The symmetric q-oscillator algebra: q-coherent states, q-Bargmann–Fock realization and continuous q-Hermite polynomials with 0 < q < 1

2016 ◽  
Vol 13 (03) ◽  
pp. 1650028 ◽  
Author(s):  
H. Fakhri ◽  
A. Hashemi
Keyword(s):  
Text Analysis ◽  
Coherent States ◽  
Hermite Polynomials ◽  
Representation Space ◽  
Oscillator Algebra ◽  
Fock Representation ◽  
Minimum Uncertainty

The symmetric [Formula: see text]-analysis is used to construct a type of minimum-uncertainty [Formula: see text]-coherent states in the Fock representation space of the symmetric [Formula: see text]-oscillator ∗-algebra with [Formula: see text]. Then, its corresponding [Formula: see text]-Hermite polynomials are derived by using the [Formula: see text]-Bargmann–Fock realization of the symmetric [Formula: see text]-oscillator algebra.

Approach of the continuous q-Hermite polynomials to x-representation of q-oscillator algebra and its coherent states

2019 ◽  
Vol 17 (02) ◽  
pp. 2050021
Author(s):  
H. Fakhri ◽  
S. E. Mousavi Gharalari
Keyword(s):  
Harmonic Oscillator ◽  
Generating Function ◽  
Coherent States ◽  
Finite Interval ◽  
Hermite Polynomials ◽  
Oscillator Algebra ◽  
Text Representation ◽  
Ladder Operators ◽  
Recursion Relations ◽  
Wilson Operator

We use the recursion relations of the continuous [Formula: see text]-Hermite polynomials and obtain the [Formula: see text]-difference realizations of the ladder operators of a [Formula: see text]-oscillator algebra in terms of the Askey–Wilson operator. For [Formula: see text]-deformed coherent states associated with a disc in the radius [Formula: see text], we obtain a compact form in [Formula: see text]-representation by using the generating function of the continuous [Formula: see text]-Hermite polynomials, too. In this way, we obtain a [Formula: see text]-difference realization for the [Formula: see text]-oscillator algebra in the finite interval [Formula: see text] as a [Formula: see text]-generalization of known differential formalism with respect to [Formula: see text] in the interval [Formula: see text] of the simple harmonic oscillator.

A MODEL OF QUANTUM OSCILLATOR WITH DISCRETE SPACE

2008 ◽  
Vol 23 (13) ◽  
pp. 943-952
Author(s):  
I. I. KACHURYK ◽  
A. U. KLIMYK
Keyword(s):  
Real Line ◽  
Coherent States ◽  
Hermite Polynomials ◽  
Heisenberg Algebra ◽  
Discrete Space ◽  
Quantum Oscillator ◽  
Fock Representation ◽  
New Model

We construct a new model of the quantum oscillator, which is related to the discrete q-Hermite polynomials of the second type. The position and momentum operators in the model are appropriate operators of the Fock representation of a deformation of the Heisenberg algebra. These operators have a discrete non-degenerate spectra. These spectra are spread over the whole real line. Coordinate and momentum realizations of the model are constructed. Coherent states are explicitly given.

Coherent states attached to the quantum disc algebra and their associated polynomials

2021 ◽  
pp. 2150078
Author(s):  
H. Fakhri ◽  
M. Refahinozhat
Keyword(s):  
Coherent States ◽  
Jacobi Polynomials ◽  
Hermite Polynomials ◽  
Hermitian Operator ◽  
Fock Representation ◽  
Disc Algebra ◽  
Variable Formula ◽  
Associated Polynomials ◽  
Hermitian Conjugate ◽  
The One

The one-variable [Formula: see text]-coherent states attached to the [Formula: see text]-disc algebra are constructed and used to obtain the [Formula: see text]-Bargmann–Fock realization of its Fock representation. Then, this realization is used to obtain the [Formula: see text]-continuous Hermite polynomials as well as continuous and discrete [Formula: see text]-Hermite polynomials by using a pair of Hermitian canonical conjugate operators and two pairs of the non-Hermitian conjugate operators, respectively. Besides, we introduce a two-variable family of [Formula: see text]-coherent states attached to the Fock representation space of the [Formula: see text]-disc algebra and its opposite algebra and obtain their simultaneous [Formula: see text]-Bargmann–Fock realization. For an appropriate non-Hermitian operator, the latter realization is served to obtain the well-known little [Formula: see text]-Jacobi polynomials used in constructing the [Formula: see text]-disc polynomials.

Nonclassicality of photon-modulated spin coherent states in the Holstein-Primakoff realization

2021 ◽  
Author(s):  
Xiaoyan Zhang ◽  
Jisuo Wang ◽  
Lei Wang ◽  
Xiangguo Meng ◽  
Baolong Liang
Keyword(s):  
Coherent States ◽  
Wigner Distribution ◽  
Hermite Polynomials ◽  
Photon Number ◽  
Spin Ladder ◽  
Bernoulli Distribution ◽  
Ladder Operators ◽  
Spin Number ◽  
Photon Number Distribution ◽  
Spin Coherent States

Abstract Two new photon-modulated spin coherent states (SCSs) are introduced by operating the spin ladder operators J &#177; on the ordinary SCS in the Holstein-Primakoff realization and the nonclassicality is exhibited via their photon number distribution, second-order correlation function, photocount distribution and negativity of Wigner distribution. Analytical results show that the photocount distribution is a Bernoulli distribution and the Wigner functions are only associated with two-variable Hermite polynomials. Compared with the ordinary SCS, the photon-modulated SCSs exhibit more stronger nonclassicality in certain regions of the photon modulated number k and spin number j, which means that the nonclassicality can be enhanced by selecting suitable parameters.

scholarly journals Generalizedq-deformed Tamm-Dancoff oscillator algebra and associated coherent states

2014 ◽  
Vol 55 (8) ◽  
pp. 081702 ◽  
Author(s):  
Won Sang Chung ◽  
Mahouton Norbert Hounkonnou ◽  
Sama Arjika
Keyword(s):  
Coherent States ◽  
Oscillator Algebra

scholarly journals Generalized fermion algebra

2014 ◽  
Vol 29 (09) ◽  
pp. 1450045 ◽  
Author(s):  
Won Sang Chung ◽  
Mohammed Daoud
Keyword(s):  
Coherent States ◽  
Polynomial Representation ◽  
Fock Representation ◽  
Fermion Algebra ◽  
Grassmann Variables ◽  
Limiting Case

A one-parameter generalized fermion algebra ℬκ(1) is introduced. The Fock representation is studied. The associated coherent states are constructed and the polynomial representation, in the Bargmann sense, is derived. A special attention is devoted to the limiting case κ → 0, where the fermionic coherent states, labeled by Grassmann variables, are obtained. The physical relevance of the algebra is illustrated throughout Calogero–Sutherland system.

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