基于逾渗理论的非晶合金屈服行为研究

从非晶合金的微观结构出发,基于处理强无序和具有随机几何结构系统常用的理论方法——逾渗理论来描述非晶合金剪切屈服时的塑性流变.为了更好地理解非晶合金剪切带萌生时的临界问题,结合已有的"自由体积(free volume)模型"和"剪切转变区(shear transformation zone)模型",建立了非晶合金剪切转变的逾渗模型.以Cu_(25)Zr_(75)二元非晶合金为例,计算了在剪切转变区内易发生塑性流动的原子团簇剪切失稳的逾渗阈值,并粗略估算了这些原子团簇的大小.研究发现,剪切失稳的逾渗阈值与临界约化自由体积浓度(x_c～2.4%)有着相似的特性,不同之处在于其值与自由体积的分散度有着密切联系.研究结果作为非晶合金的韧脆转变问题提供了新思路.     

Dynamical Localization of the Chalker-Coddington Model far from Transition

We study a quantum network percolation model which is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We show dynamical localization for parameters corresponding to edges of Landau bands, away from the expected transition point.     

Dynamical method for studying localization-delocalization transition in two dimensional percolating systems

We study quantum percolation which is described by a tight-binding Hamiltonian containing only off-diagonal hopping terms that are generally in quenched binary disorder (zero or one). In such a system, transmission of a quantum particle is determined by the disorder and interference effects, leading to interesting sharp features in conductance as the energy, disorder, and boundary conditions are varied. To aid understanding of this phenomenon, we develop a visualization method whereby the progression of a wave packet entering the cluster through a lead on one side and exiting from another lead on the other side can be tracked dynamically. Using this method, we investigate the localization-delocalization transition in a 2D system for various boundary conditions. Our results indicate the existence of two different kinds of localized regimes, namely exponential and power law localization, depending on the amount of disorder. Our study further suggests that there may be a delocalized state in the 2D quantum percolation system at very low disorder. These results are based on a finite size scaling analysis of the systems of size up to 70 × 70 (containing 4900 sites) on the square lattice.     

Resonant localized states and quantum percolation on random chains with power-law-diluted long-range couplings

We investigate the nature of one-electron eigenstates in power-law-diluted chains for which the probability of occurrence of a bond between sites separated by a distance r decays as p(r) = p/r(1+σ). Using an exact diagonalization scheme and a phenomenological finite-size scaling analysis, we determine the quantum percolation transition phase diagram in the full parameter space (p,σ). We show that the density of states displays singularities at some resonance energies associated with degenerate eigenstates localized in a pair of sites with special symmetries. This model is shown to present an intermediate phase for which there is classical percolation but no quantum percolation. Quantum percolation only takes place for σ < 0.78, a value larger than the corresponding one for the Anderson transition in long-ranged coupled chains with random diagonal disorder. The fractality of critical wavefunctions is also characterized.     

Statistical description of glass-forming alloys with chemical interaction: Application to Al-R systems

The statistical model for describing network-forming systems, developed in our previous works, is applied to study of metallic alloys with chemical bonding. The model is based on the representation of the sum of statistical weights over all possible configurations for a thermoreversible network in the form of a functional integral over a scalar field. The mean-field solution of the model is derived, and for particular case of a binary alloy having single element of chemical short-range order A₂B-type, thermodynamic and structural properties have been analyzed. This analysis allows to plot the temperature-concentration phase diagram of the model representing two immiscibility gap meeting in the distectic point. It is shown that at some temperatures and concentrations, geometry percolation of the network of chemical bonds and thus a sol-gel transition may take place. The critical percolation line was plotted in common with phase diagram. Then, the structural transitions, glass-forming ability and magnetic properties of Al-R alloys are discussed in the frames of this conception. It is proposed that the range of easy glass formation is confined on the left by the minimal concentration for the sol-gel transition and on the right by the concentration corresponding to the fractal-to-Euclidian crossover in the structure of percolation cluster. Finally, the abnormal growth of Al-REM magnetic susceptibility occurring above melting point of Al₂R compound is also explained.     

Nodal domain statistics for quantum maps, percolation, and stochastic Loewner evolution

We develop a percolation model for nodal domains in the eigenvectors of quantum chaotic torus maps. Our model follows directly from the assumption that the quantum maps are described by random matrix theory. Its accuracy in predicting statistical properties of the nodal domains is demonstrated for perturbed cat maps and supports the use of percolation theory to describe the wave functions of general Hamiltonian systems. We also demonstrate that the nodal domains of the perturbed cat maps obey the Cardy crossing formula and find evidence that the boundaries of the nodal domains are described by stochastic Loewner evolution with diffusion constant close to the expected value of 6, suggesting that quantum chaotic wave functions may exhibit conformal invariance in the semiclassical limit.     

逾渗分立时间量子行走的传输及纠缠特性

在一维分立时间量子行走中,通过静态和动态两种方式随机地断开连接边引入无序效应,研究了静态逾渗和动态逾渗对量子行走传输特性以及位置自由度和硬币自由之间纠缠的影响.随着演化时间的增加,静态逾渗会使得量子行走从弹道传输转变为安德森局域化,而动态逾渗则会使之转变为经典扩散.理想情况下,量子纠缠在较短的时间内就达到一个常数值E_0.静态逾渗量子行走的纠缠减小,并随着时间做无规振荡,而动态逾渗量子行走的纠缠则会随着时间光滑地增加,并在某一时间超过理想情况下的常数值,表现出动态逾渗增强量子纠缠的特性.     

Features of the Percolation Scheme of Vibrational Spectrum Reconstruction in the Ga1 – xAl x P Alloy

Specific features of the properties of Ga–P lattice vibrations have been investigated using the percolation model of a mixed Ga_{1 – x}Al _x P crystal (alloy) with zero lattice mismatch between binary components of the alloy. In contrast to other two-mode alloy systems, in Ga_{1 – x}Al _x P a percolation splitting of δ ~ 13 cm^–1 is observed for the low-frequency mode of GaP-like vibrations. An additional GaP mode (one of the percolation doublet components) split from the fundamental mode is observed for the GaP-rich alloy, which coincides in frequency with the gap corresponding to the zero density of one-phonon states of the GaP crystal. The vibrational spectrum of impurity Al in the GaP crystal has been calculated using the theory of crystal lattice dynamics. Upon substitution of lighter Al for the Ga atom, the calculated spectrum includes, along with the local mode, a singularity near the gap with the zero density of phonon states of the GaP crystal, which coincides with the mode observed experimentally at a frequency of 378 cm^–1 in the Ga_{1 – x}Al _x P (x < 0.4) alloy.

     

Kinetic models of a binary alloy at zero temperature

We study theoretically two types of kinetic models of a binary alloy at zero temperature. In the phase separation model, a nearest-neighbor interchange can occur if the fraction of AB bonds (where A and B denote distinct species of atoms in a binary alloy) is thereby decreased. The crystallization model is defined by the opposite evolution rule. We examine these models in one dimension and obtain exact analytical results for the densities of domain walls, defects, and for a number of other correlators. Nonergodic zero-temperature dynamics leads to final states strongly dependent on initial conditions. For generalized models, in which nearest-neighbor interchange is also performed if the portion of AB bonds is not changed, a very rich kinetic behavior is observed.     

Scaling properties of percolation models for multifragmentation

We have used scaling properties of nuclear multifragmentation, which have been observed with emulsion data, to investigate the properties of some approaches based on percolation. We have studied different percolation models on a cubic lattice and shown that they can rather well reproduce the data except for binary break up. We have described what the mean field approximation would give in this context and showed that it cannot reproduce the experimental results. Most of the paper is focused on the restructured aggregation model introduced earlier which allows to well reproduce the scaling properties observed experimentally. This model has been studied in details and extended to take account of bonds breaking. It is shown that, in some cases, a nucleus can break up in two pieces. This process cannot be obtained in conventional percolation or aggregation but is observed experimentally in the emulsion data. Other features like the dimensionality of the aggregation model, the restructuration of the clusters and a schematic constraint in momentum space have also been investigated.     

Interplay between disorder and quantum and thermal fluctuations in ferromagnetic alloys: the case of UCu2Si2-xGex

We consider, theoretically and experimentally, the effects of structural disorder, quantum fluctuations, and thermal fluctuations in the magnetic and transport properties of certain ferromagnetic alloys. We study the particular case of UCu2Si2-xGex. The low temperature resistivity, rho(T,x), exhibits Fermi liquid behavior as a function of temperature T for all values of x, which can be interpreted as a result of the magnetic scattering of the conduction electrons from the localized U spins. The residual resistivity, rho(0,x), follows the behavior of a disordered binary alloy. The observed nonmonotonic dependence of the Curie temperature, T(c)(x), with x can be explained within a model of localized spins interacting with an electronic bath. Our results clearly show that the Curie temperature of certain alloys can be enhanced due to the interplay between quantum and thermal fluctuations with disorder.     

The electrical conductivity of binary disordered systems,percolation clusters,fractals and related models

We review theoretical and experimental studies of the AC dielectric response of inhomogeneous materials, modelled as bond percolation networks, with a binary (conductor-dielectric) distribution of bond conductances. We first summarize the key results of percolation theory, concerning mostly geometrical and static (DC) transport properties, with emphasis on the scaling properties of the critical region around the percolation threshold. The frequency-dependent (AC) response of a general binary model is then studied by means of various approaches, including the effective-medium approximation, a scaling theory of the critical region, numerical computations using the transfer-matrix algorithm, and several exactly solvable deterministic fractal models. Transient regimes, related to singularities in the complex-frequency plane, are also investigated. Theoretical predictions are made more explicit in two specific cases, namely R-C and RL-C networks, and compared with a broad variety of experimental results, concerning, for example, granular composites, thin films, powders, microemulsions, cermets, porous ceramics and the viscoelastic properties of gels.     

Quantum to classical crossover under dephasing effects in a two-dimensional percolation model

Scaling theory predicts complete localization in d = 2 in quantum systems belonging to the orthogonal class(i.e., with timereversal symmetry and spin-rotation symmetry). The conductance g behaves as g^exp(-L/l) with system size L and localization length l in the strong disorder limit. However, classical systems can always have metallic states in which Ohm’s law shows a constant g in d=2. We study a two-dimensional quantum percolation model by controlling dephasing effects. The numerical investigation of g aims at simulating a quantum-to-classical percolation evolution. An unexpected metallic phase, where g increases with L, generates immense interest before the system becomes completely classical. Furthermore, the analysis of the scaling plot of g indicates a metal-insulator crossover.     

Unifying model for several classes of two-dimensional phase transition

A relatively simple and physically transparent model based on quantum percolation and dephasing is employed to construct a global phase diagram which encodes and unifies the critical physics of the quantum Hall, "two-dimensional metal-insulator," classical percolation and, to some extent, superconductor-insulator transitions. Using real-space renormalization group techniques, crossover functions between critical points are calculated. The critical behavior around each fixed point is analyzed and some experimentally relevant puzzles are addressed.     

Critical behavior in a model of correlated percolation

We study the critical behavior of certain two-parameter families of correlated percolation models related to the Ising model on the triangular and square lattices, respectively. These percolation models can be considered as interpolating between the percolation model given by the + and – clusters and the Fortuin-Kasteleyn correlated percolation model associated to the Ising model. We find numerically on both lattices a two-dimensional critical region in which the expected cluster size diverges, yet there is no percolation.     

Percolation quantum phase transitions in diluted magnets

We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are different from the classical percolation values, but in two dimensions they can nonetheless be determined exactly. We develop a complete scaling theory of this transition, and we relate it to recent experiments in La2Cu(1-p)(Zn,Mg)(p)O4. Our results are also relevant for disordered interacting boson systems.     

Quantum percolation in two-dimensional antiferromagnets

The interplay of geometric randomness and strong quantum fluctuations is an exciting topic in quantum many-body physics, leading to the emergence of novel quantum phases in strongly correlated electron systems. Recent investigations have focused on the case of homogeneous site and bond dilution in the quantum antiferromagnet on the square lattice, reporting a classical geometric percolation transition between magnetic order and disorder. In this study we show how inhomogeneous bond dilution leads to percolative quantum phase transitions, which we have studied extensively by quantum Monte Carlo simulations. Quantum percolation introduces a new class of two-dimensional spin liquids, characterized by an infinite percolating network with vanishing antiferromagnetic order parameter.     

The conductivity transition of aggregated Bi films

By analyzing the recent experimental and theoretical results, we find that the abrupt conductivity transition of an ultrathin aggregated film of bismuth during its growth is not describable by the Anderson transition or quantum percolation, but instead can be well described by a two-dimensional continuum model of classical percolation.     

Emission and percolation of excitons in dense sensembles of quantum dots on the spherical surface

We study core/shell heterostructures in which a core (SiO₂) is overcoated with a shell of ZnO quantum dots, randomly distributed on the sphere surface with the surface filling factor P∼0.45. Due to the high surface energy of SiO₂ spheres, ZnO quantum dots have the shape of disks in which, in spite of the large radii, quantum size effects of excitons are retained. The height of ZnO disks estimated by the effective mass approximation is comparable with the exciton diameter in bulk ZnO. Analysis of optical spectra has shown that, at the given density of ZnO quantum dots, the exciton system is above the percolation threshold. The quantitative parameters characterizing such phenomenon are obtained using the elements of percolation theory and the topology of the samples.     

基于纠缠态的量子通信网络的量子信道建立速率模型

针对基于纠缠态的量子通信网络, 提出了网络模型. 基于网络模型, 首先分析了基础链路的量子信道建立速率. 然后根据基础链路的量子信道建立速率, 针对不同的量子信道建立方法, 对中继长链路上的量子信道建立速率进行分析, 得到在逐点方法和分段方法下所对应的量子信道建立速率. 最后, 利用逾渗模型, 对大规模纠缠态量子通信网络中任意两点间的量子信道建立速率进行分析, 推导出n个节点量子通信网络中, 量子信道建立速率为Ω (1/n).