双参数变形多模玻色算符的代数结构及其应用(Ⅱ)

给出了双参数变形量子代数SU(2)_q,s和SU(1,1)_q,s的多模Jordan-Schwinger实现.     

双参数变形量子代数SU(1,1)_(q,s)的Nodvik实现和Holstein—Primakoff实现

给出了双参数变形量子代数SU(1,1)_q,s的Nodvik实现和Holstein-Primakoff实现,并给出了SU(1,1)_q,s,和双参数变形振子的变形映射.     

多模双参数变形相干态

借助一个满足量子Heisenberg-Weyl代数(H-W_q,s代数)的多模算符,给出了量子代数SU(2)_q,s和SU(1,1)_q,s的k(k≥2)模实现,并构造了相应的相干态.     

利用量子代数SU(1,1)q,s的 Holstein-Primakoff实现讨论双参数变形Jaynes-Cummings模型

本文利用量子代数 SU(1,1)_q,s的 Holstein-Primakoff 实现讨论了双参数变形Jaynes-Cummings 模型,并给出了布居数反转的时间演化表达式.     

双参数变形多模玻色算符的代数结构及其应用(Ⅰ)

构造了两个满足量子Heisenberg-Weyl代数的双参数变形多模玻色算符,研究了它们的代数结构,作为应用,给出了双参数变形多模量子群SU(2)_q,s和SU/(1,1)_q,s的Holstein-Primakoff实现,并分别构造了这两个玻色算符二次幂的本征态,证明了它们的完备性.     

双参数变形量子代数SU(2)q,s相干态的量子统计性质

本文研究了双参数变形量子代数SU(2)_q,s相干态的压缩效应和反聚束效应.     

利用双参变形自旋相干态计算量子代数SU(2)q,s的Clebsch-Gordan系数

利用量子代数SU(2)_q,s的双参数变形自旋相干态,通过引入量子代数SU(2)_q,s的不可约表示张量积空间的Bargmann表示,导出了这一表示中不可约表示基底、双参数变形自旋相干态以及算符的表达式.最后导出了量子代数SU(2)_q,s在双参数变形自旋相干态下的Clebsch－Gordan系数.     

量子代数SUq(4)的不可约表示

本文利用类张量的方法计算了量子代数SU_q(4)在SU_q(4)>SU_q(2)+SU_q(2)基上的不可约表示,得到了求矩阵元的递推公式.     

偶偶核基带的量子群Uqp(u2)模型的理论分析

通过对锕系和稀土偶偶核基带转动谱实验数据的拟合和Mallmann图的研究,系统地分析了量子群U_qp(u₂)模型对原子核转动谱的适用性.结果表明,U_qp(u₂)模型的理论值与实验值比较接近,明显优于单参数形变量子代数SU_q(2)模型.此外,还建立了U_qp(u₂)的形变参量q、p与核软度的关系.     

双参数变形多模玻色算符的代数结构及其应用(Ⅲ)

构造了双参数变形多模玻色算符高次幂的本征态,发现它们构成完备Hilbert空间,另外,还给出了双参数变形量子代数SL_q,s(3)的数学结构、玻色实现以及Sl_q,s(2)的阶类张量算符,指出将SL_q,s(3)的上述结果推广到多模情况是容易的.     

Two-Parameter Deformed Quantum Algebra SUq,s(4)

The commutation relations of thegenerators of the two-parameter deformed quantum algebra SU_q,s(4) are given and irreducible q,s-tensor operators of rank (1/2) of the quantum algebra SU_q,s(2) are constructed.     

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.     

双参数变形量子代数SU（1，1）_（q，s）的Nodvik实现和Holstein—Primakoff实现

给出了双参数变形量子代数ＳＵ（１，１）ｑ，ｓ的Ｎｏｄｖｉｋ实现和Ｈｏｌｓｔｅｉｎ－Ｐｒｉｍａｋｏｆｆ实现，并给出了ＳＵ（１，１）ｑ，ｓ，和双参数变形振子的变形映射。     

Clebsch-Gordan Coefficients for the Two-Parameter Deformed Quantum Algebra SU (1,1)q,s (I)

The Bargmann representations in the tensor product space of the irreducible representations for the two-parameter deformed quantum algebra SU(1,1)_q,s corresponding to the positive discrete series (a) are in trod uced, and the corresponding Bargmann expressions for the bases of irreps, the coherent state and the operators are also derived. The Clebsch-Gordan coefficients (CGC) for the two-parameter deformed quan tum algebra SU(1,1)_q,s corresponding to the positive discrete series (a) are obtained.     

双参数变形多模玻色算符的代数结构及其应用(Ⅱ)

给出了双参数变形量子代数ＳＵ（２）ｑ，ｓ和ＳＵ（１，１）ｑ，ｓ的多模Ｊｏｒｄａｎ－Ｓｃｈｗｉｎｇｅｒ实现。     

A Two-Parameter Deformed N = 2 SUSY Algebra

A two-parameter deformed N = 2 SUSY algebra is constructed by using the q-deformed bosonic and fermionic Newton oscillator algebras. The Fock space representation of the (q ₁,q ₂)-deformed N = 2 SUSY algebra is analyzed. The comparison between the algebra constructed and earlier versions of deformed N = 2 SUSY algebras is also made.     

Fermionic Realization of Two-Parameter Quantum Affine Algebra $${U_{r,s}(\widehat{\mathfrak {sl}_n})}$$

We construct all fundamental modules for the two parameter quantum affine algebra of type A using a combinatorial model of Young diagrams. In particular, we also give a fermionic realization of the two-parameter quantum affine algebra.      

Mathematical Structure of Two-Parameter Deformed Multimode Quantum Group SLqs(3)

The commutative relations of the generators ofthe two-parameter deformed multimode quantum groupSL_qs(3) are given, and irreducible qs-tensoroperators of rank 1/2 of the multi-mode quantum groupSL_qs(2) are constructed.