Related papers: Deformed squeezed states in noncommutative phase s…
We introduce a novel class of coherent states, termed $\mathcal{W}^{(\bar{\alpha},\bar{\nu})}(z)$-coherent states, constructed using a deformed boson algebra based on the generalized factorial $[n]_{\alpha,\beta,\nu}!$. This algebra extends…
Two fundamental issues about the relation between the deformed Heisenberg-Weyl algebra in noncommutative space and the undeformed one in commutative space are elucidated. First the un-equivalency theorem between two algebras is proved: the…
In two-dimensional noncommutive space for the case of both position - position and momentum - momentum noncommuting, a constraint between noncommutative parameters is investigated. The related topic of guaranteeing Bose - Einstein…
A deformation of Heisenberg algebra induces among other consequences a loss of Hermiticity of some operators that generate this algebra. Therefore, these operators are not Hermitian, nor is the Hamiltonian operator built from them. In the…
A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…
The Heisenberg algebra is first deformed with the set of parameters ${q, l, \lambda}$ to generate a new family of generalized coherent states. In this framework, the matrix elements of relevant operators are exactly computed. A proof on…
Basic idea presented in Parts (I) and (II) for the deformed boson scheme is applied to the case of the su(2,1)-algebra for describing many-body systems consisting of three kinds of boson operators. A possible form of the coherent state for…
The dynamical algebra associated to a family of isospectral oscillator Hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates. It is shown that this representation becomes similar to that of…
We study the effects of noncommutativity and deformed Heisenberg algebra on the evolution of a two dimensional minisuperspace cosmological model in classical and quantum regimes. The phase space variables turn out to correspond to the scale…
We study several classical like properties of q-deformed nonlinear coherent states as well as nonclassical behaviours of q-deformed version of the Schrodinger cat states in noncommutative space. Coherent states in q-deformed space are found…
Minimal and maximal uncertainties of position measurements are widely considered possible hallmarks of low-energy quantum as well as classical gravity. While General Relativity describes interactions in terms of spatial curvature, its…
We consider the time-dependent bi-coherent states that are essentially the Gazeau-Klauder coherent states for the two dimensional noncommutative harmonic oscillator. Starting from some q-deformations of the oscillator algebra for which the…
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…
In this paper as a continuation of Part I, the case of two kinds of boson operators is treated. The deformation of the coherent states for the su(2)- and the su(1,1)-algebra and their related deformed algebras are discussed in various forms…
We aim to analyze the consistency of the deformation of the Heisenberg algebra in the setting of constrained Hamiltonian systems, providing a procedure to induce the deformation on the Poisson algebra after symplectic reduction. We…
The full algebra of relativistic quantum mechanics (Lorentz plus Heisenberg) is unstable. Stabilization by deformation leads to a new deformation parameter $\epsilon \ell ^{2}$, $\ell $ being a length and $\epsilon$ a $\pm$ sign. The…
Extending our previous analysis on bi-coherent states, we introduce here a new class of quantum mechanical vectors, the \emph{bi-squeezed states}, and we deduce their main mathematical properties. We relate bi-squeezed states to the…
We study the possibility of exploiting superpositions of coherent states to encode qubit. A comparison between the use of deformed and undeformed bosonic algebra is made in connection with the amplitude damping errors.
In this paper, we study the noncommutative deformation of different optical states. We develop the deformed coherent state by using the raising and lowering operators of the quantum harmonic oscillator. This helps us to investigate the…
We show that the Euclidean Snyder non-commutative space implies infinitely many different physical predictions. The distinct frameworks are specified by generalized uncertainty relations underlying deformed Heisenberg algebras. Considering…