q-Deformed IWOP Technique and Its Applications

We extend the newly developed technique of integration with an ordered product (IWOP) of operators to q-deformed boson case. The ambiguity arising from defining the normal ordering of q-deformed boson operators, which satisfy aa^↑ - qa^↑a = 1, can be eliminated by following the q-deformed IWOP technique. Some new q-integration formulas and new qboson operator identities are obtained, and the P-representation of q-analogue of the chaotic state of radiation field is derived.     

Bosonic Realization for Boundary States in Quantum sine-Gordon Field with Boundary

Boundary operators and boundary ground states in sine-Gordon model with a fixed boundary condition are studied using bosonization and q-deformed oscillators. We also study the boundary bound state for this case.     

On Darboux–Bäcklund Transformations for the Q-Deformed Korteweg–de Vries Hierarchy

We study Darboux–Bäcklund transformations (DBTs) for the q-deformed Korteweg–de Vries hierarchy by using the q-deformed pseudodifferential operators. The elementary DBTs are triggered by the gauge operators constructed from the (adjoint) wave functions of the associated linear systems. Iterating these elementary DBTs, we obtain not only q-deformed Wronskian-type but also binary-type representations of the tau-function of the hierarchy.     

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.     

The q-Deformation of the Superoscillators and Their q-Supercoherent States

We discuss the superoscillators in thc supersymmetric quantum systems, and give the solution to the system. By making use of the annihilation and creation operators and their q-deformed operators, we also give the q-deformed quantum harmonic oscillator model in the supersymmetric quantum systems. The q-supercoherent states associated with the q-deformed supersymmetric quantum harmonic oscillators are constructed explicitly, and their properties are investigated. The uncertainty relations for q-supercoherent states are discussed as well.     

Wigner Function and Phase Probability Distribution of q-Analogue of Squeezed One-Photon State

In this paper, in terms of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of q-deformed annihilation and creation operators, normalizable q-analogue of the squeezed one-photon state, which is quite different from one introduced by Song and Fan [Int. 3. Theor. Phys. 41 （2002） 695], is constructed. Moreover, the Wigner function and phase probability distribution of q-analogue of the squeezed one-photon state are examined.     

q-Deformed Differential Operator Superalgebra on Quantum Superplane

The q-deformed differential operator superalgebra is proposed, and these differential operators are analyzed in the framework of quantum superplane. At the same time, a solution of graded Yang-Baxter equation is obtained.     

The q-Deformed Coherent-State Method of Normally Ordering q-Boson Operators

We extend the newly proposed coherent-state method of normally ordering boson operators to a q-deformed boson case. With the help of q-derivative, some new q-boson operator iden tities 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.     

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 Uq[sl(2|1)]. We give the bosonization of the boundary states.``     

A q-Deformed osp(1,2) Superalgebra and Its Coherent States

In this paper we present a q-deformed osp(1, 2) superalgebra, construct a type of coherent state representations and obtain a q-differential realization for the q-deformed superalgebra.We also study some quantum optical properties of the q-deformed osp(1, 2) coherent states.     

SQUEEZING PROPERTIES OF q-DEFORMED OSCILLATOR

The q-coherent states are indeed minimum uncertainty states for corresponding q-deformed operators, The time evolution of q-coherent states are given by introducing the q-boson Hamiltoninn analogous to the one for normal bosons. It is shown that initially prepared q-coherent states are no longer the eigenstates of q-annihilation operator during time evolution and eventually become squeezing states. The squeezing properties are studied numerically.     

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形变三参数吴曾公式

结合微扰论的结果详细分析了描述偶偶核基带能谱三参数吴曾公式的q形变形式. 运用阻危非线性最小二乘法对大部分稀土区和锕系区的偶偶核基带能谱进行了拟合. 计算结果表明,q形变三参数吴曾公式比原来从微扰论导出的三参数吴曾公式更为精确,并能较好地描述回弯现象.     

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。     

Boson Realization of Representations for Quantum Groups and Its Differential Correspondence in Bargmann Space

By constructing the q-analogue of the Heisenberg-Weyl algebra in terms of usual creation and annihilation operators of boson states in the Fock space, the boson realization method recently suggested^[7-11] is generalized to obtain a class of representations of quantum group in the Fock space. The q-deformed differential realization of quantum groups proposed by Alvarez-Gaume is derived by making use of the boson realization in this paper.     

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。     

The q-Deformed SU(2) Quantum Ferromagnetic Model

A q-deformed SU(2) Heisen berg (3-dimensional) spin model is set up, and the q-deformed spin-wave solution is obtained through the q-analogous Holstein-Primakoff transformation. The result is given for small γ = In q, which is the quantity characterizing the nonlinearity of the Hamiltonian. A mean-field treatment is arranged to preserve (at least some of) the nonlinearity, and the ordinary ferromagnet ground state is shown as the exact ground state of the new system. Interesting results are obtained for this nonlinear model:(i) There is an energy gap between the ground state and the first excited one, thus the ground state is stable under small perturbation of the background; (ii) the specific heat per volume is modified by a small term proportional to the (1/2)-th power of temperature and the square of γ, which is qualitatively different from the conventional model, and (iii) the magnetization M (T) is modified by a factor that depends on γ.     

Theory of q-deformed forms. III. q-deformed Hodge star,inner product,adjoint operator of exterior derivative,and self-dual yang-mills equation

In this paper we introduce the q-deformed Hodge star operator, q-deformed inner product, and q-deformed adjoint of the q-deformed exterior derivative and investigate their properties. Using this mathematical background, we construct the q-deformed self-dual Yang-Mills theory.     

Hilbert space representation of an algebra of observables forq-deformed relativistic quantum mechanics

Using a representation of theq-deformed Lorentz algebra as differential operators on quantum Minkowski space, we define an algebra of observables for a q-deformed relativistic quantum mechanics with spin zero. We construct a Hilbert space representation of this algebra in which the square of the massp ² is diagonal.