arXiv subjects

B. C. Lütfüoğlu

Publications and source records attributed to B. C. Lütfüoğlu.

At least 37 records · Page 2Linked to original sources

arXiv2025

Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential

In this manuscript, we investigate the analytical solution of the time-dependent Schrödinger equation for a harmonic oscillator with time-dependent mass and frequency, coupled with angular-dependent potential energy by utilizing the Dunkl derivatives. To obtain the solution, we employ the Lewis-Riesenfeld invariant methodology. Our approach broadens the scope of quantum mechanical analyses, offering exact solutions and new insights into dynamic quantum systems under varying conditions.

quant-ph↗

arXiv2025

Long-lived Quasinormal Modes and Gray-Body Factors of black holes and wormholes in dark matter inspired Weyl Gravity

We calculate quasinormal modes and gray-body factors of a massive scalar field in the background of three compact objects in the Weyl gravity: Schwarzschild-like black holes, known as Mannheim-Kazanas solution, non-Schwrazschild-like black holes and traversable wormholes found recently in [P. Jizba, K. Mudruňka, Phys.Rev.D 110 (2024) 12, 124006]. We show that the spectrum of the massive field is qualitatively different from massless one both in the frequency and time domains. While the mass term leads to much longer lifetime of the modes, the arbitrarily long-lived modes, known as quasi-resonances, are not achieved.

gr-qc↗

arXiv2025

Thermodynamic properties of Quantum-Corrected AdS Black Hole with Phantom Global Monopoles

In this paper, we introduce a metric ansatz designed to describe spherically symmetric quantum-corrected black hole (BH) space-time within an AdS space background, incorporating both an ordinary and a phantom global monopole. Our study focus into the thermodynamic properties of this BH, where we compute key parameters such as the Hawking temperature and specific heat capacity. We then proceed to analyze the effective potential of the system, considering both null and time-like geodesics, and investigate the shadow radius of the BH. Additionally, we calculate the emission rate of particles from the BH, providing insights into the energy dynamics. The geodesic equations of motion are explored to visualize the trajectories of massive particles within the BH. Throughout our investigation, we thoroughly examine how the inclusion of both ordinary and phantom global monopoles, combined with the quantum-corrected parameter, influences various thermal properties, the effective potential of the system, the BH shadow radius, energy emission rate, and the trajectories of massive particles. Importantly, by generating figures that depict these phenomena, we emphasize the differences in results obtained with ordinary global monopoles and phantom ones, considering a range of quantum-corrected parameter values and small energy scale parameters, which allows us to discern the distinct effects of each type of monopole in the black hole's behavior.

gr-qc↗

arXiv2025

Phantom RN-AdS black holes in noncommutative space

We analyze the effects of noncommutativity on phantom Reissner-Nordström-Anti-de Sitter black holes by modeling mass and charge distributions with Lorentzian profiles. The modified metric function exhibits significant deviations from the classical case, leading to changes in the horizon structure and the suppression of singularities. Through a comparative thermodynamic analysis, we derive expressions for the mass, Hawking temperature, entropy, and heat capacity, identifying stability conditions and phase transitions induced by noncommutative corrections. The efficiency of the black hole as a heat engine is evaluated, showing that noncommutativity influences the thermodynamic cycle differently in the presence of phantom fields. Furthermore, we investigate the orbital motion of test particles and photons, deriving the effective potential, innermost stable circular orbits, and the shadow profile. Finally, we compute quasinormal modes to assess dynamical stability, revealing that noncommutativity modifies the damping behavior and introduces a new branch of non-oscillatory modes, absent in the classical case. Our findings provide a deeper understanding of the interplay between phantom fields, noncommutative geometry, and black hole thermodynamics, offering potential observational signatures for exotic compact

hep-th↗

arXiv2024

Time-dependent Dunkl-Pauli Oscillator

This study explores the time-dependent Dunkl-Pauli oscillator in two dimensions. We constructed the Dunkl-Pauli Hamiltonian, which incorporates a time-varying magnetic field and a harmonic oscillator characterized by time-dependent mass and frequency, initially in Cartesian coordinates. Subsequently, we reformulated the Hamiltonian in polar coordinates and analyzed the eigenvalues and eigenfunctions of the Dunkl angular operator, deriving exact solutions using the Lewis-Riesenfeld invariant method. Our findings regarding the total quantum phase factor and wave functions reveal the significant impact of Dunkl operators on quantum systems, providing precise expressions for wave functions and energy eigenvalues. This work enhances the understanding of quantum systems with deformed symmetries and suggests avenues for future research in quantum mechanics and mathematical physics.

quant-ph↗

arXiv2024

Dunkl-Schrodinger Equation in Higher Dimension

This paper presents analytical solutions for eigenvalues and eigenfunctions of the Schrödinger equation in higher dimensions, incorporating the Dunkl operator. Two fundamental quantum mechanical problems are examined in their exact forms: the d-dimensional harmonic oscillator and the Coulomb potential. In order to obtain analytical solutions to these problems, both Cartesian and polar coordinate systems were employed. Firstly, the Dunkl-Schrödinger equation is derived in d-dimensional Cartesian coordinates, and then for the isotropic harmonic potential interaction, its solutions are given. Subsequently, using polar coordinates the angular and radial parts of the Dunkl-Schrödinger equation are obtained. It is demonstrated that the system permits the separation of variables in both coordinate systems, with the resulting separated solutions expressed through Laguerre and Jacobi polynomials. Then, the radial Dunkl-Schrödinger equation is solved using the isotropic harmonic, pseudoharmonic, and Coulomb potentials. The eigenstates and eigenvalues are obtained for each case and the behavior of the energy eigenvalue functions are illustrated graphically with the reduced probability densities.

quant-ph↗

arXiv2024

Dunkl-Klein-Gordon Equation in Higher Dimensions

In this study, we replace the standard partial derivatives in the Klein-Gordon equation with Dunkl derivatives and obtain exact analytical solutions for the eigenvalues and eigenfunctions of the Dunkl-Klein-Gordon equation in higher dimensions. We apply this formalism to two key quantum mechanical systems: the d-dimensional harmonic oscillator and the Coulomb potential. First, we introduce Dunkl quantum mechanics in d-dimensional polar coordinates, followed by an analysis of the d-dimensional Dunkl-Klein-Gordon oscillator. Subsequently, we derive the energy spectrum and eigenfunctions, which are expressed using confluent hypergeometric functions. Furthermore, we examine the impact of the Dunkl formalism on both the eigenvalues and eigenfunctions. In the second case, we explore both the bound-state solutions and scattering scenarios of the Dunkl-Klein-Gordon equation with the Coulomb potential. The bound-state solutions are represented in terms of confluent hypergeometric functions, while the scattering states enable us to compute the particle creation density and probability using the Bogoliubov transformation method.

quant-ph↗

arXiv2024

One-dimensional Dunkl Quantum Mechanics: A Path Integral Approach

In the present manuscript, we employ the Feynman path integral method to derive the propagator in one-dimensional Wigner-Dunkl quantum mechanics. To verify our findings we calculate the propagator associated with the free particle and the harmonic oscillator in the presence of the Dunkl derivative. We also deduce the energy spectra and the corresponding bound-state wave functions from the spectral decomposition of the propagator.

quant-ph↗

arXiv2024

Dunkl-Schrödinger equation with time-dependent harmonic oscillator potential

In this paper, using the Lewis-Riesenfeld method, we determine the explicit form of the wavefunctions of one- and three-dimensional harmonic oscillators with time-dependent mass and frequency within the framework of the Dunkl derivative, which leads to the derivation of a parity-dependent of the invariant and auxiliary equation.

quant-ph↗

arXiv2024

Exact solution of two dimensional Dunkl harmonic oscillator in Non-Commutative phase-space

In this paper, we examine the harmonic oscillator problem in non-commutative phase space (NCPS) by using the Dunkl derivative instead of the habitual one. After defining the Hamilton operator, we use the polar coordinates to derive the binding energy eigenvalue. We find eigenfunctions that correspond to these eigenvalues in terms of the Laguerre functions. We observe that the Dunkl-Harmonic Oscillator (DHO) in the NCPS differs from the ordinary one in the context of providing additional information on the even and odd parities. Therefore, we conclude that working with the Dunkl operator could be more appropriate because of its rich content.

hep-th↗

arXiv2024

Noncommutative Schwarzschild black hole surrounded by quintessence: Thermodynamics, Shadows and Quasinormal modes

{In (Sci. Rep. \textbf{12}, 8516 (2022)), Campos et al studied} the quasinormal modes and shadows of noncommutative Schwarzschild black holes. Since we know that the quintessence matter surrounding black holes has { significant effects} on the black hole quantities, {in this study, we aimed to show this influence by revisiting the same problem in the presence of quintessence matter field. To this end, we first examined the thermodynamics of noncommutative Schwarzschild black holes embedded in quintessence matter using Hawking temperature, entropy, and specific heat functions. After that,} we discussed phase transition and stability { features. We then investigated} the shadow images in the presence of plasma. After visualizing these results qualitatively, we calculated the quasinormal modes in WKB and Mashhoon approximations and we demonstrated the impacts of quintessence matter and noncommutative spacetime on the whole quantities.

gr-qc↗

arXiv2024

Black Hole Shadows in Einstein-Bel-Robinson Gravity

Gravity models given by higher-order scalar curvature corrections are believed to bear important consequences. The Einstein-Bel-Robinson gravity, with quartic curvature modification, motivated Sajadi et al to explore static spherically symmetric black hole solutions with perturbative methods. In this paper, inspired by their work, we investigate AdS black hole shadows in EBR gravity. Moreover, we demonstrate how the gravity parameter alters the energy emission rate. Finally, we handle the same problem in the presence of plasma, since the black holes are thought to be surrounded by a medium that changes the geodesic of photons.

gr-qc↗

arXiv2024

Van der Waals black holes in rainbow gravity

Recently, Rajagapol et al presented an asymptotically AdS black hole metric whose thermodynamics qualitatively mimics the behavior of the Van der Waals fluid by treating the cosmological constant as a thermodynamic pressure. In some studies in the literature, authors have discussed the effects of deformed algebras such as generalized and extended uncertainty principles on the thermal quantities of these black holes. In this manuscript, we considered another deformation, the rainbow gravity formalism, and we investigated its impact on the Van der Waal black hole thermodynamics. To this end, we first generated the modified lapse and mass functions, and then we derived the modified thermal quantities such as thermodynamic volume, Hawking temperature, entropy, and specific heat functions. Finally, we explored the thermodynamics of a black hole, which mimics the thermodynamics of an ideal gas, under the influence of the rainbow gravity formalism.

gr-qc↗

arXiv2024

Dunkl-Pauli Equation in the Presence of a Magnetic Field

The Pauli equation, an important equation of quantum mechanics, allows us to study the dynamics of spin-$1/2$ particles. The Dunkl derivative, when used instead of the ordinary derivative, leads to obtaining parity-dependent solutions. Motivated by these facts, in this work, we consider a two-dimensional nonrelativistic spin-$1/2$ particle system in the presence of an external magnetic field, and we investigate its parity-dependent dynamics by solving the Pauli equation analytically. Next, we assume the system to be in thermal equilibrium, and we examine various thermal quantities of the system.

quant-ph↗

arXiv2023

The Condensation of Ideal Dunkl-Bose Gas in Power-Law Traps

We explore the phenomenon of Bose-Einstein condensation in two and one-dimensional Dunkl-boson gases confined within a power-law potential, employing the framework of Dunkl-deformed boson theory. Our investigation involves the calculation of particle numbers and phase transition temperatures using the Dunkl formalism. To assess the validity of our findings, we compare them with the corresponding results obtained from the standard approach. We find that the impact of the Dunkl-formalism on the condensate fractions is similar in one and two-dimensional cases. However, we see that this conclusion is not fully valid for the phase transition temperature.

cond-mat.quant-gas↗

arXiv2023

Thermodynamics and Shadows of quantum-corrected Reissner-Nordström black hole surrounded by quintessence

In this work, we consider the quantum-corrected Reissner-Nordström black hole surrounded by quintessence matter and examine its thermodynamics and shadow. To this end, we handle the quantum-corrected metric of the black hole, which is given by Wu and Lui in 2022, and couple the quintessence matter field effects to the lapse function. Then, we obtain the mass, Hawking temperature, specific heat, and equation of state functions. In all these functions, we discuss two cases in which the quantum corrections are greater or smaller than the quintessence matter effects. We observe that within these two scenarios, the black hole has different characteristic thermal behaviors. Moreover, we find that the quintessence matter plays an important role in leading to a black hole remnant. Finally, we investigate the black hole shadow by Carter's approach. We find that quintessence matter and quantum corrections modify the shadow of the black hole.

gr-qc↗

arXiv2023

On Dunkl-Bose-Einstein Condensation in Harmonic Traps

The use of the Dunkl derivative, which is defined by a combination of the difference-differential and reflection operator, allows the classification of the solutions according to even and odd solutions. Recently, we considered the Dunkl formalism to investigate the Bose-Einstein condensation of an ideal Bose gas confined in a gravitational field. In this work, we address a similar problem and examine an ideal Bose gas trapped by a three-dimensional harmonic oscillator within the Dunkl formalism. To this end, we derive an analytic expression for the critical temperature of the N particle system, discuss its value at large-N limit and finally derive and compare the ground state population with the usual case result. In addition, we explore two thermal quantities, namely the Dunkl-internal energy and the Dunkl-heat capacity functions. The Wigner parameter of the Dunkl formalism can be successfully used to obtain a better agreement between experimental and theoretical results.

cond-mat.quant-gas↗

arXiv2023

Extended uncertainty principle and Van der Waals black holes

In this manuscript, we investigate the extended uncertainty principle (EUP) effects on the Van der Waals (VdW) black holes whose thermal quantities mimic the VdW liquid. We find that the considered formalism imposes an upper bound on the event horizon radius. Thus, the mass, Hawking temperature, and heat capacity become physically meaningful within a certain range of event horizon radii. At a large event horizon radius the black hole has a remnant. We observe that for a given set of parameters, the VdW black hole can be completely unstable for all horizon radii, while for another set of parameters, it can be unstable or stable depending on the horizon radius.

gr-qc↗