He原子和BH分子碰撞体系的转动激发能量转移

在碰撞体系He+BH的CCSD(T)二维势能面基础上,应用密耦方法,研究了 He+BH分子碰撞转动激发过程.计算了该体系的转动态-态激发的弹性和非弹性的微分和积分截面,分析了计算结果与势能面特征间的关系.结果表明: He原子以从H原子端共线形式碰撞BH分子对j=0→j'=2的激发最为有效;短程排斥对Δj=2的激发作用较大;态-态跃迁总截面出现振荡结构,长程部分分波只对j=0→j'=1的跃迁总截面有较大贡献,j'≥ 关键词： He+BH体系 转动激发 散射截面     

Interlaced Particle Systems and Tilings of the Aztec Diamond

Motivated by the problem of domino tilings of the Aztec diamond, a weighted particle system is defined on N lines, with line j containing j particles. The particles are restricted to lattice points from 0 to N, and particles on successive lines are subject to an interlacing constraint. It is shown that this particle system is exactly solvable, to the extent that not only can the partition function be computed exactly, but so too can the marginal distributions. These results in turn are used to give new derivations within the particle picture of a number of known fundamental properties of the tiling problem, for example that the number of distinct configurations is 2 ^N(N+1)/2, and that there is a limit to the GUE minor process, which we show at the level of the joint PDFs. It is shown too that the study of tilings of the half Aztec diamond—not known from earlier literature—also leads to an interlaced particle system, now with successive lines 2n−1 and 2n (n=1,…,N/2−1) having n particles. Its exact solution allows for an analysis of the half Aztec diamond tilings analogous to that given for the Aztec diamond tilings.     

Ne-HBr复合物CCSD(T)势能面对转动非弹性分波截面的影响

利用非线性最小二乘法拟合在CCSD(T)/aug-cc-pVQZ理论水平下计算的相互作用能，得到了基态Ne-HBr复合物势能面的解析表达式.在此基础上，采用量子密耦方法计算了入射能量分别为40，60，80 和100meV时，Ne原子与HBr分子碰撞的分波截面，详细讨论了CCSD(T)势能面的长程吸引和短程各向异性相互作用对非弹性分波截面的影响.结果表明：(1)总非弹性分波截面主要来自j=0 →j′=1, 2跃迁.高J端的尾部极大是势能面长程吸引阱的贡献，主要来自j=0 →j′=1跃迁；低J端的主极大是短程排斥的贡献，主要来自j=0 →j′=2跃迁；极小值是短程排斥和长程吸引作用相互抵消的结果.(2)尽管不同入射能量时非弹性分波截面的峰值和极小值对应的总角动量量子数J各不相同，但它们对应于几乎相同的碰撞参数，取样势能面的相同部分.     

第Ⅱ种强度不等的非对称两态叠加多模叠加态光场的偶数阶等阶N次方Y压缩

本文构造了由多模复共轭相干态的相反态|{-Z_j^(a)*}>_q与多模虚共轭相干态的相反态|{-iZ_j^(b)*}>_q这两者的线性叠加所组成的第Ⅱ种强度不等的非对称两态叠加多模叠加态光场|Ψ_Ⅱ^(ab)>_q,利用多模压缩态理论研究了态|Ψ_Ⅱ^(ab)>_q的任意偶数阶等阶N次方Y压缩特性.结果发现:1)在压缩阶数N取偶数,即N=2p的条件下,无论p=2m(m=1,2,3,…,…),还是p=2m+1(m=0,1,2,3,…,…),只要构成态|Ψ_Ⅱ^(ab)>_q的两个不同的量子光场态中各对应模的强度(即平均光子数)和初始相位都不相等,亦即R_j^(a)≠R_j^(b)和φ_j^(a)≠φ_j^(b)(j=1,2,3,…,q),并且 ,则当满足一定的量子化条件(或者在一些闭区间内连续取值)时,态|Ψ_Ⅱ^(ab)>_q总可呈现出周期性变化的、任意偶数阶的等阶N次方Y压缩效应.2)在N=2p且p=2m+1(m=0,1,2,3,…,…)的条件下,若R_j^(a)=R_j^(b)和φ_j^(a)=φ_j^(b)(j=1,2,3,…,q),态|Ψ_Ⅱ^(ab)>_q则可呈现出等阶N次方Y压缩简并现象.     

Semirigid vibrating rotor target calculation for reaction O(<Superscript>3</Superscript>P)+CH<Subscript>4</Subscript>→CH<Subscript>3</Subscript>+OH

The time-dependent quantum dynamics calculation for reaction O(³P)+CH₄ →CH₃+OH is made, using of the semirigid vibrating rotor target (SVRT) model and the time-dependent wave packet (TDWP) method. The corresponding reaction probabilities of different initial states are provided. From the calculation of initial rovibrational statej=0,v=0, 1, we can see that the excitation of the H-CH₃ stretching vibration gives significant enhancement of reaction probability and the reaction threshold decreases dramatically with the enhancement of the vibrating excitation, which indicates that the vibrating energy of reagent molecules contributes a lot to the molecular collision. As for the calculation of reaction probability of statev=0,j=0,1,2,3, the results show that the reaction probability rises significantly with the enhancement of rotational quantum numberj while the reaction threshold has no changes. The spatial steric effect of the title reaction is studied and analyzed too after the calculation of reaction probability of statesj=5,k=0–2,n=0 andj=5,k=2,n=0–2 is made.     

On the Determination of Spin-Parity of Elementary Particles Produced in Collisions of Polarized Particles

In this paper we adopt Peshkin's “maximum complexity method” for reactions 0 + 1/2 → j + s, γ + 0 → j + 0 with polarized initial particles. The produced particles undergo the decays s → 0 + 1/2, and j decays strongly into 0 + 0 + 0. Study of certain correlations in such processes allows to determine the spins of the produced particles. Because the spin of the X° (960) meson is not firmly established we apply the general results obtained to the reactions: K?p → X° Δ, πp → X°N^★, _γHe → X°He.     

Construction of positive exact (2+1)-dimensional shock wave solutions for two discrete Boltzmann models

It is proved that (2+1)-dimensional (spacex, y; timet) positive exact shock wave solutions of two discrete Boltzmann models exist. For each densityN _i, these solutions are linear combinations of three similarity shock waves,N _i =n _0i + _j n _ji /[1+d _j exp( _j y+y _j x+ _j t)],j=1,2,3. Two models with four independent densities are investigated: the square discrete-velocity Boltzmann model and the model with eight velocities oriented toward the eight corners of a cube.The positivity problem for the densities is nontrivial. Two classes of solutions are considered for which the two first similarity shock wave components depend on only one spatial dimension, _j=const· _j ,j=1,2. For the positivity, if ₁₂>0, it is sufficient to prove that the 16 asymptotic shock limitsn _0i ,n _0i +n _3i , _j=0 ² n _ji , _j=0 ³ n _ji are positive. The density solutions are built up with five arbitrary parameters and we prove that there exist subdomains of the arbitrary parameter space in which the 16 shock limits are positive. We study numerically two explicit shock wave solutions. We are interested in the movement of the shock front when the time is growing and in the possible appearance of bumps. In the space, at intermediate times, these bumps represent populations of particles which are larger than at initial time or at equilibrium time.     

Realizability of Point Processes

There are various situations in which it is natural to ask whether a given collection of k functions, ρ _j (r ₁,…,r _j ), j=1,…,k, defined on a set X, are the first k correlation functions of a point process on X. Here we describe some necessary and sufficient conditions on the ρ _j ’s for this to be true. Our primary examples are X=ℝ ^d , X=ℤ ^d , and X an arbitrary finite set. In particular, we extend a result by Ambartzumian and Sukiasian showing realizability at sufficiently small densities ρ ₁(r). Typically if any realizing process exists there will be many (even an uncountable number); in this case we prove, when X is a finite set, the existence of a realizing Gibbs measure with k body potentials which maximizes the entropy among all realizing measures. We also investigate in detail a simple example in which a uniform density ρ and translation invariant ρ ₂ are specified on ℤ; there is a gap between our best upper bound on possible values of ρ and the largest ρ for which realizability can be established.     

Dynamics in the Sherrington-Kirkpatrick model. I. The first step

We study properties of the random configuration {s _j (1)} _j=1 ^N produced by the first step of the parallel dynamics in the Sherrington-Kirkpatrick model. We show that the law of large numbers holds for the sequence of overlaps between the initial (nonrandom) configuration {s _j (0)} _j=1 ^N and {s _j (1)} _j=1 ^N , and obtain the distribution of the fluctuations around the limiting value. As a by-product we derive the average number of the fixed points {s _j (1)} _j=1 ^N with a given value of the magnetization .     

<Emphasis Type="Italic">SU</Emphasis>(2) invariants of symmetric qubit states

We express the density matrix for the N-qubit symmetric state or spin-j state (j = N/2) in terms of the well-known Fano statistical tensor parameters. Employing the multi-axial representation, where the spin-j density matrix is shown to be characterized by j(2j + 1) axes and 2j real scalars, we enumerate the number of invariants constructed out of these axes and scalars. We calculate these invariants explicitly in the particular case of the pure and mixed spin-1 state.     

He-Na2体系低温下的冷碰撞研究

在已经拟合好的He-Na₂体系势能面上,根据原子-双原子分子的非反应性碰撞动力学的相关基本理论,在空间固定坐标系下,采用严格的密耦方法求解了He原子和Na₂分子的转动非弹性碰撞动力学方程.并对He-Na₂体系的微分散射截面、积分截面作了详细的分析,结果与实验符合得比较好.结果表明：（1）弹性散射（Δj=0）截面远大于非弹性截面;（2）较小Δj的跃迁主要产生前向散射,随着Δj的增加,后向散射的几率增加 关键词： 2体系')" href="#">He-Na₂体系 密耦方法 微分散射截面 积分截面     

Bethe-Ansatz solution of the ground-state of theSU (2j+1) Kondo (Coqblin-Schrieffer) model: Magnetization,magnetoresistance and universality

The magnetization, the magnetoresistance and the populations of the spin components of the Coqblin-Schrieffer model forj5/2 are calculated from the Kondo limit of a mixed-valence model discussed previously. The results forj=1/2 andj=1 agree with those given in the literature. Forj3/2 only an approximate solution of the integral equations is given, which interpolates between the exact low and high-field results. The universality is discussed and the exact Wilson-numbers are obtained. The Kondo limit of the mixed-valent model is shown to be equivalent to the Coqblin-Schrieffer model by using the Bethe-ansatz equations.     

第Ⅱ种强度不等的两态叠加多模叠加态光场的等阶N次方H压缩1腔模总数与压缩阶数两者之积取偶数的情形

利用多模压缩态理论研究了第种强度不等的非对称两态叠加多模叠加态光场|Ψ_Ⅱ^(ab)〉q的等阶N次方H压缩特性.结果发现:1)当腔模总数q与压缩阶数N的乘积取偶数,亦即qN=2p时,无论p=2m(m=1,2,3,…,…),还是p=2m+1(m=0,1,2,3,…,…),只要各模的初始相位差(φ_j^(a)-φ_j^(b))、态间的初始相位差(θ_nq^(aR)-θ_nq^(bR))及光子干涉项的幅度 1R_j^(a)R_j^(b)等分别满足一定的条件,则态|Ψ_||^(ab)〉q的第一和第二正交分量总可分别呈现出周期性变化的等阶N次方H压缩效应.2)当qN=2p且p=2m+1(m=0,1,2,3,…,…)时,若构成态|Ψ_Ⅱ^(ab)〉q的两个不同的量子光场态中各对应模的强度(即平均光子数)和初始相位相等,亦即R_j^(a)=R_j^(b)和φ_j^(a)=φ_j^(b)(j=1,2,3,…,q),则态|Ψ_Ⅱ^(ab)〉q可呈现出“等阶N次方H压缩简并”现象.     

Non-Existence of Black Hole Solutions¶for a Spherically Symmetric, Static Einstein–Dirac–Maxwell System

We consider for j=?, … a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein–Dirac–Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner–Nordstr?m solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a “cloud” of spin-?-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon. Received: 2 November 1998 / Accepted: 23 February 1999     

The Mean-Field Limit for Solid Particles in a Navier-Stokes Flow

We propose a mathematical derivation of Brinkman’s force for a cloud of particles immersed in an incompressible viscous fluid. Specifically, we consider the Stokes or steady Navier-Stokes equations in a bounded domain Ω⊂ℝ³ for the velocity field u of an incompressible fluid with kinematic viscosity ν and density 1. Brinkman’s force consists of a source term 6π ν j where j is the current density of the particles, and of a friction term 6π ν ρ u where ρ is the number density of particles. These additional terms in the motion equation for the fluid are obtained from the Stokes or steady Navier-Stokes equations set in Ω minus the disjoint union of N balls of radius ε=1/N in the large N limit with no-slip boundary condition. The number density ρ and current density j are obtained from the limiting phase space empirical measure , where x _k is the center of the k-th ball and v _k its instantaneous velocity. This can be seen as a generalization of Allaire’s result in [Arch. Ration. Mech. Anal. 113:209–259, [1991]] who considered the case of periodically distributed x _k s with v _k =0, and our proof is based on slightly simpler though similar homogenization arguments. Similar equations are used for describing the fluid phase in various models for sprays.     

第Ⅱ种强度不等的两态叠加多模叠加态光场的等阶N次方H压缩——2腔模总数与压缩阶数两者之积取奇数的情形

构造了由多模复共轭相干态的相反态|{-Z_j^(a)*}〉q和多模虚共轭相干态的相反态|{-Z_j^(b)*}〉q的线性叠加所组成的第Ⅱ种强度不等的非对称两态叠加多模叠加态光场|Ψ(ab)Ⅱ〉q.利用多模压缩态理论,研究了态|Ψ(ab)Ⅱ〉q的等阶N次方H压缩特性.结果发现,在腔模总数与压缩阶数这两者之积取奇数,则当各对应模的初始相位、各对应模的初始相位差,态间的初始相位差、以及光子干涉项的幅度之和等分别满足一定的量子化条件时,态|Ψ(ab)Ⅱ〉q的第一及第二正交分量可分别呈现出周期性变化的等阶N次方H压缩效应.这与现有报道的结果截然不同.     

Evaluation of certain statistical sums

Summary Certain statistical ensembles,e.g. open chemical systems with randomly varying number of particles, are characterized by partition functions of the type ,n being a natural number anda _j ’s generalized temperatures. The state of the system is well defined if one knows the dependence ofa _j ’s on ensemble averages 〈n ^j 〉. For making the equations 〈n ^j 〉=〈n ^j 〉 (a ₁, ...,a _s) at least more accessible for numerical calculations a transformation of the partition function to a series of Fourier integrals is proposed. In the special case of the integrals can be calculated analytically transforming the statistical sum into a series of error functions.     

态|Ψ(3)〉q中广义电场分量的不等幂次Nj次方Y压缩

利用多模压缩态理论,研究了由多模复共轭虚相干态|{iZ_j^*}〉q、多模复共轭虚相干态的相反态|{-iZ_j^*}〉q和多模复共轭相干态|{Z_j^*}〉q的线性叠加所组成的新型三态叠加多模叠加态光场|Ψ⁽³⁾〉_q中广义电场分量的偶数次不等幂次Nj次方Y压缩特性.结果发现:在各模的压缩次数N_j=2pj且pj=2m′j+1(m′j=0,1,2,3,…,…)和Nj′=2pj′且pj′=2m′j′+1(m′j′=0,1,2,3,…,…)的条件下,当各模的初始相位φ_j与φ_j′、态间的初始相位差(θ₁-θ₃)与(θ₂-θ₃),以及各单模相干态光场总的平均光子数之和qj=1R2j等分别满足一定的取值条件时,态|Ψ⁽³⁾〉_q的广义电场分量(即第二正交相位分量)总可呈现出周期性变化的、偶数次的广义非线性不等幂次N_j次方Y压缩效应.     

Zeros of Airy Function and Relaxation Process

One-dimensional system of Brownian motions called Dyson’s model is the particle system with long-range repulsive forces acting between any pair of particles, where the strength of force is β/2 times the inverse of particle distance. When β=2, it is realized as the Brownian motions in one dimension conditioned never to collide with each other. For any initial configuration, it is proved that Dyson’s model with β=2 and N particles, $\mbox {\boldmath $\mbox {\boldmath , is determinantal in the sense that any multitime correlation function is given by a determinant with a continuous kernel. The Airy function (z){\rm Ai}(z) is an entire function with zeros all located on the negative part of the real axis ℝ. We consider Dyson’s model with β=2 starting from the first N zeros of Ai(z){\rm Ai}(z) , 0>a ₁>⋅⋅⋅>a _N , N≥2. In order to properly control the effect of such initial confinement of particles in the negative region of ℝ, we put the drift term to each Brownian motion, which increases in time as a parabolic function: Y _j (t)=X _j (t)+t ²/4+{d ₁+∑ _ℓ=1 ^N (1/a _ℓ )}t,1≤j≤N, where d₁=Ai￠(0)/Ai(0)d_{1}={\rm Ai}'(0)/{\rm Ai}(0) . We show that, as the N→∞ limit of $\mbox {\boldmath $\mbox {\boldmath , we obtain an infinite particle system, which is the relaxation process from the configuration, in which every zero of (z){\rm Ai}(z) on the negative ℝ is occupied by one particle, to the stationary state m_Ai\mu_{{\rm Ai}} . The stationary state m_Ai\mu_{{\rm Ai}} is the determinantal point process with the Airy kernel, which is spatially inhomogeneous on ℝ and in which the Tracy-Widom distribution describes the rightmost particle position.