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Abdelmalek Boumali

Publications and source records attributed to Abdelmalek Boumali.

At least 37 records · Page 2Linked to original sources
arXiv2025

Thermal properties of Klein-Gordon Oscillator in the Context of Amelino-Camelia and Magueijo-Smolin Doubly Special Relativity (DSR) frameworks

We examine the thermal and statistical properties of the one dimensional Klein-Gordon oscillator within two prominent Doubly Special Relativity (DSR) frameworks: Amelino-Camelia and Magueijo-Smolin. Using the modified dispersion relations specific to each formulation, we derive the positive energy spectra, construct the partition function via the Euler-Maclaurin method, and compute key thermodynamic quantities, including the specific heat $C_v$, as functions of temperature and the deformation scale. Planck-scale corrections produce distinct, theoretically resolvable shifts in both the position and magnitude of the $C_v$ peak in the two models. An accompanying entropy analysis reveals that these peaks correspond to smooth Schottky-type anomalies: the specific heat curves remain analytic and positive across the explored temperature range, and thus do not indicate latent or continuous thermodynamic phase transitions. These comparative results provide a robust diagnostic framework for differentiating DSR prescriptions in relativistic quantum systems and reinforce the transition-free character of their thermal response.

gr-qc↗
arXiv2025

Quantum Dynamics of Scalar Particles in a Spinning Cosmic String Background with Topological Defects: A Feshbach-Villars Formalism Perspective

We study the relativistic quantum dynamics of spin-0 particles in the spacetime of a spinning cosmic string that carries both spacelike disclination (conical deficit $α$) and screw dislocation (torsion $J_z$), as well as frame dragging ($J_t$). Using the Feshbach-Villars (FV) reformulation of the Klein-Gordon equation, we obtain a first-order Hamiltonian with a positive-definite density, enabling a clean probabilistic interpretation for bosons in curved or topologically nontrivial backgrounds. In the weak-field regime (retaining terms $\mathcal{O}(G)$ and discarding the $\mathcal{O}(G^2)$ contribution that would otherwise lead to double-confluent Heun behavior), separation of variables in a finite cylinder of radius $R_0$ yields a Bessel radial equation with an effective index $ν(α, J_t, J_z; E, k)$ that mixes rotation and torsion. The hard-wall condition $J_ν(κR_0) = 0$ quantizes the spectrum, $E_n^2 = m^2 + k^2 + \left(\frac{j_{ν,n}}{R_0}\right)^2$. Working in the stationary positive-energy sector, we derive closed-form normalized eigenfunctions and FV density, and we evaluate information-theoretic indicators (Fisher information and Shannon entropy) directly from the FV probability density. We find that increased effective confinement (via geometry/torsion) enhances Fisher information and reduces position-space Shannon entropy, quantitatively linking defect parameters to localisation/complexity. The FV framework thus provides a robust, computationally transparent route to spectroscopy and information measures for scalar particles in rotating/torsional string backgrounds, and it smoothly reproduces the pure-rotation, pure-torsion, and flat-spacetime limits.

hep-th↗
arXiv2025

Dirac Oscillator in DSR: A Comparative Study of Magueijo-Smolin and Amelino-Camelia Models

This paper investigates the energy spectrum of the Dirac oscillator within the framework of Doubly Special Relativity (DSR), focusing on two prominent models: the Magueijo--Smolin (MS) and Amelino-Camelia models. We derive the modified Dirac equations in both MS and Amelino-Camelia DSR models under the approximation of $$O(E^{2}/k^{2})$$ for a single particle and examine the resulting energy spectra. The study reveals significant corrections to the standard relativistic Dirac oscillator spectrum due to the Planck-scale deformation parameter $$k$$, which introduces distinct deviations depending on the DSR model employed. For the MS model, we observe non-uniform shifts in both positive and negative energy branches at small $$k$$, with the spectrum gradually flattening toward the canonical result as $$k$$ increases. In the Amelino-Camelia model, the energy levels show larger deviations at lower values of $$k$$, and these anomalies diminish more slowly compared to the MS model. The results provide insights into the impact of quantum gravity effects on quantum systems, with potential applications in high-precision spectroscopic or astrophysical observations at energies near the Planck scale. Furthermore, the comparative analysis of these two DSR models highlights the robustness of Planck-scale predictions and guides future experimental efforts aimed at detecting quantum-gravity signatures.

physics.gen-ph↗
arXiv2025

Dirac Oscillator for Spin-1/2 Particles in a Spinning Cosmic String Spacetime with Spacelike Disclination and Dislocation

We study the Dirac oscillator for spin-1/2 particles in a spacetime containing a spinning cosmic string endowed with both curvature (disclination) and torsion (screw dislocation). The background geometry includes off-diagonal and is analyzed through a local tetrad formalism. Working in cylindrical coordinates, we derive the covariant Dirac equation and solve it exactly via a second-order differential equation for the lower spinor component. Three distinct physical configurations are examined: (i) balanced torsion where temporal and spatial contributions are equal, (ii) purely temporal torsion (spinning string), and (iii) purely spatial torsion (screw dislocation). In all cases, we obtain exact energy spectra expressed in terms of effective angular quantum numbers that depend on the oscillator frequency, the angular deficit parameter α, the torsional parameters J_{t} and J_{z}, and the longitudinal momentum k. The resulting energy levels generalize the flat-spacetime Moshinsky oscillator spectrum by incorporating energy- and momentum-dependent shifts due to the background geometry. We show that curvature and torsion lift degeneracies and induce nontrivial modifications to the angular structure of the solutions. The flat-space spectrum is recovered as a special limit when both curvature and torsion vanish. This work provides a fully solvable model that illustrates how spacetime defects affect relativistic quantum systems, offering insights relevant to both high-energy physics and condensed-matter analogs.

gr-qc↗
arXiv2025

Quantum Dynamics of a Scalar Particle in Schwarzschild Spacetime using the Generalized Feshbach Villars Transformation

In this work, we apply the generalised Feshbach Villars transformation (GFVT) to spin-0 scalar fields in a Schwarzschild gravitational background. Starting from the covariant Klein Gordon equation, we reformulate the dynamics in the FV two-component representation, which enables a natural separation of positive- and negative-energy branches. In the far-field approximation, the system exhibits a hydrogen like bound spectrum, confirming the ability of GFVT to provide a consistent probabilistic interpretation in curved spacetime. We then extend the formalism by introducing a relativistic harmonic oscillator potential, which transforms the radial equation into a biconfluent Heun form. The requirement of square integrability leads to a discrete oscillator spectrum that remains independent of the gravitational parameter, with gravity appearing only through selection rules on the admissible quantum states. Explicit wave functions, probability densities, and graphical results are presented, illustrating the internal consistency of the method. Overall, this study demonstrates the effectiveness of GFVT as a bridge between relativistic quantum mechanics and curved geometry, and it highlights its potential for future applications in strong gravitational fields.

gr-qc↗
arXiv2025

Eigensolutions of the two Dimensional Kemmer Oscillator in Noncommutative Space with Minimal Length Effects

This paper investigates a two-dimensional Kemmer oscillator within relativistic quantum mechanics, incorporating minimal length and non-commutative phase space effects. We derive eigen solutions in configuration space $\{p\}$, examining the relationship between minimal length and non-commutative parameters. Our analysis reveals a connection to the Schrödinger equation through a Pöschl-Teller potential, enhancing our understanding of fundamental quantum phenomena in relativistic systems.

hep-th↗
arXiv2023

Dynamics of a Klein-Gordon Oscillator (KGO) in the Presence of a Cosmic String in Som-Raychaudhuri Space-Time

This paper explores the dynamics of the Klein-Gordon oscillator in the presence of a cosmic string in Som Raychaudhuri spacetime. The exact solutions for the free case and the oscillator case are obtained and discussed. These solutions reveal the effects of the cosmic string and the spacetime geometry on the bosonic particles. To illustrate these results, some figures and tables have been included.

hep-th↗
arXiv2023

Applications of the Klein-Gordon equation in the Feshbach-Villars representation in the non-inertial cosmic string space-time

We study the relativistic quantum motion of a spineless particle using the Feshbach-Villars (FV) formalism in the spinning cosmic string spacetime. The movement equations are derived using the first-order FV formulation of the Klein-Gordon (KG) equation. We apply the equation of motion (a) to study the motion of the particle confined to a rigid-wall potential, (b) motion in the presence of a Coulomb-type potential, and (c) particle interacting with the Feshbach-Villars oscillator (FVO). The energy levels and wave functions are obtained for the three cases. Our study focused on the impact of rotation and curvature on the energy levels of the particle

hep-th↗
arXiv2023

Feshbach-Villars oscillator (FVO) in Kaluza-Klein Theory (KKT)

This research investigates the relativistic quantum dynamics of spin-0 scalar massive charged particles via the relativistic Feshbach-Villars oscillator in the background of the Kaluza-Klein Theory. We solve the Feshbach-Villars equation in the abckground of a cosmic string spec-time in the context of the Kaluza-Klein and presented the eigenvalue solution. Afterward, we rewrite this system in the case of the Feshbach-Villars quantum oscillator and obtain the eigenvalue analytically. Finally, we study the interaction of the Feshbach-Villars equation and oscillator in a cosmic dislocation in the Som-Raychaudhuri in the context of the Kaluza-Klein Theory and solve the wave equation analytically. We analyze the influence of topological defect in the quantification of energy and wave function of the Feshbach-Villars oscillator and with the external fields in the last one

hep-th↗
arXiv2023

Behavior of the Feshbach-Villars oscillator (FVO) in Gürses space-time under Coulomb-type potential

Our research aims to investigate how the gravitational field influences the spectroscopic structure of the Feshbach-Villars oscillator in Gürses space-time. To achieve this, we utilize the first-order Feshbach-Villars version of the Klein-Gordon equation, which is a relativistic wave equation for spinless particles. We examine the oscillator's quantum mechanical behavior in the presence of a Coulomb-type potential, and calculate the resulting wave functions and energy levels for both free and interacting scenarios. In addition, we study the interaction between the Coulomb-type potential and Gürses space-time affects the Feshbach-Villars oscillator's behavior, specifically with regard to its spectroscopic structure. This study has important implications for our understanding of the interplay between quantum mechanics, relativity, and gravitational fields at the microscopic level.

hep-th↗
arXiv2023

On the Feshbach-Villars oscillators (FVO) under coulomb potential in the cosmic dislocation space-time

In this paper, we investigate the quantum mechanical dynamics of the massive and relativistic Feshbach-Villars oscillator in cosmic dislocation space-time induced by a coulomb-type potential. The first-order Feshbach-Villars version of the Klein-Gordon equation is used to find movement equations. Wave functions and associated energy have been calculated (both in the free case and in the interaction case). We analyse the impact of dislocation topology on this interaction. As a result, the effect of the dislocation on the quantum system under study is examined.

quant-ph↗
arXiv2023

Statistical proerties of the two-dimensional Feshbach-illars oscillator (FVO) in the rotating cosmic string

This paper is concerned with an investigation of the quantum mechanical dynamics of massive, spinless relativistic Klein-Gordon particle in the space-time generated by a rotating cosmic string. The equations of motion are found by the use of the first-order Feshbach-Villars formulation of the Klein-Gordon equation. The wave-functions and the associated energies were deduced ( both in the free and in the interaction case). Following that, the partition function was approximated using Zeta function representation. Moreover, by considering the energy spectrum of the system in question, the thermal properties are presented. We examine the behavior of these properties as a function of the physical parameters of the model such as rotation, curvature, and quantum numbers. Therefore, the impact of the topological defect on the quantum system under investigation is discussed.

hep-th↗
arXiv2018

The statistical properties of q-deformed Morse potential for some diatomic molecules

In this paper we present a closed-form expression of the vibrational partition function for the one-dimensional q-deformed Morse potential energy model. Through this function the related thermodynamic functions are derived and studied in terms of the parameters of the model. Specially, we plotted the q-deformed vibrational partition function, and vibrational specific heat for some diatomic molecule systems such as H2, HCl, LiH and CO. The idea of a critical temperature T_{C} is introduced in relation to the specific heat.

quant-ph↗
arXiv2017

Shannon Entropy and Fisher Information of the one-dimensional Klein-Gordon oscillator with energy-dependent potential

In this paper, we studied, at first, the influence of the energy-dependent potentials on the one-dimensionless Klein-Gordon oscillator. Then, the Shannon entropy and Fisher information of this system are investigated. The position and momentum information entropies for the low-lying states n=0,1,2 are calculated. Some interesting features of both Fisher and Shannon densities as well as the probability densities are demonstrated.

quant-ph↗
arXiv2016

The statistical properties of the q-deformed Dirac oscillator in one and two-dimensions

In this paper, we study the behavior of the eigenvalues of the one and two dimensions of q-deformed Dirac oscillator. The eigensolutions have been obtained by using a method based on the q-deformed creation and annihilation operators in both dimensions. For a two-dimensional case, we have used the complex formalism which reduced the problem to the problem of one dimensional case. The influence of the q-numbers on the eigenvalues has been well analyzed. Also, the connection between the q-oscillator and a quantum optics is well established. Finally, for very small deformation η, we have mentioned to existence of well-known q-deformed version of Zitterbewegung in relativistic quantum dynamics, and calculated the partition function and all thermal quantities such as the free energy, total energy, entropy and specific heat: here we consider only the case of a pure phase (q=e^{iη}). The extension to the case of graphene has been discussed

hep-th↗