Browsing by Author "Dogan, Semra Gurtas"

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Charged Fermions and Vector Bosons in Magnetic Fields Within a Spacetime Generated by a Spinning Point Source
(Elsevier, 2025) Dogan, Semra Gurtas; Mustafa, Omar; Guvendi, Abdullah
We investigate the relativistic dynamics of charged fermions and vector bosons in magnetic fields within a 2+1-dimensional spacetime background generated by a spinning point source. We derive the equations for the charged Dirac oscillator (DO) and charged vector bosons, aiming to find analytical solutions to the resulting wave equations. We identify solutions for both systems by analytically examining the allowed wave equations and analyzing the impact of each parameter on the resulting relativistic energy eigenvalues. Our observations reveal that the spin parameter ((omega) over bar) of the point source can cause symmetry breaking in particle-antiparticle energy states around the Dirac point, an effect that disappears when (omega) over bar = 0. However, for charged vector bosons in such a spinning spacetime, the asymmetry between particle-antiparticle states persists even when (omega) over bar = 0.
Coupled Fermion-Antifermion Pairs Within a Traversable Wormhole
(Elsevier, 2025) Guvendi, Abdullah; Mustafa, Omar; Dogan, Semra Gurtas
This study investigates the dynamics of fermion-antifermion (f f) pairs within a traversable wormhole (TWH) spacetime by solving the two-body covariant Dirac equation with a position-dependent mass m -> m(r). In the context of a static, radially symmetric (2+1)-dimensional TWH characterized by a constant redshift function and a given shape function, we explore two Lorentz scalar potentials: (i) a Coulomb-like potential and (ii) an exponentially decaying potential. The Coulomb potential leads to positronium-like binding energies, with the ground state (n=0) energy approximately E-n(b)approximate to-m(e)c(2)alpha(2)/4 similar to-6.803 eV. On the other hand, the exponential potential establishes critical mass thresholds, m(c)=(n+1/2)& hstrok;/2 lambda(c)c, at which the energy approaches zero, causing the system to cease to exist over time. Stability is maintained when n+1/22 leads to decay. The energy spectrum reveals essential features of the system, and the wave function reflects the influence of the wormhole's throat, shaping spatial configurations and probability distributions. This work enhances our understanding of quantum phenomena in curved spacetimes and establishes connections to condensed matter physics.
Damped Modes for a Bosonic Quantum Oscillator in the Near-Horizon Geometry of the Btz Black Hole
(Springer/Plenum Publishers, 2023) Guvendi, Abdullah; Dogan, Semra Gurtas
We analyse the evolution of a generalized bosonic oscillator in the near horizon geometry of the BTZ black hole by analytically obtaining a solution of the associated Klein-Gordon equation. We show that it is possible to obtain relativistic frequency expression in closed-form for the system in question. Here, we observe that such a system decays in time without any real oscillation and the damped modes depend explicitly on the parameters of the oscillator coupling besides the parameters of the background geometry. This result allows us to analyse the influences of both oscillator coupling and spacetime parameters on the evolution of such a test field. Also, the results indicate that the spacetime background is stable under this perturbation field.
Effect of Internal Magnetic Flux on a Relativistic Spin-1 Oscillator in the Spinning Point Source-Generated Spacetime
(World Scientific Publishing Co Pte Ltd, 2023) Guvendi, Abdullah; Dogan, Semra Gurtas
In this paper, we consider a charged relativistic spin-1 oscillator under the influence of an internal magnetic flux in a (2+1)-dimensional spacetime induced by a spinning point source. In order to analyze the effects of the internal magnetic flux and spin of the point source on the relativistic dynamics of such a vector field, we seek a non-perturbative solution of the associated spin-1 equation derived as an excited state of Zitterbewegung. By performing an analytical solution of the resulting equation, we determine exact results for the system in question. Accordingly, we analyze the effects of spin of the point source and internal magnetic flux on the relativistic dynamics of the considered test field. We see that the spin of such a field can be altered by the magnetic flux and this means that the considered system may behave as a fermion or boson according to the varying values of the magnetic flux, in principle. We observe that the internal magnetic flux and the spin of the point source impact on the relativistic energy levels and probability density functions. Also, our results indicate that the spin of the point source breaks the symmetry of the energy levels corresponding to particle-antiparticle states.
Fermion-Antifermion Pair Exposed to Magnetic Flux in an Optical Wormhole
(Springer Wien, 2023) Guvendi, Abdullah; Dogan, Semra Gurtas
We introduce an exactly soluble model for a fermion-antifermion pair exposed to magnetic flux in the hyperbolic wormhole. This model is based on an analytical solution of the corresponding two-body Dirac equation. We show a non-perturbative wave equation for such a pair in exactly soluble form. This makes it possible to acquire a complete energy spectrum. Results clearly show the effects of the magnetic flux as well as the wormhole background on the dynamics of the considered pair and such a composite system may behave as a single fermion or a single boson by depending on the magnetic flux. This implies that one can control the dynamics of such a pair in an optical background with constant negative Gaussian curvature.
Frame-Dragging and Light Deflection in Rotating Optical Wormhole Spacetimes
(Elsevier, 2025) Errehymy, Abdelghani; Guvendi, Abdullah; Dogan, Semra Gurtas; Mustafa, Omar
In this work, we present a detailed analytical study of null geodesics in a family of rotating optical wormhole spacetimes with constant negative Gaussian curvature, encompassing hyperbolic, elliptic, and Beltrami geometries. By explicitly deriving the full set of null geodesic equations, we characterize photon trajectories in these curved, rotating backgrounds. Our analysis highlights the role of rotation in shaping light paths, showing how frame-dragging effects, ergoregion emergence (despite the absence of event horizons), and alterations in causal structure influence photon dynamics. We construct exact forms of the effective potential governing radial photon motion, allowing for a systematic investigation of orbit stability and critical trajectories. Closed-form expressions for gravitational deflection angles are obtained, along with clear conditions for the presence and positioning of optical horizons unique to these geometries. Our findings demonstrate that the interplay between rotational effects and the geometry-specific radial shape functions crucially determines how light behaves in these exotic spacetimes. While some features echo those of analog gravity models, our framework remains strictly within general relativity. This study provides a rigorous foundation for understanding gravitational lensing and horizon behavior in spacetimes with nontrivial topology.
Geometric and Wave Optics in a BTZ Optical Metric-Based Wormhole
(Elsevier, 2025) Dogan, Semra Gurtas; Guvendi, Abdullah; Mustafa, Omar
We investigate the geometric and wave optical properties of a (2 + 1)-dimensional ultra-static spacetime conformally related to the static BTZ black hole, characterized by constant negative Gaussian curvature. The associated optical metric defines a hyperbolic wormhole geometry, wherein null geodesics experience a P & ouml;schl-Teller-type repulsive effective potential that suppresses circular photon orbits and directs all trajectories toward the optical origin. In the wave regime, we reformulate the Helmholtz equation into a Schr & ouml;dinger-like form, revealing a spatially localized effective potential that encodes curvature and angular momentum effects. The resulting refractive index n(p,w)) is both spatially and spectrally dispersive, leading to a position-dependent critical frequency wc(P) that delineates the boundary between propagating and evanescent modes. At high frequencies, the medium becomes asymptotically transparent, while for w
Magnetic Flux-Driven Modulation of Weyl Pair Dynamics on Catenoid Bridge: A Theoretical Analysis
(Elsevier, 2024) Guvendi, Abdullah; Dogan, Semra Gurtas
In this study, we examine the behavior of a Weyl pair influenced by magnetic flux on a catenoid bridge by obtaining analytical solutions of the corresponding fully covariant two-body Dirac equation. By deriving a non-perturbative wave equation governing their relative motion, we obtain a solution expressed in terms of the Confluent Heun function. Our findings indicate that the dynamics of this pair are influenced not only by the magnetic flux but also by the radius (rho) of the catenoid bridge. We observe that the ground state energy of the Weyl pair can vary significantly, shifting from 0.258 . 258 eV to 1.8 meV as the rho value changes from 10 nm to 1 mu m. Furthermore, our results show that the Weyl pair's behavior can resemble that of either a single fermion or boson, and intriguingly, this behavior can be modulated by adjusting the magnetic flux.
Minimally Coupled Fermion-Antifermion Pairs Via Exponentially Decaying Potential
(Springer, 2024) Guvendi, Abdullah; Dogan, Semra Gurtas; Mustafa, Omar
In this study, we explore how a fermion-antifermion (ff\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\overline{f}$$\end{document}) 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 ff\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\overline{f}$$\end{document} systems are unstable and decay over time, with the decay time depending on the Compton wavelength of the fermions.
Photonic Modes in Twisted Graphene Nanoribbons
(Elsevier, 2025) Guvendi, Abdullah; Dogan, Semra Gurtas; Mustafa, Omar; Hasanirokh, Kobra
This study investigates the behavior of photonic modes in twisted graphene nanoribbons (TGNRs) using an analytical approach based on solving the fully covariant vector boson equation. We present a model that demonstrates how helical twisting in TGNRs significantly affects the evolution of photonic modes. Our analytical solutions yield detailed expressions for mode profiles, energy spectra, and decay characteristics. We find that increasing the twist parameter shortens the decay times (tau ns) for damped modes, indicating enhanced photonic coupling due to the twisted geometry. Conversely, longer nanoribbons (NRs) exhibit increased decay times, showing a length (L)-dependent effect, where a tau ns proportional to L / e , with e representing the speed of light. These findings may enhance the understanding of light control in nanostructures and suggest potential applications in tunable photonic devices, topological photonics, and quantum optical systems.
Ray and Wave Optics in an Optical Wormhole
(Elsevier, 2025) Dogan, Semra Gurtas; Guvendi, Abdullah; Mustafa, Omar
We examine ray trajectories and wave dynamics in an optical wormhole with constant negative Gaussian curvature, analogous to a monolayer graphene sheet or graphene wormholes. Focusing on the elliptic wormhole (EWH), we derive exact solutions for ray trajectories and show that the effective potential is impenetrable at the optical origin u = 0, but rapidly vanishes at large distances, allowing trajectories to remain unaffected. By solving the Helmholtz equation on the EWH surface, we find that S-waves (m = 0) are indefinitely trapped at the origin by an infinitely attractive effective potential, whereas modes with m not equal 0 encounter an infinitely repulsive barrier. Additionally, we determine the spatially and frequency-dependent refractive index characterizing the EWH and discuss the corresponding optical response of the background.
Ray and Wave Optics in Bonnor-Melvin Domain Walls: Photon Rings
(Elsevier, 2025) Dogan, Semra Gurtas; Mustafa, Omar; Guvendi, Abdullah
In this study, we examine the propagation of light rays and wave dynamics within the (2+ 1)- dimensional analogue of the Bonnor-Melvin magnetic (BMM) spacetime, which incorporates a nonzero cosmological constant. The BMM spacetime, characterized by cylindrical symmetry, maintains Lorentz invariance along the axial direction, facilitating a systematic investigation of ray trajectories and wave behavior in the corresponding (2+1)-dimensional magnetic background. This three-dimensional spacetime can be derived as a (2+ 1 +0)-brane solution within the context of gravity coupled to nonlinear electrodynamics. Initially, we analyze general ray trajectories and derive exact solutions for the angular motion of light rays. Our findings reveal that light is confined to circular paths within a specific radial region, indicating the formation of light rings governed by the magnetic background. Extending this analysis to wave dynamics, we solve the Helmholtz equation analytically, identifying discrete wave modes with quantized frequencies. The background gravitational field induces oscillatory wave behavior, resulting in well-defined photonic states. These states are notably ring-shaped and rotate, resembling magnetic vortices.
Ray and Wave Optics in Twisted Graphene Nanoribbons
(IOP Publishing Ltd, 2025) Dogan, Semra Gurtas; Mustafa, Omar; Turgut, Guven; Guvendi, Abdullah
We investigate ray trajectories and wave propagation on a continuous helicoidal surface describing twisted graphene nanoribbons (TGNRs), treating the surface as a distortion-free structure and neglecting lattice discreteness and variations in hopping parameters. This low-dimensional curved geometry is described by a radial coordinate u is an element of [-d/2, d/2] and an angular coordinate v is an element of [ - & ell;/2, & ell;/2], where d and & ell; are the ribbon's width and total length, respectively. We derive a closed-form expression for the angular velocity of rays, with an analytical solution for the full trajectory being achievable only for narrow helicoids (u4 approximate to 0). We then solve the Helmholtz equation on the twisted surface, transforming it into a one-dimensional Schr & ouml;dinger-like form, which yields a refractive index dependent on radial position and frequency, controlled by the number of twists along the ribbon. We identify critical thresholds that distinguish regimes where the refractive index is real or complex, determined by the radial distance, twist count, and frequency. These results demonstrate that the refractive index can be continuously tuned by varying the twist count, suggesting that TGNRs could serve as frequency-selective photonic filters or waveguides.
Ray Trajectories and Wave Optics in a Traversable Wormhole: Optics of a Minimal Surface
(Elsevier, 2025) Dogan, Semra Gurtas; Guvendi, Abdullah; Mustafa, Omar
This study investigates ray trajectories and wave propagation in a static, (2 + 1)-dimensional, radially symmetric traversable wormhole (TWH) spacetime with a constant redshift function and a radial shape function proportional to 1/p. The spatial geometry forms a minimal surface (a catenoid bridge), enabling a geometric-optical interpretation. An analysis of the ray trajectories reveals how the curvature-induced structure of the wormhole (WH) governs the ray paths, depending on the relative sizes of the radial coordinate rho and the throat radius l(o). Extending the study to wave dynamics, we derive a refractive index n(rho, omega) that explicitly depends on both rho and the wave frequency w, identifying a critical frequency that marks the transition between propagation and attenuation. These results demonstrate how the WH's topology distinctly influences wave propagation and may inform future developments in analogue gravity models and advanced optical media.
Real and Damped Modes for an Interacting Fermion-Antifermion Pair: Exciton in Monolayer Medium
(Springer Heidelberg, 2024) Guvendi, Abdullah; Dogan, Semra Gurtas; Yazici, Uzeyir
In this manuscript, we investigate the interaction between a fermion-antifermion pair in ( 2 + 1 ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(2+1)$$\end{document} -dimensions, governed by a Coulomb-type inter-particle potential. We explore analytical solutions for a fully covariant two-body Dirac equation derived from quantum electrodynamics, focusing on a spinless composite system. We present a non-perturbative second-order wave equation and derive a solution using the generators of the s l 2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s\ell _{2}$$\end{document} algebra. Subsequently, we determine the relativistic frequency modes of the system and extend our findings to electron-hole pairs in a monolayer medium in the vicinity of substrate. We analyze the impact of the effective dielectric constant ( epsilon \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document} ) of the surrounding medium on the real and damped modes of an exciton. Our results indicate that the ground state binding energy of the system can vary from the order of eV to a few meV, depending on changes in epsilon \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document} . Additionally, we observe that the decay time for the ground state of such an exciton is on the order of similar to 10 - 12 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 10{-12}$$\end{document} s. These findings suggest that the evolution of such a pair can be controlled by adjusting the effective dielectric constant of the surrounding medium.
Relativistic Fermions and Vector Bosons in Magnetized Three-Dimensional Space-Time with a Cosmological Constant
(Elsevier, 2024) Guvendi, Abdullah; Ahmed, Faizuddin; Dogan, Semra Gurtas
In this manuscript, we study the relativistic dynamics of fermions and vector bosons within a (2+1)-dimensional magnetized space-time. We consider the Bonnor-Melvin magnetic spacetime, characterized by a homogeneous magnetic field aligned along the symmetry axis and a non-zero cosmological constant. This space-time background, featuring cylindrical symmetry, retains the invariance of quantum field dynamics under Lorentz boosts along the z-direction. This enables us to explore (2+1)-dimensional realms, where the associated 2+1 -dimensional spacetime background is recognized as the Bonnor-Melvin magnetic 2+1+0-brane solution within the framework of gravity coupled with nonlinear electrodynamics. We seek exact solutions for relativistic fermions and vector bosons within this space-time background. We have managed to derive the radial wave equations in both instances, securing precise eigenvalue solutions devoid of any approximations. Our findings extend seamlessly to massless fermions and vector bosons, ensuring generality. Moreover, we observe that the ground state energy of massless vector bosons (photons) within the examined space-time background is unequivocally zero.
Rotational Influence on Fermions Within Negative Curvature Wormholes
(Springer Heidelberg, 2024) Guvendi, Abdullah; Dogan, Semra Gurtas; Vitoria, R. L. L.
In this research, we examine relativistic fermions within the rotating frame of negative curvature wormholes. Initially, as is typical in our context, we introduce the wormholes by embedding a curved surface into a higher-dimensional flat Minkowski spacetime. Subsequently, we derive the spacetime metric that characterizes the rotating frame of these wormholes. We then investigate analytical solutions of the generalized Dirac equation within this framework. Through exploring a second-order non-perturbative wave equation, we seek exact solutions for fermions within the rotating frame of hyperbolic and elliptic wormholes, also known as negative curvature wormholes. Our analysis provides closed-form energy expressions, and we generalize our findings to Weyl fermions. By considering the impact of the rotating frame and curvature radius of wormholes, we discuss how these factors affect the evolution of fermionic fields, offering valuable insights into their behavior.
Twist-Induced Effects on Weyl Pairs in Magnetized Graphene Nanoribbons
(Royal Society, 2025) Dogan, Semra Gurtas; Hasanirokh, Kobra; Mustafa, Omar; Guvendi, Abdullah
This paper presents an analytical investigation into the dynamics of Weyl pairs within magnetized helicoidal graphene nanoribbons (GNRs). 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 obtains exact solutions. Our results demonstrate the influence of the uniform magnetic field and the number of twists on the dynamics of Weyl pairs in GNRs, 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 GNRs.
Vector Boson Oscillator in the Near-Horizon of the BTZ Black Hole
(IOP Publishing Ltd, 2023) Guvendi, Abdullah; Dogan, Semra Gurtas
We investigate the interaction of a generalized vector boson oscillator with the near-horizon geometry of the Ban tilde ados-Teitelboim-Zanelli (BTZ) black hole and try to determine the corresponding quasibound state frequencies. To do this, we seek an analytical solution of the relativistic vector boson equation, derived as an excited state of Zitterbewegung, with Cornell-type non-minimal coupling in the near-horizon geometry of the BTZ black hole. The vector boson equation includes a symmetric spinor of rank two and this allows to obtain an analytical solution of the corresponding equation. By imposing appropriate boundary conditions, we show that it is possible to arrive at a relativistic fre-quency (omega) expression in the form of omega = omega(Re) + omega(Im). Our results show that real (proportional to omega(Re)) and damped (proportional to 1| |omega(Im)|) oscillations depend on the parameters of the background geometry, coefficients of the non-minimal coupling and strength of the oscillator. This allows us to analyse the effects of both non-minimal coupling and spacetime parameters on the evolution of the considered vector field. We discuss the results in details and see also that the background is stable under the perturbation field in question.
Vector Bosons in the Rotating Frame of Negative Curvature Wormholes
(Springer/Plenum Publishers, 2024) Guvendi, Abdullah; Dogan, Semra Gurtas
In this study, we investigate the relativistic dynamics of vector bosons within the context of rotating frames of negative curvature wormholes. We seek exact solutions for the fully-covariant vector boson equation, derived as an excited state of zitterbewegung. This equation encompasses a symmetric rank-two spinor, enabling the derivation of a non-perturbative second-order wave equation for the system under consideration. Our findings present exact results in two distinct scenarios. Notably, we demonstrate the adaptability of our results to massless vector bosons without compromising generality. The evolution of this system is shown to correlate with the angular frequency of the uniformly rotating reference frame and the curvature radius of the wormholes. Moreover, our results highlight that the interplay between the spin of the vector boson and the angular frequency of the rotating frame can give rise to real oscillation modes, particularly evident in excited states for massless vector bosons. Intriguingly, we note that the energy spectra obtained remain the same whether the wormhole is of hyperbolic or elliptic nature.