On Universality of Local Edge Regime for the Deformed Gaussian Unitary Ensemble

We consider the deformed Gaussian ensemble H_n=H_n⁽⁰⁾+M_nH_{n}=H_{n}^{(0)}+M_{n} in which H_n⁽⁰⁾H_{n}^{(0)} is a hermitian matrix (possibly random) and M _n is the Gaussian unitary random matrix (GUE) independent of H_n⁽⁰⁾H_{n}^{(0)}. Assuming that the Normalized Counting Measure of H_n⁽⁰⁾H_{n}^{(0)} converges weakly (in probability if random) to a non-random measure N ⁽⁰⁾ with a bounded support and assuming some conditions on the convergence rate, we prove the universality of the local eigenvalue statistics near the edge of the limiting spectrum of H _n .     

From Alternating Sign Matrices to the Gaussian Unitary Ensemble

The aim of this note is to prove that fluctuations of uniformly random alternating sign matrices (equivalently, configurations of the 6-vertex model with domain wall boundary conditions) near the boundary are described by the Gaussian Unitary Ensemble and the GUE-corners process.     

Thermodynamic Phase Transition and Critical Behavior of a Spherical Symmetric Black Hole

In this paper, we builded the thermodynamics model of black hole based on the method of York. We obtained the reduced temperature reciprocal function using the action of the system. We studied the phase structure of black holes and Hawking-Page phase transition. We obtained the first order phase transition and critical values of black hole in Rerssner-NordstrÖm space time. The results showed that only when two-phase coexistence appeared only when |q| < |q_c|.     

Gaussian Fluctuation for the Number of Particles in Airy, Bessel, Sine, and Other Determinantal Random Point Fields

We prove the Central Limit Theorem (CLT) for the number of eigenvalues near the spectrum edge for certain Hermitian ensembles of random matrices. To derive our results, we use a general theorem, essentially due to Costin and Lebowitz, concerning the Gaussian fluctuation of the number of particles in random point fields with determinantal correlation functions. As another corollary of the Costin–Lebowitz Theorem we prove the CLT for the empirical distribution function of the eigenvalues of random matrices from classical compact groups.     

Phase Transition and Critical Behavior for XY Model on 2-Dimensional Random Triangle Lattice

The Monte Carlo renormalization group method is applied to discussing the nature of phase transition of XY model on 2-dimensional random triangle lattices. A line of fixed point and un-universal phase transition are found. The results are in agreement with Kosterlitz-Thouless theory. The susceptibility ehows a clear size-dependent behaviorin low temperature region. This means that it should be divergent in this region.     

Critical Behavior in Nuclear Structure from Spherical to γ-Soft Deformed Shape in IBM

Comparing with the predictions of the transitional dynamical symmetry E（5） proposed by Iachello [Phys. Rev. Lett. 85 （2000） 3580], the critical behaviors from U（5）-0（6） are studied in the space of two control parameters in the interacting boson model. A simple shape phase diagram has been presented. It is found that E（5） predictions cannot be exactly reproduced by our calculations and that the best agreement is close to the calculations with boson number N = 9. By comparing with experimental data on E（5）-like nuclei, we find that E（5） predictions and IBM calculations can reproduce the energy ratios and E2 transition ones.     

The optical Airy transform and its application in generating and controlling the Airy beam

We propose an optical Airy transform in this paper, and obtain the analytical expressions for the Airy transform of fundamental Gaussian beams and finite energy Airy beams. The setup for performing the optical Airy transform is presented. The Airy transform for Gaussian beams and finite energy Airy beams are theoretically calculated and analyzed. Our results show that the Airy beam can be conveniently generated and controlled through the optical Airy transform of the Gaussian beam. The optical Airy transform also can be used to directly modulate the beam parameters of the incident Airy beam, and it can transform the incident Airy beam into the Gaussian beam.     

Tricritical and Critical Exponents in Microcanonical Ensemble of Systems with Long-Range Interactions

We explore the tricritical points and the critical lines of both Blume Emery Griffiths and Ising model within long-range interactions in the microcanonical ensemble.For K = Kmtp,the tricritical exponents take the valuesβ = 1/4,1 =γ~-≠γ~+ = 1/2 and 0 =α~-≠α~+ =-1/2,which disagree with classical(mean ffeld) values.When K Kmtp,the phase transition becomes second order and the critical exponents have classical values except close to the canonical tricritical parameters(Kctp),where the values of the critical expoents become β = 1/2,1 = γ~-≠γ~+= 2and 0 =α~-≠α~+ = 1.     

Tricritical and Critical Exponents in Microcanonical Ensemble of Systems with Long-Range Interactions

We explore the tricritical points and the critical lines of both Blume-Emery-Griffiths and Ising model within long-range interactions in the microcanonical ensemble. For K=K_MTP, the tricritical exponents take the values β=1/4, 1=γ^-≠γ⁺=1/2 and 0=α^-≠α⁺=-1/2, which disagree with classical (mean field) values. When K>K_MTP, the phase transition becomes second order and the critical exponents have classical values except close to the canonical tricritical parameters (K_CTP), where the values of the critical expoents become β=1/2, 1=γ^-≠γ⁺=2 and 0=α⁺≠α⁺=1.     

Ffast Transient Fluorescence Technique to Study Critical Exponents at the Glass Transition

The fast transient fluorescence (FTRF) technique was used to study critical exponents at the glass transition in free-radical crosslinking copolymerization (FCC) for two different monomeric systems, methyl methacrylate (MMA) and styrene (S). Pyrene (P_y ) was used as a fluorescence probe. The fluorescence lifetimes of P_y from its decay traces were measured and used to monitor the gelation process. Changes in the viscosity of the pregel solutions due to glass formation dramatically enhance the fluorescent yield of aromatic molecules. This effect is used to study the glass transition upon gelation of MMA and S monomeric systems as a function of time, at various temperatures and crosslinker concentrations. The results are interpreted in the view of percolation theory. The gel fraction and weight average degree of polymerization exponents β and γ are found to be 0.37 ± 0.02 and 1.66 ± 0.07 in agreement with percolation results.     

Phase Transition and Critical Phenomenon Occurring in Granular Matter

We investigate the granular flow states in a channel with bottleneck by molecular dynamics simulations.Our study is restricted only on a selected key area rather than on the whole system to focus on the flow properties of a single granular state.A random force field is introduced to control the granular temperature.It is also pointed out that the flow rate in the granular flow can be correlated with the pressure,which leads us to carry out a comprehensive study similar to the classical study for general liquid-gas phase transition.Our results show that the dilute flow state and the dense flow state of the granules are similar to the gas state and the liquid state of general substances,respectively,and the properties of phase transition and critical phenomenon are also similar to those occurring in general substances.     

Crossover Critical Behavior in the Three-Dimensional Ising Model

The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by fluctuations of the order parameter. If the interaction range is finite, the critical behavior asymptotically close to the critical point is determined by fluctuations and the actual critical behavior depends on the particular universality class. A variety of systems, including fluids and anisotropic ferromagnets, belongs to the three-dimensional Ising universality class. Recent numerical studies of Ising models with different interaction ranges have revealed a spectacular crossover between the asymptotic fluctuation-induced critical behavior and mean-field-type critical behavior. In this work, we compare these numerical results with a crossover Landau model based on renormalization-group matching. For this purpose we consider an application of the crossover Landau model to the three-dimensional Ising model without fitting to any adjustable parameters. The crossover behavior of the critical susceptibility and of the order parameter is analyzed over a broad range (ten orders) of the scaled distance to the critical temperature. The dependence of the coupling constant on the interaction range, governing the crossover critical behavior, is discussed.     

有限核多重碎裂中的临界行为与临界指数的提取

利用非对称核物质状态方程可以得到有限核¹¹²Sn的压强－密度等温线, 并对其在坐标和动量空间中的分布进行了模拟, 采用了并合模型对形成的核碎片进行了构造. 通过碎片的关联分析, 寻找出了临界行为的信号, 提取了临界指数.     

PNJL模型下手征相变的临界指数

在PNJL模型下研究了临界点和旋节线边界上的临界指数。计算表明四个标准的临界指数$\alpha,\,\beta,\,\gamma,\,\delta$在 平均场近似下与朗道-金斯堡理论的预言一致。重子数涨落分布峰态的临界指数$\eta(\approx2)$大于偏态的 临界指数$\zeta(\approx1)$,这表明,如果在重离子碰撞实验中可以达到临界区域,峰态的测量比偏态的测量更加敏感。计算结果还表明,偏态(峰态)在旋节线边界上的临界指数与在临界点的临界指数具有相同的发散强度。根据重子数在不稳定相和亚稳相的剧烈涨落及峰态和偏态在旋节线边界上发散的特点,在将来的实验中用于鉴别一阶相变的信号在一定程度上会被干扰,一些偏离标准一阶相变的信号或许会在观测中发现。     

ZnO薄膜表面和边缘的发光特性

研究了分子束外延方法生长的ZnO薄膜的光学特性,首先测量样品反射光谱,然后重点研究其光致发光光谱。实验中通过改变激发光的强度,以及采用波导配置和不同的实验几何配置等手段,观察到了ZnO薄膜中起源于激子-激子散射和电子-空穴等离子体复合发光的受激辐射,同时观察到两种配置下自发辐射谱中存在巨大的差异。通过对实验数据和理论计算结果的分析,初步认为造成了从ZnO薄膜表面和侧面得到的PL谱之间的显著区别原因有两种:一是非对称薄膜波导的吸收损耗造成的波长选择效应,二是薄膜波导对掠出射光的类似薄膜微腔的微腔效应。