© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Physica Scripta

On theq-deformed coherent states of a generalizedf-oscillator

Marcelo A. Marchiolli

Published Dec 22, 2005• 10 citations

Abstract

Adopting the framework of the generalized q -deformed Heisenberg–Weyl algebra , we present a mathematical procedure which leads us to obtain analytical expressions for a general class of q -deformed coherent states associated with the different patterns of the energy spectrum exhibited by the nonlinear f -oscillator. In particular, we establish the properties of a small group of q -deformed coherent states for α > γ > 0 with emphasis on the resolution of unity. As an application of these properties, we investigate the Robertson–Schrödinger uncertainty relation and the squeezing effect for the deformed coordinate and momentum operators, which are defined in terms of the abstract elements of this algebra. Furthermore, we also obtain the Wigner function and the correct quantum-mechanical marginal distributions in phase space.

DOI: 10.1088/0031-8949/73/1/009

Related papers

Generalized q-deformed Tamm-Dancoff oscillator algebra and associated coherent states

Won Sang Chung, Mahouton Norbert Hounkonnou, Sama Arjika

In this paper, we propose a full characterization of a generalized q-deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the condition satisfied by the deformed q-number to define the algebra structure function. Particular Fock spaces involving finite and infinite dimensions are examined. A deformed calculus is performed as well as a coordinate realization for this algebra. A relevant example is exhibited. Associated coherent states are constructed. Finally, some thermodynamics aspects are computed and discussed.

arXiv:1403.1311•Journal of Mathematical Physics•Jul 17, 2014•2 citations

Maths-type q-deformed coherent states for q > 1

Quesne, C, K. A. Penson, Tkachuk, V M

Maths-type q-deformed coherent states with $q > 1$ allow a resolution of unity in the form of an ordinary integral. They are sub-Poissonian and squeezed. They may be associated with a harmonic oscillator with minimal uncertainties in both position and momentum and are intelligent coherent states for the corresponding deformed Heisenberg algebra.

•Mar 19, 2003•37 citations

Energy spectrum, potential and inertia functions of a generalizedf-oscillator

Salomon Sylvain Mizrahi, J P Camargo Lima, V. V. Dodonov

We consider a generalized four-parameter q -algebra AA † − q γ A † A = q α N +β , [ N , A ] = − A , [ N , A †] = A †, associating with operators A and A † the nonlinear f -oscillator operators, defined in terms of the usual harmonic oscillator operators as A ≡ af ( N ) and A † ≡ f *( N ) a † (where a and a † are operators of the Weyl–Heisenberg algebra and N = a † a ). The function f ( N ) is determined from the commutation relations. We write the Hamiltonian for the free f -oscillator and obtain its energy spectrum. Besides, expressing the Hamiltonian in terms of coordinate and momentum, we determine the potential and inertia functions (coordinate-dependent mass) and analyse their behaviour by varying the parameters.

Journal of Physics A Mathematical and General•Mar 2, 2004•44 citations

On the coherent states, displacement operators and quasidistributions associated with deformed quantum oscillators

Paolo Aniello, Vladimir I. Man’ko, Giuseppe Marmo +2 more

The Wigner (W), Husimi-Kano (Q) and Glauber-Sudarshan (P) quasidistributions are generalized to f-deformed quasidistributions which extend the parametric family of s-ordered quasidistributions of Cahill and Glauber. The deformation procedure is obtained via a canonical nonisometric transform of the displacement operators which preserves the form of the standard creation-annihilation commutation relation, hence the Heisenberg-Weyl algebra, but changes the scalar product in the Hilbert space of the oscillator states. A whole class of new resolutions of the identity is introduced. The time evolution equation for the new generalized quasidistributions is derived.

Journal of Optics B Quantum and Semiclassical Optics•Nov 15, 2000•60 citations

The quantum multiboson algebra and generalized coherent states of SUq(1,1)

Zhe Chang

The author gives a generalization of the deformed oscillator and shows that it satisfies the quantum Weyl-Heisenberg group. The nonlinear transformations from the usual deformed oscillator operators to the deformed k-boson operators form an Abelian group. The generalized Holstein-Primakoff realizations in terms of these multiboson operators are used to define the quantum group-theoretic coherent states of SU q (1,1).

Journal of Physics A Mathematical and General•Jun 21, 1992•10 citations

Generalized deformed oscillators in framework of unified (q;α,β,γ;ν)-deformation and their oscillator algebras

Igor Burban

The aim of this paper is to review our results on description of the multi-parameter deformed oscillators and their oscillator algebras. We define generalized (q;α,β,γ;ν)-deformed oscillator algebra and study its irreducible representations. The Arik-Coon oscillator with the main relation aa^+ - q a^+a = 1, where q > 1 is embedded in this framework. We find connection of this oscillator with the Askey (1/q)-Hermite polynomials. We construct family of the generalized coherent states associated with these polynomials and give their explicit expression in terms of standard special functions. By means of the solution of appropriate classical Stielties moment problem we prove the (over)completeness relation of these states.

arXiv:1110.1025•Oct 5, 2011•0 citations

Adopting the framework of the generalized q -deformed Heisenberg–Weyl algebra , we present a mathematical procedure which leads us to obtain analytical expressions for a general class of q -deformed coherent states associated with the different patterns of the energy spectrum exhibited by the nonlinear f -oscillator. In particular, we establish the properties of a small group of q -deformed coherent states for α > γ > 0 with emphasis on the resolution of unity. As an application of these properties, we investigate the Robertson–Schrödinger uncertainty relation and the squeezing effect for the deformed coordinate and momentum operators, which are defined in terms of the abstract elements of this algebra. Furthermore, we also obtain the Wigner function and the correct quantum-mechanical marginal distributions in phase space.

In this paper, we propose a full characterization of a generalized q-deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the condition satisfied by the deformed q-number to define the algebra structure function. Particular Fock spaces involving finite and infinite dimensions are examined. A deformed calculus is performed as well as a coordinate realization for this algebra. A relevant example is exhibited. Associated coherent states are constructed. Finally, some thermodynamics aspects are computed and discussed.

Maths-type q-deformed coherent states with

q > 1

allow a resolution of unity in the form of an ordinary integral. They are sub-Poissonian and squeezed. They may be associated with a harmonic oscillator with minimal uncertainties in both position and momentum and are intelligent coherent states for the corresponding deformed Heisenberg algebra.

We consider a generalized four-parameter q -algebra AA † − q γ A † A = q α N +β , [ N , A ] = − A , [ N , A †] = A †, associating with operators A and A † the nonlinear f -oscillator operators, defined in terms of the usual harmonic oscillator operators as A ≡ af ( N ) and A † ≡ f *( N ) a † (where a and a † are operators of the Weyl–Heisenberg algebra and N = a † a ). The function f ( N ) is determined from the commutation relations. We write the Hamiltonian for the free f -oscillator and obtain its energy spectrum. Besides, expressing the Hamiltonian in terms of coordinate and momentum, we determine the potential and inertia functions (coordinate-dependent mass) and analyse their behaviour by varying the parameters.

The Wigner (W), Husimi-Kano (Q) and Glauber-Sudarshan (P) quasidistributions are generalized to f-deformed quasidistributions which extend the parametric family of s-ordered quasidistributions of Cahill and Glauber. The deformation procedure is obtained via a canonical nonisometric transform of the displacement operators which preserves the form of the standard creation-annihilation commutation relation, hence the Heisenberg-Weyl algebra, but changes the scalar product in the Hilbert space of the oscillator states. A whole class of new resolutions of the identity is introduced. The time evolution equation for the new generalized quasidistributions is derived.

The aim of this paper is to review our results on description of the multi-parameter deformed oscillators and their oscillator algebras. We define generalized (q;α,β,γ;ν)-deformed oscillator algebra and study its irreducible representations. The Arik-Coon oscillator with the main relation aa^+ - q a^+a = 1, where q > 1 is embedded in this framework. We find connection of this oscillator with the Askey (1/q)-Hermite polynomials. We construct family of the generalized coherent states associated with these polynomials and give their explicit expression in terms of standard special functions. By means of the solution of appropriate classical Stielties moment problem we prove the (over)completeness relation of these states.