Free Boson Representation of DYh(sl2)k and the Deformation of the Feigin-Fuchs

A realization of the Yangian double with center DY_h(sl₂)_k of level-k(≠ 0, -2) in terms of free boson fields is constructed. The screening currents are also presented, which commute with DY_h(sl₂) modulo total difference. In the n → 0 limit, the currents of Yangian double DY_h(sl₂)_k become the Feigin-Fuchs realization of affine Lie Sl(2)k, while the screening currents of Yangian double DY_h(sl₂)_k become the screening currents of the affine Lie algebra sl(2)k.     

Another Free Boson Representation of Yangian Double DYħ(slN) with Arbitrary Level

We derive a free boson representation of the Yangian double DY_ħ(sl_N) with arbitrary level k by the observation that there is a correspondence between the q-affine algebra and Yangian double associated with the same Cartan matrix. Vertex operator and screening currents cannot be obtained in the same way. From this point of view, the Yangian double with centre cannot be regarded as the degenerated case of the quantum affine algebra.     

h-Miura Transformation in the DYh(sl2)k Case

The h-analogue of the Sugawara operater is constructed for the Yangian double with central extension in the sl₂ case.Using the free fields realization of the quantum currents,the h-analogue Miura transformation is obtained.     

The Unitarity of the W(3) Algebra from SU(3) Parafermion

We express the vacuum expectation value of the SU(3)k parafermion fields by that of two bosons and SU(3)_k current algebra. When k = 1,2,3, the SU(3)_k current algebra becomes an inner product of a unitary representation, and T(z), W⁽³⁾(z) are equivalent to "quasiself-adjoint" operators in this represen tation.     

Realization of the SU(N) Kondo effect in a strong magnetic field

In this Letter we suggest a realization of the SU(N) Kondo effect, using quantum dots at strong magnetic field. We propose using edge states of the quantum Hall effect as pseudospin that interact with multiple quantum dots structures. In the suggested realization one can access each pseudospin separately and hence may perform a set of experiments that were impossible until now. We focus on the realization of SU(2) and SU(3) Kondo effects and find in the unitary limit a conductivity of 3/4 quantum conductance in the SU(3) case.     

Universal R-matrix of the Super Yangian Double DY (gl(1|1))

Based on Drinfeld realization of super Yangian double DY (gl(1|1)), its pairing relations and universal R-matrix are given. By taking evaluation representation of universal R-matrix, another realization L^±(u) of DY (gl(1|1)) is obtained. These two realizations of DY (gl(1|1)) are related by the supersymmetric extension of Ding-fienkel map.     

Inhomogeneous q-Differential Realization,Inhomogeneous q-Boson Realization of Quantum Group SU(n)q and Its Indecomposable Representations

An inhomogeneous q-differential realization (q-IHDR) and its corresponding inhomogeneous q-boson realization (q-IHBR) of quantum group SU(n)_q are studied. By making use of the q-IHBR a kind of infinite dimensional indecomposable and irreducible representations of SU(n)_q is studied on the q-Fcck space. The finite dimensional irreducible representations of SU(n), are obtained on the finite dimensional subspaces of q-Fock space. As an example, these representations of SU(2)_q are studied in detail and Jimbo standard irreducible representations are obtained.     

Z-Algebra Construction of W-Algebra in the Parafermion Model

We propose a new construction — the Z-algebra construction for the W-algebra which includes the Virasoro algebra as a special case. The Z-algebra associated with the general affine Lie algebra is given. And we suggest a calculating program to make the derivation of the Z-algebra become possible. Using this technique we have derived the Virasoro algebra in general G_k parafermion case and the W-algebra in SU(2)_k parafermion case.     

Traces of Intertwining Operators for the Yangian Double

The traces over infinite-dimensional representations of the central extended Yangian double for the product of operators which intertwine these representations are calculated. For the special combinations of the intertwining operators, the traces are identified with form factors of local operators in the SU(2)-invariant Thirring model. This identification is based on the identities which are deformed analogs of the Gauss–Manin connection identities for the hyperelliptic curves.     

Application of Y（sl（2）） Algebra for Entanglement of Two-Qubit System

We construct the transition operators in terms of the generators of the general Yangian and the reduced Yangian. By acting these operators on a two-qubit pure state, we find that the entanglement degrees of the states are all decreased from the certain values to zero for the reduced Yangian algebra, which makes the state disentangled. This result sheds new light on the physical meaning of Y （sl（2） ） in quantum information.     

Universal R Matrix of Two-Parameter Deformed Quantum Group Uqs(SU(1, 1))

The universal R matrix of the two-parameterdeformed quantum group U_qs(SU(1, 1)) isderived. In previous work we suggested a method toderive the universal R matrix of the two-parameterdeformed quantum group U_qs(SU(2)). This method isdifferent from that of the quantum double; it is simpleand efficient for quantum groups of low rank at least.This paper studies the universal R matrix of thetwo-parameter deformed quantum group U_qs(SU(1, 1))using the same approach.     

两参数变形量子代数SU(1,1)q,s的相干态及其性质

利用SU(1,1)_q,s量子代数的两参数变形振子构造出归一化的SU(1,1)_q,s相干态,证明了SU(1,1)_q,s量子代数的表示基是正交的,并讨论了它的相干态的归一性和完备性。指出(SU(1,1)_q,s相干态的相干性受参数q、s的影响。     

Two-Parameter Deformations of SU(2) and SU (1,l) Algebras

The algebras SU(2) and SU(1,1) are promoted to two-parameter quantum universal enveloping algebras (QUEA) by a doubleparameter deformation in this paper. The discrete unitary irreducible representations and their deformed coherent states are studied. The deformed generators are given by a Jordan-Schwinger realization and a Bargmann-Fock representation. It is also interesting that the two-parameter deformed coherent states are found to relate to the oneparameter deformed ones by a simple scaling transformation and this can be used to derive the completeness relation of the former.     

利用SUq(2)量子代数的q变形振子实现讨论SUq(2)相干态

利用SU_q(2)量子代数的q变形振子实现构造出SU_q(2)的相干态。证明SU_q(2)代数的表示基是正交的,并讨论了它的相干态的归一性、完闭性。指出SU_q(2)相干态的相干性受q参数影响较大,它比通常的SU(2)相干态更具有一般性。 关键词：     

The Dyson Realization of the Quantum Group SU(1,1)q and Its Coherent state

The Dyson realization of the quantum group SU(1,1)_q is constructed and the transformation matrix, which turns the Dyson realization into the Holstein Primakoff realization, is given. The coherent state for the Dyson realization is discussed and is found to be the qdeformed Weyl Heisenberg coherent state.     

New 3-mode bosonic operator realization of SU（2） Lie algebra： From the point of view of squeezing

We consider the quantum mechanical SU(2) transformation e2λ JzJ± e-2λJz= e±2λJ± as if the meaning of squeezing with e±2λbeing squeezing parameter. By studying SU(2) operators(J±,Jz) from the point of view of squeezing we find that(J±,Jz) can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation(the eigenvectors of J+ or J-) of the 3-mode squeezing operator e2λ Jz. The idea of considering quantum SU(2) transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU(2) and new squeezing operators.     

Test of quantum nonlocality by full collection of polarization entangled photon pairs

We have experimentally tested the nonlocal properties of the states generated by a high brilliance source of entanglement which allows the direct measurement of virtually all the photon pairs emitted over the emission cone at a certain wavelength. By this source we could verify the Hardys ladder proof about contradiction between quantum mechanics and local realism for of entangled photon pairs. The realization of an experimental test of quantum nonlocality with no need of supplementary assumptions is also extensively discussed.     

Super Yangian Y(osp(1|2)) and the Universal R-matrix of Its Quantum Double

We present the Drinfel'd realisation of the super Yangian Y(osp(1|2)), including the explicit expression for the coproduct. We show in particular that it is necessary to introduce supplementary Serre relations. The construction of its quantum double is carried out. This allows us to give the universal R-matrix of DY(osp(1|2)).Member of Institut Universitaire de France     

A Unified Approach to the Thermodynamics and Quantum Scaling Functions of One-Dimensional Strongly Attractive SU(w) Fermi Gases

We present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional(1 D) strongly attractive Fermi gases with SU(w) symmetry. These physical quantities provide a rigorous understanding on a universality class of quantum criticality characterized by the critical exponents z=2 and correlation length exponent v=1/2. Such a universality class of quantum criticality can occur when the Fermi sea of one branch of charge bound states starts to fill or becomes gapped at zero temperature. The quantum critical cone can be determined by the double peaks in specific heat, which serve to mark two crossover temperatures fanning out from the critical point. Our method opens to further study on quantum phases and phase transitions in strongly interacting fermions with large SU(w) and non-SU(w) symmetries in one dimension.     

SU(1,1)相干态光场的统计特性及其对原子动力学行为的影响

研究了Ｂａｒｇｍａｎ指标为ｋ＝１／４和ｋ＝３／４的两种ＳＵ（１，１）相干态光场的特性，证明了两种相干态具有不同的量子统计特性，并讨论了光场初始处于ＳＵ（１，１）相干态时，双光子Ｊａｙｎｅｓ－Ｃｕｍｍｉｎｇｓ（Ｊ－Ｃ）模型中，原子的动力学行为及粒子数反转随时间的演化，证明了与初始一般相干态光场不同，原子展现出特殊的周期振荡和脉冲行为。 关键词：