Application of Fourier Slice Theorem in Wigner Operator Theory and New Complete Representation

By applying the Fourier slice theorem, S_θ(λ) =∫_{-\infty }^{\infty }P_θ(t)e^-iλt=F(λcosθ,λsinθ), where P_θ(t) is a projection of f( x,p) =∫∫_{-\infty}^{\infty }F( u,v) e^i(ux+vp)ldudv along lines of constant, to the Wigner operator we are naturally led to projection operator (pure state), which results in a new complete epresentation. The Weyl orderimg formalism of the Wigner operator is used in the derivation.     

Hermitian Operators Conjugate to Two-Mode Number-Difference Operator Studied in Entangled State Representation

In similar to the derivation of phase angle operator conjugate to the number operator by Arroyo Carrasco-Moya Cessay we deduce the Hermitian phase operators that are conjugate to the two-mode number-difference operator and the three-mode number combination operator. It is shown that these operators are on the same footing in the entangled state representation as the one of Turski in the coherent state representation.     

Convolution Theorem of Fractional Fourier Transformation Derived by Representation Transformation in Quantum Mechancis

Based on our previous paper (Commun. Theor. Phys. 39 (2003) 417) we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible.     

Multi-mode Einstein-Podolsky-Rosen Entangled State Representation and Its Applications

Our primary purpose of this work is to explicitly construct the general multipartite Einstein-Podolsky-Rosen (EPR) entangled state in multi-mode Fock space for a system with different masses of particles, which makes up a new quantum mechanical representation owing to completeness relation and orthogonal property. Its entanglement can be seen more clearly by analyzing its standard Schmidt decomposition. In addition, some applications of the multipartite entanglement are proposed including deriving the generalized Wigner operator and squeezing operator.     

n the fourth order tensor valued function of the stress in return map algorithm

针对各向同性材料,基于一组相互正交的基张量,建立了一套有 效的相关运算方法. 基张量中的两个分别是归一化的二阶单位张量和偏应力张量,另一个则 使用应力的各向同性二阶张量值函数经过归一化构造所得,三者共主轴. 根据张量函数表示 定理,本构方程和返回映射算法中所涉及到的应力的二阶、四阶张量值函数及其逆都由这组 基所表示. 推演结果表明：这些张量之间的运算,表现为对应系数矩阵之间的简单 关系. 其中,四阶张量求逆归结为对应的3\times3系数矩阵求逆,它对二阶张量的变换 则表现为该矩阵对3times 1列阵的变换. 最后,对这些变换关系应用于返回映 射算法的迭代格式进行了相关讨论.     

A Family of Integrable Rational Semi-Discrete Systems and Its Reduction

Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out.     

Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding letter (2007 Opt.Lett.32 554) we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family.In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation,which makes the complex continuous wavelet transform theory complete.A new orthogonal property of mother wavelet in parameter space is revealed.     

Two-Mode Wigner Operator in 〈ξ| Representation and 〈τ| Representation

We derive the two-mode Wigner operator in the 〈ξ| representation and 〈τ| representation, where |ξ〉 is common eigenvector of the mass-weighted relative coordinate and the mass-combinatorial momentum.and |τ〉 common eigenvector of the mass-weighted relative coordinate and the mass-combinatorial momentum. As an application,we calculate the Wigner function of some two-mode state.     

Indecomposable Representations of the Square—Root Lie Algebras of Vector Type and Their Boson Realizations

The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, R_νλ (ν, λ=0, ±1), are obtained on the space of universal enveloping algebra of two-state Heisenberg-Weyl algebra, the invariant subspaces and the quotient spaces. From Fock representations corresponding to these indecomposable representations, the inhomogeneous boson realizations of R_νλ are given. The expectation values of R_νλ in the angular momentum coherent states are calculated as well as the corresponding classical limits.