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M. Daoud

Publications and source records attributed to M. Daoud.

At least 55 records · Page 3Linked to original sources
arXiv2008

Chiral bosons on Bargmann space associated with A$_r$ Statistics

We consider a large collection of particles obeying $A_r$ statistics. The system behaves like a quantum droplet characterized by a constant Husimi distribution. We show that the excitations of this system live on the boundary of the droplet and they are described by an effective chiral boson action generalizing the Wess-Zumino-Witten theory in two dimension. Our analysis is based on the Fock-Bargmann analytical representations associated to $A_r$ statistics. The quantization of the theory describing the dynamics on the edge is achieved. As by product, we prove that the edge excitations are given by a tensorial product of $r$ abelian bosonic fields.

math-ph↗
arXiv2008

Symplectic Deformations, Non Commutative Scalar Fields and Fractional Quantum Hall Effect

We clearly show that the symplectic structures deformations lead, upon quantization, to quantum theories of non commutative fields. Two variants of deformations are considered. The quantization is performed and the modes expansions of the quantum fields are derived. The Hamiltonians are given and the degeneracies lifting induced by the deformation is also discussed. As illustration, we consider the noncommutative chiral boson fields in the context of fractional quantum Hall effect. A generalized fractional filling factor is derived and shown to reproduce the Jain Hall states. We also show that the coupling of left and right edge excitations of a quantum Hall sample, gives rise a noncommutative chiral boson theory. The coupling or the non-commutativity induces a shift of the chiral components velocities. A non linear dispersion relation is obtained corroborating some recent analytical and numerical analysis.

math-ph↗
arXiv2004

Covariance of noncommutative Grassmann star product

Using the Coherent states of many fermionic degrees of freedom labeled by Graßmann variables, we introduce the noncommutative (precisely non anticommutative) Graßmann star product. The covariance of star product under unitary transformations, particularly canonical ones, is studied. The super star product, based on supercoherent states of supersymmetric harmonic oscillator, is also considered.

math-ph↗
arXiv2004

Statistical properties of Klauder-Perelomov coherent states for the Morse potential

We present in this paper a realistic construction of the coherent states for the Morse potential using the Klauder-Perelomov approach . We discuss the statistical properties of these states, by deducing the Q- and P-distribution functions. The thermal expectations for the quantum canonical ideal gas of the Morse oscillators are also calculated.

math-ph↗
arXiv2004

Generalized intelligent states of the su(N) algebra

Schr\" odinger-Robertson uncertainty relation is minimized for the quadrature components of Weyl generators of the algebra $su(N)$. This is done by determining explicit Fock-Bargamann representation of the $su(N)$ coherent states and the differential realizations of the elements of $su(N)$. New classes of coherent and squeezed states are explicitly derived.

math-ph↗
arXiv2004

Extended Voros product in the coherent states framework

Using coherent states of the Weyl-Heisenberg algebra $h_N$, extended Voros products and Moyal brakets are derived. The covariance of Voros product under canonical transformations is discussed. Star product related to Barut-Girardello coherent states of the Lie algebra $su(1,1)$ is also considered. The star eigenvalue problem of singular harmonic osillator is investigated.

math-ph↗
arXiv2004

Extended Weyl-Heisenberg algebra and Rubakov-Spiridonov superalgebra: Anyonic realizations

We give the realizations of the extended Weyl-Heisenberg (WH) algebra and the Rubakov-Spiridonov (RS) superalgebra in terms of anyons, characterized by the statistical parameter $ν\in[0,1]$, on two-dimensional lattice. The construction uses anyons defined from usual fermionic oscillators (Lerda-Sciuto construction). The anyonic realization of the superalgebra $sl(1/1)$ is also presented.

hep-th↗
arXiv2004

A Generalized Jaynes-Cummings Model: Nonlinear dynamical superalgebra $u(1/1)$ and Supercoherent states

The generalization of the Jaynes-Cummings (GJC) Model is proposed. In this model, the electromagnetic radiation is described by a Hamiltonian generalizing the harmonic oscillator to take into account some nonlinear effects which can occurs in the experimental situations. The dynamical superalgebra and supercoherent states of the related model are explicitly constructed. A relevant quantities (total number of particles, energy and atomic inversion) are computed.

hep-th↗
arXiv2003

Generalized coherent and intelligent states for exact solvable quantum systems

The so-called Gazeau-Klauder and Perelomov coherent states are introduced for an arbitrary quantum system. We give also the general framework to construct the generalized intelligent states which minimize the Robertson-Schrödinger uncertainty relation. As illustration, the Pöschl-Teller potentials of trigonometric type will be chosen. We show the advantage of the analytical representations of Gazeau-Klauder and Perelomov coherent states in obtaining the generalized intelligent states in analytical way.

math-ph↗
arXiv2003

Generalized Intelligent States for Nonlinear Oscillators

The construction of Generalized Intelligent States (GIS) for the $x^4$% -anharmonic oscillator is presented. These GIS families are required to minimize the Robertson-Schrödinger uncertainty relation. As a particular case, we will get the so-called Gazeau-Klauder coherent states. The properties of the latters are discussed in detail. Analytical representation is also considered and its advantage is shown in obtaining the GIS in an analytical way. Further extensions are finally proposed.

quant-ph↗
arXiv2003

Coherent and generalized intelligent states for infinite square well potential and nonlinear oscillators

This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system $[ 1] $. We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states à la Gazeau-Klauder and those à la Klauder-Perelomov, we derive the generalized intelligent states in analytical ways.

quant-ph↗
arXiv2003

Generalized Intelligent States for an Arbitrary Quantum System

Generalized Intelligent States (coherent and squeezed states) are derived for an arbitrary quantum system by using the minimization of the so-called Robertson-Schrödinger uncertainty relation. The Fock-Bargmann representation is also considered. As a direct illustration of our construction, the Pöschl-Teller potentials of trigonometric type will be shosen. We will show the advantage of the Fock-Bargmann representation in obtaining the generalized intelligent states in an analytical way. Many properties of these states are studied.

quant-ph↗