Long-time limit behavior of the solution to an atom＇s master equation

We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/[1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.     

导出E=mc^2和m=m0/√1-v^2/c^2的一种方案

借助光子导出了E=mc^2和m=m0/√1-v^2/c^2。     

导出E=mc2和m=m0/1-v2√c2的一种方案

借助光子导出了E=mc2和m=(m0)/(1-v2/c2).     

Effective AC and DC Responses of Nonlinear Composites at Higher Concentration

For higher concentration of inclusions, an effective medium approximation （EMA） method is used to investigate the bulk effective response of weakly nonlinear composites, which are subject to the constitutive relation of electric displacement and electric field, Dα = εαE ＋Xα｜E｜^2 E. As an example of three dimensions, under the external AC and DC electric fields Eapp = Eα（1 ＋ sinωt）, we have derived the general effective nonh＇near response of composites by the EMA method for higher concentration of spherical inclusions. Furthermore, the effective nonlinear responses at harmonics are predicted.     

圆锥复数及其在物理学中的应用

圆锥复数是一种泛复数,由它可以非常方便地导出伽里略变化、洛伦兹变换和欧几里得变换,以及相应的速度变换规律,而这些规律分别是研究低速运动、高速运动和超光速运动的基础.下面简要地介绍圆锥复数的性质及其在物理学中的应用. 考虑某虚单位ω,它可用来定义泛复数 a=α+βω,(1)这里α,β均为实数.若ω分别取i,j,κ 且满足以下诸式 a=α+βi(i满足 i~2+1=0),(2) a=α+βj(j满足j~2-1=0),(3) a=α+βK(K满足K~2=0,(4)我们把(2),(3),(4)式的α分别称为椭圆数(简记为C)、双曲数(简记为H)和抛物数(简记为P),并统称为平面泛复数或圆锥复数. …     

导出E=mc~2和m=m_0/(1-v~2/c~2)~(1/2)的一种方案

借助光子导出了E=mc2和m=m01-v2/c2.     

Long-time limit behavior of the solution to an atom’s master equation

We study the long-time limit behavior of the solution to an atom’s master equation.For the first time we derive that the probability of the atom being in the α-th(α = j + 1-j z,j is the angular momentum quantum number,j z is the z-component of angular momentum) state is {(1- K/G)/[1-(K/G) 2j+1 ]}(K/G) α-1 as t → +∞,which coincides with the fact that when K/G > 1,the larger the α is,the larger the probability of the atom being in the α-th state(the lower excited state) is.We also consider the case for some possible generalizations of the atomic master equation.     

电场边值关系的演示

一、电分质分界面上电场的变化由于电场中电介质的极化,使得电介质界面处电场发生变化。电场在介质界面处的边值关系为 D_(1n)=D_(2n) E_(1t)=E_(2t) D_(1t)/ε_1=D_(2t)/ε_2 ε_1E_(1n)=ε_2E_(2n) (1) 很容易由(1)式及E=D/ε导出     

速度函数v(t)与时间变量t的定义域分析

1 问题的提出 质点运动学中,变加速直线运动条件下速度大小的求解是重要内容之一.由于速度在物体运动过程中是时间t的函数,求解时往往先通过求其运动方程x=x(t),再由运动方程x(t)对时间t求导,得出任一时刻的速度v(t).v=v(t)是时间t的函数,在t≥0的时域内v(t)有定义.但在某些特殊情况下,求得的速度v(t)会产生与实际物理现象不符的情况,给初学者造成误解.如一长为5 m的梯子,顶端斜靠在竖直的墙面上,设t=0时,顶端离地面4 m,当顶端以2 m/s的速度沿墙面匀速下滑时.求在t=3 s时,下端的速度[1].     

对运动电荷在匀强电场中的一点讨论

讨论一电荷沿x轴以初速υ垂直射入一匀强电场E0中(图一中的z方向).取电场E0为s’(x’,y’,z’t’)静止坐标系,观察者站在电荷q(s系)上看,s’系相对于s系以速度(-υ)运动,这时观察者将观测到原来的电场E0不再是E0.由电磁场的变换公式,在o’与o重合,即t=0时刻,在s系测得的电磁场为:式中　但在s’系看:把(2)式中的各分量代入(1)的变换式中变得s系中电磁场的分量这样站在s系看电行q的运动方程应是:但同时电场E0以速度-υ向左匀速运动,它的运动方程为 x=-υt. 于是电荷q相对于E0的等效运动方程是 解之得电荷的轨道方程:是一抛物线,轨道向x轴上…     

The calculation of the two-loop spin splitting functions $P_{ij}^{(1)}(x)$

We present the calculation of the two-loop spin splitting functions $P_{ij}^{(1)}(x)(i,j=q,g)$ contributing to the next-to-leading order corrected spin structure function g ₁ (x, Q²). These splitting functions, which are presented in the ${?erline {? MS}}$ scheme, are derived from the order $←pha_{s}^{2}$ contribution to the anomalous dimensions $αmma_{ij}^{m}(i,j=q,g)$. The latter correspond to the local operators which appear in the operator product expansion of two electromagnetic currents. Some of the properties of the anomalous dimensions will be discussed. In particular our findings are in agreement with the supersymmetric relation $αmma_{qq}^{m}+αmma_{gq}^{m}-αmma_{qg}^{m}-αmma_{gg}^{m}=0$ up to order $←pha_{s}^{2}$.     

Precise measurement of the top quark mass in the dilepton channel at D0

We measure the top quark mass (m(t)) in p ?p collisions at a center of mass energy √s = 1.96 TeV using dilepton t ?t→W(+)bW(-) ?b→?(+)ν(?)b?(-) ?ν(?) ?b events, where ? denotes an electron, a muon, or a tau that decays leptonically. The data correspond to an integrated luminosity of 5.4 fb(-1) collected with the D0 detector at the Fermilab Tevatron Collider. We obtain m(t)=174.0±1.8(stat)±2.4(syst) GeV, which is in agreement with the current world average m(t)=173.3±1.1 GeV. This is currently the most precise measurement of m(t) in the dilepton channel.     

Ableitung einer kontinuierlichen Mannigfaltigkeit von Erhaltungssätzen der modifizierten Korteweg-de-Vries-Gleichung nach dem Noetherschen Satz

Derivation of a Continuous Set of Conservation Laws for the Modified Korteweg-de Vries Equation by Noether's Theorem A method developed recently to derive a continuous set of conservation laws from extended Bäcklund transformations by means of Noether's theorem is applied to the modified Korteweg-de Vries (m. KdV) equation that describes Alfvén waves in a plasma. The corresponding conserved currents are equivalent to those found by WADATI , SANUKI and KONNO . It is shown that the extended Bäcklund transformation B?_α for the m. KdV equation, which coincides with that for the sine-Gordon equation, by MIURA'S transformation becomes the extended Bäcklund transformation β_x for the Korteweg-de Vries equation where x = 1/2α.     

Properties of Amplitude N th-power Squeezing of Even and Odd qs-Coherent States

ＰｒｏｐｅｒｔｉｅｓｏｆＡｍｐｌｉｔｕｄｅＮｔｈ┐ｐｏｗｅｒＳｑｕｅｅｚｉｎｇｏｆＥｖｅｎａｎｄＯｄｄｑｓ┐ＣｏｈｅｒｅｎｔＳｔａｔｅｓＷＡＮＧＪｉｓｕｏ１）ＳＵＮＣｈａｎｇｙｏｎｇ１）ＨＥＪｉｎｙｕ２）（１）ＤｅｐａｒｔｍｅｎｔｏｆＰｈｙｓｉｃｓ...     

全局耦合网络上的两种类集团的聚集-湮没反应动力学

利用Monte-Carlo模拟研究了全局耦合网络上扩散限制的不可逆聚集-湮没过程的动力学行为. 在系统中, 同种类集团相遇, 将发生聚集反应; 不同种类的集团相遇, 则发生部分湮没反应. 模拟结果表明:1) 当两种粒子初始浓度相等时, 系统长时间演化后, 集团浓度c(t)和粒子浓度g(t)呈现幂律形式, c(t)～t^{- α}和g(t)～t^-β, 其中幂指数α 和β 满足α=2β 的关系, 且α=2/(2 + q); 集团大小分布随时间的演化满足标度律, a_kt)=k^-τt^-ω\varPhi (k/t^z), 其中τ≈-1.27q, ω≈(3 + 1.27q)/(2 + q), z=α/2=1/(2 + q); 2) 当两种粒子初始浓度不相等时, 系统经长时间演化后, 初始浓度较小的种类完全湮没, 而初始浓度较大的那个种类的集团浓度c_A(t)仍具有幂律形式, c_A(t)～t^-α, 其中α=1/(1+q), 其集团大小分布随时间的演化也满足标度律, 标度指数为τ≈-1.27q, ω≈(2 + 1.27q)/(1 + q)和z=α=1/(1 + q). 模拟结果与已报道的理论分析结果相符得很好.     

红外杂化单光束谱的性质

同一样品不同厚度(b₁和b₂)的两单光束谱ø_b1和ø_b2经线性组合得到杂化单光束谱ø_α=αø_b1+(1-α)ø_b2=αø₀e-Kb₁+(1-α)ø₀e-Kb₂,α为杂化系数。通过改变杂化系数α,就可获得任意强度的杂化谱ø_α。系统研究了杂化光谱ø_α的性质。研究表明,只要控制合适的条件,则厚度为(b₂-αb₂+αb₁)的真实样品的单光束谱ø_b(b=b₂-αb₂+αb₁)与杂化谱ø_α高度相似,ø_α的失真程度可忽略不计。也就是说,厚度在b₁～b₂间任一厚度b的真实样品的单光束谱都可用杂化谱ø_α来表达,ø_α≈ø_b。因此,不需制备厚度为b的样品,通过改变杂化系数α就可获得研究者所希望强度的单光束谱ø_b。杂化谱方法有望在扣除背景干扰等方面得到广泛应用。     

Quantum-Statistics Behavior of the Exciton-Biexciton System In GaAs/AlAs Type-II Superlattices

We have investigated the quantum-statistics behavior of the exciton-biexciton system from the photoluminescence properties in (GaAs) m /(AlAs) m type-II superlattices with m = 12 and 13 monolayers, where the lowest-energy type-II exciton consists of the n = 1 X electron of AlAs and n = 1 o heavy hole of GaAs. The long exciton lifetime of the order of w s due to the indirect transition nature enables us to obtain precisely the density relation between the exciton and biexciton from the line-shape analysis of time-resolved photoluminescence spectra. In a relatively low exciton-density region, the biexciton density obeys a well-known square law. At an exciton density around 1 2 10 10 cm m 2 , the biexciton density suddenly increases with a threshold-like nature. This behavior, which is realized at a bath temperature up to 8 K under an excitation power of the order of 100 mW/cm 2 , results from the characteristics of Bose-Einstein statistics of the exciton-biexciton system.     

第一性原理对Al_mSi_n(m=1,2;n=1～6)团簇结构与性质的研究

本文运用第一性原理对Al_mSi_n（m=1,2;n=1～6）团簇的结构与性质进行了研究.在BLYP的水平上进行了结构优化和频率分析,得到了团簇的最低能量结构.同时计算和讨论了A1_msi_n团簇的束缚能、总能的二阶能量差分和分裂能以及费米能随原子数的变化.研究结果表明:Al_mSi_n团簇在m+n<4时的几何结构是平面结构,从4个原子开始转为空间的立体结构;除AlSi₃和Al₂Si₂团簇外,Al_mSi_n（m=1,2;n=1～6）团簇的束缚能随原子数增加而减小;分析A1_mSi_n（m=1,2;n=1～6）团簇的二阶能量差分和分裂能发现:在m+n=3,5时,团簇都出现较稳定的结构.     

Electrical Conductivity of Nonideal Quasi-Metallic Plasmas

Electrical conductivity formulas are derived from first principles for fully ionized nonideal plasmas. The theory is applicable to an electron-ion system with a 1) Maxwell electron distribution with an arbitrary interaction parameter ? = Ze2n1/3/KT (ratio of the mean coulomb interaction and thermal energies) and 2) Fermi electron distribution with an interaction parameter ? = Ze2n1/3h?2m-1 n2/3 (ratio of the coulomb interaction and Fermi energies). The momentum relaxation time of the electrons in the plasma is calculated based on plane electron wave functions interacting with the continuum oscillations (plasma waves) through a shielded coulomb potential Us(r) = esee exp (-r/?s)/r, which takes into account both electron-ion interactions (s = i) and electron-electron interactions (s = e). It is shown that the resulting conductivity formulas are applicable to higher densities, for which the ideal plasma conductivity theory breaks down because the Debye radius loses its physical meaning as a shielding length and upper impact parameter. The conductivity obtained for classical plasma is of the form ?c = ?c*(KT)3/2/m1/2e2 and agrees with the ideal plasma conductivity formula with respect to the temperature and density dependence for ?/Z ? 0, but its magnitude is significantly reduced as ?/Z increases. For quantum plasmas, the conductivity obtained is of the form ?Q = ?Q*h3n/m2Ze2, which shows that the degenerate plasma behaves like a low-temperature metal.     

Alpha decay of neutron-deficient rhenium and osmium isotopes

Neutron-deficient osmium and rhenium isotopes were produced by bombarding an enriched¹⁴⁴Sm target with beams of²⁷Al and²⁸Si. Previously reported decay data concerning^168,169,170Os were confirmed. Three newα groups, observed in the¹⁴⁴Sm+²⁷Al reaction, were assigned to the decay of^166,167,168Re based on excitation functions,α-energy systematics and theoretical half-life predictions. Their decay properties are: $$\begin{gathered} {}^{166}\operatorname{Re} , E_\alpha = 5,372 (10) keV, T_{1/2} = 2.8 (3) s; \hfill \\ {}^{167}\operatorname{Re} , E_\alpha = 5,136 (8) keV, T_{1/2} = 6.1 (2) s and \hfill \\ {}^{168}\operatorname{Re} , E_\alpha = 4,894 (10) keV, T_{1/2} = 6.9 (8) s. \hfill \\ \end{gathered}$$ It is proposed that twoα groups, observed in the¹⁴⁴Sm+²⁸Si reaction, originate from isomeric states in^168,169Re. Our measured data for the isomeric states are: $$\begin{gathered} {}^{168m}\operatorname{Re} , E_\alpha = 5,250 (10) keV, T_{1/2} = 6.6 (15) s and \hfill \\ {}^{169m}\operatorname{Re} , E_\alpha = 5,050 (10) keV, T_{1/2} = 12.9 (11) s. \hfill \\ \end{gathered} $$