用直线稳定方法控制耦合哈密顿系统的混沌运动

讨论了不稳定不动点邻域的不稳定轨道的稳定问题．通过对系统施加外部的控制信号,将直线稳定方法推广到控制高维保守系统一耦合标准映象的混沌运动．通过对外加控制信号的调整,使系统不稳定不动点邻域的不稳定轨道沿着连接任意时刻轨道点和该不动点的直线趋向不动点,从而使难于控制的高维保守系统的不稳定轨道趋于稳定．这种方法不需要事先掌握系统动力行为,而且具有较强的抗干扰能力。     

用常数周期脉冲方法控制耦合标准映象的混沌

将用常数周期脉冲方法控制保守系统的混沌运动的方法，用于控制高维系统耦合标准映象的混沌运动，计算了系统参数k=0.8和耦合常数β=0.04的有限时间李雅普诺夫指数，考察了不同系统参数和耦合常数下的有限时间李雅普诺夫指数随迭代次数的演化规律，从各次迭代的有限时间收敛区选择满足期望动力学特征的轨道片段，施加适当的脉冲强度找出其对应的周期不动点，从而得到期望的周期转道。     

催化分光光度法中的二标样计算法

本方导出了一种催化分光光度法计算公式，即二标样计算法，并进行了实验验证，结果良好。     

An Asymptotic Property of Factorizable Completely Positive Maps and the Connes Embedding Problem

We establish a reformulation of the Connes embedding problem in terms of an asymptotic property of factorizable completely positive maps. We also prove that the Holevo–Werner channels \({W_n^-}\) are factorizable, for all odd integers \({n\neq 3}\). Furthermore, we investigate factorizability of convex combinations of \({W_3^+}\) and \({W_3^-}\), a family of channels studied by Mendl and Wolf, and discuss asymptotic properties for these channels.     

溶液阴极辉光放电光谱信号的内标法定量分析研究

溶液阴极辉光放电-原子发射光谱是一种新颖的快速、高效、实时在线的元素分析方法,它可用于水体金属元素的检测。为提高其测量精确度和稳定性,将内标法应用于溶液阴极辉光放电-原子发射光谱技术。对K元素建立了标准定标曲线和以H_β为内标元素的定标曲线,内标法测得样品的相对误差和相对标准偏差分别为1.11%,2.14%,精确度和稳定性较之标准曲线法有一定的提高。实验考察了元素谱线强度在同一时段的波动情况,发现元素K和H_β的谱线强度变化趋势稍有不同,而同主族元素K和Rb,Ca和Mg的谱线强度有相同的变化趋势,提出选择与待测元素同主族且谱线强度变化趋势较为一致的元素作为内标元素能更大化校正实验波动的观点。同时探讨了K以Rb为内标元素、Ca以Mg为内标元素以及Mg以Ca为内标元素时的内标法测量的精确度和稳定性,得其相对误差分别为0.49%,0.02%和0.30%,相对标准偏差分别为1.11%,1.13%和0.87%,与标准曲线法和以H_β为内标元素的内标法相比效果更佳。测得自来水样品中Ca元素以Mg为内标的相对误差和相对标准偏差为0.58%,1.03%,Mg元素以Ca为内标的相对误差和相对标准偏差为1.57%和1.10%。研究结果表明,将溶液阴极辉光放电-原子发射光谱技术应用于水体金属元素检测时,内标法可以有效校正实验波动的影响,提高测量的精确度和稳定性。     

Quantum Entanglement Dynamics of Two Atoms in Two Coupled Cavities

Quantum entanglement dynamics for two atoms trapped in two coupled cavities is investigated.Numerical results show that the present of the two atomic excitations is mainly accounted for the entanglement-sudden-death(ESD) effect with the two cavities initially in the vacuum.The entanglement can also be controlled by the hopping rate and the imbalances between the two atom-cavity coupling rates.     

高效毛细管电泳内标法与外标法含量测定的比较

比较研究高效毛细管电泳内标法与外标法进行含量测定结果的差异.采用高效毛细管电泳内标法(以二苯胍为内标物)和外标法分别测定三黄泻心汤3种不同剂型中盐酸小檗碱的含量,并进行了比较.外标法测得结果较内标法偏低,高效毛细管电泳内标法比外标法含量测定结果理想.     

Breaking of Ergodicity in Expanding Systems of Globally Coupled Piecewise Affine Circle Maps

To identify and to explain coupling-induced phase transitions in coupled map lattices (CML) has been a lingering enigma for about two decades. In numerical simulations, this phenomenon has always been observed preceded by a lowering of the Lyapunov dimension, suggesting that the transition might require changes of linear stability. Yet, recent proofs of co-existence of several phases in specially designed models work in the expanding regime where all Lyapunov exponents remain positive. In this paper, we consider a family of CML composed by piecewise expanding individual map, global interaction and finite number $N$ of sites, in the weak coupling regime where the CML is uniformly expanding. We show, mathematically for $N=3$ and numerically for $N\ge 3$ , that a transition in the asymptotic dynamics occurs as the coupling strength increases. The transition breaks the (Milnor) attractor into several chaotic pieces of positive Lebesgue measure, with distinct empiric averages. It goes along with various symmetry breaking, quantified by means of magnetization-type characteristics. Despite that it only addresses finite-dimensional systems, to some extend, this result reconciles the previous ones as it shows that loss of ergodicity/symmetry breaking can occur in basic CML, independently of any decay in the Lyapunov dimension.     

耦合集团展开方法的改进

改进了耦合集团展开方法,计算出的2+1维SU(2)格点规范场的真空波函数的μ₀和μ₂比用改进前的方法所得到的结果好,在弱耦合区表现出良好的标度行为     

Kinetic Theory of Area-Preserving Maps. Application to the Standard Map in the Diffusive Regime

The evolution of the distribution function of a dynamical system governed by a general two-dimensional area-preserving iterative map is studied by the methods of nonequilibrium statistical mechanics. A closed, non-Markovian master equation determines the angle-averaged distribution function (the density profile). The complementary, angle-dependent part (the fluctuations) is expressed as a non-Markovian functional of the density profile. Whenever there exist two widely separated intrinsic time scales, the master equation can be markovianized, yielding an asymptotic kinetic equation. The general theory is applied to the standard map in the diffusive regime, i.e., for large stochasticity parameter and large scale length. The non-Markovian master equation can be written and solved analytically in this approximation. The two characteristic time scales are exhibited. This permits the thorough study of the evolution of the density profile, its tendency toward the Markovian approximation, and eventually toward a diffusive Gaussian packet. The evolution of the fluctuations is also described in detail. The various relaxation processes are governed asymptotically by a single diffusion coefficient, which is calculated analytically. This model appears as a testing bench for the study of kinetic equations. The various previous approaches to this problem are reviewed and critically discussed.     

Correlation of Two Coupled Particles in Viscoelastic Medium

Considering the viscoelastic memory effect, we study the correlated motion of two hydrodynamically coupled colloidal particles, each of which confined in a harmonic potential well, in a Kelvin-type and Maxwell-type viscoelastic medium. We find that viscoelastic relaxation plays a significant role in modifying the correlation, particularly the cross correlation. We also find that both the real and imaginary parts of the response function are significantly different from the viscous medium case. In particular there is a phase shift between the vanishing imaginary part and the maximal real part of the response function in a viscoelastic medium. In addition imaginary part of the cross correlation response function exhibits a net energy loss （gain） behavior when the elasticity parameter of the medium is larger （smaller） than the critical value for Kelvin （Maxwell） viscoelastic fluid. Some implication of our results and their connection with previous works are discussed.     

Correlation of Two Coupled Particles in Viscoelastic Medium

Considering the viscoelastic memory effect, we study the correlated motion of two hydrodynamically coupled colloidal particles, each of which confined in a harmonic potential well, in a Kelvin-type and Maxwell-type viscoelastic medium. We find that viscoelastic relaxation plays a significant role in modifying the correlation, particularly the cross correlation. We also find that both the real and imaginary parts of the response function are significantly different from the viscous medium case. In particular there is a phase shift between the vanishing imaginary part and the maximal real part of the response function in a viscoelastic medium. In addition imaginary part of the cross correlation response function exhibits a net energy loss (gain) behavior when the elasticity parameter of the medium is larger (smaller) than the critical value for Kelvin (Maxwell) viscoelastic fluid. Some implication of our results and their connection with previous works are discussed.     

The Dynamics of Quantum Correlations Between Two Atoms in Two Coupled Cavities

The dynamics of the quantum correlation between two atoms in two single-mode cavities is studied. For the initial Bell state |Ψ ⁺〉, the quantum consonance is equal to the entanglement, and larger than quantum discord. For the initial Bell state |Φ ⁺〉, the quantum consonance is larger than entanglement, but not larger than quantum discord all the time. As the increase of the cavity-cavity coupling strength, the evolution period of quantum correlation becomes smaller. Consonance is not smooth at some points while cavities are coupled with each other.     

Dynamical Properties of Two Coupled Dissipative QED Cavities Driven by Coherent Fields

When two identical QED cavities driven by the coherent fields are located in a uniform environment, in addition to dissipation, there appears an indirect coupling between the two cavities induced by the background fields. We investigate the effects of the coherent fields, the dissipation as well as the incoherent coupling on the following dynamical properties of the system： photon transfer, reversible decoherence, and quantum state transfer, etc. We find that the photons in the cavities do not leak completely into the environment due to the collective coupling between the cavities and the enviroment, and the photons are transferred irreversibly from the cavity with more photons to the cavity with less ones due to the incoherent coupling so that they are equally distributed among the two cavities. The coherent field pumping on the two cavities increases the mean photons, complements the revived magnitude of the reversible decoherence, but hinders the quantum state transfer between the two cavities. The above phenomena may find applications in quantum communication and other basic fields.     

Dynamical Properties of Two Coupled Dissipative QED Cavities Driven by Coherent Fields

When two identical QED cavities driven by the coherent fields are located in a uniform environment, in addition to dissipation, there appears an indirect coupling between the two cavities induced by the background fields. We investigate the effects of the coherent fields, the dissipation as well as the incoherent coupling on the following dynamical properties of the system: photon transfer, reversible decoherence, and quantum state transfer, etc. We find that the photons in the cavities do not leak completely into the environment due to the collective coupling between the cavities and the enviroment, and the photons are transferred irreversibly from the cavity with more photons to the cavity with less ones due to the incoherent coupling so that they are equally distributed among the two cavities. The coherent field pumping on the two cavities increases the mean photons, complements the revived magnitude of the reversible decoherence, but hinders the quantum state transfer between the two cavities. The above phenomena may find applications in quantum communication and other basic fields.     

Tip-Nanoparticle Near-Field Coupling in Scanning Near-Field Microscopy by Coupled Dipole Method

We use the couple dipole method to investigate the scanning near-field optical microscopy metallic tip-nanoparticle near-field interaction. Dependences of the local field intensity inside the nanoparticle on the nanosized tip shape,the tip open angle and the illumination angle are revealed. In combination with the previous results, we establish a complete model to understand the tip-nanoparticle near-field coupling mechanism.     

A New Solution to the Hirota-Satsuma Coupled KdV Equations by the Dressing Method

The Hirota-Satsuma coupled KdV equations associated 2×2 matrix spectral problem is discussed by the dressing method, which is based on the factorization of integral operator on a line into a product of two Volterra integral operators. A new solution is obtained by choosing special kernel of integral operator.     

Method of Coupled Waves in the Theory of Diffraction of Light by Elastic Waves in Crystals

Diffraction of light by elastic waves in crystals is described by the method of coupled waves in a form different from that used by other researchers. The difference is determined by the treatment of two pairs of orthogonal coordinate systems whose principal axes are oriented along the directions of phase and energy transfer of two optical waves interacting on a sound wave. Due to this, the equations of coupled waves assume the most compact form, which was previously unknown for crystals. These equations are easily solved by the conventional methods in terms of quasi-plane waves and also admit of a wider class of solutions for bounded interaction regions. Two different diffraction regimes are compared in the present work, namely, the transmission and reflection diffraction. It is indicated that the suggested approach allows one to refine the parameters that define the efficiency of diffraction of light by elastic waves in crystals.     

Transportation of Two Coupled Particles in an Asymmetric Saw-Tooth Potential

Based on a simple model,we theoretically show the transport behaviors of two harmonically coupled Brownian particles in an asymmetric saw-tooth potential with two slopes.The coupled particles are subject to stochastic fluctuations.It is found that when the equilibrium distance of the coupled particles is between the two slopes of the potential,the transport direction of the coupled particles will be reversed with a certain harmonic coupling strength.This current reversal can be easily understood with the near rigid approximation,where the two coupled particles can be regarded as a single particle in an effective potential.Compared with the original saw-tooth potential,the asymmetry of the effective potential could be reversed when the equilibrium distance is between the two slopes of the original potential,which results in the current reversal.