The two-parameter deformation of the supergroup GL(1|1), its differential calculus and its Lie algebra

We construct a right-invariant differential calculus on the quantum supergroup GL _q,s (1|1) and we show that its quantum Lie algebra with comultiplication is isomorphic to that which we obtain using the Reshetikhin-Takhtajan-Faddeev approach.     

q-Difference Realization of Uq(sl(M|N)) and Its Application to Free Boson Realization of Uq $$(\widehat{{\text{sl}}}(2|1))$$

We present a q-difference realization of the quantum superalgebra U_q(sl(M|N)), which includes Grassmann even and odd coordinates and their derivatives. Based on this result, we obtain a free boson realization of the quantum affine superalgebra U_q of an arbitrary level k.     

Universal R-matrix of the quantum superalgebra osp(2 | 1)

A quantum analogue of the simplest superalgebra osp(2 | 1) and its finite-dimensional, irreducible representations are found. The corresponding constant solution to the Yang-Baxter equation is constructed and is used to formulate the Hopf superalgebra of functions on the quantum supergroup OSp(2 | 1).     

Differential calculus on the quantum superspace and deformation of phase space

We investigate non-commutative differential calculus on the supersymmetric version of quantum space in which quantum supergroups are realized. Multiparametric quantum deformation of the general linear super-group,GL _q(m|n), is studied and the explicit form for the \(\hat R - matrix\) is presented. We apply these results to the quantum phase-space construction ofOSp _q(2n|2m) and calculate their \(\hat R - matrices\) .     

\hat sl(2) \oplus \hat sl(2)/\hat sl(2) coset theory is a Hamiltonian reduction of the \hat D(2|1;\alpha ) superalgebra

It is shown that $\hat sl(2)_{k_1 } \oplus \hat sl(2)_{k_2 } /\hat sl(2)_{k_1 + k_2 } $ coset theory is a quantum Hamiltonian reduction of the exceptional affine Lie superalgebra $\hat D(2|1;\alpha )$ . In addition, the W algebra of this theory is the commutant of the U _q D(2|1;a) quantum group.     

基于p1-p2与a1+a2共同本征态的相干纠缠态表象的构建及性质

利用有序算符乘积内的积分技术（IWOP）,建立了一种称之为相干纠缠态的两粒子体系的新表象,研究了这种新表象的性质,从理论上探讨了这种相干纠缠态的产生方法.结果表明：本文建立的这种p₁-p₂与a₁+a₂的共同本征态|p,β〉,既具有相干态的特性,又体现了纠缠态的特征,具有超完备性,完全可以作为一个表象使用. 物理上可以用光分束器来实现|< 关键词： IWOP技术 相干纠缠态表象 分束器     

Nonrelativistic Shifted-1 Expansion Technique for Three- and Two-Dimensional Schrodinger Equation

The shifted-1 expansion techniques (SLET) has been developed to get eigenvalues of Schrödinger equation in three (30) and two dimensions (2D). SLET simply consists of 1/l as a perturbation parameter, where l= 1 -β.β is a suitable shift, l is the angular-momentum quantum number for the 3D-case, l = |m| for the 2D-case, and m is the magnetic quantum number. Unlike the shifted large-N expansion theory (SLNT), SLET seems to be applicable to a wider number of problems of significant interest in physics.     

The construction of the generalized continuously variable two-mode entangled state and its application

The generalized continuous variable two-mode entangled state |ς> is proposed by using the technique of integration within an ordered product (IWOP) of operators. The characteristics of this new entangled representation and its application in quantum teleportation are analyzed in detail. These results indicate that such real parameters |ς> indeed make up a new entangled representation owing to its completeness and orthogonal relation. By employing the |ς> as quantum transmission channel, the teleportation of any single-mode quantum state 3 |ψ>₃ can be realized by a unitary transformation.     

Large enhancement of the thermoelectric Seebeck coefficient for amorphous oxide semiconductor superlattices with extremely thin conductive layers

Herein we demonstrate that amorphous oxide semiconductor (AOS) superlattices composed of a‐In–Zn–O (well) and a‐In–Ga–Zn–O (barrier) layers, fabricated on SiO₂ glass substrate by pulsed laser deposition at room temperature, exhibited an enhanced Seebeck coefficient |S |. The |S | value increases drastically with decreasing a‐In–Zn–O thickness (d_IZO) when d_IZO < ∼5 nm, and reached 73 µV K^–1 (d_IZO = 0.3 nm), which is ∼4 times larger than that of bulk |S |_3D (19 µV K^–1), while it kept its high electrical conductivity, clearly demonstrating that the quantum size effect can be utilized in AOS superlattices. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cartan-Weyl Basis For Quantum Affine SuperalgebraU q (\widehat{osp}(1|2))(1|2))

A Cartan-Weyl basis for the quantum affine superalgebraU _q (osp(1|2)) is constructed in an explicit form. Presented at the 6th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 19–21 June 1997. Supported by KNB grant No. 2P 30208706. Supported by Russian Foundation for Fundamental Research, grant No. 96-01-01421.     

非均匀磁场和杂质磁场对自旋1系统量子关联的影响

通过负值度和测量诱导的扰动, 研究了非均匀磁场和杂质磁场对自旋为1的Heisenberg系统量子关联的影响. 研究发现非均匀磁场的增加会降低纠缠, 但也可用来产生纠缠, 并且会提高临界非线性作用K_c的值, 测量诱导的扰动的临界磁场要高于负值度的临界磁场, 而且测量诱导的扰动不会随着非线性作用|K| 的减小而消失, 它能全面反映量子关联的存在. 研究还发现, 不同杂质磁场对测量诱导的扰动的影响彼此间无交叉. 杂质磁场下, 相互作用|J| 必须小于非线性作用|K| 才会有纠缠存在, 但是测量诱导的扰动却可以在相互作用|J| 大于非线性作用|K| 时依然存在, |J| 与|K| 相同时只是测量诱导的扰动的最小取值点. 此外, 系统粒子数目对量子关联也具有重要影响.     

Effect of Dissipative Environments on Atomic-State Quantum Teleportation

In the paper, taking the atomic EPR entanglement states as quantum channel, we investigate the fidelity of quantum teleportation of atomic state in thermal environment and vacuum reservoir by means of quantum theory of damping-density operator approach, and the average fidelities are calculated. the resultsshow that the atomic quantum channel state |ø> = (1/2^1/2)(| 00>+ |11>) is more robust than | Φ> = (1/2^1/2)(|01> + |10>) in teleportation process when they are subject to the dissipative environments.     

Quantum entanglement and quantum nonlocality for N-photon entangled states

Quantum entanglement and quantum nonlocality of N-photon entangled states |\psi_{N m}\rangle =C_m[\cos\gamma|N-m\rangle₁|m\rangle₂ +\e^{\i\θ_m}\sin\gamma|m\rangle₁|N-m\rangle₂] and their superpositions are studied. We point out that the relative phase θ_m affects the quantum nonlocality but not the quantum entanglement for the state |\psi_{N m}\rangle. We show that quantum nonlocality can be controlled and manipulated by adjusting the state parameters of |\psi_{N m}\rangle, superposition coefficients, and the azimuthal angles of the Bell operator. We also show that the violation of the Bell inequality can reach its maximal value under certain conditions. It is found that quantum superpositions based on |\psi_{N m}\rangle can increase the amount of entanglement, and give more ways to reach the maximal violation of the Bell inequality.     

Entanglement in spin-1 Heisenberg <Emphasis Type="Italic">XY</Emphasis> chain

We investigated the quantum entanglement in spin-1 Heisenberg XY chain for two-spin-qutrit and multi-particle systems. As a measure of the entanglement, the negativity of this state was analyzed as a function of the temperature and the magnetic field. We gave some numerical results and discussed them in detail. We found that the negativity increases monotonously with the coupling constants |J ₁| and |J ₂|, and it showed a symmetry with respect to the point of J ₁ = 0 and J ₂ = 0. In addition to the above features, there is evidence that the critical temperature is independent of the length of the chain.     

Quantum Teleportation and State Sharing via a Generalized Seven-Qubit Brown State

In this paper, a novel scheme is investigated for quantum teleportation (QT) and quantum state sharing (QSTS). The generalized seven-qubit Brown state |B ₇〉 is used as information carrier. Firstly, for an arbitrary single-qubit state, we perfectly present a QT protocol and three QSTS ones, which is among three participants via |B ₇〉. Then we make an overall comparison among three QSTS protocols and present an almost even distribution principle of particles. Secondly, for two- and three-qubit cases, based on the almost even distribution principle we design several QT and QSTS protocols. Finally, we mainly consider our scheme’s security against dishonest participant attacks. Furthermore, for an arbitrary N-qubit state, there is a conjecture that QT and QSTS can be designed by using the generalized (2N+1)-qubit Brown state |B _2N+1〉 in Eq. (3) (N≥2) in theoretical aspects.     

Wigner function for the generalized excited pair coherent state

This paper introduces the generalized excited pair coherent state （GEPCS）. Using the entangled state 〈η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, the variations of the Wigner function distributions with the parameters q, α, k and l are discussed. The tomogram of the GEPCS is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state ｜η1, η2, τ1, τ2｜. The entangled states ｜η〉 and ｜η1, η2, τ1, τ2〉 provide two good representative space for studying the Wigner functions and tomograms of various two-mode correlated quantum states.     

Strain effects on the polarized optical properties of InGaN with different In compositions

Strain effects on the polarized optical properties of c-plane and m-plane In_x1-xN were discussed for different In compositions (x=0, 0.05, 0.10, 0.15) by analyzing the relative oscillator strength (ROS) and energy level splitting of the three transitions related to the top three valence bands (VBs). The ROS was calculated by applying the effective-mass Hamiltonian based on k. p perturbation theory. For c-plane In_xGa_1-xN, it was found that the ROS of | X > and | Y >-like states were superposed with each other. Especially, under compressive strain, they dominated in the top VB whose energy level also went up with strain, while the ROS of the | Z >-like state decreased in the second band. For m-plane In_xGa_1-xN under compressive strain, the top three VBs were dominated by | X >, | Z >, and | Y >-like states, respectively, which led to nearly linearly-polarized light emissions. For the top VB, ROS difference between | X > and | Z >-like states became larger with compressive strain. It was also found that such tendencies were more evident in layers with higher In compositions. As a result, there would be more TE modes in total emissions from both c-plane and m-plane InGaN with compressive strain and In content, leading to a larger polarization degree. Experimental results of luminescence from InGaN/GaN quantum wells (QWs) showed good coincidence with our calculations.     

Quantum Affine Superalgebra Uq(gl(1|1)) and Its

Drinfeld's realization of quantum affine superalgebra U_q(gl(1|1)) is given based on the super version of RS construction method and Gauss decomposition.     

态|ψ5(3)〉q中广义电场的2(2m+1)次方Y压缩特性

利用多模压缩态理论,研究了由多模复共轭相干态|{Z_j^*}〉_q(j =1,2,3,…,…,q)、多模复共轭相干态的相反态|{-Z_j^*}〉_q和多模虚相干态|{iZ_{j}〉q的线性叠加所组成的第Ⅴ类三态叠加多模叠加态光场|ψ5⁽³⁾〉q中广义电场分量的等幂次N次方Y压缩特性 .结果发现 :当压缩次数N=2 p且p=2m+1(m=0,1,2,…,…)时,在一定的条件下,态|ψ5⁽³⁾〉q的广义电场分量(即第二正交相位分量)可呈现出周期性变化的、偶数次的等幂次2(2m+1)次方Y压缩效应 .}     

Quantum deformation of compactified Minkowski space

The quantum GrassmanianG(2|0; ? _q ^4|0 ) of “quantum 2-planes ? _q ^2|0 in the quantum 4-plane ? _q ^4|0 ”, which provides aq-deformation of compactified complexified Minkowski space, is proposed. A quantum analogue of classical Plücker embedding of the usual GrassmanianG(2; ?²) into a non-degenerate quadric in ??⁵ is found.