Quantum entangled fractional Fourier transform based on the IWOP technique

In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.

Rapid Sample Product Trial Manufacture Technique for Developing Water Meter New Products

This paper advances the viewpoints and methods of the rapid sample product trial manufacture technique for developing water meter new products by CAD and simulation, computer virtual assembling and optimizing, rapid machining process and measurement etc. as the design and sample product trial manufacture process of water meter new products are long in product development period, and low in product development efficiency in the present time.

Influence of main dietary chemical constituents on the in vitro gas and methane production in diets for dairy cows

Background： Modification of chemical composition of diets fed to dairy cows might be a good strategy to reduce methane（CH4） production in the rumen. Notable reductions of CH4 production compared to conventional highroughages rations were more frequently observed for very concentrated diets or when fat supplements were used. In these cases, the reduction in the gas emission was mainly a consequence of an overall impairment of rumen function with a reduction of fiber digestibility. These strategies do not always comply with feeding standards used in intensive dairy farms and they are usually not applied owing to the risks of negative health and economic consequences.Thus, the present study evaluated the effects of seven commercial diets with contents of neutral detergent fiber（NDF）,protein and lipids ranging 325 to 435 g/kg DM, 115 to 194 g/kg DM, and 26 to 61 g/kg DM, respectively, on in vitro degradability, gas（GP）, and CH4 production.Results： In this experiment, changes in the dietary content of NDF, crude protein（CP） and lipids were always obtained at the expense or in favor of starch. A decreased of the dietary NDF content increased NDF（NDFd） and true DM（TDMd） degradability, and increased CH4 production per g of incubated DM（P 〈 0.001）, but not that per g of TDMd. An increase of the dietary CP level did not change in vitro NDFd and TDMd, decreased GP per g of incubated DM（P 〈 0.001）, but CH4 production per g of TDMd was not affected. An increased dietary lipid content reduced NDFd, TDMd,and GP per g of incubated DM, but it had no consequence on CH4 production per g of TDMd.Conclusions： It was concluded that, under commercial conditions, changes in dietary composition would produce small or negligible alterations of CH4 production per unit of TDMd, but greater differences in GP and CH4 production would be expected when these amounts are expressed per unit of DM intake. The use of TDMd as a standardizing parameter is proposed to account for possible difference in DM intake and productivity.

STEREOSTRUCTURAL DETERMINATION OF ADDITION PRODUCTS FROM ISOFURANOGERMACRENE AND MALEIMIDE BY NMR TECHNIQUES

The stereostructures of the title compounds were shown to be represented by (A) and (B).

An effective technique to improve photosynthetic productivity and adaptability of rice

High photosynthetic productivity and widephotosynthetic adaptability are two importantphysiological characteristics for the sustained highyield and wider growing range of rice.Preliminaryexperiments indicated that the utilization ofbeterosis between two different ecotype rices,US

The N-mode squeezed state with enhanced squeezing

It is known that exp [iA （Q] P1 - i/2）] is a unitary single-mode squeezing operator, where Q1, P1 are the coordinate and momentum operators, respectively. In this paper we employ Dirac＇s coordinate representation to prove that the exponential operator Sn ≡exp[iλi=1∑n（QiPi＋1＋Qi＋1Pi））],（Qn＋1=Q1,Pn＋1=P1）,is an n-mode squeezing operator which enhances the standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive Sn＇s normally ordered expansion and obtain new n-mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.

Wigner function and density operator of the photon-subtracted squeezed thermal state

By using the technique of integration within an ordered product of operators, the normal ordered density operator of the photon-subtracted squeezed thermal state （PSSTS） is derived. Then the corresponding Wigner function is presented by using the coherent state representation of the Wigner operator. The nonclassical properties of the PSSTS are discussed based on the negativity of the Wigner function.

New decomposition of the Fresnel operator corresponding to the optical transformation in ABCD-systems

By virtue of the coherent state representation of the newly introduced Fresnel operator and its group product property we obtain new decomposition of the Fresnel operator as the product of the quadratic phase operator, the squeezing operator, and the fractional Fourier transformation operator, which in turn sheds light on the matrix optics design of ABCD-systems The new decomposition for the two-mode Fresnel operator is also obtained by the use of entangled state representation.

New formulas for normalizing photon-added(-subtracted) two-mode squeezed thermal states

For the first time,we derive the compact forms of normalization factors for photon-added（-subtracted） two-mode squeezed thermal states by using the P-representation and the integration within an ordered product of operators（IWOP） technique.It is found that these two factors are related to the Jacobi polynomials.In addition,some new relationships for Jacobi polynomials are presented.

Four-mode continuous-variables entangled state:generation from beam splitter,a parametric down-conversion and a polarizer

We introduce a new kind of four-mode continuous variable entangled state in Fock space. The completeness relation and the partly nonorthonormal property of such a state are proven. The scheme to generate this state is presented by combining a symmetrical beamsplitter, a parametric down-conversion and a polarizer. After making a single-mode quadrature amplitude measurement, the remaining three modes are kept in entanglement. And its applications are also discussed.

The squeezing entangled state of two particles with unequal mass

For two unequal-mass particles,we construct the entangled state representation and then derive the corresponding squeezing operator.This squeezing operator has a natural realization in the entangled state representation,which exhibits the intrinsic relation between squeezing and quantum entanglement.This squeezing operator involves both two-mode squeezing and the direct product of two single-mode squeezings.The maximum squeezing occurs when the two particles possess equal mass.When the two particles＇ mass difference becomes large,the component of the two single-mode squeezings becomes dominant.

Unifying the theory of integration within normal-,Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators

By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.

Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum optics

We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m（x）,∞∑n=0sntm/n!m!H2n,2m（x,y）,and ∞∑n=0sntm/n!m!H2n＋l,2m＋k（x,y）.We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.

Two mutually conjugated tripartite entangled states and their fractional Fourier transformation kernel

We newly construct two mutually-conjugate tripartite entangled state representations, based on which we propose the formulation of three-mode entangled fractional Fourier transformation （EFFT） and derive the transformation kernel. The EFFT＇s additivity property is proved and the eigenmode of EFFT is derived. As an application, we calculate the EFFT of the three-mode squeezed vacuum state.

Evolution of quantum states via Weyl expansion in dissipative channel

Based on the Weyl expansion representation of Wigner operator and its invariant property under similar transformation,we derived the relationship between input state and output state after a unitary transformation including Wigner function and density operator.It is shown that they can be related by a transformation matrix corresponding to the unitary evolution.In addition,for any density operator going through a dissipative channel,the evolution formula of the Wigner function is also derived.As applications,we considered further the two-mode squeezed vacuum as inputs,and obtained the resulted Wigner function and density operator within normal ordering form.Our method is clear and concise,and can be easily extended to deal with other problems involved in quantum metrology,steering,and quantum information with continuous variable.

The s-parameterized Weyl-Wigner correspondence in the entangled form and its applications

Based on the theory of integration within s-ordering of operators and the bipartite entangled state representation we introduce s-parameterized Weyl-Wigner correspondence in the entangled form. Some of its applications in quantum optics theory are presented as well.

Wigner functions and tomograms of the even and odd binomial states

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, the Wigner functions of the even and odd binomial states （EOBSs） are obtained. The physical meaning of the Wigner functions for the EOBSs is given by means of their marginal distributions. Moreover, the tomograms of the EOBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics.

Influence of Characteristics of Alumina-silicate Raw Materials on the Formation Process of Clinker

The traditional alumina-silicate raw materials, for example, clays, in the precalcining technique of cement production, have been replaced by low grade and high silica content sandstones, shales, and industrial waste residues, including fly ashes, slag, and others. The results are the change of compositions and characteristics of raw materials applied and a great effect on cement calcination process and clinker formation. In this work, the cement clinker formation process of different alumina-silicate raw materials to replace clay raw material was studied by chemical analysis, X-ray diffraction, differential thermal analysis, and high temperature microscope based on the characteristics of the alumina-silicate raw materials. The formation heat of the clinker was determined by the acid dissolution method. Influence of different alumina-silicate raw materials on the clinker burnability and formation process was studied. The results show that the changing of alumina- silicate raw materials, especially using industrial waste residues, can reduce the formation temperature of high temperature liquid phases, improve the burnability of raw materials, reduce the formation temperature and formation heat of clinker. And this study also observed the formation temperature and transformation of high temperature liquid phases in the heating process of raw materials by high temperature microscope.