arXiv subjects

B. Hamil

Publications and source records attributed to B. Hamil.

At least 37 records · Page 2Linked to original sources

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

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↗

arXiv2023

Quantum-corrected Schwarzschild AdS black hole surrounded by quintessence: Thermodynamics and Shadows

In this manuscript, we study the quantum-corrected Schwarzschild AdS black hole surrounded by quintessence matter in two folds: its thermal quantities and shadows. For this purpose, first, we present a detailed analysis of the influences of the quintessence matter field on Hawking temperature, mass, and specific heat functions. Then, we examine the shadows by following Carter's approach. We find that the shadow radius value takes smaller values for greater quintessence state parameter values. On the other hand, we see that the shadow radius takes greater values for greater values of the normalization parameter. Finally, in a brief section, we discuss the energy emission rate and show that the Gaussian-type plots' peak values are also affected by the quintessence matter field parameters.

gr-qc↗

arXiv2023

The condensation of ideal Bose gas in a gravitational field in the framework of Dunkl-statistic

In the framework of the theory of Dunkl-deformed bosons, Bose-Einstein condensation of two and three-dimensional Dunkl-boson gases confined in the one-dimensional gravitational field is investigated. Using the semi-classical approximation method, we calculate the expressions of the Dunkl-critical temperature $T_{c}^{D}$, the ground state population $\frac{N_{0}^{D}}{N}$ and the Dunkl-mean energy and Dunkl-specific heat functions. Further numerical calculation shows that the condensation temperature ratio $\frac{T_{c}^{D}}{T_{c}^{B}}$ increases with the increasing Wigner parameter.

cond-mat.quant-gas↗

arXiv2023

Ideal Bose Gas and Blackbody Radiation in the Dunkl Formalism

Recently, deformed quantum systems gather lots of attention in the literature. Dunkl formalism differs from others by containing the difference-differential and reflection operator. It is one of the most interesting deformations since it let us discuss the solutions according to the even and odd solutions. In this work, we studied the ideal Bose gas and the blackbody radiation via the Dunkl formalism. To this end, we made a liaison between the coordinate and momentum operators with the creation and annihilation operators which allowed us to obtain the expressions of the partition function, the condensation temperature, and the ground state population of the Bose gas. We found that Dunkl-condensation temperature increases with increasing θ value. In the blackbody radiation phenomena, we found how the Dunkl formalism modifies total radiated energy. Then, we examined the thermal quantities of the system. We found that the Dunkl deformation causes an increase in entropy and specific heat functions as well as in the total radiation energy. However, we observed a decrease in the Dunk-corrected Helmholtz free energy in this scenario. Finally, we found that the equation of state is invariant even in the considered formalism.

cond-mat.stat-mech↗

arXiv2022

The effect of modified dispersion relations on the thermodynamics of Schwarzschild black hole surrounded by quintessence

In this manuscript, we investigate the effects of a modified dispersion relation on the thermodynamics of Schwarzschild black hole surrounded by the quintessence matter. We find that the MDR-correction states the same lower bound on the horizon, while the quintessence matter specifies the upper bound to the horizon depending on the state parameter. Due to MDR-correction and quintessence matter presence, we observe modifications in equation of state and specific heat functions of black hole. We show that a remnant can occur according to quintessence matter, and the black hole's stability depends only on the modified dispersion relation.

gr-qc↗

arXiv2022

Thermodynamics of Schwarzschild black hole surrounded by quintessence in gravity's rainbow

According to some quantum gravity models, Lorentz invariance can be violated in the Planck energy scale. With this motivation, we analyze the thermal quantities and the stability of Schwarzschild black hole surrounded by quintessence in gravity's rainbow formalism. To do that, we consider the rainbow functions which are motivated by loop quantum gravity and gamma-ray bursts, and we derive Hawking temperature, specific heat, entropy and the equation of state function. We observe that the presence the quintessence matter field and rainbow gravity affect the stability of the black hole.

gr-qc↗

arXiv2022

Dunkl-Graphene in constant magnetic field

Graphene-based materials are thought to revolutionize entire industries. Therefore, many research are being carried on graphene theoretically and experimentally. On the other hand, recent studies show that the use of Dunkl derivative, instead of ordinary derivative, allows the concept of parity to be interpreted together with other physical quantities. In this manuscript, we investigate the thermal quantities of graphene under the constant magnetic field with the Dunkl-formalism. We observe that only at low temperatures Dunkl-parameters, thus parity, modify the conventional results.

cond-mat.mes-hall↗

arXiv2022

Thermal Properties of Relativistic Dunkl Oscillators

For a better understanding of the physical systems, even at the quantum level, the thermal quantities can be investigated. Recently, we realized that the parity of the system can also be examined simultaneously, by substituting the Dunkl operator with the ordinary differential operator in quantum mechanics. In this manuscript, we consider two relativistic Dunkl-oscillators and investigate their thermal quantities with well-known statistical methods. Besides, we establish a relationship between the Dunkl-Dirac oscillator and the Dunkl-Anti-Jayne-Cummings model by defining the Dunk creation and annihilation operators. Therefore, we conclude that our model can be regarded as an appropriate scenario for the theory of an open quantum system coupled to a thermal bath.

quant-ph↗

arXiv2022

Quantum corrections to the thermodynamics of rotating charged BTZ black hole in gravity's rainbow

In this manuscript, we investigate the thermal properties of the rotating charged BTZ black hole under the gravity's rainbow (GR) and generalized uncertainty principle (GUP) formalism. At first, we study the GR-corrected thermal quantities according to the usual Heisenberg algebra. Then, we consider a deformed algebra that leads to a change in the Heisenberg uncertainty principle and compare the Hawking temperature, entropy, thermodynamical volume, pressure, and heat capacity functions with the previous results. Thus, we understand and interpret the quantum effects on the BTZ black hole.

gr-qc↗