Remarks on the q-Deformation of Fermionic Oscillators

The properties of the q-deformed fermionic oscillator opcrators arc esarnir~cd. The difference between the deformed oscillators and the ordinary ones is closely related to the mullivalueness of the deformation parameter η= ln q.     

Boson Representations of Subalgebra Chain for Quantum Algebra (Cl)q with q a Root of Unity

The method of q-deformed boson realization is extended to the caee that q is a root of unity. By using thb method, many irreducible and indecomposable representations of each su balgebra in a su balgebra chain of the quantum universal enveloping algebra (quan tum algebra) (C_l)_q are obtained on the q-deformed Fock space and its quotient space. AB an example, the representations of (C₃)_q are constructed in explicit forms. Besides, by embedding (A₁)_q = (C_l)_q, into the subalgebra chain, a new realisation of (A₁)_q and its representations are obtained.     

Spinor and Oscillator Representations of Quantum Enveloping Algebras of Type Bn,Cn and Dn

With the help of the q-deformed bosonic and fermionic oscillation operators, which can be conetructed from the ordinary ones, the quantum enveloping algebras of the classical Lie algebras B, C and D are written down explicitly. Under these representations the highest roots are given.     

On Solutions to the q-Deformed Oscillator Systems and the q-Oscillator Algebra Hq (4)

Discussions upon the q-oscillator systems and the q-oscillator algebra H_q(4) are provided,and the case of |q| = 1 ia detailed. A remarkable connection between SH_q(2) and H_q(4) is indicated and investigated. The single q-oscillator system t solved and shown to be analogous to the parafermion (PF), with the specific case analogous to the third order PF discussed in detail. The properties of the representations and a finite chain model are exploited.     

A (p,q)-Deformation of Quantum Mechanics

On a one-dimensional lattice with a geometric sequence spacing, the Hermitian conjugation of a (p, q)-derivative operator is discussed by means of (p, q)-integration. Then a (p, q)-deformation of both the Heisenberg algebra for the canonical coordinates and the Heisen berg-Weyl algebra for the harmonic oscillator is presented. It is shown that although in the algebraic aspect the (p, q)-deformation discussed here is identical with 9-deformation given by Truong, the (p, q)-deformed SchrGdinger picture is in fact different from the q-deformed one.     

A New q-Deformed Boson Realization of the Quantum Algebra Cq(l) and Its Representations

A new q-deformed boson realization of the quantum algebra C_q(l) is given and some of its finite dimensional representations are explicitly presented when q is a root of unity.     

The Characteristic Equation of q-Deformed Bosonic Oscillator

The main goal of this paper is to deduce the characteristic equation of [N]. From the fundamental relation of q-deformed bosonic oscillator, we deduce a strict algebraic equation. After introducing a moderate boundary condition, we obtain the characteristic equation of number operator [N].Using this equation, we extract all the eigenvalues of operator [N] and write out the corresponding eigenstates. Then we obtain the completeness of the Hilbert space.     

q变形量子振子的Glauber相干态

利用具有量子群对称性的q变形量子谐振子Fock态│n>_q生成q变形量子谐振子的Glauber相干态(q-Glauber相干态│a>_q)。还讨论了q-Glauber相干态│a>_q的完备性、粒子数分布、振子强度分布和最小测不准关系,指出q-Glauber相干态│a>_q的相干程度可以用q参数来描述。     

Energy Level of Three-Mode Harmonic Oscillator for Coordinate Operators Satisfying Cyclic Commutative Relations Obtained by IEO Method

Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator (IEO) method to solving the energy spectrum of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative elations, [X₁, X₂] = X₂, X₃] =[ X₃, X₁] =iθ, and this method seems effective and concise.     

The Boundary States of the q-Deformed Supersymmetric t-J Model with a Boundary

The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra U_q[\widehat{sl(2|1)}]. We give the bosonization of the boundary states.     

q变形叠加态及其特性

利用ｑ－振子代数提出了一种由ｑ变形振子的本征态（ｑ变形光子数态）叠回由成的态。给出了这种ｑ有叠加态的定义,研究了它们的量子统计性质。也讨论了这种态的压缩和ｑ压缩,并进一步研究了它们的寻常高阶压缩和ｑ高阶压缩。ｑ变形振子是一种非线性振子,通过这些讨论,推广通常的叠加态。     

General Solution and Localized COherent Soliton Structures of the （2＋1）—Dimensional Generalized Davey—Stewarson Equations

In this paper,the variable separation approach is used to obtain localized coherent structures of the (2 1)-dimensional generalized Davey-Stewarson equations:iqt 1/2(qxx=qyy) (R S)q=0,Rx=-σ/2|q|y^2,Sy=-σ/2|q|2/x.Applying a special Baecklund transformation and introducing arbitrary functions of the seed solutions.and abundance of the localized structures of this model is derived,By selceting the arbitrary functions appropriately,some special types of localized excitations such as dromions,dromion lattice,breathers,and instantons are constructed.     

The Q-deformed Oscillator Algebra with an Integer Number Eigenvalue and a Half Odd Integer Number Eigenvalue

In this paper a new q-deformed oscillator algebra with an integer number eigenvalue and a half odd integer number eigenvalue is proposed. For this algebra, the associated energy spectrum and thermodynamic behavior is discussed.     

有限维q非谐振子广义相干态振幅N次方压缩

利用Zhang等人提出的单模辐射场的振幅N次方压缩理论,研究了有限维希尔伯特空间中单参数q变形非简谐振子广义相干态的振幅N次方压缩效应.结果发现:该量子光场的确存在场的振幅N次方压缩效应,其压缩条件分别与相位角Φ、维度参数s、压缩幂次N、平均光子数的方根r和变形参数q相关;这一结果与无限维希尔伯特空间单参数q变形广义相干态的情形截然不同.     

THE CONVERSION OF GLUONS INTO QUARKS AND THE MULTIQUARK STATES

The rate for the conversion of the gluon into a color octet quark pair which subsequently forms a multiquark state with another quark pair or a gluon is discussed. The static potential in a [(QQ)₈(qq)_8,1] state where Q=c,b and q=u, d is studied in the MIT bag model. It is shown that the repulsive Coulomb force between Q and Q is dominant at small QQ separations, which would significantly suppress the QQ wave function at the origin. For the charm quark (Q=c) the ratio of |Ψ(O)|² for the ordinary (QQ)₁ to that for the(QQ)₈ in the [(QQ)₈(qq)_8,1] state is estinated to be 2-5. Therefore the assumption |Ψ₈(O)|²=|Ψ₁(O)|² would lead to an overestimation for the rate of g*→QQ and it is necessary to take the suppression effect of the repulsive Coulomb force into consideration.     

A q-deformation of the harmonic oscillator

The q-deformed harmonic oscillator is studied in the light of q-deformed phase space variables. This allows a formulation of the corresponding Hamiltonian in terms of the ordinary canonical variables x and p. The spectrum shows unexpected features such as degeneracy and an additional part that cannot be reached from the ground state by creation operators. The eigenfunctions show lattice structure, as expected.     

q形变光场与级联型三能级原子相互作用中场的压缩效应

建立了q形变光场与级联型三能级原子相互作用的非线性理论,求得相互作用绘景中薛定谔方程的形式解,利用数值计算讨论了q形变对相互作用中场压缩效应的影响并与q-偶相干光场的情形做了对比分析。研究发现,q偏离1的程度越大,q形变对场压缩效应的调控能力越强,反映出q形变的非线性行为对量子相干性的干扰以及对量子特性的影响。当q→1时,恢复为普通线性理论。和q-偶相干光场的情形做的对比分析,反映出q-奇相干光场不仅不存在压缩效应,还会弱化压缩效应。这与q-偶相干光场和q-奇相干光场存在不同的量子效应的结论完全一致。     

Tensor Products of Hecke Algebras

Tensor product of irreducible representations of Hecke algebras are discussed. It is found that the tensor product of irreps of Hecke algebras generates representations of Birman-Wenzl algebra C_ƒ(γ, q) with γ = q³ or-q^-3. A procedure for the evaluation of tensor product coefficients (TPC's) of H_ƒ (q)oH_ƒ(q) ↓ C_ƒ(γ,q) is established when the representations of Cƒ(γ, q) remain irreducible. An example of deriving TPC's of H_ƒ (q)oH_ƒ(q) ↓ C_ƒ(γ, q) is given. It is also found that indecomposable representation of C₄(γ q) occurs in the tensor product [211]o[31].     

New Application of Weyl Correspondence in Studying Husimi Operator

In this paper, the so-cMled Husimi operator △h（q,p; κ）, which is introduced by smoothing out the Wigner operator △ω（q,p） br averaging over the ＂coarse graining＂ function exp[-κ（q＇ - q）^2- （p＇- p）^2/κ], is now regarded as a Weft correspondence connecting the Husimi operator △h（q, p; κ） with its classical correspondence, since the integration kernel is just the Wigner operator. In this way we can easily identify ｜p, q; κ ） such that △ h （ q, p; κ ） = ｜p, q;κ ） （P, q; κ｜, where ｜P, q;κ） is a new kind of squeezed coherent states. The entangled Husimi operator is also treated in this way. Thus a simple way to tnd the Husimi operator is presented.     

q变形非简谐振子奇偶广义相干态的高阶压缩效应及反聚束效应

研究了q变形非简谐振子奇偶广义相干态的高阶压缩效应和反聚束效应,并就q变量[χ]的两种不同表示情况进行了讨论.数值计算结果表明,q变形非简谐振子奇偶广义相干态均可呈现奇次方阶压缩效应和反聚束效应,这与谐振子情况的光学统计特性是不同的.