New Exact Ground States for One-Dimensional Quantum Many-Body Systems

We consider one-dimensional quantum many-body systems with pair interactions in external fields and (re)investigate the conditions under which exact ground-state wave functions of product type can be found. Contrary to a claim in the literature that an exhaustive list of such systems is already known, we show that this list can still be enlarged considerably. In particular, we are able to calculate exact ground-state wave functions for a class of quantum many-body systems with Ax ^–2+Bx ² interaction potentials and external potentials given by sixth-order polynomials.     

Exponential decay of bound state wave functions

The spatial decay properties of the wave functions of multiparticle systems are investigated. The particles interact through pair potentials in the classR+L . The bound states lie below the bottom of the continuous spectrum of the system. Exponential decay, in anL ² sense, is proven for these wave functions. The result is the best possible one which will cover every potential in this class.Based on a thesis submitted to Princeton University in partial fulfillment of the degree of Doctor of Philosophy.     

利用Gordon-Kim模型对NaCl物态方程的研究

 本文对孤立离子Hartree-Fock波函数的数值解出发，直接计算了NaCl晶体中各种离子对的相互作用势。结果表明，对不同的离子对，其短程作用势性质不同。对Na⁺-Cl^-离子对，其短程作用势为正，而对Cl^--Cl^-离子对和Na⁺-Na⁺离子对，对物理上感兴趣的大部分距离范围内，其短程作用势为负。在对以上的离子对势进行了解析拟合后，通过晶格动力学的方法计算了晶体的Grüneisen参数和物态方程，其结果与实验符合程度是令人满意的。     

金属电子关联函数的实空间变分计算

本文求解了在相关基函数理论框架下得到的实空间关联函数的积分方程,得到了金属铝(r_s=2.07)和铯(r_s=5.65)的关联函数,关联能和多体波函数。改进了其它多体理论,本文得到的关联函数是恒正的,并且满足归一化条件。 关键词：     

The phase statistics of a multichannel radar interferometer

Abstract

The analysis in this paper is concerned with the problem of determining the phase statistics of the output of a multichannel coherent radar interferometer. The 2N channels of the radar consist of the outputs from N pairs of antennae. Each antenna receives a random electromagnetic wave field which has circular normal first-order statistics with an arbitrary coherence function. Each antenna in each pair receives a wave at a different time, the time difference Δt between each antenna in each pair being the same for all pairs. The signals received by each pair are independent. The signals from each pair are combined to give G(t, Δt)=Σ_k=1 ^N S_k(t) S_k*(t+Δt) where, for example, the signals from each antenna in the kth pair are S_k(t) and S_k(t+Δt).

The probability density function of the modulus and phase of G(t, Δt) is worked out. The joint density is shown to be a type of generalized K distribution, and the phase distribution is shown to be a hypergeometric function. The results show that it is possible to measure the phase of the coherence function of an electromagnetic wave field scattered from a randomly moving extended object (such as the ocean surface) using such a multichannel radar. This phase is related to asymmetry of the Doppler power spectrum. Furthermore, if this asymmetry is a result of surface currents on the ocean interacting with the surface waves which cause the electromagnetic scattering, then the surface currents may be measured in some sense.     

Localization of a pair of bound particles in a random potential

We study the localization length l_c of a pair of two attractively bound particles moving in a one-dimensional random potential. We show in which way it depends on the interaction potential between the constituents of this composite particle. For a pair with many bound states N the localization length is proportional to N, independently of the form of the two particle interaction. For the case of two bound states, we present an exact solution for the corresponding Fokker–Planck equation and demonstrate that l_c depends sensitively on the shape of the interaction potential and the symmetry of the bound state wave functions.     

Ultrasonic high frequency lamb waves for evaluation of plate structures

The potentials of high frequency Lamb wave modes are investigated in the inspection of plate-like structures. The wave propagation characteristics of higher order wave modes and the corresponding sensitivity and detectability are studied. Finite element simulations are carried out using infinite elements to model the ultrasonic wedge transducer and the inspection system. Experimental pulse–echo measurements are conducted to verify the influence of different modes characteristics predicted from the finite element simulations. The experimental measurements show a good agreement with the obtained numerical results for the fundamental modes, S₀ and A₀, and the higher order modes, S₁ and A₁, at 4 MHz mm of frequency–thickness.     

On perturbations of solutions of the Einstein-Maxwell equations

By using the expressions for the solutions of the Einstein-Maxwell equations in terms of potentials, valid in the case where the spacetime admits a shear-free geodesic null congruence and the electromagnetic field is aligned to it, we show that a pair of complex potentials generates simultaneous perturbations of the gravitational and the electromagnetic fields. We also show that if the background electromagnetic field is null, then the pair of complex potentials is determined by a pair of coupled, linear, second-order differential equations.     

Activation energy of self-diffusion along symmetric tilt grain boundaries 〈111〉 in the Ni3Al intermetallic compound

Activation energy of self-diffusion along symmetric tilt grain boundaries 〈111〉 in the Ni₃Al inter-metallic compound has been calculated depending on the temperature and misorientation angle. For comparison, two types of potentials of interatomic interaction have been used: pair Morse potentials and multi-particle Cleri-Rosato potentials. It has been shown that the activation energy of grain-boundary diffusion increases with temperature on applying the additional diffusion mechanisms. Three temperature ranges with various activation energies have been found.     

On the Crystallization of 2D Hexagonal Lattices

It is a fundamental problem to understand why solids form crystals at zero temperature and how atomic interaction determines the particular crystal structure that a material selects. In this paper we focus on the zero temperature case and consider a class of atomic potentials V = V ₂ + V ₃, where V ₂ is a pair potential of Lennard-Jones type and V ₃ is a three-body potential of Stillinger-Weber type. For this class of potentials we prove that the ground state energy per particle converges to a finite value as the number of particles tends to infinity. This value is given by the corresponding value for a optimal hexagonal lattice, optimized with respect to the lattice spacing. Furthermore, under suitable periodic or Dirichlet boundary condition, we show that the minimizers do form a hexagonal lattice. Dedicated with admiration to Professor Tom Spencer on occasion of his 60th birthday     

低温下Au959团簇负载于MgO(100)表面后结构变化的分子动力学研究

采用基于Chen-Mbius反演方法,从金属/金属氧化物界面第一性原理计算的粘结能结果中推导出的Au/MgO原子间相互作用势的正则系综（NVT）分子动力学,模拟了在10 K条件下,Au₉₅₉团簇负载于MgO（100）表面后团簇结构的变化.根据原子对分析技术和对分布函数的分析表明,由于团簇界面处原子间距与载体原子间距相匹配,置于载体上的Au团簇经过一个变形过程后,较其孤立自由表面时的团簇体积变大. 关键词： 团簇 分子动力学 计算机模拟 表面     

Electronic structure reconstruction of CaFe2As2 in the spin density wave state

The electronic structure of CaFe₂As₂, a parent compound of iron-based superconductors, is studied with high-resolution angle-resolved photoemission spectroscopy. The electronic structure of CaFe₂As₂ in the paramagnetic state is consistent with that of density-functional theory calculations. We show that the electronic structure of this compound is significantly reconstructed when entering the spin density wave state. We could resolve two hole-like pockets and four electron-like pockets around the (0, 0) point, and one electron-like pocket surrounded with a pair of electron- and hole-like pockets around the (π, π) point in the spin density wave state. Therefore, the complicated Fermi surface topology and electronic structure near Fermi surface of CaFe₂As₂ illustrate that there exists unconventional electronic reconstruction in the spin density wave state, which cannot be explained by the band folding and Fermi surface nesting pictures.     

The liquid-state structure of difluoromethane

Neutron scattering experiments have been performed on liquid difluoromethane (CH₂F₂, R32) resulting in the first experimental determination of the total structure factor and total pair distribution function of difluoromethane. Analysis of the measurements has led to the liquidstate intramolecular structure of this fluid. The structure has been compared with that obtained for some other halogenated methanes. A comparison with results obtained for trifluoromethane (CHF₃, R23) suggests that there is less long-range order in liquid-state difluoromethane than trifluoromethane. Subtraction of the intramolecular structure leads to an intermolecular structure factor and an intermolecular pair distribution function, both of which are crucially important for assessing the reliability of models of the pair potentials used in computer simulations.     

The potential curve of the He-α-quartz surface interaction

One of the fundamental problems for gas-surface interaction physics is to relate the pairwise gas atom-surface atom interaction characteristics to that of the aggregate collision complex. One method of studying the problem on a microscopic scale is to model the surface lattice structure and calculate the interaction characteristics using the Monte Carlo technique. We describe the calculation of the He-α-quartz (SiO₂) interaction potential applying this method assuming pairwise He-surface atom Lennard-Jones (12, 6) potentials. The results show that the interaction potential follows a (13.5, 3.8) shape function in the gas-surface interaction range below 8 Å, and an asymptotic dependence with 3.8 < m < 6 for the region beyond 8 Å. This potential well shape function differs substantially from the (9, 3) function suggested by earlier work. The calculated potential curve shows a weak dependence on surface and gas temperature. The potential well depth of the gas-surface interaction shows a strong nonlinear relationship to the equilibrium internuclear distance of the HeSi pair potential applied to the calculation. We find that the empirically determined parameters for the HeSi pair potential provide resultant gas-surface potentials with well depth remarkably close to those required by the measured heat of adsorption.     

A molecular dynamics study of the structural change differences between Au225 and Au369 clusters on MgO surfaces at low temperature

The differences in structural change between Au₂₂₅ and Au₃₆₉ clusters with their (111) facets supported on MgO(100) surfaces at 5 K are studied by using molecular-dynamics simulations with the atomic interchange potentials of the Au/MgO interface. The parameters are obtained from the ab initio energies using the Chen-Möbius inversion method. Analyses of the pair distribution functions show that the two Au clusters use different deformation processes to adjust the distances between the interface atoms, owing to the misfit between the atom distances among the clusters and the substrates. The local structural changes are identified by atomic density profiles.     

High energy elastice + − O2 scattering

Theoretical differential cross-sections are obtained for the elastic scattering of fast (E _i ⩾ 200 eV) positrons by oxygen molecules. Employing the independent atom model, the atomic scattering amplitudes are calculated with the (static + polarization) model potentials, in the partial wave analysis (PWA). Comparisons made with the theory and experiments on the incident electrons, show significant differences at small angles.     

Fast atom diffraction during grazing scattering from a MgO(001) surface

Fast neutral atoms and molecules with energies from 0.4 up to 3 keV are scattered under a grazing angle of incidence from a clean and flat MgO(001) surface. For “axial surface channeling” conditions, we observe defined diffraction patterns in the angular intensity distributions for scattered ³He and ⁴He atoms as well as H₂ molecules. The diffraction patterns are analyzed in terms of semiclassical trajectory calculations making use of projectile surface interaction potentials derived from density functional theory and from pair potentials calculated from Hartree–Fock wave functions. From comparison of measured and calculated diffraction patterns we deduced the rumpling of the topmost surface layer of MgO(001), i.e. an inward shift of Mg²⁺ ions with respect to O^2? ions, of (0.03±0.03) Å.     

铁磁-p波超导结中的自旋极化隧道谱与散粒噪声

考虑到界面的势垒散射和铁磁层中的磁交换作用，依照Sr2RuO4超导体具有自旋三重配对态的p波对称结构，研究铁磁-p波超导结中的自旋极化隧道谱与散粒噪声，研究表明：1.对于幺正配对态，随着铁磁层中磁交换劈裂增强，隧道谱与散粒噪声都减少；2.对于非幺正配对态，隧道谱与散粒噪声都依赖于铁磁层的磁化轴方向，当磁化轴平行于非幺正配对态的自旋轴时，在低偏压下磁交换作用能使隧谱与散粒噪声增强，而当磁化轴反平行于自旋转轴时，其结果相反。