arXiv subjects

Mohammed Daoud

Publications and source records attributed to Mohammed Daoud.

49 records · Page 3Linked to original sources

arXiv2010

Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets

We show that the integer quantum Hall effect systems in plane, sphere or disc, can be formulated in terms of an algebraic unified scheme. This can be achieved by making use of a generalized Weyl--Heisenberg algebra and investigating its basic features. We study the electromagnetic excitation and derive the Hamiltonian for droplets of fermions on a two-dimensional Bargmann space (phase space). This excitation is introduced through a deformation (perturbation) of the symplectic structure of the phase space. We show the major role of Moser's lemma in dressing procedure, which allows us to eliminate the fluctuations of the symplectic structure. We discuss the emergence of the Seiberg--Witten map and generation of an abelian noncommutative gauge field in the theory. As illustration of our model, we give the action describing the electromagnetic excitation of a quantum Hall droplet in two-dimensional manifold.

hep-th↗

arXiv2010

Phase operators, temporally stable phase states, mutually unbiased bases and exactly solvable quantum systems

We introduce a one-parameter generalized oscillator algebra A(k) (that covers the case of the harmonic oscillator algebra) and discuss its finite- and infinite-dimensional representations according to the sign of the parameter k. We define an (Hamiltonian) operator associated with A(k) and examine the degeneracies of its spectrum. For the finite (when k < 0) and the infinite (when k > 0 or = 0) representations of A(k), we construct the associated phase operators and build temporally stable phase states as eigenstates of the phase operators. To overcome the difficulties related to the phase operator in the infinite-dimensional case and to avoid the degeneracy problem for the finite-dimensional case, we introduce a truncation procedure which generalizes the one used by Pegg and Barnett for the harmonic oscillator. This yields a truncated generalized oscillator algebra A(k,s), where s denotes the truncation order. We construct two types of temporally stable states for A(k,s) (as eigenstates of a phase operator and as eigenstates of a polynomial in the generators of A(k,s)). Two applications are considered in this article. The first concerns physical realizations of A(k) and A(k,s) in the context of one-dimensional quantum systems with finite (Morse system) or infinite (Poeschl-Teller system) discrete spectra. The second deals with mutually unbiased bases used in quantum information.

quant-ph↗

arXiv2009

Magnetism of Two Coupled Harmonic Oscillators

The thermodynamical properties of a system of two coupled harmonic oscillators in the presence of an uniform magnetic field B are investigated. Using an unitary transformation, we show that the system can be diagonalized in simple way and then obtain the energy spectrum solutions. These will be used to determine the thermodynamical potential in terms of different physical parameters like the coupling parameter α. This allows us to give a generalization of already significant published work and obtain different results, those could be used to discuss the magnetism of the system. Different limiting cases, in terms of αand B, have been discussed. In fact, quantum corrections to the Landau diamagnetism and orbital paramagnetism are found.

cond-mat.stat-mech↗

arXiv2008

Quantum Hall Effect on the Flag Manifold F_2

The Landau problem on the flag manifold ${\bf F}_2 = SU(3)/U(1)\times U(1)$ is analyzed from an algebraic point of view. The involved magnetic background is induced by two U(1) abelian connections. In quantizing the theory, we show that the wavefunctions, of a non-relativistic particle living on ${\bf F}_2$, are the SU(3) Wigner ${\cal D}$-functions satisfying two constraints. Using the ${\bf F}_2$ algebraic and geometrical structures, we derive the Landau Hamiltonian as well as its energy levels. The Lowest Landau level (LLL) wavefunctions coincide with the coherent states for the mixed SU(3) representations. We discuss the quantum Hall effect for a filling factor $ν=1$. where the obtained particle density is constant and finite for a strong magnetic field. In this limit, we also show that the system behaves like an incompressible fluid. We study the semi-classical properties of the system confined in LLL. These will be used to discuss the edge excitations and construct the corresponding Wess-Zumino-Witten action.

hep-th↗

arXiv2008

Quantum Hall Droplets on Disc and Effective Wess-Zumino-Witten Action for Edge States

We algebraically analysis the quantum Hall effect of a system of particles living on the disc ${\bf B}^1$ in the presence of an uniform magnetic field $B$. For this, we identify the non-compact disc with the coset space $SU(1,1)/U(1)$. This allows us to use the geometric quantization in order to get the wavefunctions as the Wigner ${\cal D}$-functions satisfying a suitable constraint. We show that the corresponding Hamiltonian coincides with the Maass Laplacian. Restricting to the lowest Landau level, we introduce the noncommutative geometry through the star product. Also we discuss the state density behavior as well as the excitation potential of the quantum Hall droplet. We show that the edge excitations are described by an effective Wess-Zumino-Witten action for a strong magnetic field and discuss their nature. We finally show that LLL wavefunctions are intelligent states.

hep-th↗

arXiv2007

Effective Wess-Zumino-Witten Action for Edge States of Quantum Hall Systems on Bergman Ball

Using a group theory approach, we investigate the basic features of the Landau problem on the Bergman ball {\bf B}^k. This can be done by considering a system of particles living on {\bf B}^k in the presence of an uniform magnetic field B and realizing the ball as the coset space SU(k,1)/U(k). In quantizing the theory on {\bf{B}}^k, we define the wavefunctions as the Wigner \cal{D}-functions satisfying a set of suitable constraints. The corresponding Hamiltonian is mapped in terms of the right translation generators. In the lowest Landau level, we obtain the wavefunctions as the SU(k,1) coherent states. This are used to define the star product, density matrix and excitation potential in higher dimensions. With these ingredients, we construct a generalized effective Wess-Zumino-Witten action for the edge states and discuss their nature.

hep-th↗

arXiv2006

Fractional supersymmetry and hierarchy of shape invariant potentials

Fractional supersymmetric quantum mechanics is developed from a generalized Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional supersymmetric dynamical systems are built in terms of the generators of this algebra. The Hamiltonian gives rise to a hierarchy of isospectral Hamiltonians. Special cases of the algebra lead to dynamical systems for which the isospectral supersymmetric partner Hamiltonians are connected by a (translational or cyclic) shape invariance condition.

quant-ph↗

arXiv2006

Representations and Properties of Generalized $A_r$ Statistics, Coherent States and Robertson Uncertainty Relations

The generalization of $A_r$ statistics, including bosonic and fermionic sectors, is performed by means of the so-called Jacobson generators. The corresponding Fock spaces are constructed. The Bargmann representations are also considered. For the bosonic $A_r$ statistics, two inequivalent Bargmann realizations are developed. The first (resp. second) realization induces, in a natural way, coherent states recognized as Gazeau-Klauder (resp. Klauder-Perelomov) ones. In the fermionic case, the Bargamnn realization leads to the Klauder-Perelomov coherent states. For each considered realization, the inner product of two analytic functions is defined in respect to a measure explicitly computed. The Jacobson generators are realized as differential operators. It is shown that the obtained coherent states minimize the Robertson-Schrödinger uncertainty relation.

math-ph↗

arXiv2006

Representations of Generalized a$_r$ Statistics and Eigenstates of Jacobson Generators

We investigate a generalization of $A_r$ statistics discussed recently in the literature. The explicit complete set of state vectors for the $A_r$ statistics system is given. We consider a Bargmann or an analytic function description of the Fock space corresponding to $A_r$ statistics of bosonic kind. This brings, in a natural way, the so-called Gazeau-Klauder coherent states defined as eigenstates of the Jacobson annihilation operators. The minimization of Robertson uncertainty relation is also considered.

math-ph↗

arXiv2006

Representations and Properties of Generalized $A_r$ Statistics

A generalization of $A_r$ statistics is proposed and developed. The generalized $A_r$ quantum statistics is completely specified by a set of Jacobson generators satisfying a set of triple algebraic relations. Fock-Hilbert representations and Bargmann-Fock realizations are derived.

math-ph↗

arXiv2004

On supersymmetric quantum mechanics

This paper constitutes a review on N=2 fractional supersymmetric Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl-Heisenberg algebra W_k. It is shown how a general Hamiltonian can be associated with the algebra W_k. This general Hamiltonian covers various supersymmetrical versions of dynamical systems (Morse system, Poschl-Teller system, fractional supersymmetric oscillator of order k, etc.). The case of ordinary supersymmetric Quantum Mechanics corresponds to k=2. A connection between fractional supersymmetric Quantum Mechanics and ordinary supersymmetric Quantum Mechanics is briefly described. A realization of the algebra W_k, of the N=2 supercharges and of the corresponding Hamiltonian is given in terms of deformed-bosons and k-fermions as well as in terms of differential operators.

quant-ph↗

arXiv2000

D-dimensional Ideal Quantum Gases in $Ar^{n}+Br^{-n}$ Potential

The paper is concerned with thermostatistics of both $D$-dimensional Bose and Fermi ideal gases in a confining potential of type $Ar^{n}+Br^{-n}$. The investigation is performed in the framework of the semiclassical approximation. Some physical quantities for such systems are derived, like density of states, density profiles and number of particles. Bose-Einstein condensation (BEC) is discussed in the high and low temperature regimes.

hep-th↗

arXiv1999

A Fractional Supersymmetric Oscillator and Its Coherent States

We review some basic elements on k-fermions, which are objects interpolating between bosons and fermions. In particular, we define k-fermionic coherent states and study some of their properties. The decomposition of a Q-uon into a boson and a k-fermion leads to a definition of fractional supercoherent states. Such states involve bosonic coherent states and k-fermionic coherent states. We construct an Hamiltonian which generalizes the ordinary (or Z_2-graded) supersymmetric oscillator Hamiltonian. Our Hamiltonian describes a fractional (or Z_k-graded) supersymmetric oscillator for which the fractional supercoherent states are coherent states.

math-ph↗