Thermodynamic Comparison and the Ideal Glass Transition of Antiferromagnetic Ising Model on Multi-branched Husimi and Cubic Recursive Lattice with the Identical Coordination Number

Two types of recursive lattices with the identical coordination number but different unit cells (2-D square and 3-D cube) are constructed and the antiferromagnetic Ising model is solved exactly on them to study the stable and metastable states. A multi-branched structure of the 2-D plaquette model, which we introduced in this work, makes it possible to be an analog to the cubic lattice. Two solutions of each model can be found to exhibit the crystallization of liquid, and the ideal glass transition of supercooled liquid respectively. Based on the solutions, the thermodynamics on both lattices, e.g. the free energy, energy density, and entropy of the supercooled liquid, crystal, and liquid state of the model are calculated and compared with each other. Interactions between particles farther away than the nearest neighbor distance and multi-spins interactions are taken into consideration, and their effects on the thermal behavior are examined. The two lattices show comparable properties on the thermodynamics, which proves that both of them are practical to describe the regular 3-D case, especially to locate the ideal glass transition, while the 2-D multi-branched plaquette model is less accurate with the advantage of simpler formulation and less computation time consumption.     

二维卡门涡街的格子Boltzmann仿真

格子气自动机和格子Boltzmann方法的迅速发展提供了一类求解流体力学问题的新的方法。本文中，我们介绍了Boltzmann方法，解决了格子气方法中的缺点，通过选择适当平衡分布及其参数，导出了Navier－Stokers方程，并得到了声速和粘性系数。最后在微机上模拟了在无限长平板流动问题及绕单分离板的流动问题，得到了卡门涡街。结果表该模型有格子气方法及其它的数值方法所没有的优点，计算更精确、更直观、更有效。     

Phase diagram of Cu-Au-type alloys

We investigate the ordering phase diagram of an binary alloy on a face centered cubic lattice. In Ising spin language the nearest-neighbor interactions are antiferromagnetic with strengthJ, the next-nearest-neighbor interactions are ferromagnetic with strength J, and the external magnetic field ish. For > 0 and allh, the ground state is only finitely degenerate, so Pirogov-Sinai theory gives the exact form of the phase diagram in the limit of vanishing temperature. For=0 and vhv 12J the ground state is infinitely degenerate, and indeed the zero temperature entropy is nonvanishing at the four super-degenerate pointsh=± 47 or ±1Z7. We investigate the finite temperature behavior of the model using Monte Carlo simulations and (for=0) low temperature expansions. The most interesting portions of the phase diagram are those near the superdegenerate points. We rigorously map these points onto certain hard constraint lattice gases, but can draw no firm conclusions concerning the phase diagram in their vicinity.Supported in part by the National Science Foundation through Grant No. DMR81-14726. The simulations were carried out at the Center for Materials Science at Los Alamos National Laboratory.     

The number of smallest knots on the cubic lattice

It has been shown that the smallest knots on the cubic lattice are all trefoils of length 24. In this paper, we show that the number of such unrooted knots on the cubic lattice is 3496.     

Lattice Green's Function for the Body-Centered Cubic Lattice

An expression for the Green's function (GF) of Body-Centered Cubic (BCC) lattice is evaluated analytically and numerically for a single impurity lattice. The density of states (DOS), phase shift, and scattering cross section are expressed in terms of complete elliptic integrals of the first kind.     

Unified treatment for accurate and fast evaluation of the Fermi-Dirac functions

A new analytical approach to the computation of the Fermi-Dirac(FD) functions is presented,which was suggested by previous experience with various algorithms.Using the binomial expansion theorem,these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions.This simplification and the use of the memory of the computer for the calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation,should such limits be required in practice.Some numerical results are presented for significant mapping examples and they are briefly discussed.     

Constructing New Discrete Integrable Coupling System for Soliton Equation by Kronecker Product

It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of soliton equation hierarchy in this paper. A direct application to the fractional cubic Volterra lattice spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is also indicated that the study of discrete integrable couplings by using the Kronecker product is an efficient and straightforward method. This method can be used generally.     

On the evaluation of generalized exponential integral functions

This paper deals with generalized exponential integral (GEI) functions arising in the study of anisotropic scattering in a multidimensional media. These functions are represented as finite linear combinations of basic GEIs introduced in this work. The recurrence relations are derived for the linear combination coefficients and basic GEIs. Numerical results are also given. The extensive test calculations show that the work proposed in this algorithm is the most efficient practical computations of GEI functions.     

Analytical evaluation of the plasma dispersion function for a Fermi—Dirac distribution

An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed.The new method has been developed using the binomial expansion theorem and the Gamma functions.The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function.The resulting series present better convergence rates.Several acceleration techniques are combined to further improve the efficiency.The obtained results for the plasma dispersion function are in good agreement with the known numerical data.     

Analytical evaluation of Askerov functions arising from anisotropy of the thermoelectric power in superlattices

In this work, we propose an analytical approach which enables more accurate calculation of Askerov functions arising from components of the thermoelectric power in superlattices. Using the binomial expansion theorem, these functions are expressed through the binomial coefficients and familiar basic functions. This work is the first attempt in the literature to analytically evaluate Askerov functions. The convergence of the series is tested by concrete cases of parameters. The exact analytical and numerical solutions are compared with each other and good agreements are obtained.     

Multiple-Photon-Added and -Subtracted Two-Mode Binomial States:Nonclassicality and Entanglement *

We theoretically analyze the nonclassicality and entanglement of two new non-Gaussian entangled states generated by applying multiple-photon addition and subtraction to a two-mode binomial state. The nonclassical properties are investigated in terms of the partial negativity of the Wigner functions, whose results show that their nonclassicality can be enhanced via one-mode even-number photon operations and two-mode symmetrical operations for the initial two-mode binomial state. We also find that there exists some enhancement in the entanglement properties in certain parameter ranges via one-mode photon-addition and two-mode symmetrical operations.     

格点规范场的真空波函数和真空能量的无规相近似计算

采用无规相近似(RPA)耦合集团展开方法,计算出2?+1维SU(2?)格点规范场的三到六阶真空波函数和真空能量.在计算中,用空心图构成试探波函数,得到的三到六阶真空波函数的计算结果在弱耦合区1g²〉1.2都表现出良好的标度行为.与较早的计算结果比较,采用RPA方法计算的真空波函数比采用非RPA方法计算的结果的标度行为有大幅度的改善.采用RPA方法计算的真空能量比采用非RPA方法计算的真空能量略低,这表明此方法是成功的方法.     

Dispersion relation for two-dimensional simple cubic lattices

The linear wave equation for the simple cubic lattice is given in this paper. The dispersion relations of both longitudinal and transverse waves are given analytically for the acoustic mode and the optical mode, respectively.      

Excited Binomial States and Excited Negative Binomial States of the Radiation Field and Some of Their Statistical Properties

We introduce excited binomial states and excited negative binomial states of theradiation field by repeated application of the photon creation operator on binomialstates and negative binomial states. They reduce to Fock states and excitedcoherent states in certain limits and can be viewed as intermediate states betweenFock states and coherent states. We find that both the excited binomial statesand excited negative binomial states can be exactly normalized in terms ofhypergeometric functions. Base on this interesting characteristic, some of thestatistical properties are discussed.     

Quantum and classical binomial distributions for the charge transmitted through coherent conductor

We discuss controversial results for the statistics of charge transport through coherent conductors. Two distribution functions for the charge transmitted was obtained previously, one actually coincides with classical binomial distribution, the other is different, and we call it here quantum binomial distribution. We show that high-order charge correlators, determined by the either distribution functions, all can be measured in different setups. The high-order current correlators, starting with the third order, reveal (missed in previous studies) special oscillating frequency dependence on the scale of the inverted time flight from the obstacle to the measuring point. Depending on setup, the oscillating terms give substantially different contributions.     

Resistance Calculation for an Infinite Simple Cubic Lattice Application of Green's Function

It is shown that the resistance between the origin and any lattice point (l,m,n) in an infinite perfect Simple Cubic (SC) lattice is expressible rationally in terms of the known value of G ₀ (0,0,0). The resistance between arbitrary sites in an infinite SC lattice is also studied and calculated when one of the resistors is removed from the perfect lattice. The asymptotic behavior of the resistance for both the infinite perfect and perturbed SC lattice is also investigated. Finally, experimental results are obtained for a finite SC network consisting of 8×8×8 identical resistors, and a comparison with those obtained theoretically is presented.     

纳米晶体线的晶格动力学格林函数及晶格振动

通过求解差分方程,推导了纳米晶体线的晶格动力学格林函数,分析了其晶格振动,并推导了声子数表象中的原子位移及晶格振动哈密顿公式.研究结果表明,纳米晶体线的晶格振动能带分裂为一系列的子带,格波只能沿纳米晶体线的纵向传播,沿纳米晶体线的横截面只存在驻波.     

The Atiyah–Hitchin bracket and the open Toda lattice

The dynamics of the finite nonperiodic Toda lattice is an isospectral deformation of the finite three-diagonal Jacobi matrix. It is known since the work of Stieltjes that such matrices are in one-to-one correspondence with their Weyl functions. These are rational functions mapping the upper half-plane into itself. We consider representations of the Weyl functions as a quotient of two polynomials and exponential representation. We establish a connection between these representations and recently developed algebraic-geometrical approach to the inverse problem for Jacobi matrix. The space of rational functions has natural Poisson structure discovered by Atiyah and Hitchin. We show that an invariance of the AH structure under linear-fractional transformations leads to two systems of canonical coordinates and two families of commuting Hamiltonians. We establish a relation of one of these systems with Jacobi elliptic coordinates.     

导心轨道模拟中对磁场计算方法的改进

在导心轨道的计算中,用离散傅立叶变换对二维磁场信息沿角向进行变换,得到各阶谐波分量随极向磁通变化的拟合公式,用此生成磁场。数值模拟结果表明,该方法在精度上和传统的样条插值一致,可以在角向和极向上求任意阶导数,为磁岛和撕裂膜的计算提供了便利.     

Correspondence between generalized binomial field states and coherent atomic states

We show that the N-photon generalized binomial states of electromagnetic field may be put in a bijective mapping with the coherent atomic states of N two-level atoms. We exploit this correspondence to simply obtain both known and new properties of the N-photon generalized binomial states. In particular, an over-complete basis of these binomial states and an orthonormal basis are obtained. Finally, the squeezing properties of generalized binomial state are analyzed.