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Omar Mustafa

Publications and source records attributed to Omar Mustafa.

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

Twist-Induced Effects on Weyl Pairs in Magnetized Graphene Nanoribbons

This paper presents an analytical investigation into the dynamics of Weyl pairs within magnetized helicoidal graphene nanoribbons. By embedding a curved surface into flat Minkowski space-time, we derive a fully covariant two-body Dirac equation specific to this system. We begin by formulating a non-perturbative wave equation that governs the relative motion of the Weyl pairs and obtain exact solutions. Our results demonstrate the influence of the uniform magnetic field and the number of twists on the dynamics of Weyl pairs in graphene nanoribbons, providing precise energy values that lay a robust foundation for future research. Furthermore, we examine the material's response to perturbation fields by calculating the polarization function and investigating how twisting and magnetic fields affect this response. Our findings indicate that, in principle, the material's properties, which are crucial for practical applications, can be effectively controlled by precisely tuning the magnetic field and the number of twists in graphene nanoribbons.

cond-mat.mes-hall↗
arXiv2025

On the Klein-Gordon bosonic fields in the Bonnor-Melvin spacetime with a cosmological constant in rainbow gravity: Bonnor-Melvin Domain Walls

We investigate the effect of rainbow gravity on Klein-Gordon (KG) bosons in the background of the magnetized Bonnor-Melvin (BM) spacetime with a cosmological constant. We first show that the very existence of the sinusoidal term \(\sin^2(\sqrt{2Λ}r)\), in the BM space-time metric, suggests that \(\sin^2(\sqrt{2Λ}r) \in [0,1],\) which consequently restricts the range of the radial coordinate \(r\) to \(r \in [0,π/\sqrt{2Λ}]\). Moreover, we show that at \(r = 0\) and \(r = π/\sqrt{2Λ}\), the magnetized BM-spacetime introduces domain walls (infinitely impenetrable hard walls) within which the KG bosonic fields are allowed to move. Interestingly, the magnetized BM-spacetime introduces not only two domain walls but a series of domain walls. However, we focus on the range \(r \in [0,π/\sqrt{2Λ}]\). A quantum particle remains indefinitely confined within this range and cannot be found elsewhere. Based on these findings, we report the effects of rainbow gravity on KG bosonic fields in BM-spacetime. We use three pairs of rainbow functions: \( f(χ) = \frac{1}{1 - \tildeβ |E|}, \, h(χ) = 1 \); \( f(χ) = (1 - \tildeβ |E|)^{-1}, \, h(χ) = 1 \); and \( f(χ) = 1, \, h(χ) = \sqrt{1 - \tildeβ |E|^\upsilon} \), with \(\upsilon = 1,2\). Here, \(χ= |E| / E_p\), \(\tildeβ = β/ E_p\), and \(β\) is the rainbow parameter. We found that while the pairs \((f,h)\) in the first and third cases fully comply with the theory of rainbow gravity and ensure that \(E_p\) is the maximum possible energy for particles and antiparticles, the second pair does not show any response to the effects of rainbow gravity. We show that the corresponding bosonic states can form magnetized, spinning vortices in monolayer materials, and these vortices can be driven by adjusting an out-of-plane aligned magnetic field.

gr-qc↗
arXiv2025

Amelino-Camelia DSR effects on charged Dirac oscillators: Modulated spinning magnetic vortices

This work explores the two-dimensional Dirac oscillator (DO) within the framework of Amelino-Camelia doubly special relativity (DSR), employing a modified Dirac equation that preserves the first-order nature of the relativistic wave equation. By introducing non-minimal couplings, the system provides an exact analytical solution in terms of confluent hypergeometric functions, along with closed-form expressions for the energy spectrum (indulging a Landau-like signature along with accidental spin-degeneracies)-. In the low-energy limit, the results reproduce the well-known two-dimensional Dirac oscillator spectrum, and in the nonrelativistic regime, the results reduce the Schrödinger oscillator spectrum. First-order corrections in this DSR model introduce a mass-splitting term proportional to $\pm \mathcal{E}_{\circ}/\mathcal{E}_p$, where $\mathcal{E}_{\circ} = mc^2$ is the rest energy and $\mathcal{E}_p$ is the Planck energy. These corrections preserve the symmetry between the energies of particles and antiparticles around zero energy, but induce a shift in the energy levels that becomes more significant for higher excited states ($n > 0$). By mapping the system to a DSR-deformed charged Dirac oscillator in the presence of an out-of-plane uniform magnetic field, we show that the leading-order Planck-scale corrections vanish at a critical magnetic field $\mathcal{B}^{c}_{0}$, and as the magnetic field approaches this critical value, the relativistic energy levels approach $\mathcal{E}_{n,\pm} = \pm \mathcal{E}_{\circ}$. Finally, we identify a previously undetermined feature in two-dimensional charged Dirac oscillator systems in a magnetic field, revealing that the corresponding modes manifest as spinning magnetic vortices.

physics.gen-ph↗
arXiv2025

Ray geodesics and wave propagation on the Beltrami surface: Optics of an optical wormhole

This study investigates ray geodesics and wave propagation on the Beltrami surface, with a particular emphasis on the effective potentials governing photon dynamics. We derive the geodesic equations and analyze the Helmholtz equation within this curved geometry, revealing that the resulting potentials are purely repulsive. For ray trajectories, the potential is determined by wormhole parameters such as the throat radius ($\ell$), radial optical distance ($u$), scale parameter ($R$), and the angular momentum of the test field. Near the wormhole throat, the potential remains constant, preventing inward motion below a critical energy threshold, whereas at larger radial distances, it decays exponentially, allowing free propagation. In the context of wave propagation, the potential exhibits a centrifugal barrier along with a constant repulsive term at large $u$. The Beltrami surface, characterized by constant negative Gaussian curvature, serves as a model for graphene sheets and optical wormholes in condensed matter systems. These results allow us to determine the space- and frequency-dependent refractive index of the medium, providing a coherent framework for understanding photon behavior in such systems, with promising implications for material applications.

physics.class-ph↗
arXiv2025

Probing quantum criticality near the BTZ black hole horizon: Insights from coupled fermion-antifermion pairs

In this study, we analytically examine the behavior of a fermion-antifermion pair near the horizon of a static BTZ black hole using a fully covariant two-body Dirac equation with a position-dependent mass. This formulation leads to a set of four first-order equations that can be reduced to a second-order wave equation, enabling the analysis of gravitational effects on quantum interactions. Two mass modifications are considered: (i) \(m \rightarrow m - a/r\), representing an attractive Coulomb interaction, and (ii) \(m \rightarrow m - a/r + b r\), corresponding to a Cornell potential. For case (i), an exact analytical solution is obtained, while for case (ii), conditionally exact solutions involving biconfluent Heun functions are derived. For the lowest mode (\(n=0\)), the results indicate that real oscillations without energy loss occur when \(a > 0.25\) in scenario (i) and \(a > 0.75\) in scenario (ii), suggesting stable oscillatory behavior. When \(a < 0.25\) in scenario (i) or \(a < 0.75\) in scenario (ii), the state exhibits decay, indicating instability below these critical thresholds. At \(a = 0.25\) (scenario (i)) and \(a = 0.75\) (scenario (ii)), the system reaches a state where its evolution ceases over time. These findings provide insights into the stability conditions of fermion-antifermion pairs near the black hole horizon and may have relevance for determining critical coupling strengths in systems such as holographic superconductors. Furthermore, this work adopts an effective semi-classical quantum gravity approach, offering a practical framework for incorporating gravitational effects.

gr-qc↗
arXiv2025

KG- oscillators in a spinning cosmic string spacetime and an external magnetic field

We study the Klein-Gordon (KG) oscillators in a spinning cosmic string spacetime and an external magnetic field. The corresponding KG-equation is shown to admit a solution in the form of the confluent hypergeometric functions/polynomials. Consequently, the corresponding energies are shown to be given in a quadratic equation of a delicate nature that has to be solved in an orderly manner (for it involves the energies for KG-particles/antiparticles, $E=E_{\pm}=\pm\left\vert E\right\vert $ along with the magnetic quantum number $m=m_{\pm }=\pm |m|$). Following a case-by-case strategy allowed us to clearly observe the effects of the spinning cosmic string on the spectroscopic structure of the KG-oscillators. We have observed that, under some parametric settings, whilst the Landau-like energies of the KG-particles ($E=E_{+}$), with $m=m_{+}$, have no explicit dependence on the spinning string parameter or wedge parameter $α$, the KG-antiparticles ($E=E_{-}$), with $m=m_{-}$, have such explicit dependence. Interestingly, the co-existence of a spinning cosmic string and external magnetic field eliminates the effect of the wedge parameter ( a byproduct of the string) for KG-particles ($E=E_{+}$), with $m=m_{+}$, but not for the KG-antiparticles ($E=E_{-}$), with $m=m_{-}$. Such co-existence is observed to break the symmetry of the energies of the KG-particles and antiparticles about $E=0$ for KG-oscillators. However, for KG-particles ($E=E_{+}$), with $m=m_{-}$, and KG-antiparticles ($E=E_{-}$), with $m=m_{+}$, are observed to be unfortunate for being indeterminable. Moreover, for the spinning parameter $β>>1$, clustering of the energy levels is observed eminent to indicate that there is no distinction between energy levels at such values of $β$.

gr-qc↗
arXiv2025

KG-oscillators in Eddington-inspired Born-Infeld gravity: Wu-Yang magnetic monopole and Ricci scalar curvature effects

We investigate the bosonic Klein-Gordon (KG) oscillators in a global monopole (GM) spacetime in Eddington-inspired Born-Infeld (EiBI) gravity and a Wu-Yang magnetic monopole (WYMM). We discuss the gravitational effects in the presence of Ricci scalar curvature $R=R_{\upsilon }^{\upsilon }$. It is observed that the presence of the Ricci scalar curvature, effectively and manifestly, introduces a force field that makes the corresponding quantum mechanical repulsive core more repulsive. Similar effect is also observed for the EiBI-gravitational field. We reiterate and report that the corresponding bosonic KG-oscillator quantum mechanical system admits a solution in the form of confluent Heun functions, the truncation of which into a physically admissible polynomial is shown to be associated with some parametric correlations/conditions. The use of such conditions/correlations is mandatory and yields a set of allowed/restricted quantum mechanical orbital $\ell $-excitations, for all radial quantum numbers $n_{r}\geq 0$. Our procedure is shown to be quite handy, in the since that it allows one to retrieve results for KG-oscillators in GM-spacetime in different EiBI-gravity and Ricci scalar curvature settings.

gr-qc↗
arXiv2024

Klein-Gordon oscillators in traversable wormhole rainbow gravity spacetime: Conditional exact solvability via a throat radius and oscillator frequency correlation

In this study, we discuss an analytical solution for a set of the Klein-Gordon (KG) oscillators' energies through a correlation between the frequency of the KG-oscillators and the traversable wormhole (TWH) throat radius. Under such restricted parametric correlation (hence the notion of conditionally exact solvability is unavoidable in the process), we report the effects of throat radius, rainbow parameter, disclination parameter, and oscillator frequency on the spectroscopic structure of a vast number of $\left( n,m\right) $-states (the radial and magnetic quantum numbers, respectively). In the process, we only use two loop quantum gravity motivated rainbow functions pairs. The only rainbow functions that clearly and reliably fully adhere to the rainbow gravity model and secure Planck energy $E_p$ as the maximum possible energy for particles and anti-particles alike. Near the asymptotically flat upper and lower universes connected by the TWH, i.e., for the throat radius $r_{0 }>>1 $, the energies tend to cluster around the rest mass energies, i.e., $|E_{\pm }|\sim m_{0 }$. Whereas, for $r_{0 }<<1$ the energies tend to approach $|E_{\pm }| \leq E_{P}$.

gr-qc↗
arXiv2024

Minimally coupled fermion-antifermion pairs via exponentially decaying potential

In this study, we explore how a fermion-antifermion ($f\overline{f}$) pair interacts via an exponentially decaying potential. Using a covariant one-time two-body Dirac equation, we examine their relative motion in a three-dimensional flat background. Our approach leads to coupled equations governing their behavior, resulting in a general second-order wave equation. Through this, we derive analytical solutions by establishing quantization conditions for pair formation, providing insights into their dynamics. Notably, we find that such interacting $f\overline{f}$ systems are unstable and decay over time, with the decay time depending on the Compton wavelength of the fermions.

quant-ph↗
arXiv2024

An innovative model for coupled fermion-antifermion pairs

Understanding the behavior of fermion-antifermion (\(f\overline{f}\)) pairs is crucial in modern physics. These systems, governed by fundamental forces, exhibit complex interactions essential for particle physics, high-energy physics, nuclear physics, and solid-state physics. This study introduces a novel theoretical model using the many-body Dirac equation for \(f\overline{f}\) pairs with an effective position-dependent mass (i.e., \(m \rightarrow m + \mathcal{S}(r)\)) under the influence of an external magnetic field. To validate our model, we show that by modifying the mass with a Coulomb-like potential, \(m(r) = m - α/r\), where \(-α/r\) is the Lorentz scalar potential \(\mathcal{S}(r)\), our results match the well-established energy eigenvalues for \(f\overline{f}\) pairs interacting through the Coulomb potential, without approximation. By applying adjustments based on the Cornell potential (i.e., \(\mathcal{S}(r) = kr - α/r\)), we derive a closed-form energy expression. We believe this unique model offers significant insights into the dynamics of \(f\overline{f}\) pairs under various interaction potentials, with potential applications in particle physics. Additionally, it could be extended to various \(f\overline{f}\) systems, such as positronium, relativistic Landau levels for neutral mesons, excitons in monolayer transition metal dichalcogenides, and Weyl pairs in monolayer graphene sheets.

hep-ph↗
arXiv2024

KG-oscillators in Som-Raychaudhuri rotating cosmic string spacetime in a mixed magnetic field

We investigate Klein-Gordon (KG) oscillators in a Gö% del-type Som-Raychaudhuri spacetime in a mixed magnetic field (given by the vector potential $A_{μ}=\left( 0,0,A_{φ},0\right) $, with $% A_{φ}=B_{1}r^{2}/2+B_{2}r$). The resulting KG equation takes a Schr% ödinger-like form (with an oscillator plus a linear plus a Coulomb-like interactions potential) that admits a solution in the form of biconfluent Heun functions/series $H_{B}\left( α,β,γ,δ,z\right) $% . The usual power series expansion of which is truncated to a polynomial of \ order $n_{r}+1=n\geq 1$ through the usual condition $γ=2\left( n_{r}+1\right) +α$. However, we use the very recent recipe suggested by Mustafa \cite{1.29} as an alternative parametric condition/correlation. i.e., $δ=-β\left( 2n_{r}+α+3\right) $, to facilitate conditional exact solvability of the problem. We discuss and report the effects of the mixed magnetic field as well as the effects of the Gödel-type SR-spacetime background on the KG-oscillators' spectroscopic structure.

gr-qc↗
arXiv2024

KG-particles in a cosmic string rainbow gravity spacetime in mixed magnetic fields

We investigate and report the effects of rainbow gravity on the spectroscopic structure of KG-oscillators in a mixed magnetic field (in the sense that it has the usually described as a uniform and a non-uniform magnetic fields, each at a time) introduced by the 4-vector potential $A_μ=(0,0,A_φ,0)$, where $A_φ=B_1 r^2/2+B_2 r$, and $B_1$ and $B_2$ are magnetic field strengths. We also discuss and report the effects of such a mixed magnetic field on the spectra of KG-oscillators in cosmic string rainbow gravity. In so doing, we introduce a new and quite handy \textit{conditionally exact solution} associated with the truncation of the biconfluent Heun functions into polynomials. Using a loop quantum gravity motivated rainbow functions, we observe interesting effects when the magnetic field strength $B_2$ grows up from zero. Such effects include energy levels crossings which, in this case, turns the spectra of the KG-oscillators upside down. Moreover, Landau-like signature on the spectra are observed and discussed. Yet, interestingly, we also observe that rainbow gravity affects the magnetic field as well, in the sense that the magnetic field becomes probe particle energy-dependent one.

gr-qc↗
arXiv2024

On the Klein-Gordon oscillators in Eddington-inspired Born-Infeld gravity global monopole spacetime and a Wu-Yang magnetic monopole

We consider Klein-Gordon (KG) particles in a global monopole (GM) spacetime within Eddington-inspired Born-Infeld gravity (EiBI-gravity) and in a Wu-Yang magnetic monopole (WYMM). We discuss a set of KG-oscillators in such spacetime settings. We propose a textbook power series expansion for the KG radial wave function that allows us to retrieve the exact energy levels for KG-oscillators in a GM spacetime and a WYMM without EiBI-gravity. We, moreover, report some \textit{conditionally exact}, closed form, energy levels (through some parametric correlations) for KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity, and for massless KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity under the influence of a Coulomb plus linear Lorentz scalar potential. We study and discuss the effects of the Eddington parameter $κ$, GM-parameter $α$, WYMM strength $σ$, KG-oscillators' frequency $Ω$, and the coupling parameters of the Coulomb plus linear Lorentz scalar potential, on the spectroscopic structure of the KG-oscillators at hand. Such effects are studied over a vast range of the radial quantum number $n_r\geq 0$ and include energy levels clustering at $κ>>1$ (i.e., extreme EiBI-gravity), and at $|σ|>>1$ (i.e., extreme WYMM strength).

gr-qc↗
arXiv2023

Fermion-antifermion pairs in Bonnor-Melvin magnetic space-time with non-zero cosmological constant

We study the relativistic dynamics of fermion-antifermion pairs in the Bonnor-Melvin magnetic (BMM) spacetime in non-zero cosmology. We focus on the $(1+2)$-dimensional cylindrically symmetric BMM-spacetime background. Within the context of such a magnetized universe, we rigorously investigate the fully-covariant two-body Dirac equation. We derive the corresponding radial part of the equation and obtain an exact closed form analytical solution for the problem at hand. Moreover, we report some intriguing parallels with relativistic and non-relativistic quantum oscillators in flat spaces. Notably, our findings suggest a compelling correlation between the cosmological constant and the energy spectrum of fermion-antifermion systems, hinting at profound connections between quantum realms and cosmology.

physics.gen-ph↗
arXiv2023

Dynamics of the Modified Emden and pseudo-Modified Emden Equations: position-dependent mass, invariance and exact solvability

We consider the modified Emden equation (MEE) and introduce its most general solution, using the most general solution for the simple harmonic oscillator's linear dynamical equation (i.e., the initial conditions shall be identified by the PDM-MEE problem at hand) . We use a general nonlocal point transformation and show that modified Emden dynamical equation is transformed to describe position-dependent mass (PDM) classical particles. Two PDM-MEE-type classical particles are used as illustrative examples, and their exact solutions are reported. Under specific parametric considerations, the phase-space trajectories are reported for the MEE-type and for PDM-MEE-type classical particles.

physics.class-ph↗
arXiv2023

Klein-Gordon particles in a quasi-pointlike global monopole spacetime and a Wu-Yang magnetic monopole: invariance and isospectrality

We use two correlated metric functions and transform/deform the pointlike global monopole (PGM) spacetime metric into a quasi-PGM (QPGM) spacetime one. We study Klein-Gordon (KG) particles (manifestly introduced by the non-minimal coupling form of the operator $% \tilde{D}_{μ}=D_{μ}+\mathcal{F}_{μ}$, with $\mathcal{F}_{μ}$ $% \in %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion $, and $D_{μ}=\partial _{μ}-ieA_{μ}$) in such QPGM spacetime background. We show that the KG-particles in the QPGM spacetime are isospectral and invariant with KG-particles in the PGM spacetime, provided that the two metric functions are correlated. The Wu-Yang magnetic monopole (WYMM) is also included in the process. We report the effects of both monopoles PGM/QPGM and WYMM on the spectroscopic structure of two models, KG-oscillators and KG-Coulomb particles in such spacetime background. Moreover, we discuss KG-Coulomb particles and shifted KG-oscillators in a PGM spacetime and a WYMM, where such models are manifestly introduced by some Lorentz scalar interaction potentials $S(r)$. The current study is not only of fundamental observability nature but also of pedagogical interest in quantum gravity.

gr-qc↗
arXiv2023

Schrödinger oscillators in a deformed point-like global monopole spacetime and a Wu-Yang magnetic monopole: position-dependent mass correspondence and isospectrality

We show that a specific transformation/deformation in a point-like global monopole (PGM) spacetime background would yield an effective position-dependent mass (PDM) Schrödinger equation (i.e., a von Roos PDM Schrödinger equation). We discuss PDM Schrödinger oscillators in a PGM spacetime in the presence of a Wu-Yang magnetic monopole. Within our transformed/deformed global monopole spacetime, we show that all PDM Schrödinger oscillators admit isospectrality and invariance with the constant mass Schrödinger oscillators in the regular global monopole spacetime in the presence of a Wu-Yang magnetic monopole. The exclusive dependence of the thermodynamical partition function on the energy eigenvalues manifestly suggests that the Schrödinger oscillators and the PDM Schrödinger oscillators share the same thermodynamical properties as mandated by their isospectrality. Moreover, we discuss the hard-wall effect on the energy levels of the PDM Schrödinger oscillators in a PGM spacetime without and with a Wu-Yang magnetic monopole. Drastic energy levels' shift-ups are observed as a consequence of such hard-wall effect.

gr-qc↗