Parametric number variance of disordered systems in the multifractal regime

Abstract

We study the effect of an external field X on the energy levels of a disordered system by evaluating the parametric number variance (PNV). The weak disorder regime is studied within the Gaussian random matrix theory, while the multifractal regime is studied by considering the q-deformed random matrices. The PNV at both small and large values of X has distinct features in the weak disorder and multifractal regimes that should be observable in numerical studies.     

Mean displacement moments and survival times in the trapping model with strong fields

The mean displacement moments for the strong field trapping model are calculated. Their asymptotic behaviour is Xⁿ(t) (V_efft)ⁿ, where V_eff is an effective drift velocity. This is in sharp contrast with the weak field case, for which Xⁿ(t) t^n/3. The mean survival (first passage) time and the upstream and downstream trapping probabilities are also obtained.     

周期受击陀螺系统随时间演化波函数的多重分形

研究了周期受击陀螺系统波函数的多重分形. 发现: 1)在打击次数较小时, 周期受击陀螺系统波包的扩散速度、扩散方向与打击强度相关, 打击强度越大扩散越混乱、扩散速度也越大; 2)波函数在相空间的精细结构的分布范围随着打击强度的增大而扩大, 最后充满整个相空间; 3)局部分维a的分布范围对应波函数在相空间的分布, 规则态时a 的分布范围最宽, 过渡态的a的分布范围较窄, 而混沌态的a的分布范围则最狭窄且稳定.     

The crystallographic symmetries of single BaPb1−xBixO3 crystals grown from BaCO3-PbO2-Bi2O3 solutions

Single crystals of Perovskite-type oxide BaPb_1−xBi_xO₃ are grown from BaCO₃-PbO₂-Bi₂O₃ solutions which are weighed in two kinds of mixing ratios: X/2 mol % BaCO₃ − (100−X) mol % PbO₂ − X/2 mol % Bi₂O₃ and (10+X/2) mol % BaCO₃ − (90−X) mol % PbO₂ − X/2 mol % Bi₂O₃ These room temperature crystal structures are examined by using an X-ray powder diffraction method. The crystals grown from X/2−(100−X)−X/2 mol % solutions are orthorhombic at room temperature, while the structures are tetragonal with crystals grown from relatively Ba rich and Pb poor ( (10+X/2)−(90−X)−X/2 mol % ) solutions. This result indicates that the difference in the mixing ratio of the initial materials brings about a drastic structural change. The orthorhombic and the tetragonal crystals of x0.25 exhibit superconducting transition at 10K and 12K, respectively. The transition temperature in the latter is 2K higher than the former. In the light of this result, some difference between orthorhombic and tetragonal crystals is considered to influence superconductivity in this system.     

Binding energy of an exciton bound to ionized donors in quantum dots

Binding energies for an exciton (X) trapped in the two-dimensional quantum dot by a positive ion located on the z axis at a distance d from the dot plane are calculated by using the method of few-body physics. This configuration is called a barrier (D⁺,X) center. The dependence of the binding energy of the ground state of the barrier (D⁺,X) center on the dot radius for a few values of the distance d between the fixed positive ion on the z axis and the dot plane is obtained. We find that when d<0.2nm the barrier (D⁺,X) center does not form a bound state.     

Thermal transport properties in a He---He mixture near and below the superfluid transition

Measurements of the thermal conductivity and of X/T are reported for a ³He---⁴He mixture with a ³He mole fraction X = 0.622. At T_λ, X/T passes through a sharp peak. A comparison with the theory of Khalatnikov is presented. The relaxation times τ(T) to reach steady state conditions show qualitatively the same behaviors as X/T.     

倾斜度及温度震荡频率对三维多孔介质方腔自然对流换热的影响

对三维多孔介质倾斜方腔内非稳态自然对流换热进行数值研究.腔体右壁面(X=1)保持恒温T₀,左壁面(X=0)基于温度T₀按正弦规律变化,其他所有壁面保持绝热.采用Brinkman扩展达西模型及SIMPLE算法模拟方腔内的流动.方腔沿y轴转动倾角α1的变化范围为0°~90°,沿x轴转动倾角α2的变化范围为0°~45°,无量纲温度震荡频率f的变化范围为5π~90π.详细研究倾角和温度震荡频率对三维方腔自然对流换热的影响.计算结果表明:当倾角α1=46°,α2=45°及温度震荡频率f=45π时,方腔内的换热最强.     

Direct observation of double diffraction patterns

The double diffraction light intensity of two identical gratings placed parallel in the Fresnel region is sensitive to the lateral displacement ΔX, and is also affected by the air gap R between the gratings. In this note, the dependence of the double diffraction light intensity on ΔX and R for each order beam has been obtained directly by observing the intensity pattern on a screen.     

A density-functional theory investigation on disorption of O2 on Sn(111) and its comparison with initial oxidation on the X(111) (X=Si,Ge, Sn,Pb) surfaces

The first-principles calculations are performed to investigate the adsorption of O₂ molecules on an Sn(111) 2×2 surface. The chemisorbed adsorption precursor states for O₂ are identified to be along the parallel and vertical channels, and the surface reconstructions of Sn(111) induced by oxygen adsorption are studied. Based on this, the adsorption behaviours of O₂ on X(111) (X=Si, Ge, Sn, Pb) surfaces are analysed, and the most stable adsorption channels of O₂ on X(111) (X=Si, Ge, Sn, Pb) are identified. The surface reconstructions and electron distributions along the most stable adsorption channels are discussed and compared. The results show that the O₂ adsorption ability declines gradually and the amount of charge transferred decreases with the enhancement of metallicity.     

A Fourier transform for sheaves on real tori: Part II. Relative theory

If X is a symplectic family of Lagrangian tori, the dual family has a natural complex structure. We define, for any dimension of X, a Fourier transform which yields a bijective correspondence between local systems supported on Lagrangian submanifolds of X and holomorphic vector bundles supported on complex subvarieties of (suitable conditions being verified on both sides).     

Using X(3823)→J/ψπ+π− to identify coupled-channel effects

Very recently, the Belle and BESIII experiments observed a new charmonium-like state X(3823), which is a good candidate for the D-wave charmonium ψ(1³D₂). Because the X(3823) is just near the D ¯D^∗ threshold, the decay X(3823)→ J/ψπ⁺π⁻ can be a golden channel to test the significance of coupled-channel effects. In this work, this decay is considered including both the hidden-charm dipion and the usual quantum chromodynamics multipole expansion (QCDME) contributions. The partial decay width, the dipion invariant mass spectrum distribution dΓ[X(3823) → J/ψπ⁺π⁻]/dm_π⁺_π⁻, and the corresponding dΓ[X(3823) → J/ψπ⁺π⁻]/d cos θ distribution are computed. Many parameters are determined from existing experimental data, so the results depend mainly only on one unknown phase between the QCDME and hidden-charm dipion amplitudes.     

磁共振碳谱研究:应用分子子图指数估计与预测卤代烃化学位移

系统研究了核磁共振碳谱(¹³C NMR)与化学位移规律及其定量构谱关系(QSSR).本文提出了一组含多元素组成的分子子图指数矢量(VMSG),并发现它与卤代烃化学位移(CSRX)有很好线性相关性.采用多元线性回归(MVLR)进行准确估计与预测,结果良好.     

薄膜生长的多重分形谱的计算

规则分形具有理想的标度不变性,而随机分形(如薄膜生长)概率分布曲线及标度不变性的范围与计算方法有关:以偏离平均高度的方差值求概率,标度不变性不好,多重分形谱也不光滑;而以薄膜平均底面为基准面求概率得到的标度不变性可延伸到3个数量级,多重分形谱光滑.采用外延的方法修正灰度设置的偏移可以对多重分形谱有所改善.另外,讨论了权重因子q取值范围的影响,确定了q的取值范围.     

Phonon dispersion on Ag(100) surface:A modified analytic embedded atom method study

Within the harmonic approximation, the analytic expression of the dynamical matrix is derived based on the modified analytic embedded atom method(MAEAM) and the dynamics theory of surface lattice. The surface phonon dispersions along three major symmetry directionsΓˉXˉ, Γˉ Mˉ, and Xˉ Mˉ are calculated for the clean Ag(100) surface by using our derived formulas. We then discuss the polarization and localization of surface modes at points Xˉ and Mˉ by plotting the squared polarization vectors as a function of the layer index. The phonon frequencies of the surface modes calculated by MAEAM are compared with the available experimental and other theoretical data. It is found that the present results are generally in agreement with the referenced experimental or theoretical results, with a maximum deviation of 10.4%. The agreement shows that the modified analytic embedded atom method is a reasonable many-body potential model to quickly describe the surface lattice vibration. It also lays a significant foundation for studying the surface lattice vibration in other metals.     

混沌光注入垂直腔面发射激光器混沌输出的时延和带宽特性

提出并仿真论证了利用一个双光反馈垂直腔面发射激光器(定义为主VCSEL,M-VCSEL)产生的混沌光平行单向注入到另一个VCSEL(定义为副VCSEL,S-VCSEL)使所产生的混沌信号的延时特征(TDS)和带宽特性得以优化的技术方案.首先,基于VCSELs自旋反转模型,结合自相关分析方法,通过对系统参量进行优化,可使双光反馈M-VCSEL的X偏振分量(X-PC)和Y偏振分量(Y-PC)均输出混沌信号,且两路混沌信号的平均强度相当、TDS均较弱;在此基础上,将双光反馈M-VCSEL在优化条件下得到的混沌信号平行单向注入到S-VCSEL中,以获得两路TDS得到抑制、带宽更宽的混沌信号.通过考察两个偏振分量输出混沌信号的TDS以及混沌带宽在注入强度和频率失谐构成的参数空间的演化规律,确定了系统获取两路TDS被抑制、宽带宽的混沌信号所需的注入参数范围.     

Differential operators on a Riemann surface with projective structure

Let X be a Riemann surface equipped with a projective structure and a theta characteristic on X, or in other words, is a holomorphic line bundle equipped with a holomorphic isomorphism with the holomorphic cotangent bundle Ω_X. The complement of the zero section in the total space of the line bundle has a natural holomorphic symplectic structure, and using , this symplectic structure has a canonical quantization. Using this quantization, holomorphic differential operators on X are constructed. The main result is the construction of a canonical isomorphism

, n≥0, provided i[−2(k−1),0].     

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.     

From weak to strong pinning I: A finite size study

We have used linear stability analysis to study the depinning of an elastic chain with long range interactions submitted to a random pinning potential. In this paper, we provide, for the first time, evidence of a pronounced change from a strong pinning regime to a weak pinning regime. This change depends on the strength of disorder, and takes place only in finite size systems. For a given disorder, we show a characteristic length separating the weak pinning regime from the strong pinning regime. This length depends on the long range of the algebraic decay of the elastic couplings. The weak pinning regime is very well described by perturbation theory. As an example, we discuss more specifically the case of wetting of heterogeneous surfaces, where the change from a strong to a weak pinning regime could be induced in the wetting front by varying the surface tension of the liquid-air interface.Received: 12 September 2003, Published online: 20 April 2004PACS: 05.10.-a Computational methods in statistical physics and nonlinear dynamics - 68.08.Bc Wetting - 02.50.Fz Stochastic analysis     

A continuum model of a solid with a free surface: I. Normal mode analysis of the model

A complete analysis is made of the normal modes of an isotropic continuum model of a solid which occupies the region (0, 0, 0) < (x, y, z) < (X, Y, Z), the limit (X, Y, Z) → (∞,∞,∞) being taken. The surface z = 0 is a free surface and that z = Z is fixed; cyclic boundary conditions are used in the x and y directions. The modal displacements (vectors), modal frequencies (as a function of the wave-vectors), and wave-vector-densities are obtained for all types of normal modes; the work is a modification and extension of that of earlier workers.