再谈相干态在算符编序中的应用

利用广义Weyl对应导出了相干态密度算符的S-编序表示.通过此表示并结合S-编序内的算符积分技术,导出了若干量子玻色算符的S-编序形式(包含了正规编序、Weyl编序和反正规编序).此方法进一步推广了相干态在算符编序中的应用.     

General Formalism for Setting Up Unitary Transform Operators from Classical Transforms via IWOP Technique

We present a general formalism for setting up unitary transform operators from classical transforms via the technique of integration within an ordered product of operators, their normally ordered form can be obtained too.     

光场位相算符和逆算符的Weyl编序展开

用有序算符内的积分技术, 推导了光场位相算符和逆算符的Weyl编序展开形式, 并利用该结果获得了相算符的经典对应以及某些新的特殊函数的生成函数和新的积分公式, 尤其是导出了带负次幂的复高斯积分的积分公式. 关键词： Weyl编序 位相算符 有序算符内的积分     

Quantum Mechanical Hilbert Transformation for Normally Ordering Coulomb Potential-Type Operators

We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.     

Quantum Mechanical Hilbert Transformation for Normally Ordering Coulomb Potential-Type Operators

We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.     

Normally Ordered Quantum Gate Operators for Continuum Variables as Images of Classical Transforms

We derive normally ordered quantum gate operators for continuum variables by mapping classical transforms onto Fock space. Successive gate operations can be treated in a unified way that is using the technique of integration within an ordered product of operators.     

Normally Ordered and Antinormally Ordered Expansions of Some Exponential Operators in Hilbert Space

In this paper, the completeness relations of the fundamental representations in quantum mechanics, together with the "integration within orderd product" technique are exploited to derive normally ordered and antinormally ordered expansions of some exponential operators in Hilbert space. Applications of the normally ordered exponential operators to evaluating Feynman matrix element in coherent state representation are given, which seems to be a new approach.     

General Formalism for Mapping of Two-Mode Classical Canonical Transformations to Quantum Unitary operators

Two types of canonical transformations in two-mode classical phase space are mapped into the quantum mechanical Hilbert space to produce some new normally ordered unitary operators. These operators are evaluated in the coordinate (momentum) representations using the "integration within ordered product technique, and the mapping is maniferrtly apparent in the derivation. New generalixed coherent states are constructed in terms of these operators, and the uncertainty relations for these states are analysed.     

Physics of a Kind of Normally Ordered Gaussian Operators in Quantum Optics

Based on the technique of integration within an ordered product of operators we investigate a completeness relation of pure states （such as the coordinate eigenstate, the momentum eigenstate and the coherent state） into normally ordered Gaussian forms. The Weyl ordering invariance under similarity transformations is employed to reveal physical meaning of a kind of normally ordered Gaussian operators, which have the similar forms to the bivariate normal distributions in statistics, i.e., the thermo mixed state density matrix.     

The IWOP Method of Normally Ordering Multimode Exponential Operators

This paper states that the technique of integration within ordered product (IWOP) provides us with a generally effective approach to normally ordering multimode exponential operators. In fact, all the operators listed in Ref. [5] can be normally ordered by virtue of IWOP, in contrast to the comment of Ref. [5].     

New Formulation of Weyl Quantization Scheme in Coherent State Representation

By virtue of the technique of integration within an ordered product of operators we present a new formulation of the Weyl quantization scheme in the coherent state representation, which not only brings convenience for calculating the Weyl correspondence of normally ordered operators, but also directly leads us to find both the coherent state representation and the Weyl ordering representation of the Wigner operator.     

Newton-Leibniz integration for ket-bra operators in quantum mechanics (V)—Deriving normally ordered bivariate-normal-distribution form of density operators and developing their phase space formalism

We show that Newton-Leibniz integration over Dirac’s ket-bra projection operators with continuum variables, which can be performed by the technique of integration within ordered product (IWOP) of operators [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480], can directly recast density operators and generalized Wigner operators into normally ordered bivariate-normal-distribution form, which has resemblance in statistics. In this way the phase space formalism of quantum mechanics can be developed. The Husimi operator, entangled Husimi operator and entangled Wigner operator for entangled particles with different masses are naturally introduced by virtue of the IWOP technique, and their physical meanings are explained.     

Differential-Form Relations Between Density Operators and Their P-Representations in Coherent State Basis

By virtue of the technique of integration within an ordered product of operators, we derive differential-form relations between density operators and their P-representations in the coherent state basis. Some applications of these new relations in normally ordering operators are given.     

Normally Ordered Bivariate-Normal-Distribution Forms of Two-Mode Mixed States with Entanglement Involved

Based on the technique of integration within an ordered product of operators we have demonstrated that singlemode mixed states＇ density matrices can be recast into the normally ordered Gaussian forms [Chin. Phys. Lett. 24 （2007） 3322]. Here we employ the Weyl ordering invariance under similar transformations to show that some two-mode mixed states with entanglement involved can be put into normally ordered form in the bivariate normal distribution too and its marginal distributions can be analysed. In this way, density operators of quantum statistics can be analogous to mathematical statistics, and calculation of variances can be simplified.     

Antinormally Ordering the Power of Radial Operator in Quantum Optics Theory

We derive a general formula for arranging the power of radial operators into antinormal ordering productof optical fields by using the technique of integration within antinormally ordered product of operators.     

A New Kind of Two-Fold Integration Transformation in Phase Space and Its Uses in Weyl Ordering of Operators

We propose a new two-fold integration transformation in p-q phase space ∫∫_-∞^∞(dp dq/π)e^2i(p-x)(q-y)f(p,q)≡G( x,y), which possesses some well-behaved transformation properties. We apply this transformation to the Weyl ordering of operators, especially those Q-P ordered and P-Q ordered operators.     

Antinormally Ordering the Power of Radial Operator in Quantum Optics Theory

We derive a general formula for arranging the power of radial operators into antinormal ordering product of optical fields by using the technique of integration within antinormally ordered product of operators.     

The Normal- and Antinormal-Ordered Decomposition Formulas of Multimode Exponential Operators

We obtain the normally ordered form of the general multimode exponential operator by means of parameter differentiation method and its antinormally ordered form by virtue of the technique of integration within an ordered product of operators.As an application,we obtain a new comp[leteness relation in n-mode Fock space.     

Dissipation of Gaussian-Enhenced Chaotic State

We investigate how an optical Gaussian-enhenced chaotic state (GECS) evolves in an amplitude dissipation channel. We have used the integration within ordered product of operators technique to derive its evolution law and show that the dacay of photon number. Also both the normally ordered and anti-normally ordered of the evolution law are given.     

Entanglement Rule of Wigner Operators at a Beamsplitter

It is known that beamsplitter can be used to produce quantum entanglement, in this paper we examine this topic from the point of view of Wigner operators. Using Weyl-ordering of the Wigner operator and the Weyl ordering invariance of Weyl ordered operators under similarity transformation we derive the entanglement rule of Wigner operators at a beamsplitter.