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M. Daoud

Publications and source records attributed to M. Daoud.

69 records · Page 4Linked to original sources
arXiv2001

On Fractional Supersymmetric Quantum Mechanics: The Fractional Supersymmetric Oscillator

The Hamiltonian for a fractional supersymmetric oscillator is derived from three approaches. The first one is based on a decomposition in which a Q-uon gives rise to an ordinary boson and a k-fermion (a k-fermion being an object interpolating between boson and fermion). The second one starts from a generalized Weyl-Heisenberg algebra. Finally, the third one relies on the quantum algebra Uq(sl(2)) where q is a root of unity.

math-ph↗
arXiv2000

Fractional Spin through Quantum Affine Algebra $\hat A(n)$ and quantum affine superalgebra $\hat A(n,m)$

Using the splitting of a $Q$-deformed boson, in the $Q \to q= e^{\frac{\rm 2πi}{\rm k}}$ limit, the fractional decomposition of the quantum affine algebra $\hat A(n)$ and the quantum affine superalgebra $\hat A(n,m)$ are found. This decomposition is based on the oscillator representation and can be related to the fractional supersymmetry and k-fermionic spin. We establish also the equivalence between the quantum affine algebra $\hat A(n)$ and the classical one in the fermionic realization.

hep-th↗
arXiv1998

Two-Photon Laser Spectroscopy of Transition Ions in Crystals: Inter- Configurational Transitions

Symmetry adaptation techniques are applied to the determination of the intensity of two-photon absorption transitions, between Stark levels of configurations with opposite parities, for transition ions in finite symmetry environments. The equivalence between third-order mechanisms and second- plus first-order mechanisms is clearly established. A compact formula is derived for the intensity of a two-photon transition between two levels with well-defined symmetries. A set of (selection) rules which controls the number of intensity parameters for inter-configurational transitions is given. The formalism is illustrated with the case of an ion with 4f configuration in tetragonal symmetry.

physics.atm-clus↗
arXiv1998

Symmetry Adaptation and Two-Photon Spectroscopy of Ions in Molecular or Solid-State Finite Symmetry

Finite symmetry adaptation techniques are applied to the determination of the intensity strength of two-photon transitions for ions with one partly-filled shell nl in crystalline environments of symmetry G. We treat the case of intra- configurational transitions as well as the case of inter-configurational transitions. In both cases, the Wigner-Racah algebra of the chain O(3) > G allows to extract the polarization dependence from the intensity. The reported results are valid for any strength of the crystalline field.

physics.atm-clus↗
arXiv1998

Sum Rules for Multi-Photon Spectroscopy of Ions in Finite Symmetry

Models describing one- and two-photon transitions for ions in crystalline environments are unified and extended to the case of parity-allowed and parity- forbidden p-photon transitions. The number of independent parameters for characterizing the polarization dependence is shown to depend on an ensemble of properties and rules which combine symmetry considerations and physical models.

physics.atm-clus↗
arXiv1998

Symmetry Adaptation Techniques in n-Photon Absorption Spectroscopy

We present some recent progress achieved in the application of symmetry adaptation techniques to n-photon absorption spectroscopy of rare earth ions in finite symmetry. More specifically, this work is concerned with the determination of the intensity of n-photon transitions between Stark levels (rather than J levels) of an ion in an environment with a given symmetry. The role of symmetry is taken into account through the use of initial and final state vectors characterized by irreducible representations of the (double) group for the ion site symmetry. Two distinct situations are considered, viz., the case of parity-allowed and parity-forbidden n-photon transitions.

physics.atm-clus↗
arXiv1998

Two-Photon Spectroscopy of Transition-Metal Ions in Cubical Symmetry

Symmetry adaptation techniques are applied to the determination of intensities of intra-configurational two-photon transitions for transition-metal ions in cubical symmetry. This leads to a simple model giving the polarization dependence of intensities of two-photon (electric dipolar) transitions between Stark levels of the configuration 3dN (N = even or odd).

physics.atm-clus↗
arXiv1998

Intensity of Two-Photon Absorption Transitions for Ni2+ in MgO

The parity-allowed two-photon transitions between the ground state 3A2(T2) of the configuration 3d8 in cubical symmetry and the excited states of the same configuration are obtained via a simple model. This model is developed in a symmetry adapted framework by using second-order mechanisms and ionic wave-functions. It is applied to the recent experimental results obtained by McClure and co-workers for Ni2+ in MgO.

physics.atm-clus↗
arXiv1998

On Generalized Super-Coherent States

A set of operators, the so-called k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of an algebra arising from two non-commuting quon algebras. The deformation parameters q and 1/q for these quon algebras are roots of unity with q to the power k being equal to 1. The case k = 2 corresponds to fermions and the case k going to infinity to bosons. Generalized coherent states (connected to the k-fermionic states) and super-coherent states (involving a k-fermionic sector and a purely bosonic sector) are investigated.

quant-ph↗
arXiv1997

An Alternative Basis for the Wigner-Racah Algebra of the Group SU(2)

The Lie algebra of the classical group SU(2) is constructed from two quon algebras for which the deformation parameter is a common root of unity. This construction leads to (i) a not very well-known polar decomposition of the ladder generators of the SU(2) Lie algebra and to (ii) an alternative to the (J,M) quantization scheme, viz., the (J,alpha) quantization scheme. The key ideas for developing the Wigner-Racah algebra of the group SU(2) in the (J,alpha) scheme are given. In particular, some properties of the coupling and recoupling coefficients as well as the Wigner-Eckart theorem in the (J,alpha) scheme are briefly discussed.

math-ph↗
arXiv1997

The k-fermions as objects interpolating between fermions and bosons

Operators, refered to as k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of two noncommuting quon algebras. The deformation parameters for these quon algebras are roots of unity connected to an integer k. The case k=2 corresponds to fermions and the limiting case k going to infinity to bosons. Generalized coherent states and supercoherent states are investigated. The Dirac quantum phase operator and the Fairlie-Fletcher-Zachos algebra are also considered.

quant-ph↗
arXiv1996

On $qp$-Deformations in Statistical Mechanics of Bosons in D Dimensions

The Bose distribution for a gas of nonrelativistic free bosons is derived in the framework of $qp$-deformed second quantization. Some thermodynamical functions for such a system in D dimensions are derived. Bose-Einstein condensation is discussed in terms of the parameters q and p as well as a parameter $ν_0'$ which characterizes the representation space of the oscillator algebra.

cond-mat.stat-mech↗
arXiv1996

Statistical Mechanics of $qp$-Bosons in $D$ Dimensions

This paper is concerned with statistical properties of a gas of $qp$-bosons without interaction. Some thermodynamical functions for such a system in $D$ dimensions are derived. Bose-Einstein condensation is discussed in terms of the parameters $q$ and $p$. Finally, the second-order correlation function of a gas of photons is calculated.

quant-ph↗
arXiv1995

Two-Photon Spectroscopy Between States of Opposite Parities

Magnetic- and electric-dipole two-photon absorption (MED-TPA), recently introduced as a new spectroscopic technique for studying transitions between states of opposite parities, is investigated from a theoretical point of view. A new approximation, referred to as {\it weak quasi-closure approximation}, is used together with symmetry adaptation techniques to calculate the transition amplitude between states having well-defined symmetry properties. Selection rules for MED-TPA are derived and compared to selection rules for parity-forbidden electric-dipole two-photon absorption (ED-TPA).

atom-ph↗