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1.
《Journal of Nonlinear Mathematical Physics》2013,20(3):333-347
Abstract A method is proposed in this paper to construct a new extended q-deformed KP (q-KP) hiearchy and its Lax representation. This new extended q-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey hierarchy with self-consistent sources and the constrained q-deformed KP hierarchy, which include two types of q-deformed KdV equation with sources and two types of q-deformed Boussinesq equation with sources. All of these results reduce to the classical ones when q goes to 1. This provides a general way to construct (2+1)- and (1+1)-dimensional q-deformed soliton equations with sources and their Lax representations. 相似文献
2.
H. Wachter M. Wohlgenannt 《The European Physical Journal C - Particles and Fields》2002,23(4):761-767
In this paper we present explicit formulas for the *-product on quantum spaces which are of particular importance in physics,
i.e., the q-deformed Minkowski space and the q-deformed Euclidean space in 3 and 4 dimensions, respectively. Our formulas are complete and formulated using the deformation
parameter q. In addition, we worked out an expansion in powers of up to second order, for all considered cases.
Received: 6 June 2001 / Published online: 15 March 2002 相似文献
3.
J.-z. Zhang 《The European Physical Journal C - Particles and Fields》2003,28(3):389-393
In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators.
There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians; one originates from the perturbation expansion of the potential in one configuration space, the
other one originates from the perturbation expansion of the kinetic energy in another configuration space. In order to establish
a general foundation of the q-perturbation theory, two perturbation equivalence theorems are proved. The first is Equivalence Theorem I: Perturbation expressions
of the q-deformed uncertainty relations calculated by two pairs of undeformed operators are the same, and the two q-deformed uncertainty relations undercut Heisenberg's minimal one in the same style. The general Equivalence Theorem II is:
for any potential (regular or singular) the expectation values of two q-perturbation Hamiltonians in the eigenstates of the undeformed Hamiltonian are equivalent to all orders of the perturbation
expansion. As an example of singular potentials the perturbation energy spectra of the q-deformed Coulomb potential are studied.
Received: 6 September 2002 / Revised version: 21 October 2002 / Published online: 14 April 2003
RID="a"
ID="a" e-mail: jzzhang@physik.uni-kl.de, jzzhang@ecust.edu.cn 相似文献
4.
S. Kharchev D. Lebedev M. Semenov-Tian-Shansky 《Communications in Mathematical Physics》2002,225(3):573-609
The paper deals with the analytic theory of the quantum q-deformed Toda chains; the technique used combines the methods of representation theory and the Quantum Inverse Scattering
Method. The key phenomenon which is under scrutiny is the role of the modular duality concept (first discovered by L. Faddeev)
in the representation theory of noncompact semisimple quantum groups. Explicit formulae for the Whittaker vectors are presented
in terms of the double sine functions and the wave functions of the N-particle q-deformed open Toda chain are given as a multiple integral of the Mellin–Barnes type. For the periodic chain the two dual
Baxter equations are derived.
Received: 11 April 2001 / Accepted: 8 October 2001 相似文献
5.
Miura and auto-Backlund transformations for the q-deformed KP and q-deformed modified KP hierarchies
Jipeng Cheng 《Journal of Nonlinear Mathematical Physics》2017,24(1):7-19
The Miura and anti-Miura transformations between the q-deformed KP and the q-deformed modified KP hierarchies are investigated in this paper. Then the auto-Backlund transformations for the q-deformed KP and q-deformed modified KP hierarchies are constructed through the combinations of the Miura and anti-Miura transformations. And the corresponding results are also generalized to the constrained cases. At last, some examples of Miura and auto-Backlund transformations are given. 相似文献
6.
The differences among quon operators, q
a-math oscillator operators and q-deformed oscillator operators are pointed out. The q-deformed ocsillator and q
a-math oscillator are constructed in terms of q
q = 0 quon. 相似文献
7.
We present explicit formulae for q-exponentials on quantum spaces which could be of particular importance in physics, i.e. the q-deformed Minkowski space and the q-deformed Euclidean space with two, three or four dimensions. Furthermore, these formulae can be viewed as 2-, 3- or 4-dimensional analogues of the well-known q-exponential function.Received: 21 January 2004, Revised: 19 May 2004, Published online: 7 September 2004 相似文献
8.
In this paper, we solve the Schrödinger equation for q-deformed hyperbolic Pöshel-Teller (PT) potential and we obtain the wave function and ladder operators for it. We show that these operators satisfy commutation relations of su(2) Lie algebra. Then we build the generalized coherent states for this q-deformed potential. We show that for the case q=1, we can obtain the same generalized coherent states for usual hyperbolic PT potential. 相似文献
9.
D. Mikulovic A. Schmidt H. Wachter 《The European Physical Journal C - Particles and Fields》2006,45(2):529-544
Attention is focused on antisymmetrized versions of quantum spaces that are of particular importance in physics, i.e. two-dimensional
quantum plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. For each case standard techniques for dealing with q-deformed Grassmann variables are developed. Formulae for multiplying supernumbers are given. The actions of symmetry generators
and fermionic derivatives upon antisymmetrized quantum spaces are calculated. The complete Hopf structure for all types of
quantum space generators is written down. From the formulae for the coproduct a realization of the L-matrices in terms of symmetry generators can be read off. The L-matrices together with the action of symmetry generators determine how quantum spaces of different type have to be fused
together.
Arrival of the final proofs: 6 December 2005 相似文献
10.
The solutions of the q-deformed equations of quantum conformal Weyl gravity in terms of q-deformed plane waves are given.
The text was submitted by the authors in English. 相似文献
11.
Properties of the simplest class of self-similar potentials are analyzed. Wave functions of the corresponding Schrödinger equation provide bases of representations of theq-deformed Heisenberg-Weyl algebra. When the parameterq is a root of unity, the functional form of the potentials can be found explicitly. The generalq
3 = 1 and the particularq
4 = 1 potentials are given by the equi-anharmonic and (pseudo) lemniscatic Weierstrass functions, respectively. 相似文献
12.
三维各向同性q变形振子的双波描述 总被引:2,自引:1,他引:1
利用双波函数理论描述三维各向同性q变形振子力学量随时间的演化方程,结果显示粒子做非线性振动.同时,当r→0时,所有结论退化为普通三维各向同性谐振子的相关结果. 相似文献
13.
In this article we present explicit formulae for q-differentiation on quantum spaces which could be of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three or four dimensions. The calculations are based on the covariant differential calculus of these quantum spaces. Furthermore, our formulae can be regarded as a generalization of Jacksons q-derivative to three and four dimensions.Received: 26 September 2002, Revised: 18 June 2003, Published online: 2 October 2003 相似文献
14.
In the present paper we show that the Lorentz algebra as defined in [5] is isomorphic to an algebra closely related to a q-deformed algebra. On this algebra we define a Hopf algebra structure and show its action on q-spinor modules. This algebra is related to the q-deformed Minkowski space algebra by a non invertible factorisation.
Received: 12 June 1998 / Published online: 5 October 1998 相似文献
15.
Aq-deformed,q-Hermitian kinetic energy operator is realised and hence aq-Schrödinger equation (q-SE) is obtained. Theq-SE for a particle confined in an infinite potential box is solved and the energy spectrum is found to have an upper bound. 相似文献
16.
I. Benkaddour M. Hssaini M. Kessabi B. Maroufi M. B. Sedra 《International Journal of Theoretical Physics》2002,41(12):2339-2368
We build in this paper the algebra of q-deformed pseudo-differential operators, shown to be an essential step toward setting a q-deformed integrability program. In fact, using the results of this q-deformed algebra, we derive the q-analogues of the generalized KdV hierarchy. We focus in particular on the first leading orders of this q-deformed hierarchy, namely the q-KdV and q-Boussinesq integrable systems. We also present the q-generalization of the conformal transformations of the currents u
n
,n 2, and discuss the primary condition of the fields W
n
, n 2, by using the Volterra gauge group transformations for the q-covariant Lax operators. An induced su(n)-Toda(su(2)-Liouville) field theory construction is discussed and other important features are presented. 相似文献
17.
Whenq is a root of unity, the representations of the quantum universal enveloping algebra sl
q
(2) with multiplicity two are constructed from theq-deformed boson realization with an arbitrary parameter which is in a very general form and is first presented in this Letter. The new solutions to the Yang-Baxter equation are obtained from these representations through the universalR-matrix.This work is supported in part by the National Foundation of Natural Science of China. 相似文献
18.
The supersymmetric quantization condition is used to study the wave functions of SWKB equivalent q-deformed harmonic oscillator which are obtained by using only the knowledge of bound-state spectra of q-deformed harmonic oscillator. We have also studied the nonuniqueness of the obtained interactions by this spectral inverse
method. 相似文献
19.
D. Agboola 《Few-Body Systems》2012,52(1-2):31-38
In this paper, we investigate the spin symmetry case of a spin ${-\frac{1}{2}}$ particle governed by a q-deformed Morse potential by presenting an approximate bound-state solutions of the Dirac equation with the spin-orbit coupling term for spin symmetry vector and scalar q-deformed Morse potential within framework of the Pekeris approximation. The relativistic energy levels are obtained using the Nikiforov–Uvarov (NU) method and the two-components spinor wave functions are obtain in terms of the Jacobi polynomials. It is found that there exist only positive-energy for the bound states of some diatomic molecules under spin symmetry. 相似文献
20.
A three-dimensional representation of the double quantum algebrasu
q((J)) is given. By the use of this representation and a Lax pair, we obtain a nonlinear Ernst equation system. By the harmonic function method, a solution of theq-deformed double complex Ernst equation is given. 相似文献