单一多体不可逆聚集方程的解

本文研究的是单一多体不可逆聚集方程的解,从广义Smoluchovski方程出发,分别讨论凝结核为K(i₁,i₂,…,i_n)=const和凝结核为K(i₁,i₂,…,i_n)=sumfrom i=1 to n(i_l)的精确解,求出集团的体积分布C_m(t)。并且还讨论它们的长时行为。 关键词：     

在源作用下的n体不可逆聚集过程集团尺寸分布

把在源作用下两体作用的Smoluchovski方程推广到n体相互作用的广义Smoluchovski方程,讨论了系统在源作用下,核为K(i₁,i₂,…,i_n)＝(i₁·i₂…i_n)ω(0≤ω≤1),源项为I(t)＝Iδ_m,1的非凝胶系统广义Smoluchovski方程的定态解,得到了不可逆聚集过程的集团尺寸分布．同时,讨论了凝胶系统的广义Smoluchovski方程发生胶凝相变在相变点附近集团尺寸分布的渐进行为. 关键词：     

热阴极电离真空计的线性理论

从繁流放电理论可直接导出热阴极电离真空计的特性方程,证明通常的概念即在热计的电子流i_e一定时其离子流i₊与压强P成正比的关系,只在离子流甚小于电子流时才能成立。在被测气体的压强较高时,离子流和压强之间呈现下列指数关系: i₊/i_e=1-e^{(-(K₁P-K₂P2))}(K₁及K₂为常数),且随着压强的增长而逐步趋于饱和。进一步的推导则得出,当容许测量误差为1％时,热计的线性上限(临界压强)为P_c=0.22/Г,此处Г为热计的灵敏度。这种理论可以容易地解释近年来一些实验工作者例如Nottingham,Schultz,Goto,Hinzpeter等的实验结果。此外我们还使用了特殊设计的“封闭式”电离计作实验,得到的结果和理论预计十分符合。这种电离计本身则可用作10^-7～0.6托的宽程量具。 关键词：     

电子的原子散射因子解析表达式的拟合

本文用阻尼最小二乘法将国际X射线结晶学手册中全部中性原子的电子散射因子数据,从(sinθ)/λ等于0.0到2.0的范围内,拟合成包含九个参数的解析式 f(s)=sumfrom i=1to4 (a_ie^{-b_is2))+c.用相对偏离因子R=sumfrom k=1toN (f_ok+f_ok)/sumfrom k=1toN (f_ok)作为估计原子散射因子计算值与观测值之间相对偏离程度的判据。计算结果表明,各种原子散射因子的相对偏离因子R约为10-3。文中除列出参数表外,还给出了相对偏离因子、最大误差、平均误差、均方差以及偏差方和。 关键词：}     

新系列超导相TlBaCan-1CunO2n+2.5(n=2,3)的晶体结构和超导电性

本文用粉末烧结法合成了Tl-Ba-Ca-Cu-O体系TlBa₂Ca_n-1Cu_nO_2n+2.5新系列超导相,用粉末衍射法测定了n=2和3的晶体结构,属简单四方单胞,空间群为D_4h¹-P4/mmm,点阵常数a相同,而c值不同,随n值而增大。a=3.847?,c分别为12.73?和15.89?,每单胞含一个化合式单位,阳离子沿四方晶系的(0,0,z)和(1/2,1/2,z)位置交替排列,排列的顺序相同,n=3比n=2依次多增加Ca和Cu及相应的氧离子。TlBa₂Ca_nCu_nO_2n+2.5,n=3时,零电阻超导转变温度T_c(0)=112K;n=2时,T_c(0)=101K,与Tl₂Ba₂Ca_n-1Cu_nO_2n+4型体心四方晶胞超导相不同,TlBa₂Ca_n-1Ca_nO_2n+2.5结构中缺氧类钙钛矿型结构单元[Ba₂Ca_n-1Cu_nO_2n+1]仅被TI-O单层所隔开,当n相同时,Tl-O双隔层的体心四方单胞比Tl-O单层的简单四方单胞的超导转变温度高10K左右,这说明Tl-Ba-Ca-Cu-O体系中超导相的转变温度不仅与类钙钛矿结构单元的[CuO₄]和[CuO₅]的数目有关,而且与Tl-O的隔层数目有关。 关键词：     

正偏离Bragg定律的二元化合物靶中离子射程参数研究

研究了正偏离Bragg定律,即计算S_e(E)值高于实测S_e(E)的二元系化合物靶的离子射程特性。文中应用“regular”观点引入了“双原子模型”,在二元化合物靶的射程计算中,不仅考虑相同“原子对”对离子的阻止本领S₁₁(E),S₂₂(E),而且考虑不同“原子对”对离子的阻止本领S₁₂(E),S₂₁(E)。文中还应用Berthelot关系,使S₁₂(E)=S₂₁(E)=(S₁₁(E)·S₂₂(E))^1/2,则二元系靶的阻止本领及总的射程为NS(E)=1/2[(N₁S₁₁(E))^1/2+(N₂S₂₂(E)^1/2)]², R=4/a[x-A₁(arctg(2x+f)/△^1/2-arctg(f/△^1/2))-B₁(ln(x+g)²/g²·e/(x²+fx+e)) -b/2 ln(x²+fx+e/e)。这里X=E^1/2,E为离子注入能量,所有其它常数是与离子和靶的质量、原子序数有关的常数。结合文献[1]提出的R与R_p,R_p与△R_p的关系式,可计算得正偏离系统的投影射程R_p及其偏差量△R_p。并对各关系式的物理意义作了阐明。 关键词：     

一维准周期体系中的电子延展态

本文采用动力学映象方法,研究了作为泛Fibonacci序列一个子集的一系列一维准周期体系的电子性质,该一维准周期体系S_∞由递推公式S_l+1=S_l^2j-1S_l-1²ⁱ构造,其中l≥1,i,j为正整数,初始条件为S₀和S₁,结果表明,该一维准周期体系无论是对角模型和非对角模型,都存在电子延展态。 关键词：     

KdVB方程行波解的渐近分析

本文利用奇异摄动的理论和方法,研究v²?4μ时KdVB方程的行波解,得到行波解的三阶渐近展开式的显式,同时得到行波解的一般渐近展开式的表达式:u≈u⁽⁰⁾+εu⁽¹⁾+ε¹u⁽²⁾+…+εⁿu⁽ⁿ⁾+…;并且证明u^(j)(j=1,2,…,n,…)都是有界函数。 关键词：     

Co2+-Ti4+和Cu2+-Nb5+离子取代BaFe12O19单晶体中Fe3+离子的研究

本文对用Co²⁺-Ti⁴⁺和Cu²⁺-Nb⁵⁺离子取代BaFe₁₂O₁₉单晶体中Fe³⁺离子进行了研究,以Bi₂O₃作为助熔剂生长出了BaFe_12-2xCo_x²⁺Ti_x⁴⁺O₁₉(x=0;0.04;0.09;0.13;0.27和0.68)以及BaFe_12-x[Nb_1/3⁵⁺Cu_2/3²⁺]_xO₁₉(x=0;0.28;0.44和0.60)这两系列的单晶体,测定了100—300K温度范围内样品的磁化强度σ与单轴各向异性常数K₁,我们发现,对Co²⁺-Ti⁴⁺取代的样品,当x≤0.09时,其σ与K₁随x的增加而缓慢增加;当x>0.09时,其σ与K₁随x的增加而迅速降低,至x=1.1时,K₁变为零,对Nb⁵⁺-Cu²⁺取代的样品,其σ值在整个成份范围内基本保持不变,且有缓慢增加趋势;而K₁值则随x增加而单调下降,提出了取代离子在M型六角铁氧体中可能的分布模型来解释我们的结果。 关键词：     

Rydberg原子nS1/2→(n+1)S1/2双光子激发EIT-AT光谱

主要研究了热原子蒸气池中铯Rydberg原子nS_1/2→(n+1)S_1/2微波耦合的双光子光谱.铯原子基态(6S_1/2)、第一激发态(6P_3/2)、Rydberg态(69S_1/2)形成阶梯型三能级系统,弱探测光作用于基态到激发态6S_1/2→6P_3/2的跃迁,强耦合光则作用于6P_3/2→69S_1/2的Rydberg跃迁形成电磁感应透明(EIT)效应,实现对Rydberg原子的光学探测.频率fMW=11.735 GHz的微波场耦合69S_1/2→70S_1/2的Rydberg跃迁,形成微波双光子光谱.利用EIT-AT分裂光谱研究微波电场强度对双光子光谱的影响.研究表明:在强微波场作用时,EIT-AT分裂与微波场功率成正比,而弱微波场时的EIT-AT分裂与微波场功率成非线性依赖关系,理论计算与实验测量结果相一致.本文的研究对微波电场的精密测量具有一定的指导意义.     

Mass distribution in n—polymer stochastic aggregation and large—mass behaviour

The exact solutions of the rate equations of the n-polymer stochastic aggregation involving two types of clusters, active and passive for the kernel \dprⁿ_k=1s_(ik)(s_(ik)=i_k) and \dsumⁿ_k=1s_(ik)(s_(ik)=i_k), are obtained. The large-mass behaviours of the final mass distribution of the active and passive clusters have scaling-like forms, although the models exhibit different properties. Respectively, they have different decay exponents γ=\dfrac{2n+1}{2(n-1)} and γ=q+\dfrac{2n+1}{2(n-1)} for \dprⁿ_{k=1}s(ik)(s(ik)=ik) and γ=\dfrac 3{2(n-1)} and γ=q+\dfrac 3{2(n-1)} for \dsumⁿk=1}s(ik)(s(ik)=ik), which include exponents of two-polymer stochastic aggregation. We also find that gelation is suppressed for kernel \dprⁿk=1s(ik)(s(ik)=ik) which is different from the deterministic aggregation.}     

Johnson's SB distribution function as applied in the mathematical representation of particle size distributions. Part 1: Theoretical background and numerical simulation

An investigation was carried out of the transformation between the number, length, surface and volume size distributions expressed by Johnson's S_B distribution function – the bounded log-normal distribution function. As is well known, if any of the number, length, surface and volume distributions is log-normal, all the others will also be log-normal. Theoretical analysis suggests that the S_B function may have a similar property. This was confirmed by a computer-aided numerical simulation, in which emphasis was given to the transformation between successive order size distributions, i.e. ?_i(x) → ?_{i + 1}(x) or ?_i(x) → ?_{i ? 1}(x). The numerical results can be applied to the particle size distribution transformation because this transformation can generally be made step by step, for example, ?_i → ?_i?1 (x) → ?_{i ? 2}(x) → … → ?_j(x) for ?_i(x) → ?_j(x) ( i > j).     

Degree Complexity of Birational Maps Related to Matrix Inversion

For a q × q matrix x = (x _{i, j} ) we let ${J(x)=(x_{i,j}^{-1})}For a q × q matrix x = (x _{i, j} ) we let J(x)=(x_i,j^-1){J(x)=(x_{i,j}^{-1})} be the Hadamard inverse, which takes the reciprocal of the elements of x. We let I(x)=(x_i,j)^-1{I(x)=(x_{i,j})^{-1}} denote the matrix inverse, and we define K=I°J{K=I\circ J} to be the birational map obtained from the composition of these two involutions. We consider the iterates Kⁿ=K°?°K{K^n=K\circ\cdots\circ K} and determine the degree complexity of K, which is the exponential rate of degree growth d(K)=lim_n?￥( deg(Kⁿ) )^1/n{\delta(K)=\lim_{n\to\infty}\left( deg(K^n) \right)^{1/n}} of the degrees of the iterates. Earlier studies of this map were restricted to cyclic matrices, in which case K may be represented by a simpler map. Here we show that for general matrices the value of δ(K) is equal to the value conjectured by Anglès d’Auriac, Maillard and Viallet.     

Eine scheinbare Abschwächung der Lokalitätsbedingung. II

If for a relativistic field theory the expectation values of the commutator (Ω|[A (x),A(y)]|Ω) vanish in space-like direction like exp {? const|(x-y ²|^α/2#x007D; with α>1 for sufficiently many vectors Ω, it follows thatA(x) is a local field. Or more precisely: For a hermitean, scalar, tempered fieldA(x) the locality axiom can be replaced by the following conditions 1. For any natural numbern there exist a) a configurationX(n): $$X_1 ,...,X_{n - 1} X_1^i = \cdot \cdot \cdot = X_{n - 1}^i = 0i = 0,3$$ with \(\left[ {\sum\limits_{i = 1}^{n - 2} {\lambda _i } (X_i^1 - X_{i + 1}^1 )} \right]^2 + \left[ {\sum\limits_{i = 1}^{n - 2} {\lambda _i } (X_i^2 - X_{i + 1}^2 )} \right]^2 > 0\) for all λ _i ≧0i=1,...,n?2, \(\sum\limits_{i = 1}^{n - 2} {\lambda _i > 0} \) , b) neighbourhoods of theX _i 's:U _i (X _i )?R ⁴ i=1,...,n?1 (in the euclidean topology ofR ⁴) and c) a real number α>1 such that for all points (x):x ₁, ...,x _n?1:x _i ∈U _i (X _r ) there are positive constantsC ⁽ⁿ⁾{(x)},h ⁽ⁿ⁾{(x)} with: $$\left| {\left\langle {\left[ {A(x_1 )...A(x_{n - 1} ),A(x_n )} \right]} \right\rangle } \right|< C^{(n)} \left\{ {(x)} \right\}\exp \left\{ { - h^{(n)} \left\{ {(x)} \right\}r^\alpha } \right\}forx_n = \left( {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \\ r \\ \end{array} } \right),r > 1.$$ 2. For any natural numbern there exist a) a configurationY(n): $$Y_2 ,Y_3 ,...,Y_n Y_3^i = \cdot \cdot \cdot = Y_n^i = 0i = 0,3$$ with \(\left[ {\sum\limits_{i = 3}^{n - 1} {\mu _i (Y_i^1 - Y_{i{\text{ + 1}}}^{\text{1}} } )} \right]^2 + \left[ {\sum\limits_{i = 3}^{n - 1} {\mu _i (Y_i^2 - Y_{i{\text{ + 1}}}^{\text{2}} } )} \right]^2 > 0\) for all μ _i ≧0,i=3, ...,n?1, \(\sum\limits_{i = 3}^{n - 1} {\mu _i > 0} \) , b) neighbourhoods of theY _i 's:V _i(Y _i )?R ⁴ i=2, ...,n (in the euclidean topology ofR ⁴) and c) a real number β>1 such that for all points (y):y ₂, ...,y _n y _i ∈V _i (Y _i there are positive constantsC _(n){(y)},h _(n){(y)} and a real number γ_(n){(y)∈a closed subset ofR?{0}?{1} with: γ_(n){(y)}\y ₂,y ₃, ...,y _n totally space-like in the order 2, 3, ...,n and $$\left| {\left\langle {\left[ {A(x_1 ),A(x_2 )} \right]A(y_3 )...A(y_n )} \right\rangle } \right|< C_{(n)} \left\{ {(y)} \right\}\exp \left\{ { - h_{(n)} \left\{ {(y)} \right\}r^\beta } \right\}$$ for \(x_1 = \gamma _{(n)} \left\{ {(y)} \right\}r\left( {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \\ 1 \\ \end{array} } \right),x_2 = y_2 - [1 - \gamma _{(n)} \{ (y)\} ]r\left( {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \\ 1 \\ \end{array} } \right)\) and for sufficiently large values ofr.     

The N-mode squeezed state with enhanced squeezing

It is known that exp [iλ (Q1P1i/2)] is a unitary single-mode squeezing operator,where Q1,P1 are the coordinate and momentum operators,respectively.In this paper we employ Dirac’s coordinate representation to prove that the exponential operator S n ≡ exp [iλ sum((QiPi+1+Qi+1Pi))) from i=1 to n ],(Qn+1=Q1,Pn+1=P1),is an n-mode squeezing operator which enhances the standard squeezing.By virtue of the technique of integration within an ordered product of operators we derive S n ’s normally ordered expansion and obtain new n-mode squeezed vacuum states,its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.     

Reliability of the data on the cross sections of the partial photoneutron reaction for <Superscript>63,65</Superscript>Cu and <Superscript>80</Superscript>Se nuclei

The cross sections of partial photoneutron reactions are evaluated for the ^63,65Cu and ⁸⁰Se isotopes. The cross sections are free of systematic uncertainties from shortcomings of the experimental methods for neutron multiplicity sorting based on measurements of neutron energy used in experiments with quasimonoenergetic annihilation photon beams. An experimental-theoretical method is used to evaluate cross sections σ^eval(γ, in)= F_i^theor σ^exp(γ, xn), where ratios F_i^theor = σ^theor(γ, in)/σ^theor(γ, xn) = σ^theor(γ, in)/σ^theor[(γ, 1n) + 2(γ, 2n) + …] are calculated using a combined model of photonuclear reactions, and σ^exp(γ, xn) is the experimental cross section of the neutron yield reaction free from neutron multiplicity sorting problems. The cross sections are evaluated for reactions (γ, 1n) and (γ, 2n) for the ^63,65Cu and ⁸⁰Se isotopes, and for the total photoneutron reaction σ(γ, Sn) = σ[(γ, 1n) + (γ, 2n) + …]. It is shown that noticeable deviations of the experimental cross sections from the evaluated values result from the unreliable sorting of neutrons between the channels with multiplicities 1 and 2.     

On observability of N-level quantum systems

The purpose of this paper is to discuss necessary and sufficient conditions for observability of N-level quantum systems. We assume that the information about a physical system is given by the mean values Tr(?(t_j)A_i) = m_Ai(t_j), of n self-adjointoperators A₁,…,A_n on $\text{H}$ at some instants t₁ < t₂ <…<t_s. The question of theminimal number n of operators A₁,…,A_n (physical quantities $\text{A}{}_1\text{, …,}\text{A}{}_{\mathrm{n}}$) for which the quantum system $\text{S}$ is (A₁,…,A_n)-observableis discussed.     

Real space renormalization group approach to the two-dimensional antiferromagnetic Heisenberg model (I) – The singlet triplet gap

The low energy behaviour of the two-dimensional antiferromagnetic Heisenberg model is studied in the sector with total spins S = 0,1,2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix Δ_S ⁽ⁿ⁺¹⁾ of 4 neighbouring “n clusters” of size 2ⁿ × 2ⁿ, n = 1,2,3,... from the corresponding quantities Δ_S ⁽ⁿ⁾. Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies E_S ⁽ⁿ⁺¹⁾, S = 0,1,2 approach each other for increasing n, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions 〈S’,m’;n+1|S_q ^*|S,m;n+1〉 between the ground states |S,m;n+1〉 (m = -S,...,S) on an (n+1)-cluster of size 2ⁿ⁺¹ × 2ⁿ⁺¹, mediated by the staggered spin operator S_q ^*.