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Luis B. Castro

Publications and source records attributed to Luis B. Castro.

At least 19 recordsLinked to original sources
arXiv2026

Scalar and vector bosons in a Bonnor-Melvin-$\Lambda$ spacetime: an exact Duffin-Kemmer-Petiau analysis

We study scalar and vector bosons in the Bonnor--Melvin--$\Lambda$ spacetime within the Duffin--Kemmer--Petiau (DKP) formalism. By employing Umezawa's projection operators, we separate the physical spin-0 and spin-1 sectors and derive the corresponding exact second-order equations in the full curved spacetime, without relying on the conical approximation. For the scalar sector, the radial equation reduces to a Schr\"odinger-like equation with a trigonometric P\"oschl--Teller effective potential. In the vector sector, the longitudinal mode is governed by the same effective potential, whereas the transverse polarizations are described by generalized trigonometric P\"oschl--Teller potentials. Because the me\-tric function vanishes at a discrete set of radial points, the radial dynamics is naturally formulated as a singular Sturm--Liouville problem on a fundamental interval, with the physical radial domain fixed by the Friedrichs self-adjoint extension of the corresponding singular radial operators. As a result, all physical sectors exhibit purely discrete radial spectra, and their eigenfunctions are obtained in closed form. These results provide a unified exact treatment of scalar and vector bosons in the Bonnor--Melvin--$\Lambda$ spacetime, complement previous analyses based on the conical approximation, and clarify the role of the global geometric structure of the background in shaping confinement and spectral properties.

gr-qc↗
arXiv2026

Scattering, bound states, and resonances in the one-dimensional Dirac equation via supersymmetric quantum mechanics

We develop a unified treatment of scattering and discrete spectra for the one-dimensional Dirac equation with scalar and vector interactions. Under the spin-symmetry condition, the coupled first-order Dirac system maps exactly onto an effective Sturm--Liouville (Schr\"o\-din\-ger-like) problem for a single spinor component. This mapping provides a convenient framework for analyzing transmission, reflection, and analytic continuation. As an explicit application, we consider effective interactions of hyperbolic P\"oschl--Teller type and exploit supersymmetric quantum mechanics and shape invariance to obtain a closed-form expression for the transmission probability. The bound-state spectrum is then recovered from the poles of the analytically continued transmission amplitude, reproducing known results and offering a unified description of scattering and bound states. For the barrier configuration, we briefly comment on the resulting pole pattern in the complex momentum plane and its connection with resonance and quasi-normal-mode behavior. Moreover, we use the chiral transformation to relate the spin- and pseudospin-symmetry sectors and translate results between them without repeating the full derivation.

quant-ph↗
arXiv2025

Effects of the Lorentz symmetry violation on relativistic neutral scalar bosons: Scattering and bound states

In this letter, we investigate the effects of Lorentz symmetry violation on a relativistic neutral scalar boson within the framework of the Klein-Gordon formalism. We consider a tensor $(K_F)_{\mu \nu \alpha \beta}$ out of the Standard Model Extension, which describes the field configuration consisting of a constant magnetic field $\vec{B}=B\hat{z}$ and a cylindrical electric field $\vec{E}=\frac{\lambda}{r}\hat{r}$. We analyze and discuss the effects of Lorentz symmetry violation on the equation of motion and show that the presence of a specific Lorentz symmetry violation parameter is essential to obtain analytical solutions for scattering and bound states. Employing the partial wave approach in cylindrical coordinates, we calculate the relativistic phase shift, scattering amplitude and $S$-matrix, and discuss the effects of Lorentz symmetry violation on the phase shift. Furthermore, we obtain bound-state solutions by examining the poles of the $S$-matrix and compare our findings with those reported in the literature. Our results reveal that bound-state solutions are only feasible for a restrict range of Lorentz symmetry violation parameters, which contradict previous studies.

hep-th↗
arXiv2024

Oscillatory properties of strange quark stars described by the vector MIT bag model

We investigated the radial and non-radial fundamental ($f$) mode oscillations of self-bound (quark) stars obtained after employing the Vector MIT (vMIT) bag model. Within this model, we computed the equation of state for strange quark matter satisfying thermodynamic consistency. This allowed us to obtain the corresponding behavior of the speed of sound, mass-radius relation, and gravitational redshift. In particular, our choice of $G_V$ = 0.30 fm$^2$ produces masses and radii in agreement with recent astronomical data (e.g. from NICER and HESS J1731). In fact, we tested that variations of the remaining vMIT parameters slightly modify this conclusion. Then, we proceeded to compute the radial oscillation frequencies of the $f$-mode, which is tightly connected to the dynamical stability of these compact stars. We found that increments of the $G_V$ parameter have a stabilizing property around the maximal-mass stars for a given stellar family. We also calculated the gravitational-wave frequencies of the non-radial $f$-mode. Our results show that they are restricted to be in the range (1.6 - 1.8) kHz for high-mass stars and to (1.5 - 1.6) kHz for low-mass stars. Finally, we propose a universal relation between these frequencies and the square root of the average density. All these last results are important in distinguishing strange stars from ordinary neutron stars in future gravitational-wave detections coming from compact sources with activated non-radial modes.

hep-ph↗
arXiv2024

Charged scalar bosons in a Bonnor-Melvin-$Λ$ universe at conical approximation

The quantum dynamics of charged scalar bosons in a Bonnor-Melvin-$Λ$ universe is considered. In this study, the behavior of charged scalar bosons is explored within the framework of the Duffin-Kemmer-Petiau (DKP) formalism. Adopting a conical approximation ($Λ\ll 1$), we are considered two scenarios for the vector potential: a linear and quadratic vector potentials. In particular, the effects of this background in the equation of motion, phase shift, $S$-matrix, energy spectrum and DKP spinor are analyzed and discussed.

gr-qc↗
arXiv2024

On the electromagnetic interaction and the anomalous term in the Duffin-Kemmer-Petiau theory

The problem of vectorial mesons embedded in an electromagnetic field via Duffin-Kemmer-Petiau (DKP) formalism is reinvestigated. Considering the electromagnetic interaction as a minimal coupling, an incorrect value $(g=1)$ is identified for the gyromagnetic factor ($g$-factor). Furthermore, it is shown that is cumbersome to find analytical solutions due to the presence of the so-called anomalous term for the spin-1 sector of the DKP theory. Suspecting that the anomalous term results from an incomplete version of the DKP equation to describe the electromagnetic interaction, we consider the addition of a non-minimal coupling. This leads to the correct $g$-factor $(g=2)$, and as a consequence, the anomalous term becomes proportional to an external four current. As an application, the DKP equation with a static uniform magnetic field is considered, yielding the corresponding Landau levels.

hep-th↗
arXiv2024

Remarks on the ($2+1$)-dimensional Duffin-Kemmer-Petiau oscillator in an external magnetic field

This work re-examines the issue of spin-$1$ particles in a ($2+1$)-dimensional Duffin-Kemmer-Petiau oscillator (DKPO) in the presence of an external magnetic field. By following the appropriate procedure for the spin-$1$ sector of the Duffin-Kemmer-Petiau (DKP) theory, the previously used $6\times 6$ representation in the literature is shown to be reducible to a $3\times 3$ irreducible representation. This approach enabled us to find new aspects of the results recently disseminated in various studies, as well as other considerations overlooked and requiring revision. Finally, we present some applications of two-dimensional DKP theory in condensed matter systems, particularly in Lieb lattices.

quant-ph↗
arXiv2024

Effect of a critical magnetic field on the control of scalar neutral boson pair production in the context of Lorentz-symmetry violation

This study investigates the production of neutral scalar boson pairs in static electromagnetic fields resulting from Lorentz-symmetry violation (LSV), with a focus on the parity-even sector of the CPT-even photon sector in the Standard Model Extension (SME). Utilizing a cross-configuration involving inhomogeneous static electric fields and homogeneous static magnetic fields, the analysis of the probability of bosons pair production identifies three different regimes determined by critical magnetic field. Below the critical value, creation is exponentially suppressed; at the critical value, the number density of created bosons remains constant, and above the critical field, there is exponential amplification. This behavior prompts an additional investigation using von Neumann entanglement entropy to analyze fluctuations in the bosonic vacuum.

hep-th↗
arXiv2023

Effects of a uniform magnetic field on twisted graphene nanoribbons

In the present work, the relativistic quantum motion of massless fermions in a helicoidal graphene nanoribbon under the influence of a uniform magnetic field is investigated. Considering a uniform magnetic field ($B$) aligned along the axis of helicoid, this problem is explored in the context of Dirac equation in a curved space-time. As this system does not support exact solutions due to considered background, the bound-state solutions and local density of state (LDOS) are obtained numerically by means of the Numerov method. The combined effects of width of the nanoribbon ($D$), length of ribbon ($L$), twist parameter ($\omega$) and $B$ on the equations of motion and local density of states (LDOS) are analyzed and discussed. It is verified that the presence of $B$ produces a constant minimum value of local density of state on the axis of helicoid, which is possible only for values large enough of $\omega$, in contrast to the case for $B=0$ already studied in the literature.

cond-mat.mes-hall↗
arXiv2022

Non-radial oscillations and global stellar properties of anisotropic compact stars using realistic equations of state

In this work, we have made a systematic study of how the gravitational wave frequency of the fundamental mode from compact stars is affected by anisotropic effects using realistic equations of state. Our study is an extension of the seminal research performed by Doneva [Phys. Rev. D 85 (2012) 124023], where a polytropic equation of state was used. To achieve our objective, we considered compact stars which were built by using equations of state in the framework of a relativistic mean field theory for the case of hadronic stars and in the framework of the MIT model for the case of quark stars. In order to obtain some pertinent information that could give us the possibility to detect the anisotropy in compact stars, we also studied and analized the behaviour of various global stellar quantities, e.g., gravitational redshift, stellar mass, radius, among others. We concluded that the anisotropic effects can have important consequences, which are strongly related to the anisotropic parameter and the equation of state of high density matter. Additionally, a comparison with observational data has been made and we have shown that the anisotropic parameter $λ$ can be used as a tuning parameter to reproduce mass and radius observational data of neutron stars.

gr-qc↗
arXiv2020

Remarks on thermodynamic properties of a double ring-shaped quantum dot at low and high temperatures

In a recent paper published in this Journal, Khordad and collaborators [J Low Temp Phys (2018) 190:200] have studied the thermodynamics properties of a GaAs double ring-shaped quantum dot under external magnetic and electric fields. In that meritorious research the energy of system was obtained by solving the Schrödinger equation. The radial equation was mapped into a confluent hypergeometric differential equation and the differential equation associated to $z$ coordinate was mapped into a biconfluent Heun differential equation. In this paper, it is pointed out a misleading treatment on the solution of the biconfluent Heun equation. It is shown that the energy $E_{z}$ can not be labeled with $n_{z}$ and this fact jeopardizes the results of this system. We calculate the partition function with the correct energy spectrum and recalculate the specific heat and entropy as a function of low and high temperatures.

cond-mat.mes-hall↗
arXiv2020

Comment on "Chern-Simons theory and atypical Hall conductivity in the Varma phase''

In a recent paper published in this Journal [Phys. Rev. B 97, 075135 (2018)], Menezes et al. analyze the topological behavior of a effective bosonic model defined on the Lieb lattice in presence of an electromagnetic field. In this context, the authors claim to have found an atypical quantum Hall effect for the quasiparticles. However, some inconsistencies related to the treatment of the propagator jeopardizes the main result in this system.

hep-th↗
arXiv2020

Gravitational Wave Signatures of Highly Magnetized Neutron Stars

Motivated by the recent gravitational wave detection by the LIGO-VIRGO observatories, we study the Love number and dimensionless tidal polarizability of highly magnetized stars. We also investigate the fundamental quasi-normal mode of neutron stars subject to high magnetic fields. To perform our calculations we use the chaotic field approximation and consider both nucleonic and hyperonic stars. As far as the fundamental mode is concerned, we conclude that the role played by the constitution of the stars is far more relevant than the intensity of the magnetic field and if massive stars are considered, the ones constituted by nucleons only present frequencies somewhat lower than the ones with hyperonic cores, a feature that can be used to point out the real internal structure of neutron stars. Moreover, our studies clearly indicate that strong magnetic fields play a crucial role in the deformability of low mass neutron stars, with possible consequences on the interpretation of the detected gravitational waves signatures.

nucl-th↗
arXiv2020

Comment on "Dirac fermions in Som-Raychaudhuri space-time with scalar and vector potential and the energy momentum distributions"

We point out a misleading treatment and incorrect expressions in a recent paper published in this Journal [Eur. Phys. J. C (2019) 79: 541] regarding solutions for the Dirac equation in presence of scalar and vector potentials in a class of flat Gödel-type space-time called Som-Raychaudhuri space-time. Following the appropriate procedure we obtain the solution for this system.

hep-th↗
arXiv2019

Comment on "Comment on linear confinement of a scalar particle in a Gödel-type space-time"

We show that from an appropriate manipulation of the biconfluent Heun differential equation can obtain the correct expression for the energy eigenvalues for the Klein-Gordon equation without potential in the background of Som-Raychaudhuri space-time with a cosmic string as a case particular ($k_{L}=0$) of [Vitória et al. Eur. Phys. J. C (2018) 78:44], in opposition what was stated in a recent paper published in this journal [F. Ahmed, Eur. Phys. J. C (2019) 79:682].

gr-qc↗
arXiv2019

Scalar bosons with Coulomb potentials in a cosmic string background: Scattering and bound states

The relativistic quantum motion of scalar bosons under the influence of a full vector (minimal $A^μ$ and nonminimal $X^μ$) and scalar ($V_{s}$) interactions embedded in the background of a cosmic string is explored in the context of the Klein-Gordon equation. Considering Coulomb interactions, the effects of this topological defect in equation of motion, phase shift and S-matrix are analyzed and discussed. Bound-state solutions are obtained from poles of the S-matrix and it is shown that bound-state solutions are possible only for a restrict range of coupling constants.

hep-th↗
arXiv2019

On the 2D Dirac oscillator in the presence of vector and scalar potentials in the cosmic string spacetime in the context of spin and pseudospin symmetries

The Dirac equation with both scalar and vector couplings describing the dynamics of a two-dimensional Dirac oscillator in the cosmic string spacetime is considered. We derive the Dirac-Pauli equation and solve it in the limit of the spin and the pseudo-spin symmetries. We analyze the presence of cylindrical symmetric scalar potentials which allows us to provide analytic solutions for the resultant field equation. By using an appropriate ansatz, we find that the radial equation is a biconfluent Heun-like differential equation. The solution of this equation provides us with more than one expression for the energy eigenvalues of the oscillator. We investigate these energies and find that there is a quantum condition between them. We study this condition in detail and find that it requires the fixation of one of the physical parameters involved in the problem. Expressions for the energy of the oscillator are obtained for some values of the quantum number $n$. Some particular cases which lead to known physical systems are also addressed.

hep-th↗