The Plateau and Symmetrical Structure of Lyapunov Exponents in 2-Dimensional Homogeneous. Dissipative Map

The universal crossover behavior of Lyapunov exponents in transition from conservative limit to dissipative limit of dynamical system is studied. We discover numerically and prove analytically that for homogeneous dissipative two-dimensional maps, along the equal dissipation line in parameter space, two Lyapunov exponents λ₁ and λ₂ of periodic orbits possess a plateau structure, and around this exponent plateau value, there is a strict symmetrical relation between λ₁ and λ₂ no matter whether the orbit is periodic, quasiperiodic, or chaotic.The method calculating stable window and Lyapunov exponent plateau widths is given. For Hénon map and 2-dimensional circle map, the analytical and numerical results of plateau structure of Lyapunov exponents for period-1,2 and 3 orbits are presented.     

THE UNIVERSAL TRANSITION OF PLATEAU STRUCTURE OF LYAPUNOV EXPONENTS

The universal transition of Lyapunov exponents between conservative limit and dissipa-tire limit of nonlinear dynamical system is studied. It is discovered numerically and proved analytically that for homogeneous dissipative two-dimensional maps, along the equal dissi-pation line in parameter space, the Lyapunov exponents of attractor orbits possess a plateau structure and strict symmetry about its plateau value, The ratios between the plateau width and the stable window width of period 1-4 orbits for Henon map are calculated. The result shows that the plateau structure of Lyapunov exponents remains invariant for the attractor orbits belonging to a period doubling bifurcation sequence. This fact reveals a new universal transition behavior between order and chaos when the dissipation of the dynamical system is weakened to zero.     

Critical Behavior of Nonlinear Properties in Percolating Superconductor/Nonlinear-Normal Conductor Networks

The critical behavior of nonlinear response in random networks of superconductor/nonlinear-normal conductors below the percolation threshold is investigated. Two cases are examined: (i) The nonlinear normal conductor has weakly nonlinear current (i)-voltage (ν) response of the form ν = ri + bi^α (bi^α-1《t and α > 1). Both the crossover current density and the crossover electric field are introduced to mark the transition between the linear and nonlinear responses of the network and are found to have power-law dependencies ～(f_c - f)^H and ～(f_c - f)^M as the percolation threshold f_c of the superconductor is approached from below, where H = ν_d - s_d > 0, M = ν_d > 0, ν_d and s_d are the correlation length exponent and the critical exponent of linear conductivity in percolating S/N system respectively; (ii) The nonlinear-normal conductor has strongly nonlinear ν-i response, i.e., i = X^να The effective nonlinear response X_e, behaves as X_e ～(f_c - f)^-W(α), where W ( α ) is the critical exponent of the nonlinear response x_e(α) and is α-dependent in general. The results are compared with recently published data, reasonable agreement is found.     

纳米SrHPO4：RE（RE=Eu3+或Tb3+）磷光体的水热合成与光谱特性

利用水热法合成了α-SrHPO₄：RE（RE=Eu³⁺,Tb³⁺）纳米磷光体,并研究了材料的形貌与光谱特性。α-SrHPO₄纳米粒子为长度90~200 nm的棒状结构,直径为24~36 nm。Eu³⁺和Tb³⁺的掺杂均会降低α-SrHPO₄的结晶度,并减小其长径比。α-Sr_0.97HPO₄：0.03Eu³⁺在395 nm近紫外光的激发下,存在分别由⁵D₀→⁷F₁和⁵D₀→⁷F₁₂跃迁引起的590 nm和614 nm发射峰,最终发射橙红光。α-Sr_0.97HPO₄：0.03Tb³⁺在217 nm近紫外光的激发下,存在由⁵D₄→⁷F₅跃迁引起的543 nm绿光发射。     

Baryon ＋ Baryon→（ΩΩ）J^π=0＋ ＋ X Cross Section Calculation

The cross sections of Ω Ξ→（ΩΩ）J^π=0 K(K^*) and Ω Ω→（ΩΩ）J^π=0 η‘(φ) are studied by using an effective Hamiltonian method.For the two pseudo-scalar meson production processes,the cross sections are still in the order of several μbs,but for the two vector meson production processes,the cross sections are about 10 times larger than those in pseudo-scalar meson production case when the coupling constants of vector meson fields are fixed according to gNNρ and fNNρ in NN scattering and the SU(3) relation.     

Quantization of Space in the Presence of a Minimal Length

In this article,we apply the Generalized Uncertainty Principle(GUP),which is consistent with quantum gravity theories to an elementary particle in a finite potential well,and study the quantum behavior in this system.The generalized Hamiltonian contains two additional terms,which are proportional to αp~3(the result of the maximum momentum assumption) and α~2p~4(the result of the minimum length assumption),where α ~ 1/M_(PIC) is the GUP parameter.On the basis of the work by Ali et al.,we solve the generalized Schrodinger equation which is extended to include the α~2 correction term,and find that the length L of the finite potential well must be quantized.Then a generalization to the double-square-well potential is discussed.The result shows that all the measurable lengths especially the distance between the two potential wells are quantized in units of α_0l_(PI) in GUP scenario.     

Parameterization of Nuclear Hulthén Potential for Nucleus-Nucleus Elastic Scattering

In contrast to Gaussian or Woods-Saxon potential a two-term four parameter nuclear Hulth′en type interaction is considered to describe the α-α, α-~3He and α-~3H systems. By exploiting the phase function method, scattering phase shifts are computed up to ELab = 100 MeV for the α-α system and ELab = 15 Me V for α-~3He and α-~3H systems.The S-wave phase shift δ_0 for the α-α system tends to 2π and δ_(3/2)-for the α-~3He system tends to π, in the limit of zero energy. Reasonable agreements in phase shifts with the standard data are obtained with this simple potential model except for the 5/2~- states of α-~3He and α-~3H systems. With an additional energy-dependent correction factor to our potential, a good agreement with experimental data is obtained for 5/2~- states. We have also compared our results with the convenient Born approximations.     

The Uniqueness Theorem of the First Integral for a Quartic Potential System

The first integrals for a quartic potential system are of the form of I_m=Σ_i=0^4m Σ_j=0^4m-i α_ij(t)q^jp^j, where m is a positive integer m = 1,2,3,..., this paper finds the expression of I_m by the recurrence method. Furthermore it shows that any I, (for which m≥2) must be a polynomial in fundamental invariant I₁ (m = 1) of degree m, and hence there is no new invariant which is independent of I₁. Thus we generalize the results of the previous papers from m = 2 to m = any positive integer, and prove the uniqueness theorem of the first integral for a quartic potential system.     

锐钛矿金红石的高温原位X射线衍射研究

对TiO₂粉末进行了空气和真空条件下从室温到1200℃的加热原位X射线衍射实验, 得到了空气和真空条件下微米级锐钛矿颗粒转变为金红石的起始温度分别为850℃ 和855℃; 分别修正了空气条件下锐钛矿在(27–850℃)范围和金红石在(900–1200℃) 范围内的晶胞参数和真空条件下锐钛矿在(27–850℃)范围和金红石在(950–1200℃) 范围的晶胞参数, 从而得到了晶胞参数随温度变化的关系, 得到了锐钛矿和金红石在空气中和真空中的热膨胀系数, 并总结了热膨胀系数随温度变化的规律. 室温下锐钛矿在空气条件下的热膨胀系数为 α_a=4.55063×10^-6/℃, α_c=7.7543×10^-6/℃, β=16.85836×10^-6/℃; 真空下为 α_a=4.69429×10^-6/℃, α_c=9.02850×10^-6/℃, β=18.69688×10^-6/℃. 室温下, 金红石在空气条件下的热膨胀系数为 α_a=6.81243×10^-6/℃, α_c=8.71644×10^-6/℃, β=22.22178×10^-6/℃; 真空条件下为 α_a=6.05834×10^-6/℃, α_c= 8.39280×10^-6/℃, β=20.52362×10^-6/℃. 关键词： 2')" href="#">TiO₂ 原位X射线衍射 相转变 热膨胀     

Tricritical and Critical Exponents in Microcanonical Ensemble of Systems with Long-Range Interactions

We explore the tricritical points and the critical lines of both Blume-Emery-Griffiths and Ising model within long-range interactions in the microcanonical ensemble. For K=K_MTP, the tricritical exponents take the values β=1/4, 1=γ^-≠γ⁺=1/2 and 0=α^-≠α⁺=-1/2, which disagree with classical (mean field) values. When K>K_MTP, the phase transition becomes second order and the critical exponents have classical values except close to the canonical tricritical parameters (K_CTP), where the values of the critical expoents become β=1/2, 1=γ^-≠γ⁺=2 and 0=α⁺≠α⁺=1.     

Reconstructing Equation of State for Dark Energy in Double Complex Symmetric Gravitational Theory

We propose to study the accelerating expansion of the universe in the double complex symmetric gravitational theory (DCSGT). The universe we live in is taken as the real part of the whole spacetime M4C(J), which is double complex. By introducing the spatially flat FRW metric, not only the double Friedmann equations but also the two constraint conditions pJ = 0 and J2 = 1 are obtained. Furthermore, using parametric DL(z) ansatz, we reconstruct the ω′(z) and V(φ) for dark energy from real observational data. We find that in the two cases of J = i, pJ = 0, and J = ε, pJ ≠ 0, the corresponding equations of state ω′(z) remain close to -1 at present (z = 0) and change from below -1 to above -1. The results illustrate that the whole spacetime, i.e. the double complex spacetime M4C(J), may be either ordinary complex (J = i, pJ = 0) or hyperbolic complex (J = ε, pJ ≠ 0). And the fate of the universe would be Big Rip in the future.     

微乳液法制备NaYF4：Yb3+, Er3+粉体及其发光性能

采用微乳液法制备了纯相立方和六方晶相NaYF₄：Yb³⁺,Er³⁺发光材料,微乳液体系选择了CTAB（十六烷基三甲基溴化铵）-正丁醇-正辛烷-水。研究了NaF/Y³⁺比例、反应温度、反应时间和体系pH值等对相形成的影响,以及陈化、后续热处理温度和时间对颗粒尺寸和发光性能的影响。结果表明：在NaF/Y³⁺比例小于5、体系pH=5~6、反应温度为140 ℃、反应时间为24 h的条件下,可得到立方相α-NaYF₄：Yb³⁺,Er³⁺,粒径约为200 nm;在NaF/Y³⁺比例大于5、体系pH=1~4、反应温度为160 ℃、反应时间为60 h以上的条件下,可得到六方相β-NaYF₄：Yb³⁺,Er³⁺,粒径约为1 μm。样品在980 nm激光激发下,在521,529,541,549 nm 处有发光峰,最强发光峰为541 nm,表现为明亮的绿色。     

Electroexcitation of Low-Lying Particle-Hole RPA States of 16O with WBP Interaction

The nuclear structure of ¹⁶O is studied in the framework of the particle-hole random phase approximation (ph RPA). The Hamiltonian is diagonalized within a model space with particle orbits {1d_5/2,1d_3/2 , and 2s_1/2} and the hole orbits {1p_3/2 and 1p_1/2} using Warburton and Brown interaction WBP. The ph RPA calculations are tested, by comparing the electron scattering form factors with the available experimental data. The results of electron scattering form factors and reduced transition strength for the states: 1^-, T=0 (7.116 MeV); 2^-, T=1 (12.968 MeV); 2^-, T=1 (20.412 MeV); and 3^-, T=0 (6.129 MeV) are interpreted in terms of the harmonic-oscillator (HO) wave functions of size parameter b. The occupation probabilities of the single particle and hole orbits are calculated. The spurious states are removed by adding the center of mass (CM) correction to the nuclear Hamiltonian. A comparison with the available experiments data is presented.     

Energy Spectra and g Factors of α-A1203:Cr3+ and α-A1203:Mn4+

By diagonalizing the complete d³ energy matrix in a trigonally distorted cubicfield and using the wavefunctions from it, unified calculations of the whole energy spectrum as well as the g factors of the ground state and t₂^{3 2} E excited states for α-A1₂0₃:Cr³⁺ and α-A1₂0₃:Mn⁴⁺ have been carried out respectively. A11 the calculated results are in very good agreement with the experimental data. The comparison between the results of the two crystals has been made, which demonstrates that the covalency of α-A1₂0₃:Mn⁴⁺ is stronger than the one of α-A1₂0₃:Cr³⁺. For the zero-field splittings of the ground state and t₂^{3 2} E , their physical origins are revealed; the comparison and analysis of their values of the two crystals have been made.     

红色长余辉材料Zn3(PO4)2：Mn2+,Ga3+的合成及光谱性质

采用高温固相法合成α、β和γ-Zn₃(PO₃)₂:Mn²⁺,Ga³⁺(ZPMG),XRD分析表明,高温合成过程中淬火条件有利于β相的形成,退火条件有利于γ相的形成。三种磷光粉的激发光谱分别位于246nm(α)、234nm(β和γ)的宽带谱。α相的发射光谱为位于508nm的锐线谱,β和γ相的发射光谱均存在两个谱带,分别位于508nm的绿色光谱区和616nm的红色光谱区。两种发射均归属为Mn²⁺的⁴T₁(⁴G)→⁶A_1g(⁶S)跃迁,但是由于Mn²⁺在Zn₃(PO₃)₂结构中的配位数不同,故发光颜色及强度均不同。对于余辉发射,只能观察到红色余辉光谱。     

Ground States of a Generalized Frenkel-Kontorova Model

We studied the modulated structures and commensurate-incommensurate transitions in a generalized Ftenkel-Kontorova (FK) model where the chain is composed of three kinds of atoms. For the classical ground states, the phase diagram and the phonon spectrum show the multi-atomic effects. For the quantum ground states, the multi-atomic effects are reflected by the distribution of atoms in external potential, the phase diagram, the correspondences between the ground states and the orbits of the area-preserving maps, as well as the phonon spectrum and coherence length. For the most incommensurate structure, the critical point K_c at which the transition by breaking of analyticity occurs does not vary monotonically with A. For the case of μ_A= μ_B = 1 and μ_c = 2, with the increasing of A, the critical point K_c first decreases, then increases. The minimum value of K_c occurs at nearly h = 0.035. When K < K_c, the phonon gap Ω_G = 0 and the Lyapunov exponent γ = 0, the system is in the sliding state. When K > K_c, the phonon gap and the Lyapunov exponent show great difference from those of the standard FK model.     

Controlling hyperchaos and synchronizing periodic states in the DOPO

It has been found out that hyperchaotic behaviors can be controlled to enter periodicity state by modulating the detuned parameters in degenerated optical parameter oscillator (DOPO) with different periodic orbits from different modulation index at the same modulation frequency, or from different modulation frequency at the same modulation index. It was shown that the periodic orbits of the DOPOs modulated through sinusoid can be resulted in identical synchronization or inversed synchronization only in the case that the largest Lyapunov exponent exponent of the system is negative.PACS: 42.65.Sf     

Upper Bounds on Top Quark Mass,Z Boson Decay Widths and Mass Ratio MW/MZ

In this paper we made a comprehensive analysis of some latest esperimental data-the Z boson decay widths, the mass ratio M_W/M_Z and effective vector coupling constant g_v, within the framework of standard model. We considered the 0(α_s²), order QCD corrections in tlte calculation of T_h and T_z. The analysis shows that the mass ratio (M_W/M_Z)² is rather sensitive to the change of the strong coupling constant α_s(M_Z), and the smaller value α_s(M_Z)≤0.128 is preferred. The upper bounds on top quark Inass M_t are obtained from different analyses. The final averaged result is M_t= 102 37 GeV, or M_t< 186 GeV at 95% C.L. for Higgs boson mass M_H in the range of 50～1000 GeV.     

Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

Using the bosonic numerical renormalization group method, we studied the equilibrium dynamical correlation function C(ω) of the spin operator σ_z for the biased sub-Ohmic spin-boson model. The small-ω behavior C(ω) ∝ω~s is found to be universal and independent of the bias ε and the coupling strength α(except at the quantum critical point α = αc and ε = 0). Our NRG data also show C(ω) ∝χ~2ω~s for a wide range of parameters, including the biased strong coupling regime(ε = 0 and α α_c), supporting the general validity of the Shiba relation. Close to the quantum critical point αc,the dependence of C(ω) on α and ε is understood in terms of the competition between ε and the crossover energy scale ω_0~*of the unbiased case. C(ω) is stable with respect to ε for ε《ε~*. For ε》ε~*, it is suppressed by ε in the low frequency regime. We establish that ε~*∝(ω_0~*)~(1/θ)holds for all sub-Ohmic regime 0≤s 1, with θ = 2/(3s) for 0 s≤1/2 and θ = 2/(1 + s) for 1/2 s 1. The variation of C(ω) with α and ε is summarized into a crossover phase diagram on the α–ε plane.