by finding the system-size-independent characteristic of the wave function.     

Delocalization in weakly coupled disordered wires: application to conjugated polymers

It is well known that even for minimal disorder one-dimensional wires are insulators: all 1D electron states are localized. Here, the influence of interwire coupling on delocalization of 1D states is examined. Based on perturbation theoretic arguments for the formation of 3D states in coupled wires and subsequent scaling analysis, practical expressions for the microscopic conditions of electronic delocalization and coherent conductivity of coupled 1D wires are obtained. The model quantitatively explains the temperature dependent dc conductivity in conducting polymers at both sides of the metal-insulator transition and links the experimental data to microscopic material parameters.     

Suppression of the virtual anderson transition in the impurity band of doped quantum well structures

We have previously observed activation-type conductivity with low activation energies of heavily doped p-GaAs/AlGaAs quantum well structures at low temperatures. It has been attributed to the delocalization of the electron states near the maximum of a narrow impurity band in the sense of the Anderson transition. The possibility of this delocalization at a relatively low impurity concentration is associated with the narrowness of the impurity band in the presence of weak disorder. In this case, charge carriers were activated from the tail of the band and their presence was due to the background (weak) compensation. In this work, we study the dependence of the above virtual Anderson transition on the external compensation and impurity concentration. It has been found that an increase in the compensation does not initially affect the Anderson transition; however, at a higher compensation, it leads to the suppression of the transition owing to the growing disorder. An increase in the impurity concentration also initially leads to the suppression of the Anderson transition due to the disorder associated with the partial overlap of the Hubbard bands. However, the conductivity becomes metallic at a fairly high concentration due to the Mott transition.     

A colloidal model system with tunable disorder: Solid-fluid transition and discontinuities in the limit of zero disorder

We study a colloidal model system where disorder can be continuously tuned from no disorder --corresponding to a system that can crystallize-- to large disorder where geometrical frustration occurs. The model system consists of colloidal particles with screened electrostatic repulsion. They can only move on single lines which are parallel and equidistant to each other. We introduce disorder by modulating the particle line density. The system exhibits a solid-to-fluid transition which we study by the structure factor and the temporal evolution of the mean-square distance of nearest neighbors on neighboring lines. A determining feature is the occurrence of discontinuities when disorder is tuned to zero. We observe that the peak height of the pair correlation function in the solid phase does not extrapolate to the value of the perfect crystal. Similarly, the mean interaction energy and the screening length at which the solid-fluid transition occurs seem to be discontinuous when the limit of zero disorder is approached.     

Scaling and localization lengths of a topologically disordered system

We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical evidence that this model displays the same universal behavior as the standard Anderson model. We use finite-size scaling to find the localization length as a function of energy and density, including localized states away from the delocalization transition. Results at many energies all fit onto the same universal scaling curve.     

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.     

无序度对一维长程关联无序系统中局域化-退局域化转变的影响

对长程幂律关联能量序列进行了修正,使其能体现出无序度在一维长程关联无序系统中的影响,并利用重正化群方法,计算了能反映该系统局域化-退局域化转变的Lyapunov指数.结果表明,在由于关联指数p的影响而在系统中出现的局域化向退局域化的转变中,无序度起着相反的作用.当关联指数p一定而无序度W增大时,系统中心能区范围内由于长程关联而引起的扩展态逐渐向局域态转变.当无序度W增大到某一临界值W_c时,系统中所有本征态均转变为局 关键词： 长程关联 Lyapunov指数 无序度 局域化-退局域化转变     

耗散量子隧道系统的变分法研究

本文用变分法研究了耗散量子系统中的声于基态及其对局域一退局域相变条件的影响.发现: 1. 声子基态不仅存在通常的位移效应, 而且还有形变效应. 本文提出的位移一压缩态可同时描述这两种效应; 2. 声子基态的选择对相变条件有很大影响.随着声子基态能量下降,相变曲线将向强祸合方向移动. 关键词：     

Ultracold atoms in a disordered crystal of light: towards a bose glass

We use a bichromatic optical lattice to experimentally realize a disordered system of ultracold strongly interacting 87Rb bosons. In the absence of disorder, the atoms are pinned by repulsive interactions in the sites of an ideal optical crystal, forming one-dimensional Mott-insulator states. We measure the excitation spectrum of the system as a function of disorder strength and characterize its phase-coherence properties with a time-of-flight technique. Increasing disorder, we observe a broadening of the Mott-insulator resonances and the transition to a state with vanishing long-range phase coherence and a flat density of excitations, which suggest the formation of a Bose-glass phase.     

Influence of weak nonlinearity on the 1D Anderson model with long-range correlated disorder

We investigate theoretically the nature of the states and the localization properties in a one-dimensional Anderson model with long-range correlated disorder and weak nonlinearity. Using the stationary discrete nonlinear Schrödinger equation, we calculate the disorder-averaged logarithm of the transmittance and the localization length in the fixed input case in a numerically exact manner. Unlike in many previous studies, we strictly fix the intensity of the incident wave and calculate the localization length as a function of other parameters. We also calculate the wave functions in a given disorder configuration. In the linear case, flat phased localized states appear near the bottom of the band and staggered localized states appear near the top of the band, while a continuum of extended states appears near the band center. We find that the focusing Kerr-type nonlinearity enhances the Anderson localization of flat phased states and suppresses that of staggered states. We observe that there exists a perfect symmetry relationship for the localization length between focusing and defocusing nonlinearities. Above a critical value of the strength of nonlinearity, delocalization due to the long-range correlations of disorder is destroyed and all states become localized.     

Delocalization in one-dimensional tight-binding models with fractal disorder

In the present work, we investigated the correlation-induced localization-delocalization transition in the one-dimensional tight-binding model with fractal disorder. We obtained a phase transition diagram from localized to extended states based on the normalized localization length by controlling the correlation and the disorder strength of the potential. In addition, the transition of the diffusive property of wavepacket dynamics is shown around the critical point.     

Critical Properties and Finite-Size Estimates for the Depinning Transition of Directed Random Polymers

We consider models of directed random polymers interacting with a defect line, which are known to undergo a pinning/depinning (or localization/delocalization) phase transition. We are interested in critical properties and we prove, in particular, finite-size upper bounds on the order parameter (the contact fraction) in a window around the critical point, shrinking with the system size. Moreover, we derive a new inequality relating the free energy F and an annealed exponent μ which describes extreme fluctuations of the polymer in the localized region. For the particular case of a (1+1)-dimensional interface wetting model, we show that this implies an inequality between the critical exponents which govern the divergence of the disorder-averaged correlation length and of the typical one. Our results are based on the recently proven smoothness property of the depinning transition in presence of quenched disorder and on concentration of measure ideas.     

Competitive localization of vortex lines and interacting bosons

We present a theory for the localization of three-dimensional vortex lines or two-dimensional bosons with a short-ranged repulsive interaction which are competing for a single columnar defect or potential well. For two vortices we use a necklace model approach to find a new kind of delocalization transition between two different states with a single bound particle. This exchange-delocalization transition is characterized by the onset of vortex exchange on the defect for sufficiently weak vortex-vortex repulsion or sufficiently weak binding energy corresponding to high temperature. We calculate the transition point and order of the exchange-delocalization transition. A generalization of this transition to an arbitrary vortex number is proposed.     

Anomalously localised electronic states in three-dimensional disordered systems

We study the Anderson model of localisation at the metal-insulator transition in the band centre of three-dimensional disordered samples. For the critical disorder we determine a large number of wave functions of the model and study the distribution of the wave function amplitudes. Deviations from scaling of multifractal correlation functions allow us to discriminate anomalously localised states from the usual critical states. The thus identified anomalously localised states lead to deviations of the critical properties and should be eliminated from the ensemble average for a characterisation of criticality.     

On the Mean Pair Correlation Function of ±J Ising Spin Glasses

We provide a formula and an upper bound for the average over the disorder of the pair correlation function of ±J Ising spin glasses by using the symmetries of the system, We show the decay of the mean spin pair correlation function when the proportion of antiferromagnetic bonds is larger than the critical parameter associated with the pair dissociation phase transition.     

二级相变理论和Lifshitz条件不成立的论证

系统的自由能是序参量的泛函。在二级相变点附近,自由能密度是序参量及其关联项的幂次展式。按本文给定的方法,无论关联项是定域还是非定域的,由对自由能的一级变分等于零,都能求得表示平衡态位形的序参量。在求解过程,必须将序参量进行傅氏变换,这与序参量以系统对称群的基函数展开是一致的,由此对二级相变中对称改变进行了分析。利用变分法中极值的充要条件(或充分条件),我们讨论了二级相变过程中状态的稳定性条件。由于我们对自由能求极值时没有略去关联项,因此不存在Lifshitz的对称改变限制条件。这里强调指出:实质上,Lif