arXiv subjects

B. C. Lütfüoğlu

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

At least 73 records · Page 4Linked to original sources

arXiv2021

Interaction of the magnetic quadrupole moment of a non-relativistic particle with an electric field in the background of screw dislocations with a rotating frame

In this study, we considered a moving particle with a magnetic quadrupole moment in an elastic medium in the presence of a screw dislocation. We assumed a radial electric field in a rotating frame that leads a uniform effective magnetic field perpendicular to the plane of motion. We solved the Schrödinger equation to derive wave and energy eigenvalue functions by employing analytical methods for two interaction configurations: in the absence of potential and in the presence of a static scalar potential. Due to the topological defect in the medium, we observed a shift in the angular momentum quantum number which affects the energy eigenvalues and the wave function of the system.

quant-ph↗

arXiv2021

Graphene in curved Snyder space

The Snyder-de Sitter (SdS) model which is invariant under the action of the de Sitter group, is an example of a noncommutative spacetime with three fundamental scales. In this paper, we considered the massless Dirac fermions in graphene layer in a curved Snyder spacetime which are subjected to an external magnetic field. We employed representation in the momentum space to derive the energy eigenvalues and the eigenfunctions of the system. Then, we used the deduced energy function obtaining the internal energy, heat capacity, and entropy functions. We investigated the role of the fundamental scales on these thermal quantities of the graphene layer. We found that the effect of the SdS model on the thermodynamic properties is significant.

hep-th↗

arXiv2021

Electric quadrupole moment of a neutral non-relativistic particle in the presence of screw dislocation

In this contribution, we investigate the interaction between electric and magnetic fields with an electric quadrupole moment of a spinless particle moving in an elastic medium which has a topological defect (screw dislocation). By considering this interaction, the Schrödinger equation is exactly solved by using the analytical method. Thus, the eigenfunction and energy eigenvalues for two configurations are found. Meanwhile, by observing a shift in the angular momentum quantum number, the energy eigenvalues and the wave function of the system are modified, due to the screw dislocation in the medium.

quant-ph↗

arXiv2021

The spin-one DKP Equation with a nonminimal vector interaction in the presence of minimal uncertainty in momentum

In this work, we consider the relativistic Duffin-Kemmer-Petiau equation for spin-one particles with a nonminimal vector interaction in the presence of minimal uncertainty in momentum. By using the position space representation we exactly determine the bound-states spectrum and the corresponding eigenfunctions. We discuss the effects of the deformation and nonminimal vector coupling parameters on the energy spectrum analytically and numerically.

quant-ph↗

arXiv2020

The generalized Klein-Gordon oscillator in a Cosmic Space-Time with a Space-Like Dislocation and the Aharonov-Bohm Effect

In the present work, we investigated the quantum behavior of a charged particle that is under the effect of a uniform magnetic external field. We assumed that space-time has a space-like dislocation with an internal magnetic flux. We examined two different types of potential energies that are known as the pseudo harmonic and Cornell type potential energies, with the nonminimal coupling. We observed the Aharonov-Bohm effect in both cases. We extended the analysis on the energy spectrum functions to the different limits.

quant-ph↗

arXiv2020

Thermal properties of a two-dimensional Duffin-Kemmer-Petiau oscillator under an external magnetic field in the presence of a minimal length

Generalized uncertainty principle puts forward the existence of the shortest distances and/or maximum momentum at the Planck scale for consideration. In this article, we investigate the solutions of a two-dimensional Duffin-Kemmer-Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) scale. First, we obtain the eigensolutions in ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of an ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions in the non-relativistic limit. We show that in the ordinary quantum mechanic limit, where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler-Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale.

physics.gen-ph↗

arXiv2020

Effect of the modified Heisenberg algebra on the Black hole thermodynamics

In this letter, we introduce two new forms of uncertainty relations by extending the usual Heisenberg algebra with higher terms. Within these scenarios, at first, we study on the Unruh temperature. We find that the Unruh temperature increases in one of the new forms while it decreases in the other form. Next, we explore the thermodynamic properties of a Schwarzschild black hole by relying on these two new forms of the Heisenberg uncertainty relation. We present the modifications in the mass-temperature, specific heat, and entropy functions of the black hole according to the extension parameters.

gr-qc↗

arXiv2020

New higher-order generalized uncertainty principle: Applications

Last year, Chung and Hassanabadi proposed a higher order general uncertainty principle (GUP$^\ast$) that predicts a minimal length as well as possesses a upper bound momentum limit. In this article, we have discussed an ideal gas system and its thermal properties using that deformed canonical algebra introduced by them. Moreover, we examined blackbody radiation spectrum and the cosmological constant in the presence of the GUP$^\ast$. After a comparison with the existing literature, we concluded that the given formalism of Chung and Hassanabadi yields more accurate results.

gr-qc↗

arXiv2020

Bound state solutions of the Klein Gordon equation with energy-dependent potentials

In this manuscript, we investigate the exact bound state solution of the Klein-Gordon equation for an energy-dependent Coulomb-like vector plus scalar potential energies. To the best of our knowledge, this problem is examined in literature with a constant and position dependent mass functions. As a novelty, we assume a mass-function that depends on energy and position and revisit the problem with the following cases: First, we examine the case where the mixed vector and scalar potential energy possess equal magnitude and equal sign as well as an opposite sign. Then, we study pure scalar and pure vector cases. In each case, we derive an analytic expression of the energy spectrum by employing the asymptotic iteration method. We obtain a non-trivial relation among the tuning parameters which lead the examined problem to a constant mass one. Finally, we calculate the energy spectrum by the Secant method and show that the corresponding unnormalized wave functions satisfy the boundary conditions. We conclude the manuscript with a comparison of the calculated energy spectra versus tuning parameters.

quant-ph↗

arXiv2019

A statistical mechanical analysis on the bound state solution of an energy-dependent deformed Hulthén potential energy

In this article, we investigate the bound state solution of the Klein Gordon equation under mixed vector and scalar coupling of an energy-dependent deformed Hulthén potential in D-dimensions. We obtain a transcendental equation after we impose the boundary conditions. We calculate energy spectra in four different limits and in arbitrary dimension via the Newton-Raphson method. Then, we use a statistical method, namely canonical partition function, and discuss the thermodynamic properties of the system in a comprehensive way. We find out that some of the thermodynamic properties overlap with each other, some of them do not.

quant-ph↗

arXiv2018

On the Role of Differentiation Parameter in a Bound State Solution of the Klein-Gordon Equation

Recently, the bound state solutions of a confined Klein-Gordon particle under the mixed scalar-vector generalized symmetric Woods-Saxon potential in one spatial dimension have been investigated. The obtained results reveal that in the spin symmetric limit discrete spectrum exists, while in the pseudo-spin symmetric limit it does not. In this manuscript, new insights and information are given by employing an analogy of the variational principle. The role of the difference of the magnitudes of the vector and scalar potential energies, namely the differentiation parameter, on the energy spectrum is examined. It is observed that the differentiation parameter determines the measure of the energy spectrum density by modifying the confined particle's mass-energy in addition to narrowing the spectrum interval length.

quant-ph↗

arXiv2018

A Comparative Interpretation of the Thermodynamic Functions of a Relativistic Bound State problem proposed with an Attractive or a Repulsive Surface Effect

Generalized symmetric Woods-Saxon potential (GSWSP) energy well has a significant importance not only in nuclear physics but also in atomic and molecular physics. A GSWSP energy well takes the surface effects (describing e.g. repulsive interaction at the nucleus edge in nuclear physics) into account in addition to the volume effect. These effects can be, in general, both repulsive or attractive. In this paper, the recently obtained bound state solution of the Klein-Gordon equation with vector and scalar GSWSP energy in the spin symmetry limit is used to calculate a neutral pion's energy spectra in attractive and repulsive cases via various potential parameters. Then, the spectra are employed to find the thermodynamic functions such as Helmholtz free energy, entropy, internal energy, and specific heat. These functions in the attractive and repulsive cases are compared comprehensively. Finally, the role of the shape parameters on the thermodynamic functions in repulsive and attractive cases, respectively, is analyzed.

nucl-th↗

arXiv2018

Analytical solution of the Klein Gordon equation with a Multi-parameter q-Deformed Woods-Saxon Type Potential

In this manuscript, we present analytical solution of the Klein-Gordon equation with the multi-parameter q-deformed Woods-Saxon type potential energy under the spin symmetric limit in $(1+1)$ dimension. In the scattering case, we obtain the reflection and transmission probabilities and prove the conservation of the total probability. Moreover, we analyze the correlation between the potential parameters with the reflection and transmission probabilities. In the bound state case, we use the continuity conditions and derive a quantization scheme. To confirm our results numerically, in both cases we randomly assign values to the potential parameters and find numerical results by using the Newton Raphson method.

quant-ph↗

arXiv2018

Surface Interaction Effects to a Klein-Gordon Particle Embedded in a Woods-Saxon Potential Well in terms of Thermodynamic Functions

Recently, it has been investigated how the thermodynamic functions vary when the surface interactions are taken into account for a nucleon which is confined in a Woods-Saxon potential well, with a non-relativistic point of view. In this manuscript, the same problem is handled with a relativistic point of view. More precisely, the Klein-Gordon equation is solved in presence of mixed scalar-vector generalized symmetric Woods-Saxon potential energy that is coupled to momentum and mass. Employing the continuity conditions the bound state energy spectra of an arbitrarily parameterized well are derived. It is observed that, when a term representing the surface effect is taken into account, the character of Helmholtz free energy and entropy versus temperature are modified in a similar fashion as this inclusion is done in the non-relativistic regime. Whereas it is found that this inclusion leads to different characters to internal energy and specific heat functions for relativistic and non-relativistic regimes.

nucl-th↗

arXiv2018

Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential

Recently, it has been shown that the generalized symmetric Woods-Saxon potential energy, in which surface interaction terms are taken into account, describes the physical processes better than the standard form. Therefore in this study, we investigate the scattering of Klein-Gordon particles in the presence of both generalized symmetric Woods-Saxon vector and scalar potential. In one spatial dimension we obtain the solutions in terms of hypergeometric functions for spin symmetric or pseudo-spin symmetric cases. Finally, we plot transmission and reflection probabilities for incident particles with negative and positive energy for some critical arbitrary parameters and discuss the correlations for both cases.

nucl-th↗

arXiv2018

Comparative effect of an addition of a surface term to the Woods-Saxon potential on the thermodynamics of a nucleon

In this study, we reveal the difference between Woods-Saxon (WS) and Generalized Symmetric Woods-Saxon (GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schrödinger eq. for the two potentials. The additional term squeezes the WS potential well, which leads an upward shift in the spectrum, resulting in a more realistic picture. The resulting GSWS potential does not merely accommodate extra quasi bound states, but also has modified bound state spectrum. As an application, we apply the formalism to a real problem, an $α$ particle confined in Bohrium-$270$ nucleus. The thermodynamic functions Helmholtz energy, entropy, internal energy, specific heat of the system are calculated and compared for both wells. The internal energy and the specific heat capacity increase as a result of upward shift in the spectrum. The shift of the Helmholtz free energy is a direct consequence of the shift of the spectrum. The entropy decreases because of a decrement in the number of available states.

nucl-th↗

arXiv2017

Properties of an $α$ particle in a Bohrium $270$ Nucleus under the Generalized Symmetric Woods-Saxon Potential

The energy eigenvalues and the wave functions of an $α$ particle in a Bohrium $270$ nucleus were calculated by solving Schrödinger equation for Generalized Symmetric Woods-Saxon potential. Using the energy spectrum by excluding and including the quasi-bound eigenvalues, entropy, internal energy, Helmholtz energy, and specific heat, as functions of reduced temperature were calculated. Stability and emission characteristics are interpreted in terms of the wave and thermodynamic functions. The kinetic energy of a decayed $α$ particle was calculated using the quasi-bound states, which is found close to the experimental value.

nucl-th↗

arXiv2017

Klein-Gordon equation particles in exponential-type molecule potentials and its thermodynamic properties in D- dimensions

In this paper we use the Nikiforv-Uvarov method to obtain the approximate solutions of the Klein-Gordon equation with deformed five parameter exponential type potential (DFPEP) model. We also obtain the solutions of the Schrödinger equation in the presence of the DFPEP in the non-relativistic limits. In addition, we calculate in the nonrelativistic limits the thermodynamics properties such as vibrational mean energy U, free energy F and the specific heat capacity C . Special cases of the potential are also discussed.

quant-ph↗