Generalized algebra within a nonextensive statistics

By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators: addition, subtraction, product and division, are generalized. The properties of the generalized operators are investigated. Some standard properties are preserved, e.g. associativity, commutativity and existence of neutral elements. On the contrary, the distributivity law and the opposite element are no more universal within the generalized algebra.     

Skew-gradient representation of generalized Birkhoffian system

The skew-gradient representation of a generalized Birkhoffian system is studied. A condition under which the generalized Birkhoffian system can be considered as a skew-gradient system is obtained. The properties of the skew-gradient system are used to study the properties, especially the stability, of the generalized Birkhoffian system. Some examples are given to illustrate the application of the result.     

Correspondence between generalized binomial field states and coherent atomic states

We show that the N-photon generalized binomial states of electromagnetic field may be put in a bijective mapping with the coherent atomic states of N two-level atoms. We exploit this correspondence to simply obtain both known and new properties of the N-photon generalized binomial states. In particular, an over-complete basis of these binomial states and an orthonormal basis are obtained. Finally, the squeezing properties of generalized binomial state are analyzed.     

Optimal dynamical systems of Navier-Stokes equations based on generalized helical-wave bases and the fundamental elements of turbulence

In this paper, we present the theory of constructing optimal generalized helical-wave coupling dynamical systems. Applying the helical-wave decomposition method to Navier-Stokes equations, we derive a pair of coupling dynamical systems based on optimal generalized helical-wave bases. Then with the method of multi-scale global optimization based on coarse graining analysis, a set of global optimal generalized helical-wave bases is obtained. Optimal generalized helical-wave bases retain the good properties of classical helical-wave bases. Moreover, they are optimal for the dynamical systems of Navier-Stokes equations, and suitable for complex physical and geometric boundary conditions. Then we find that the optimal generalized helical-wave vortexes fitted by a finite number of optimal generalized helical-wave bases can be used as the fundamental elements of turbulence, and have important significance for studying physical properties of complex flows and turbulent vortex structures in a deeper level.     

Amplitude-squared squeezing of the generalized odd-even coherent states of the anharmonic oscillator in a finite-dimensional Hilbert space

This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.     

广义Birkhoff系统的两类广义梯度表示

提出了两类广义梯度系统, 即广义斜梯度系统以及具有对称负定矩阵的广义梯度系统. 分别讨论了这两类梯度系统与动力学系统稳定性的关系. 研究了广义Brikhoff系统的两类广义梯度表示, 分别给出条件和表达式. 给出了广义Brikhoff系统稳定性的梯度判别法, 利用广义梯度系统的性质来研究广义Birkhoff系统的稳定性. 并举例说明了方法的应用.     

Quantum phase distribution and the number—phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems

The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states:solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.     

Bifurcation for the generalized Birkhoffian system

The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper,the condition under which the generalized Birkhoffian system can be a gradient system is given. The stability of equilibrium of the generalized Birkhoffian system is discussed by using the properties of the gradient system. When there is a parameter in the equations, its influences on the stability and the bifurcation problem of the system are considered.     

Generalized stokes parameters of random electromagnetic beams

A generalization of the Stokes parameters of a random electromagnetic beam is introduced. Unlike the usual Stokes parameters, which depend on one spatial variable, the generalized Stokes parameters, depend on two spatial variables. They obey precise laws of propagation, both in free space and in any linear medium, whether deterministic or random. With the help of the generalized Stokes parameters, the changes in the ordinary Stokes parameters upon propagation can be determined. Numerical examples of such changes are presented. The generalized Stokes parameters contain information not only about the polarization properties of the beam but also about its coherence properties. We illustrate this fact by expressing the degree of coherence of the electromagnetic beam in terms of one of the generalized Stokes parameters.     

Semi-Cats: Nonclassicality and Generation

We define generalized cat states as linear superpositions of the semi-coherent states. They can be considered as superpositions of two distinguishable components of the Schrödinger cat states. We study the statistical properties of the introduced states in detail. The physical properties of these states, like the sub-Poissonian statistics and normal-order as well as amplitude-squared squeezing effect, are discussed analytically. Moreover, we find some interesting properties of their optical tomogram derived in terms of the exponential function. Finally, we suggest a new theoretical framework for preparing generalized cat states.     

环状平顶光束的传输特性研究

利用偏心高斯光束相干叠加方法，建立了柱坐标系下环状平顶光束模型.采用广义强度二阶矩定义，推导出环状光束广义M2因子的解析表达式.利用广义衍射积分理论，给出环状光束经过近轴ABCD光学系统的传输公式，并进一步给出了环状平顶光束修正的菲涅耳数定义.分析了环状平顶光束在自由空间的传输规律.研究结果表明，该模型可统一描述基模高斯光束、环状高斯光束以及环状平顶光束.环状平顶光束的广义M2因子和环状平顶光束的传输特性与其阶数及遮拦比有关.     

Squeezing Properties of the Generalized Multimode Squeezed States

By means of the invariance of Weyl ordering under similar transformations we derive the explicit form of the generalized multimode squeezed states.Moreover,the completeness relation and the squeezing properties of the generalized multimode squeezed states are discussed.     

量子叠加态光场中广义电场的N次方H压缩效应

利用多模压缩态理论,研究了一种新型的三态叠加多模量子叠加态光场|Ψ(3)〉q中广义电场分量的等幂次N次方H压缩特性.结果发现,在一定条件下,态|Ψ(3)〉q的广义电场分量总可呈现出周期性变化的广义非线性等幂次N次方H压缩效应.     

A unified approach to classical and quantum K.M.S. theory

We study a generalized K.M.S. condition which includes the classical and quantum mechanical K.M.S. conditions as special cases. We consider also a generalized centre of the von Neumann algebra and prove that with respect to the above K.M.S. condition it has properties analogous to the properties of the centre with respect to the quantum mechanical K.M.S. condition.     

约束系统的变换和推广的Killing方程

本文从约束系统的作用量和约束方程的普遍变换性质出发,得到了约束系统的推广Killing方程组,此方程组的解所生成的变换可产生经典Noether定理的守恒量。讨论了连续系统的时空变换和内禀变换,在变换保持约束方程不变时,指出此变换能导致守恒流的充要条件,给出了对不可压缩连续介质的应用,讨论了对广义力学和经典力学的应用,并给出了推广Killing方程组解的某些实例,将Poincare不变量推广到了受约束广义力学系统。 关键词：     

Scattering properties of polluted dust in 1.6-μm wavelength

Three typical polluted dust particles （i.e., single coated dust, two-sphere/spheroid system, and coated dust with ag- gregate） including internal and semi-external mixtures are modeled, and their scattering properties at 1.6-μm wavelength are calculated by using the generalized multi-sphere Mie-solution （GMM） method. We investigate the influences of par- ticle size, morphology, and chemical composition on the scattering parameters of polluted dust particles. The analysis results demonstrate that the single scattering albedo of coated dust is much smaller than that of pure dust, especially for the spheroidal black carbon （BC） coated dust. When a dust particle semi-mixes with another aerosol particle to form a two-sphere/spheroid system, its scattering properties are much more sensitive to the size and species of monomers than the monomer shape. If an aggregated BC attaches to the coated dust, the scattering properties of whole particle mainly depend on the host particle （coated dust）.     

Noether-type theory for discrete mechanico-electrical dynamical systems with nonregular lattices

We investigate Noether symmetries and conservation laws of the discrete mechanico-electrical systems with nonregular lattices.The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems.Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the dissipation forces under the infinitesimal transformations with respect to the time,generalized coordinates and generalized charge quantities,we work out the discrete analog of the generalized variational formula.From this formula we derive the discrete analog of generalized Noether-type identity,and then we present the generalized quasi-extremal equations and properties of these equations for the systems.We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems.Finally we use an example to illustrate these results.     

Wave scattering functions and their application to multiple scattering problems

Scattering functions arise naturally in standard treatments of the effects of a material object or surface embedded in a uniform field. The most commonly used scattering function describes the far-field modulation imparted at large distances to a spherical wavefront eminating from the scatterer. The purpose of this is to develop the properties of the spectrum of scattered plane waves as an exact generalized scattering function. The linearity of the wave equations guarantees that such a representation exists; moreover, it is possible to derive the generalized scattering function from the far-field scattering function by analytic continuation. Although these properties are known, recent theoretical developments have motivated us to reexplore the interrelations among the far-field scattering function, the Green's function and various forms of the generalized scattering function as well as the symmetry properties of the generalized scattering function imposed by reciprocity. For multiple-scattering objects that can be separated by parallel planes, a system of difference equations is developed that fully accommodates the mutual interaction among the scatterers. The mutual interaction equations were developed earlier, but we show here that they can be transformed into the form that would be obtained by using the Foldy-Lax-Twersky formalism. This reinforces the equivalence between wave-space and configuration space formulations of the scattering problems.     

Superposition of Generalized q-Coherent States of the Non-harmonicOscillator and Their Nonclassical Properties

The superposition states, which are composed of the generalized q-coherent states of the non-harmonic oscillator, are presented. The quantum statistical properties of these states are studied. Then the influence of the superposition phase δ and the deformation parameter q on these nonclassical properties are discussed. It is shown that the superposition states exhibit higher-order (order of odd number) squeezing effect and antibunching effect respectively. When the superposition phase δ is taken values approach to 0 or π/2, these results approach the properties of the even or odd generalized q-coherent states of the non-harmonic oscillator. Especially, the effects are influenced by the parameter q. When the values of q is taken departure from 1 greatly, the nonclassical properties are more evidently.