Generalized deformed algebra

Chung, Won Sang; Chung, K.S.; Nam, Sang-Tack; Um, Chung-In

doi:10.1016/0375-9601(93)90589-r

Cited by 81 publications

(57 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Most of deformations of a boson algebra have been accomplished until now [29][30][31][32][33]. Some of them are constructed by using the Jackson's qcalculus [34], while others are not.…”

Section: Introductionmentioning

confidence: 99%

Cat-states in the framework of Wigner–Heisenberg algebra

et al. 2015

View full text Add to dashboard Cite

A one-parameter generalized Wigner-Heisenberg algebra( WHA) is reviewed in detail. It is shown that WHA verifies the deformed commutation rule [x,p λ ] = i(1+ 2λR) and also highlights the dynamical symmetries of the pseudo-harmonic oscillator( PHO). The present article is devoted to the study of new cat-states built from λ-deformed Schrödinger coherent states, which according to the Barut-Girardello scheme are defined as the eigenstates of the generalized annihilation operator. Particular attention is devoted to the limiting case where the Schrödinger cat states are obtained. Nonclassical features and quantum statistical properties of these states are studied by evaluation of Mandel's parameter and quadrature squeezing with respect to the λ−deformed canonical pairs (x,p λ ). It is shown that these states minimize the uncertainty relations of each pair of the su(1, 1) components.

show abstract

“…Most of deformations of a boson algebra have been accomplished until now [29][30][31][32][33]. Some of them are constructed by using the Jackson's qcalculus [34], while others are not.…”

Section: Introductionmentioning

confidence: 99%

Cat-states in the framework of Wigner–Heisenberg algebra

et al. 2015

View full text Add to dashboard Cite

show abstract

“…In [18] we have been generalized two-parameter deformed oscillator algebra [11] by introducing additional parameters α, γ, l in the structure function. This is a generalization of the well-known deformations [6,4,5,11,14,15,23] of these algebras. The generators {I, a, a + , N }, structure function (7) and the defining relations…”

Section: Some Aspects Of Generalized (P Q; α γ L)-deformed Oscillamentioning

confidence: 99%

“…In this paper we propose the unified deformation of the oscillator algebra which envelop as particular cases the well known deformations [6,4,5,11,14,15]. The structure function ("generalized (p, q; α, γ, l)-number") of this deformation…”

Section: Introductionmentioning

confidence: 99%

“…On the level of oscillator algebra, the study of multi-parameter deformations of the oscillator algebra was continued in the works [14,15,16,17,18].…”

Section: Introductionmentioning

confidence: 99%

“…Naturally, the increasing of the number of the deformation parameters makes the application of the deformed oscillator algebras more flexible in the practical applications. In the framework of one-parameter deformation this scheme combined with scheme of construction of the generalized deformed oscillator algebras [22] has given possibility to unify in unified framework [14,15,23,16,18] the well-known deformations of the oscillator algebra [6,4,5].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Unified -deformation of oscillator algebra and two-dimensional conformal field theory

Burban

2013

Physics Letters A

View full text Add to dashboard Cite

Two types of q‐deformed Wigner algebra

Chung

2014

Fortschritte der Physik

View full text Add to dashboard Cite

In this paper we introduce two types of q‐deformed Wigner algebras. One is q‐deformation of Wigner algebra with q‐reflection symmetry and another is q‐deformation of Wigner algebra with reflection symmetry. For two types of q‐deformed Wigner algebras, we investigate the representation and the eigenvalue of the position operator. Like q‐calculus, we introduce the (q; ν)‐ numbers, (q; ν)‐derivatives and (q; ν)‐Hermite polynomials for two algebras. For the deformation parameter q = 1 ‐ ϵ with small ϵ, we discuss the thermodynamics of the particle obeying the q‐deformed Wigner algebra.

show abstract

Generalized deformed algebra

Cited by 81 publications

References 14 publications

Cat-states in the framework of Wigner–Heisenberg algebra

Cat-states in the framework of Wigner–Heisenberg algebra

Unified -deformation of oscillator algebra and two-dimensional conformal field theory

Two types of q‐deformed Wigner algebra

Contact Info

Product

Resources

About