Asymptotic Energy Expansion for Rational Power Polynomial Potentials

Asymptotic energy expansion method is extended for polynomial potentials having rational powers. New types of recurrence relations are derived for the potentials of the form V(x)=x^2n/m+b₁x^n1/m1+b₂x^n2/m2 +··· + b_Nx^n_N/m_N where n,m,n₁,m₁,...,n_N,m_N are positive integers while coefficients b_k∈ C. As in the case of even degree polynomial potentials with integer powers, all the integrals in the expansion can be evaluated analytically in terms of Γ functions. With the help of two examples, we demonstrate the usefulness of these expansions in getting analytic insight into the quantum systems having rational power polynomial potentials.     

On Diagonal P-Representation of Superposition Field of Two Light Modes

For the superposition field a₁^†+a₂^† of two light modes we introduce an appropriate diagonal P-representation which is constructed on the common eigenvectors |z,x〉of (X₁-X₂) and a₁+a₂, where X_i=(a_i+ a_i^†)/√(2), [a_i,a_i^†] =δ_ij. It is remarkable that |z,x〉make up a new quantum mechanical representation.     

Rational Solutions for the Fokas System

Fokas system is the simplest (2+1)-dimensional extension of the nonlinear Schrödinger equation (Eq. (2), Inverse Problems 10 (1994) L19-L22). By using the bilinear transformation method, general rational solutions for the Fokas system are given explicitly in terms of two order-N determinants τn (n = 0, 1) whose elements m_i,j⁽ⁿ⁾ (n = 0, 1; 1 ≤ i, j ≤ N) are involved with order-n_i and order-n_j derivatives. When N = 1, three kinds of rational solution, i.e., fundamental lump and fundamental rogue wave (RW) with n₁ = 1, and higher-order rational solution with n₁ ≥ 2, are illustrated by explicit formulas from τn (n = 0, 1) and pictures. The fundamental RW is a line RW possessing a line profile on (x, y)-plane, which arises from a constant background with at t << 0 and then disappears into the constant background gradually at t >> 0. The fundamental lump is a traveling wave, which can preserve its profile during the propagation on (x, y)-plane. When N ≥ 2 and n₁ = n₂ = ··· = n_N = 1, several specific multi-rational solutions are given graphically.     

水溶液中稀土离子与甘氨酸、丝氨酸、天冬氨酸作用的13C NMR研究

测定了酸性水溶液中甘氨酸、丝氨酸和天冬氨酸稀土络合物(Ln=La、Pr、Nd、Eu、Tb、Dy、Ho、Er、Tm和Yb)的¹³C诱导位移。对位移试剂的分析指出,三种氨基酸通过α-羧基以双齿形式配位于稀土,配位键长为0.23nm~0.25nm,天冬氨酸的γ-羧基也是配位基团。由本文与文献中已报道的各种氨基酸稀土络合物的¹³C诱导位移的系统分析表明,配体¹³C超精细偶合常数A值和结构因子G值有如下规律:(1)│A(C₀)│<│A(C_α)│;A(C₀)为正,A(C_α)为负;(2)│G(C₀)│>│G(C_α)│;配体碳核的G均为负值。     

General Solution and Localized COherent Soliton Structures of the （2＋1）—Dimensional Generalized Davey—Stewarson Equations

In this paper,the variable separation approach is used to obtain localized coherent structures of the (2 1)-dimensional generalized Davey-Stewarson equations:iqt 1/2(qxx=qyy) (R S)q=0,Rx=-σ/2|q|y^2,Sy=-σ/2|q|2/x.Applying a special Baecklund transformation and introducing arbitrary functions of the seed solutions.and abundance of the localized structures of this model is derived,By selceting the arbitrary functions appropriately,some special types of localized excitations such as dromions,dromion lattice,breathers,and instantons are constructed.     

Mn掺杂后三元黄铜矿结构半导体CuInTe2的缺陷特征与热电性能

三元黄铜矿结构(也称类金刚石结构)半导体是一类具有热电转换潜力的新型热电材料. 本次工作中采用电负性更小的Mn元素替换CuInTe₂黄铜矿结构半导体中的Cu元素, 设计制备贫Cu化合物Cu_1-xInMn_xTe₂. 研究表明, 当Mn含量较低时, Mn优先占位在In 位置产生受主缺陷Mn_In^-. 因此随着Mn含量的增大, 载流子浓度和电导率均得到改善. 但当Mn含量进一步增大后, Mn可同时占位在In位置和Cu位置, 除产生受主缺陷Mn_In^-外, 还能产生施主缺陷Mn_Cu⁺. 由于两类极性相反的缺陷之间的湮灭现象, 使得缺陷浓度及载流子浓度开始降低, 晶格结构畸变有变小趋势, 因此在高温下晶格热导率仅略有提高. 研究结果表明, 在某一特定的Mn含量(x=0.05)时, 材料具有最优的热电性能(ZT=0.84@810.0 K), 这一性能约是未掺杂CuInTe₂的2倍.     

Universal Associated Legendre Polynomials and Some Useful Definite Integrals

We first introduce the universal associated Legendre polynomials, which are occurred in studying the non-central fields such as the single ring-shaped potential and then present definite integrals I_A^±(a, τ)=∫_-1⁺¹x^a[P_l'^m'(x)]²/(1±x)^τdx, a=0, 1, 2, 3, 4, 5, 6, τ=1, 2, 3, I_B(b, σ)=∫_-1⁺¹x^b[P_l'^m'(x)]²/(1- x²)^σdx, b=0, 2, 4, 6, 8, σ=1, 2, 3, and I_C^±(c, κ)=∫_-1⁺¹x^c[P_l'^m'(x)]²/[(1-x²)^κ(1±x)]dx, c=0, 1, 2, 3, 4, 5, 6, 7, 8, κ=1, 2. The superindices “±” in I_A^±(a, τ) and I_C^±(c, κ) correspond to those of the factor (1±x) involved in weight functions. The formulas obtained in this work and also those for integer quantum numbers l' and m' are very useful and unavailable in classic handbooks.     

Ω＋Ω→（ΩΩ）Jπ=0＋＋X Cross section Calculation

The cross sections of Ω+Ω→(ΩΩ)_J^π=0⁺+X are studied by using an effective Hamiltonian method. The results are σ_{Ω+Ω→(ΩΩ)0⁺+γ}=0.03～0.16×10^-29 cm² for p_Ω=100～400 MeV, and the cross sections of η production are about 10^-28 cm² for p_Ω > 880 MeV.     

Features of the electrochemical lithium insertion into monophosphate tungsten bronzes (PO2)4(WO3)2m (m=9 and 10)

Electrochemical lithium insertion into (PO₂)₄(WO₃)_2m, where m=9 and 10, has allowed the determination of several phases Li_x(PO₂)₄(WO₃)_2m between 3.4 and 0.01 V vs Li⁺/Li⁰. After the first cycle the electrochemical system was unable to maintain the high specific capacity of the cells (540 Ah/kg) due to irreversible processes. Nevertheless at high voltage values, above 1.4 V vs Li⁺/Li⁰, the lithium insertion proceeded through a reversible mechanism. By means of X-ray diffraction experiments we have detected the nature of different phases Li_x(PO₂)₄(WO₃)_2m formed and we have established a correlation with the reversible/irreversible processes detected during the electrochemical insertion.     

Study on υμ, υγ, Decays and CP Non-Invariance at Early Epoch of the Universe

We study the υ_μ and υ_γ decays in the early epoch of the universe. If m_υγ > 2m_e, there would be a CP asymmetry between υ_γ→e⁺+e^-+υ_e and υ_γ→e⁺+ e^-+ υ_e. The resultant CP non-invariance is a function of temperature and density and can reach l0^-7 for a reasonable temperature range, but it is noticed that if m_υγ > 2υ_μ～200 MeV, the CP non-invariance can be much larger.     

THE CONVERSION OF GLUONS INTO QUARKS AND THE MULTIQUARK STATES

The rate for the conversion of the gluon into a color octet quark pair which subsequently forms a multiquark state with another quark pair or a gluon is discussed. The static potential in a [(QQ)₈(qq)_8,1] state where Q=c,b and q=u, d is studied in the MIT bag model. It is shown that the repulsive Coulomb force between Q and Q is dominant at small QQ separations, which would significantly suppress the QQ wave function at the origin. For the charm quark (Q=c) the ratio of |Ψ(O)|² for the ordinary (QQ)₁ to that for the(QQ)₈ in the [(QQ)₈(qq)_8,1] state is estinated to be 2-5. Therefore the assumption |Ψ₈(O)|²=|Ψ₁(O)|² would lead to an overestimation for the rate of g*→QQ and it is necessary to take the suppression effect of the repulsive Coulomb force into consideration.     

The Mass Bounds on Exotic Particles in an SU(3)L×U(1)X Model

We study an SU(3)_L×U(1)_X electroweak model. By requiring M²_Z1-M²_W/cos²θ_W to be less than experimental value we obtain a lower bound on Z' boson mass, M_Z' >600 GeV. The relation between M_Z' and M_U (M_V) then gives a lower bound on M_U (M_V):M_U (M_V)>490 GeV. From the constraint sin² θ_W(M_Z')<0.3, the upper bounds on M_Z' and M_U (M_V) are computed to be M_Z'<5.8×10⁴ TeV and M_U (M_V)<4.6×10⁴ TeV. We estimate further the K_L-K_S mass difference due to Z' exchange and try to use the result to obtain stronger lower bounds. On cosmological grounds we find that M_N<390 eV for T_f=2.3 GeV and M_N<740 eV for T_f=300 GeV.     

Unified Treatment of Systematics for Even-Even Nuclei with A≥70

By the concept of effective boson numbers, systematics of E₂₁+E₄₁+E₆₁+, R=E₂₁+/E₄₁, B(E2, 0₁⁺→2₁⁺) and Q₀ for even-even nuclei with A≥70 are presented. New features of energy spectra are noticed and an intuitive understanding is given.     

Four-Particle Entangled State Representation and Its Squeezing Transformation

The four-particle EPR entangled state | p,χ₂,χ₃,χ₄〉is constructed. The corresponding quantum mechanical operator with respect to the classical transformation p→e^λ₁p, χ₂→ e^λ₂χ₂, χ₃→e^λ₃χ₃, and χ₄→e^λ₄χ₄ in the state |p,χ₂ ,χ₃ ,χ₄〉is investigated, and the four-mode realization of the SU(1,1) Lie algebra as well as the corresponding squeezing operators are presented.     

New red Y0.85Bi0.1Eu0.05V1−yMyO4 (M=Nb, P) phosphors for light-emitting diodes

The Y_0.85Bi_0.1Eu_0.05V_1−yM_yO₄ (M=Nb, P) as new near-ultraviolet excited phosphors were synthesized and their luminescence properties under 365 nm excitation were investigated in detail. It indicated that by doping small amount of P⁵⁺ into V⁵⁺ sites, the excitation intensity of charge transfer (CT) band of Bi–O (330–400 nm) was greatly improved. By substituting Nb⁵⁺ for V⁵⁺, both the CT bands of Bi–O and Eu–O (240–320 nm) were significantly enhanced. As a result, the emission intensity of Y_0.85Bi_0.1Eu_0.05V_1−yM_yO₄ (M=Nb, P) could be improved about 90% by doping 5 mol% P⁵⁺ and 110% by doping 5 mol% Nb⁵⁺. Comparing with the commercial Y₂O₂S:Eu³⁺ phosphors, the Y_0.85Bi_0.1Eu_0.05V_0.95M_0.05O₄ (M=Nb, P) phosphors exhibited excellent color purity and much higher brightness. The results showed that these Y_0.85Bi_0.1Eu_0.05V_1−yM_yO₄ (M=Nb, P) phosphors could be considered as promising red phosphors for application in LED.     

The angular intensity correlation functions C(1) and C(10) for the scattering of light from randomly rough dielectric and metal surfaces

We study the statistical properties of the scattering matrix S(q|k) for the problem of the scattering of light of frequency ω from a randomly rough one-dimensional surface, defined by the equation x₃=ζ(x₁), where the surface profile function ζ(x₁) constitutes a zero-mean, stationary, Gaussian random process. This is done by studying the effects of S(q|k) on the angular intensity correlation function C(q,k|q',k')=〈I(q|k)I(q'|k')〉-〈I(q|k)〉〈I(q'|k')〉, where the intensity I(q|k) is defined in terms of S(q|k) by I(q|k)=L^-1₁(ω/c)|S(q|k)|², with L₁ the length of the x₁ axis covered by the random surface. We focus our attention on the C⁽¹⁾ and C⁽¹⁰⁾ correlation functions, which are the contributions to C(q,k|q',k') proportional to δ(q-k-q'+k') and δ(q-k+q'-k'), respectively. The existence of both of these correlation functions is consistent with the amplitude of the scattered field obeying complex Gaussian statistics in the limit of a long surface and in the presence of weak surface roughness. We show that the deviation of the statistics of the scattering matrix from complex circular Gaussian statistics and the C⁽¹⁰⁾ correlation function are determined by exactly the same statistical moment of S(q|k). As the random surface becomes rougher, the amplitude of the scattered field no longer obeys complex Gaussian statistics but obeys complex circular Gaussian statistics instead. In this case the C⁽¹⁰⁾ correlation function should therefore vanish. This result is confirmed by numerical simulation calculations.     

Gelation in Generalized Smoluchovski Equation

We consider a system of substances A_j reacting according to the scheme: A_i + A_j +A_k A_i+j+k, which is described by the generalized Smoluchovski equation. We discuss the existence of global solutions of this kinetic equation, and show that the total number of monomers may decrease as the result of the formation of infinite clustere (gelation) for some special coagulation kernels. We also solve the case R(i, j, κ) = s_is_js_κ with s_κ = Ak + B explicitly, and find that the gelation indeed occurs at t_c = (6A + B)/6A²(A + B)².     

金属螺旋型碳纳米管的Peierls相变研究

根据描述电子声子相互作用的Fr?hlich哈密顿量,推导出了金属螺旋型碳纳米管(n₁,n₂)的Peierls相变温度的一般表达式,并利用该式计算了(6,3)的Peierls相变温度.结果表明金属螺旋型碳纳米管在远离室温下都不会发生Peierls相变,仍然保持其金属性 关键词： 螺旋型碳纳米管 电子声子相互作用 Peierls相变     

计算自旋-s算子幺正演化矩阵ds(t)的新方法及其应用

提出了一种严格求解任意自旋-s算子幺正演化矩阵的方法,该方法不同于群论的方法和直接计算的方法,是一种间接的算法.方法的核心是利用两个系统表示的等价性：即自旋-s算子Hamiltonian量H_s=S_x与Heisenberg XX开链带相互作用J_n=n(N-n)的Hamiltonian量的等价性,由于存在这种等价性,自旋-s算子幺正演化矩阵的计算可通过Heisenberg XX开链中态的演化来实现.采用该方法计算了s=3/2,s=2和s=5/2时对应的幺正演化矩阵.由于初始态|sm〉在算子e^-itS_x下的演化实质上相当于对态|sm〉进行一个绕x轴转角为β＝t的转动,演化矩阵元d^s_m'm(t)=〈sm′|e^-itS_x|sm〉就是转动后的态e^-itS_x|sm〉在|sm′〉态上的投影值,所以在t＝π时刻的演化矩阵刚好对应Heisenberg XX开链上量子态的理想传输. 关键词： s算子')" href="#">自旋-s算子 幺正演化矩阵 量子态传输     

Total Quantum Statistical Entropy of Reissner-Nordstrom Black Holes: in Dirac Field Case

The total quantum statistical entropy of Reissner-Nordstrom black holes in Dirac field case is evaluated in this article. The space-time of the black holes is divided into three regions: region 1 (r>r_o), region 2 ( r_o > r > r_i), and region 3 (r_i >r>0), where r_o is the radius of the outer event horizon, and r_i is the radius of the inner event horizon. The total quantum statistical entropy of Reissner-Nordstrom black holes is S=S₁+S₂+S₃, where S_i (i=1,2,3) is the entropy, contributed by regions 1,2,3. The detailed calculation shows that S₂ is neglectfully small. S₁=w_t(π²/45)k_b(A_o/ε²β³), S₃=-w_t(π²/45)k_b(A_i/ε²β³), where A_o and A_i are, respectively, the areas of the outer and inner event horizons, w_t=2^s[1- 2^-(s+1)], s=d/2, d is the space-time dimension, here d=4, s=2. As r_i approaches r_o in the extreme case the total quantum statistical entropy of Reissner-Nordstrom black holes approaches zero.