Correlations of Eigenvalues on¶Multi-Dimensional Flat Tori

We show that, for almost all k-dimensional flat tori, the eigenvalues of the Laplacian follow a uniform distribution with respect to their 2-, 3-, …, and [k/2]-level correlations.     

Discrete Polynuclear Growth and Determinantal Processes

We consider a discrete polynuclear growth (PNG) process and prove a functional limit theorem for its convergence to the Airy process. This generalizes previous results by Prähofer and Spohn. The result enables us to express the F ₁ GOE Tracy- Widom distribution in terms of the Airy process. We also show some results, and give a conjecture, about the transversal fluctuations in a point to line last passage percolation problem. Furthermore we discuss a rather general class of measures given by products of determinants and show that these measures have determinantal correlation functions.     

Deposition of Aerosol Nanoparticles on Flat Substrate Surfaces

The deposition process in a homogeneous electric field, and the subsequent microscopic arrangement of charged, metallic aerosol nanoparticles in the size range of 30 nm on flat substrate surfaces is described. The first aspect of the investigation is the transfer of the particles from a three-dimensional distribution in the gas phase into their arrangement on the substrate surface, in dependence on particle-particle interactions and on Brownian motion. The theoretical results obtained with a trajectory model are compared with experimental results obtained by scanning electron microscope investigation of the deposition patterns. The second aspect of the investigation is the nanostructured arrangement of nanoparticles by means of inhomogeneous electric microfields. We demonstrate a parallel process for the transfer of charge patterns on oxidized silicon surfaces followed by the deposition of monodisperse singly charged nanoparticles, which allows the creation of particle arrangements reaching from 100 nm resolution up to structures in the upper micrometer range. The charge patterns are transferred using a polydimethylsiloxane (PDMS)-stamp, which is covered with a metal layer.     

Elastic and Plastic Deformations of Carbon Nanotubes Multilayer Packing on a Flat Substrate

Journal of Experimental and Theoretical Physics - It is shown by molecular dynamics method using the chain model that the transverse compression of a multilayer packing of identical parallel...     

Limiting Distributions for a Polynuclear Growth Model with External Sources

The purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by Prähofer and Spohn. Depending on the strength of the sources, the limiting distribution functions are either the Tracy–Widom functions of random matrix theory or a new explicit function which has the special property that its mean is zero. Moreover, we obtain transition functions between pairs of the above distribution functions in suitably scaled limits. There are also similar results for a discrete totally asymmetric exclusion process.     

Fluctuations of the One-Dimensional Polynuclear Growth Model in Half-Space

We consider the multi-point equal time height fluctuations of the one-dimensional polynuclear growth model in half-space. For special values of the nucleation rate at the origin, the multi-layer version of the model is reduced to a process with a determinantal weight, for which the asymptotics can be analyzed. In the scaling limit, the fluctuations near the origin are shown to be equivalent to those of the largest eigenvalue of the orthogonal/symplectic to unitary transition ensemble at soft edge in random matrix theory.     

Influences of Fractal Substrate Structures on Dynamic Scaling Behaviors of Etching Model

The Etching model on various fractal substrates embedded in two dimensions was investigated by means of kinetic Mento Carlo method in order to determine the relationship between dynamic scaling exponents and fractal parameters. The fractal dimensions are from 1.465 to 1.893, and the random walk exponents are from 2.101 to 2.578.It is found that the dynamic behaviors on fractal lattices are more complex than those on integer dimensions. The roughness exponent increases with the increasing of the random walk exponent on the fractal substrates but shows a non-monotonic relation with respect to the fractal dimension. No monotonic change is observed in the growth exponent.     

Universality of a Double Scaling Limit near Singular Edge Points in Random Matrix Models

We consider unitary random matrix ensembles on the space of Hermitian n × n matrices M, where the confining potential V _s,t is such that the limiting mean density of eigenvalues (as n→∞ and s,t→ 0) vanishes like a power 5/2 at a (singular) endpoint of its support. The main purpose of this paper is to prove universality of the eigenvalue correlation kernel in a double scaling limit. The limiting kernel is built out of functions associated with a special solution of the P _I ² equation, which is a fourth order analogue of the Painlevé I equation. In order to prove our result, we use the well-known connection between the eigenvalue correlation kernel and the Riemann-Hilbert (RH) problem for orthogonal polynomials, together with the Deift/Zhou steepest descent method to analyze the RH problem asymptotically. The key step in the asymptotic analysis will be the construction of a parametrix near the singular endpoint, for which we use the model RH problem for the special solution of the P _I ² equation. In addition, the RH method allows us to determine the asymptotics (in a double scaling limit) of the recurrence coefficients of the orthogonal polynomials with respect to the varying weights on . The special solution of the P _I ² equation pops up in the n ^−2/7-term of the asymptotics.     

Anomalous Minimum and Scaling Behavior of Localization Length Near an Isolated Flat Band

Using one‐dimensional tight‐binding lattices and an analytical expression based on the Green's matrix, we show that anomalous minimum of the localization length near an isolated flat band, previously found for evanescent waves in a defect‐free photonic crystal waveguide, is a generic feature and exists in the Anderson regime as well, i.e., in the presence of disorder. Our finding reveals a scaling behavior of the localization length in terms of the disorder strength, as well as a summation rule of the inverse localization length in terms of the density of states in different bands. Most interestingly, the latter indicates the possibility of having two localization minima inside a band gap, if this band gap is formed by two flat bands such as in a double‐sided Lieb lattice.     

Evaluation of ensemble averages for simple Hamiltonians perturbed by a GOE interaction

Using an expansion in powers of N^?1, where N is the dimension of the Hamiltonian matrix, we evaluate ensemble averages of the resolvent, of products involving several resolvents, and of the moments of the Hamiltonian H₀ + λV. Here, H₀ is arbitrary but fixed, and V is a GOE ensemble. The nature of the N^?1 expansion is also discussed.     

Growth and Crystallization Habit of a Novel Substrate Crystal LiGaO_2

ＧｒｏｗｔｈａｎｄＣｒｙｓｔａｌｌｉｚａｔｉｏｎＨａｂｉｔｏｆａＮｏｖｅｌＳｕｂｓｔｒａｔｅＣｒｙｓｔａｌＬｉＧａＯ_２￥ＨＵＡＮＧＷｅｉｍｉｎｇ；ＸＵＪｕｎ；ＷＵＧｕａｎｇｚｈａｏ；ＤＥＮＧＰｅｉｚｈｅｎ；ＧＡＮＦｕｘｉ（ＳｈａｎｇｈａｉＩｎｓｔｉ?..     

生长温度对ZnO薄膜晶体质量和发光特性的影响

采用激光脉冲沉积法在Si(100)衬底上生长ZnO薄膜,衬底温度分别为室温,200℃,300℃,400℃和500℃.用X射线衍射仪、拉曼光谱、扫描电子显微镜对薄膜的微结构进行了测量,并测量了室温下薄膜的光致发光特性.结果表明,300℃时.ZnO具有最佳择优取向,随着衬底温度升高.衍射峰半峰全宽减小,薄膜晶粒尺寸增大,400℃时,薄膜具有各向等大的品粒尺寸.同时拉曼谱结果显示,薄膜内部的缺陷随衬底温度变化无明显差别,应力表现为张应力,400℃时应力最小,紫外发光峰在衬底温度为400℃时最强,而黄绿光带最弱.在减少薄膜缺陷,提高择优长向和晶粒尺寸的同时.使晶粒横向尺寸和纵向尺寸尽可能相同,可极大提高薄膜的发光特性.     

Destruction of order in nuclear spectra by a residual GOE interaction

We consider hamiltonians of the type H = H₀ + λV_GOE where H₀ is a fixed N × N matrix and V_GOE represents a gaussian orthogonal ensemble. The change as a function of λ of the average level density and of the eigenvector correlations is studied, and related to the distribution of branch points of H. It is shown that the GOE interaction completely dominates the spectral properties of H when its spectrum covers the spectrum of H₀.     

Growth of High Quality Strained-Si on Ultra-Thin SiGe-on-Insulator Substrate

Ultra-thin and near-fully relaxed SiCe substrate is fabricated using a modified Ce condensation technique, and then a 25-nm-thiek biaxially tensile strained-Si with a low rms roughness is epitaxially deposited on a SiGe- on-Insulator （SGOI） substrate by ultra high vacuum chemical vapor deposition （UHVCVD）. High-Resolution cross-sectional transmission electron microscope （HR-XTEM） observations reveal that the strained-Si/SiGe layer is dislocation-free and the atoms at the interface are well aligned. Furthermore, secondary ion mass spectrometry （SIMS） results show a sharp interface between layers and a uniform distribution of Ge in the SiCe layer. One percent in-plane tensile strain in the strained-Si layer is confirmed by ultraviolet （UV） Raman spectra, and the stress maintained even after a 30-s rapid thermal annealing （RTA） process at 1000℃. According to those results, devices based on strained-Si are expected to have a better performance than the conventional ones.     

Si衬底上ZnSe外延膜的低压MOCVD生长

以硒化氢（H2Se）和二甲基锌为源材料，生长温度是300℃时，用低压金属有机化学气相沉积（LP－MOCVD）系统在Si(111)衬底上外延生长了ZnSe薄膜。通过X射线衍射（XRD）、扫描电子显微镜的能量色散（EDS）以及光致发光（PL）实验验证ZnSe外延膜的质量，在X射线衍射谱中只有一个强的ZnSe(111)面衍射峰，这说明外延膜是（111）取向的单晶薄膜，在能量色散谱中除了Si,Zn和Se原子外，没有观测到其他原子，说明ZnSe外延膜中杂质含量较少。ZnSe外延膜中Zn/Se原子比接近1，有较好的化学配比。在ZnSe外延膜的77K光致发光谱中没有观测到与深中心发射相关的发光峰，表明ZnSe外延膜的晶格缺陷密度较小。77K时的近带边发射峰447nm在室温时移至465nm附近。     

Nucleation, Growth, and Scaling in Slow Combustion

We study the nucleation and growth of flame fronts in slow combustion. This is modeled by a set of reaction-diffusion equations for the temperature field, coupled to a background of reactants and augmented by a term describing random temperature fluctuations for ignition. We establish connections between this model and the classical theories of nucleation and growth of droplets from a metastable phase. Our results are in good agreement with theoretical predictions.     

Eigenvalues and eigenfunctions of a clover plate

We report a numerical study of the flexural modes of a plate using semi-classical analysis developed in the context of quantum systems. We first introduce the Clover billiard as a paradigm for a system inside which rays exhibit stable and chaotic trajectories. The resulting phase space explored by the ray trajectories is illustrated using the Poincare surface of section, and shows that it has both integrable and chaotic regions. Examples of the stable and the unstable periodic orbits in the geometry are presented. We numerically solve the biharmonic equation for the flexural vibrations of the Clover shaped plate with clamped boundary conditions. The first few hundred eigenvalues and the eigenfunctions are obtained using a boundary elements method. The Fourier transform of the eigenvalues show strong peaks which correspond to ray periodic orbits. However, the peaks corresponding to the shortest stable periodic orbits are not stronger than the peaks associated with unstable periodic orbits. We also perform statistics on the obtained eigenvalues and the eigenfunctions. The eigenvalue spacing distribution P(s) shows a strong peak and therefore deviates from both the Poisson and the Wigner distribution of random matrix theory at small spacings because of the C_4v symmetry of the Clover geometry. The density distribution of the eigenfunctions is observed to agree with the Porter-Thomas distribution of random matrix theory. Received 12 February 2001 and Received in final form 17 April 2001     

两步生长法生长的Inx Ga1-x As/GaAs材料及性质

利用LP-MOCVD技术,采用两步生长法在GaAs(100)单晶衬底上外延生长InxGa1-xAs材料。通过扫描电子显微镜( SEM)与原子力显微镜( AFM)观察了缓冲层厚度对外延层表面形貌、表面粗糙度的影响;利用X射线衍射( XRD)分析了缓冲层厚度对外延层结晶质量的影响;利用拉曼光谱分析了缓冲层厚度对外延层材料合金有序度的影响;通过透射电子显微镜( TEM)观察了外延层材料位错的分布状态,计算了外延层的位错密度。实验结果表明,两步生长法生长的Inx Ga1-x As/GaAs异质结材料的缓冲层厚度存在一个最优值。     

ZnMgO生长中压强和衬底对薄膜性质的影响

利用金属有机源化学气相沉积(MOCVD)生长方法,在2.5 kPa和5 kPa生长压强下,分别以sapphire (Al2O3)和ZnO为衬底生长ZnMgO薄膜.研究分析了样品的晶体结构、表面形貌、光电学性质.结果表明,衬底和生长压强对ZnMgO薄膜的生长有重要影响.5 kPa高压生长和以ZnO为衬底均有利于ZnMgO...