一维长程关联无序系统中的电子态

利用傅里叶滤波法在一维Anderson无序系统中产生了具有幂律谱密度公式s(q)∝q^-p形式的长程关联随机能量序列，并利用传输矩阵方法计算了系统中引入了长程关联后的局域长度，同时应用负本征值理论对系统中的电子态密度进行了分析，并分别把计算结果与系统中不具有长程关联时的局域长度与电子态密度进行了比较.结果表明，长程幂律关联的引入对电子态的性质产生了很大的影响，当关联指数p≥2.0时，在系统能带中心范围内发生了部分局域态向退局域态的转变，而同时电子态密度也发生了很大的变化，出现了六个范霍夫奇点，系统的能带范围也相应地得到展宽. 关键词： 无序系统 长程关联 局域长度 电子态密度     

Atoms in double-delta-kicked periodic potentials: chaos with long-range correlations

We report an experimental and theoretical study of the dynamics of cold atoms subjected to pairs of closely spaced pulses in an optical lattice. For all previously studied delta-kicked systems, chaotic classical dynamics shows diffusion with short-time (2- or 3-kick) correlations; here, chaotic diffusion combines with new types of long-ranged global correlations, between all kick pairs, which control transport through trapping regions in phase space. Correlations are studied in the classical regime, but the diffusive behavior observed in experiment depends on the quantum dynamical localization.     

Electronic properties of one-dimensional systems with long-range correlated binary potentials

We study numerically the electronic properties of one-dimensional systems with long-range correlated binary potentials.The potentials are mapped from binary sequences with a power-law power spectrum over the entire frequency range,which is characterized by correlation exponent β.We find the localization length ξ increases with β.At system sizes N →∞,there are no extended states.However,there exists a transition at a threshold β c.When β > β c,we obtain ξ > 0.On the other hand,at finite system sizes,ξ≥ N may happen at certain β,which makes the system "metallic",and the upper-bound system size N (β) is given.     

The wavefunction envelope in one-dimensional random potentials

We propose a formalism for the study of mean resistance of a one dimensional chain of random potentials. We obtain the resistance as a function of the length of the chain. In the asymptotic limit, this is related to the wavefunction envelope. The formalism demands loss of translational symmetry, but is general enough to include potentials with spatial correlations which are not long ranged and also those whose randomness is inhomogeneous.     

Absence of phase transitions in certain one-dimensional long-range random systems

An Ising chain is considered with a potential of the formJ(i, j)/|i–j|, where theJ(i, j) are independent random variables with mean zero. The chain contains both randomness and frustration, and serves to model a spin glass. A simple argument is provided to show that the system does not exhibit a phase transition at a positive temperature if>1. This is to be contrasted with a ferromagnetic interaction which requires>2. The basic idea is to prove that the surfacefree energy between two half-lines is finite, although the surface energy may be unbounded. Ford-dimensional systems, it is shown that the free energy does not depend on the specific boundary conditions if>(1/2)d.     

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     

Absence of long-range order with long-range potentials

A particular form of Mermin's inequality is analyzed for repulsive inverse power potentials [V(r)=e ² r ^–m/m] in ad-dimensional space. For long-range potentials (m d) the system is put into a stabilizing background. Long-range order is shown to be excluded ford (m + 2)/2 whenm d, while for short-range potentials (m > d) we recover Mermin's result (d 2). For Coulomb systems (m=d – 2) and the experimentally studied electron surface layer (d = 2,m=1), long-range order cannot be excluded by the present argument.     

Anderson localization of expanding Bose-Einstein condensates in random potentials

We show that the expansion of an initially confined interacting 1D Bose-Einstein condensate can exhibit Anderson localization in a weak random potential with correlation length sigma(R). For speckle potentials the Fourier transform of the correlation function vanishes for momenta k>2/sigma(R) so that the Lyapunov exponent vanishes in the Born approximation for k>1/sigma(R). Then, for the initial healing length of the condensate xi(in)>sigma(R) the localization is exponential, and for xi(in)相似文献   

Upper bound on the decay of correlations in the plane rotator model with long-range random interaction

We give an upper bound on the decay of correlation function for the plane rotator model with Hamiltonian $$ - \frac{1}{2}\mathop \sum \limits_{xy} \frac{{J_{xy} \cos (\theta _x - \theta _y )}}{{\| {x - y} \|^{({3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2} + \varepsilon )^d } }}$$ in dimensiond=1 andd=2 when (J _xy are independent random variables with mean zero.     

Elastic wave localization in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity

The band structures of in-plane elastic waves propagating in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity are analyzed in this paper. The localization of wave propagation is discussed by introducing the concept of the localization factor, which is calculated by the plane-wave-based transfer-matrix method. By treating the random disorder and aperiodicity as the deviation from the periodicity in a special way, three kinds of aperiodic phononic crystals that have normally distributed random disorder, Thue-Morse and Rudin-Shapiro sequence in one direction and translational symmetry in the other direction are considered and the band structures are characterized using localization factors. Besides, as a special case, we analyze the band gap properties of a periodic planar layered composite containing a periodic array of square inclusions. The transmission coefficients based on eigen-mode matching theory are also calculated and the results show the same behaviors as the localization factor does. In the case of random disorders, the localization degree of the normally distributed random disorder is larger than that of the uniformly distributed random disorder although the eigenstates are both localized no matter what types of random disorders, whereas, for the case of Thue-Morse and Rudin-Shapiro structures, the band structures of Thue-Morse sequence exhibit similarities with the quasi-periodic (Fibonacci) sequence not present in the results of the Rudin-Shapiro sequence.     

Influence of a quasiclassical random potential on electron correlations in a one-dimensional system

The influence of a quasiclassical random potential on the behaviour of the correlation functions in a one-dimensional electron system is investigated in the generalized Luttinger model. We prove rigorously that in the case of a not-half-filled band the quasiclassical electron scattering suppresses dielectric and antiferromagnetic correlations, but has no effect on superconductive correlations. The case of a half-filled band, in which the existence of a gap Δ_ρ in the density excitation spectrum results in the exponential decrease of superconductive correlations in the pure system, is also considered. It is shown that in the “dirty” limit, Δ_ρτ ⪡ 1 (τ is the electron relaxation time), the quasiclassical random potential recovers a long-range, power law behaviour of superconductive correlations, typical for a gapless regime.     

Tailoring Anderson localization by disorder correlations in 1D speckle potentials

We study Anderson localization of single particles in continuous, correlated, one-dimensional disordered potentials. We show that tailored correlations can completely change the energy-dependence of the localization length. By considering two suitable models of disorder, we explicitly show that disorder correlations can lead to a nonmonotonic behavior of the localization length versus energy. Numerical calculations performed within the transfer-matrix approach and analytical calculations performed within the phase formalism up to order three show excellent agreement and demonstrate the effect. We finally show how the nonmonotonic behavior of the localization length with energy can be observed using expanding ultracold-atom gases.     

Solitons in random media with long-range correlation

Abstract

A statistical approach of the propagation of solitons in media with a spatially random potential is developed. Applying the inverse scattering transform several regimes are demonstrated which are determined by the mass and the velocity of the incoming soliton as well as by the correlation length of the random potential. Namely, the mass of the soliton is conserved if its initial amplitude is large enough. If the initial mass is small, then the mass decays with the length of the system. The decay rate is exponential in the case of a white noise perturbation, but it obeys a power law if the carrier wavenumber of the soliton lies in the tail of the spectrum of the potential. Furthermore, the scattered radiation propagates in a backward direction in the case of a white noise perturbation, while it propagates in a forward direction (with the same carrier wavenumber as the soliton) in the case of a coloured noise with long-range correlation.     

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     

Analyticity for one-dimensional systems with long-range superstable interactions

We consider unbounded spin systems and classical continuous particle systems in one dimension. We assume that the interaction is described by a superstable two-body potential with a decay at large distances at least asr ^?2(lnr)^?(2+ε), ε > 0. We prove the analyticity of the free energy and of the correlations as functions of the interaction parameters. This is done by using a “renormalization group technique” to transform the original model into another, physically equivalent, model which is in the high-temperature (small-coupling) region.     

Decay of correlations in classical fluids with long-range forces

We show with simple arguments that, as a consequence of the Poisson equation, the correlations of a charged system at equilibrium decay faster than any inverse power, if they are integrable and monotonous at infinity. For all other longrange systems (with potential(x)b¦x¦^–s , ¦x¦ , 0v,s} 2), the decay is bounded below by an inverse power.Partially supported by the Swiss National Foundation for Scientific Research.     

Critical point estimation and long-range behavior in the one-dimensional XY model using thermal quantum and total correlations

We investigate the thermal quantum and total correlations in the anisotropic XY spin chain in transverse field. While we adopt concurrence and geometric quantum discord to measure quantum correlations, we use measurement-induced non-locality and an alternative quantity defined in terms of Wigner–Yanase information to quantify total correlations. We show that the ability of these measures to estimate the critical point at finite temperature strongly depend on the anisotropy parameter of the Hamiltonian. We also identify a correlation measure which detects the factorized ground state in this model. Furthermore, we study the effect of temperature on long-range correlations.