An observation of quadratic algebra, dual family of nonlinear coherent states and their non-classical properties, in the generalized isotonic oscillator

V. Chithiika Ruby, Murugaian Senthilvelan

arXiv:1202.5104Journal of Mathematical PhysicsAug 1, 20126 citations

$(q;l,λ)-$deformed Heisenberg algebra: representations, special functions and quantization

Mahouton Norbert Hounkonnou, Sama Arjika, Ezinvi Baloïtcha

arXiv:1301.7028Jan 29, 20130 citations

arXiv:1309.3100 · Journal of Nonlinear Mathematical Physics

On nonlinear coherent states properties for electron-phonon dynamics

Isiaka Aremua, Mahouton Norbert Hounkonnou, Ezinvi Baloïtcha

Published Feb 18, 2014• 0 citations

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Abstract

DOI: 10.1080/14029251.2014.894723

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On nonlinear coherent states properties for electron-phonon dynamics

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V. Chithiika Ruby, Murugaian Senthilvelan

In this paper, we construct nonlinear coherent states for the generalized isotonic oscillator and study their non-classical properties in detail. By transforming the deformed ladder operators suitably, which generate the quadratic algebra, we obtain Heisenberg algebra. From the algebra, we define two non-unitary and one unitary displacement type operators. While the action of one of the non-unitary type operators reproduces the original nonlinear coherent states, the other one fails to produce a new set of nonlinear coherent states (dual pair). We show that these dual states are not normalizable. For the nonlinear coherent states, we evaluate the parameter A3 and examine the non-classical nature of the states through quadratic and amplitude-squared squeezing effect. Further, we derive analytical formula for the P-function, Q-function, and the Wigner function for the nonlinear coherent states. All of them confirm the non-classicality of the nonlinear coherent states. In addition to the above, we obtain the harmonic oscillator type coherent states from the unitary displacement operator.In this paper, we construct nonlinear coherent states for the generalized isotonic oscillator and study their non-classical properties in detail. By transforming the deformed ladder operators suitably, which generate the quadratic algebra, we obtain Heisenberg algebra. From the algebra, we define two non-unitary and one unitary displacement type operators. While the action of one of the non-unitary type operators reproduces the original nonlinear coherent states, the other one fails to produce a new set of nonlinear coherent states (dual pair). We show that these dual states are not normalizable. For the nonlinear coherent states, we evaluate the parameter A3 and examine the non-classical nature of the states through quadratic and amplitude-squared squeezing effect. Further, we derive analytical formula for the P-function, Q-function, and the Wigner function for the nonlinear coherent states. All of them confirm the non-classicality of the nonlinear coherent states. In addition to the above, we obtain the harmonic oscillator type coherent states from the unitary displacement operator.

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$(q;l,λ)-$ deformed Heisenberg algebra: representations, special functions and quantization$(q;l,λ)-$deformed Heisenberg algebra: representations, special functions and quantization

Mahouton Norbert Hounkonnou, Sama Arjika, Ezinvi Baloïtcha

This paper addresses a new characterization of Sudarshan's diagonal representation of the density matrix elements $ρ(z',z)$ , derivedfrom $(q;l,λ)-$ deformed boson coherent states.The induced $ρ(z',z)$ self-reproducing property with the associated self-reproducing kernel $K(z',z)$ is computed and analyzed. An explicit construction of novel classes of generalized continuous $(q;l,λ)-$ Hermite polynomials is provided with the corresponding recursion relations and exact resolution of the moment problems giving their orthogonality weight functions. Besides, the Berezin-Klauder-Toeplitz quantization of classical phase space observables and relevant normal and anti-normal forms are investigated and discussed.This paper addresses a new characterization of Sudarshan's diagonal representation of the density matrix elements $ρ(z',z)$, derivedfrom $(q;l,λ)-$deformed boson coherent states.The induced $ρ(z',z)$ self-reproducing property with the associated self-reproducing kernel $K(z',z)$ is computed and analyzed. An explicit construction of novel classes of generalized continuous $(q;l,λ)-$Hermite polynomials is provided with the corresponding recursion relations and exact resolution of the moment problems giving their orthogonality weight functions. Besides, the Berezin-Klauder-Toeplitz quantization of classical phase space observables and relevant normal and anti-normal forms are investigated and discussed.

arXiv:1301.7028Jan 29, 20130 citations

(q;l,λ)-

deformed Heisenberg algebra: representations, special functions and quantization

This paper addresses a new characterization of Sudarshan's diagonal representation of the density matrix elements

ρ(z',z)

, derivedfrom

(q;l,λ)-

deformed boson coherent states.The induced

ρ(z',z)

self-reproducing property with the associated self-reproducing kernel

K(z',z)

is computed and analyzed. An explicit construction of novel classes of generalized continuous

(q;l,λ)-

Hermite polynomials is provided with the corresponding recursion relations and exact resolution of the moment problems giving their orthogonality weight functions. Besides, the Berezin-Klauder-Toeplitz quantization of classical phase space observables and relevant normal and anti-normal forms are investigated and discussed.