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Ilyas Haouam

Publications and source records attributed to Ilyas Haouam.

11 recordsLinked to original sources
arXiv2026

Thermal Properties of Gauge-Invariant Graphene in Noncommutative Phase-Space

We study graphene in an external magnetic field within a noncommutative (NC) framework. A gauge-invariant NC Hamiltonian is derived, and the system is analyzed using the ladder-operator formalism, yielding deformed Landau levels and eigenstates. A mapping to the anti-Jaynes-Cummings model is established, providing a bridge to quantum-optical interpretation. The thermal properties of gauge-invariant NC graphene are then investigated via the partition function, constructed using Euler and zeta functions. Analytical expressions for the partition function, free energy, internal energy, entropy, and specific heat are obtained and numerically evaluated. The results show that the NC phase-space deformation modifies the effective Landau-level spacing and consequently alters the thermal behavior of the graphene system. In particular, the deformation suppresses the thermal accessibility of excited states and produces measurable deviations from the commutative case while preserving the correct low- and high-temperature asymptotic limits.

math-ph↗
arXiv2026

Schrodinger Oscillator and its Thermal Properties in a Dynamical Noncommutative Space

In this paper, we study the two-dimensional Schrodinger oscillator within a dynamical noncommutative (DNC) space. By leveraging perturbation theory, we derive the energy eigenvalues and eigenvectors and systematically analyze the effects of both dynamical and non-dynamical noncommutative settings. First-order corrections to the eigensystem are obtained, revealing that the energy shift explicitly depends on the DNC parameter tau. Furthermore, we explore the thermal properties of the system by employing the partition function. Numerical results are presented to provide a comprehensive analysis of the system behavior under the considered effects. Notably, in the DNC framework, the commutation relations and the deformation parameter are position-dependent. Using the two-dimensional Bopp-shift, we effectively map the noncommutative problem to its commutative counterpart.

quant-ph↗
arXiv2023

Ehrenfest's Theorem for the Dirac Equation in Noncommutative Phase-Space

In this article, we investigate Ehrenfest's theorem from the Dirac equation in a noncommutative phase-space where we calculate the time derivative of the position and the kinetic momentum operators for Dirac particles in interaction with electromagnetic field and within a noncommutative setting. This allows examining the effect of the phase-space noncommutativity on Ehrenfest's theorem. Knowing that with both the linear Bopp-Shift and Moyal-Weyl product, the noncommutativity is inserted.

quant-ph↗
arXiv2023

Quantum mechanics on a circle with a finite number of α-uniformly distributed points

In this paper, quantum mechanics on a circle with finite number of α-uniformly distributed points is discussed. The angle operator and translation operator are defined. Using discrete angle representation, two types of discrete angular momentum operators and Hermitian Hamiltonian on a circle with d α-distributed discrete angles are constructed. The energy levels are computed for a free particle on a circle where the wave function is defined in the d α-distributed discrete angles.

quant-ph↗
arXiv2021

Dynamical Noncommutative Graphene

We study graphene in a two-dimensional dynamical noncommutative space in the presence of a constant magnetic field. The model is solved using perturbation theory and to the second order of perturbation. The energy levels of the system are calculated and the corresponding eigenstates are obtained. For all cases, the energy shift depends on the dynamical noncommutative parameter τ. Using the accuracy of energy measurement we put an upper bound on the noncommutativity parameter τ. In addition, we investigate some of the thermodynamic quantities of the system at zero temperature limit and extreme relativistic case, which reveals interesting differences between commutative and dynamical noncommutative spaces.

quant-ph↗
arXiv2021

Two-dimensional pauli equation in noncommutative phase-space

In this paper, we investigated the Pauli equation in a two-dimensional noncommutative phase-space by considering a constant magnetic field perpendicular to the plane. We mapped the noncommutative problem to the equivalent commutative one through a set of two-dimensional Bopp-shift transformation. The energy spectrum and the wave function of the two-dimensional noncommutative Pauli equation are found, where the problem in question has been mapped to the Landau problem. Further, within the classical limit, we have derived the noncommutative semi-classical partition function of the two-dimensional Pauli system of one-particle and N-particle systems. Consequently, we have studied its thermodynamic properties, i.e. the Helmholtz free energy, mean energy, specific heat and entropy in noncommutative and commutative phase-spaces. The impact of the phase-space noncommutativity on the Pauli system is successfully examined.

hep-th↗
arXiv2020

On the Three-Dimensional Pauli Equation in Noncommutative Phase-Space

In this paper, we obtained the three-dimensional Pauli equation for a spin-1/2 particle in the presence of an electromagnetic field in noncommutative phase-space, as well the corresponding deformed continuity equation, where the cases of a constant and non-constant magnetic field are considered. Due to the absence of the current magnetization term in the deformed continuity equation as expected, we had to extract it from the noncommutative Pauli equation itself without modifying the continuity equation. It is shown that the non-constant magnetic field lifts the order of the noncommutativity parameter in both the Pauli equation and the corresponding continuity equation. However, we successfully examined the effect of the noncommutativity on the current density and the magnetization current. By using a classical treatment, we derived the semi-classical noncommutative partition function of the three-dimensional Pauli system of the one-particle and N-particle systems. Then, we employed it for calculating the corresponding Helmholtz free energy followed by the magnetization and the magnetic susceptibility of electrons in both commutative and noncommutative phase-spaces. Knowing that with both the three-dimensional Bopp-Shift transformation and the Moyal-Weyl product, we introduced the phase-space noncommutativity in the problems in question.

math-ph↗
arXiv2020

Analytical Solution of (2+1) Dimensional Dirac Equation in Time-Dependent Noncommutative Phase-Space

In this article, we studied the system of (2+1) dimensional Dirac equation in time-dependent noncommutative phase-space. Exactly, we investigated the analytical solution of the corresponding system by the Lewis-Riesenfeld invariant method based on the construction of the Lewis-Riesenfeld invariant. Knowing that we obtained the time-dependent Dirac Hamiltonian of the problem in question from a time-dependent Bopp-Shift translation, then it used to set the Lewis-Riesenfeld invariant operators. Thereafter, the obtained results used to express the eigenfunctions that lead to determining the general solution of the system.

quant-ph↗
arXiv2020

On the Fisk-Tait Equation for Spin-3/2 Fermions Interacting With an External Magnetic Field in Noncommutative Space-Time

In this paper, we investigated the Fisk-Tait equation in interaction with an external magnetic field in noncommutative space-time. Knowing that the space-time noncommutativity is introduced through the Moyal-Weyl product known method. Consequently, we studied the continuity equation in both commutative and noncommutative space-time; there we examined the influence of the space-time noncommutativity on the current density quadri-vector. Moreover, we find that the total charge obtained from the probability density still indefinite even when space does not commute. Furthermore, we found the spin current density in the two different spin directions. We also investigated the linking between the fermions and the bosons in the Fock space using the Holstein-Primakoff transformation.

hep-th↗
arXiv2019

Continuity Equation in Presence of a Non-local potential in Non-Commutative Phase-Space

We studied the continuity equation in presence of a local potential, and a non-local potential arising from electron-electron interaction in both commutative and non-commutative phase-space. Furthermore, we examined the influence of the phase-space non-commutativity on both the locality and the non-locality, where the definition of current density in commutative phase-space cannot satisfy the condition of current conservation, but with the steady state, in order to solve this problem, we give a new definition of the current density including the contribution due to the non-local potential. We showed that the calculated current based on the new definition of current density maintains the current. As well for the case when the non-commutativity in phase-space considered, we found that the conservation of the current density completely violated; and the non-commutativity is not suitable for describing the current density in presence of non-local and local potentials. Nevertheless, under some conditions, we modified the current density to solve this problem. Subsequently, as an application we studied the Frahn-Lemmer non-local potential, taking into account that the employed methods concerning the phase-space non-commutativity are both of Bopp-shift linear transformation through the Heisenberg-like commutation relations, and the Moyal-Weyl product.

math-ph↗