arXiv subjects

Ahmed Jellal

Publications and source records attributed to Ahmed Jellal.

At least 163 records · Page 9Linked to original sources

arXiv2012

Entanglement in Coupled Harmonic Oscillators via Unitary Transformation

We develop an approach to study the entanglement in two coupled harmonic oscillators. We start by introducing an unitary transformation to end up with the solutions of the energy spectrum. These are used to construct the corresponding coherent states through the standard way. To evaluate the degree of the entanglement between the obtained states, we calculate the purity function in terms of the coherent and number states, separately. The result is yielded to two parameters dependance of the purity, which can be controlled easily. Interesting results are derived by fixing the mixing angle of such transformation as π/2. We compare our results with already published work and point out the relevance of these findings to a systematic formulation of the entanglement effect in two coupled harmonic oscillators.

quant-ph↗

arXiv2012

Massless Dirac Fermions in Electromagnetic Field

We study the relations between massless Dirac fermions in an electromagnetic field and atoms in quantum optics. After getting the solutions of the energy spectrum, we show that it is possible to reproduce the 2D Dirac Hamiltonian, with all its quantum relativistic effects, in a controllable system as a single trapped ion through the Jaynes--Cummings and anti-Jaynes--Cummings models. Also we show that under certain conditions the evolution of the Dirac Hamiltonian provides us with Rashba spin-orbit and linear Dresselhaus couplings. Considering the multimode multiphoton Jaynes-Cummings model interacting with N modes of electromagnetic field prepared in general pure quantum states, we analyze the Rabi oscillation. Evaluating time evolution of the Dirac position operator, we determine the Zitterbewegung frequency and the corresponding oscillating term as function of the electromagnetic field.

hep-th↗

arXiv2011

Solution of One-dimensional Dirac Equation via Poincare Map

We solve the general one-dimensional Dirac equation using a "Poincare Map" approach which avoids any approximation to the spacial derivatives and reduces the problem to a simple recursive relation which is very practical from the numerical implementation point of view. To test the efficiency and rapid convergence of this approach we apply it to a vector coupling Woods--Saxon potential, which is exactly solvable. Comparison with available analytical results is impressive and hence validates the accuracy and efficiency of this method.

hep-th↗

arXiv2011

Diamagnetism of Confined Dirac Fermions in Disordered Graphene

The diamagnetism of confined Dirac fermions submitted to a uniform magnetic field in disordered graphene is investigated. The solutions of the energy spectrum are used to discuss the orbital magnetism from a statistical mechanical point of view. More precisely, by the technique of Green functions the self-energy for short and long-ranged disorders is obtained. This allows us to determine the susceptibility for short and long-ranged disorders together with confinement. We compare our results with already published work and point out the relevance of these findings to a systematic formulation of the diamagnetism in a confining potential.

cond-mat.mes-hall↗

arXiv2011

Noncommutative Description of Quantum Spin Hall Effect

We propose an approach based on a generalized quantum mechanics to deal with the basic features of the intrinsic spin Hall effect. This can be done by considering two decoupled harmonic oscillators on the noncommutative plane and evaluating the spin Hall conductivity. Focusing on the high frequency regime, we obtain a diagonalized Hamiltonian. After getting the corresponding spectrum, we show that there is a Hall conductivity without an external magnetic field, which is noncommutativity parameter θ-dependent. This allows us to make contact with the spin Hall effect and also give different interpretations. Fixing θ, one can recover three different approaches dealing with the phenomenon.

hep-th↗

arXiv2011

Fractional Quantum Hall States in Graphene

We quantum mechanically analyze the fractional quantum Hall effect in graphene. This will be done by building the corresponding states in terms of a potential governing the interactions and discussing other issues. More precisely, we consider a system of particles in the presence of an external magnetic field and take into account of a specific interaction that captures the basic features of the Laughlin series ν={1\over 2l+1}. We show that how its Laughlin potential can be generalized to deal with the composite fermions in graphene. To give a concrete example, we consider the SU(N) wavefunctions and give a realization of the composite fermion filling factor. All these results will be obtained by generalizing the mapping between the Pauli--Schrödinger and Dirac Hamiltonian's to the interacting particle case. Meantime by making use of a gauge transformation, we establish a relation between the free and interacting Dirac operators. This shows that the involved interaction can actually be generated from a singular gauge transformation.

hep-th↗

arXiv2011

Tunneling for Dirac Fermions in Constant Magnetic Field

The tunneling effect of two-dimensional Dirac fermions in a constant magnetic field is studied. This can be done by using the continuity equation at some points to determine the corresponding reflexion and transmission coefficients. For this, we consider a system made of graphene as superposition of two different regions where the second is characterized by an energy gap t'. In fact, we treat concrete systems to practically give two illustrations: barrier and diode. For each case, we discuss the transmission in terms of the ratio of the energy conservation and t'. Moreover, we analyze the resonant tunneling by introducing a scalar Lorentz potential where it is shown that a total transmission is possible.

hep-th↗

arXiv2011

Electromagnetic Excitations of Hall Systems on Four Dimensional Space

The noncommutativity of a four-dimensional phase space is introduced from a purely symplectic point of view. We show that there is always a coordinate map to locally eliminate the gauge fluctuations inducing the deformation of the symplectic structure. This uses the Moser's lemma; a refined version of the celebrated Darboux theorem. We discuss the relation between the coordinates change arising from Moser's lemma and the Seiberg--Witten map. As illustration, we consider the quantum Hall systems on CP^2. We derive the action describing the electromagnetic interaction of Hall droplets. In particular, we show that the velocities of the edge field, along the droplet boundary, are noncommutativity parameters-dependents.

hep-th↗

arXiv2010

Dirac Fermions in Inhomogeneous Magnetic Field

We study a confined system of Dirac fermions in the presence of inhomogeneous magnetic field. Splitting the system into different regions, we determine their corresponding energy spectrum solutions. We underline their physical properties by considering the conservation energy where some interesting relations are obtained. These are used to discuss the reflexion and transmission coefficients for Dirac fermions and check the probability condition for different cases. We generalize the obtained results to a system with gap and make some analysis. After evaluating the current-carrying states, we analyze the Klein paradox and report interesting discussions.

cond-mat.mes-hall↗

arXiv2010

Electromagnetic Excitations of A_n Quantum Hall Droplets

The classical description of A_n internal degrees of freedom is given by making use of the Fock--Bargmann analytical realization. The symplectic deformation of phase space, including the internal degrees of freedom, is discussed. We show that the Moser's lemma provides a mapping to eliminate the fluctuations of the symplectic structure, which become encoded in the Hamiltonian of the system. We discuss the relation between Moser and Seiberg--Witten maps. One physics applications of this result is the electromagnetic excitation of a large collection of particles, obeying the generalized A_n statistics, living in the complex projective space CP^k with U(1)background magnetic field. We explicitly calculate the bulk and edge actions. Some particular symplectic deformations are also considered.

hep-th↗

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

A Noncommutative Space Approach to Confined Dirac Fermions in Graphene

A generalized algebra of noncommutative coordinates and momenta embracing non-Abelian gauge fields is proposed. Through a two-dimensional realization of this algebra for a gauge field including electromagnetic vector potential and two spin-orbit-like coupling terms, a Dirac-like Hamiltonian in noncommutative coordinates is introduced. We established the corresponding energy spectrum and from that we derived the relation between the energy level quantum number and the magnetic field at the maxima of Shubnikov-de Haas oscillations. By tuning the non-commutativity parameter θin terms of the values of magnetic field at the maxima of Shubnikov-de Haas oscillations we accomplished the experimentally observed Landau plot of the peaks for graphene. Accepting that the experimentally observed behavior is due to the confinement of carriers, we conclude that our method of introducing noncommutative coordinates provides another formulation of the confined massless Dirac fermions in graphene.

cond-mat.mes-hall↗

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↗

arXiv2009

Confined Dirac Fermions in a Constant Magnetic Field

We obtain an exact solution of the Dirac equation in (2+1)-dimensions in the presence of a constant magnetic field normal to the plane together with a two-dimensional Dirac-oscillator potential coupling. The solution space consists of a positive and negative energy solution, each of which splits into two disconnected subspaces depending on the sign of an azimuthal quantum number, k = 0, \pm 1, \pm 2,... and whether the cyclotron frequency is larger or smaller than the oscillator frequency. The spinor wavefunction is written in terms of the associated Laguerre polynomials. For negative k, the relativistic energy spectrum is infinitely degenerate due to the fact that it is independent of k. We compare our results with already published work and point out the relevance of these findings to a systematic formulation of the relativistic quantum Hall effect in a confining potential.

hep-th↗

arXiv2008

Periodic Structures with Rashba Interaction in Magnetic Field

We analyze the behaviour of a system of particles living on a periodic crystal in the presence of a magnetic field B. This can be done by involving a periodic potential U(x) and the Rashba interaction of coupling constant k_{so}. By resorting the corresponding spectrum, we explicitly determine the band structures and the Bloch spinors. These allow us to discuss the system symmetries in terms of the polarizations where they are shown to be broken. The dynamical spin will be studied by calculating different quantities. In the limits: k_{so} and U(x)=0, we analyze again the system by deriving different results. Considering the strong $B$ case, we obtain an interesting result that is the conservation of the polarizations. Analyzing the critical point λ_{k,σ}=\pm\sq{1\over 2}, we show that the Hilbert space associated to the spectrum in z-direction has a zero mode energy similar to that of massless Dirac fermions in graphene. Finally, we give the resulting energy spectrum when B=0 and U(x) is arbitrary.

hep-th↗

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↗

arXiv2008

Anomalous Quantum Hall Effect on Sphere

We study the anomalous quantum Hall effect exhibited by the relativistic particles living on two-sphere S^2 and submitted to a magnetic monopole. We start by establishing a direct connection between the Dirac and Landau operators through the Pauli--Schrödinger Hamiltonian H_{s}^{SP}. This will be helpful in the sense that the Dirac eigenvalues and eigenfunctions will be easily derived. In analyzing H_{s}^{SP} spectrum, we show that there is a composite fermion nature supported by the presence of two effective magnetic fields. For the lowest Landau level, we argue that the basic physics of graphene is similar to that of two-dimensional electron gas, which is in agreement with the planar limit. For the higher Landau levels, we propose a SU(N) wavefunction for different filling factors that captures all symmetries. Focusing on the graphene case, i.e. N=4, we give different configurations those allowed to recover some known results.

hep-th↗