arXiv subjects

R. R. S. Oliveira

Publications and source records attributed to R. R. S. Oliveira.

At least 19 recordsLinked to original sources

arXiv2026

The Dirac oscillator in the curved spacetime of a cloud of strings

In this paper, we determine the relativistic bound-state solutions for the Dirac oscillator (DO) in the curved spacetime of a cloud of strings in $(3+1)$-dimensions, where such solutions are given by the four-component normalized Dirac spinor and by the relativistic energy spectrum. However, unlike in literature, here, we work with the spacetime in two different forms/configurations, that is, both in its original form and in its modified form. To achieve our objective, we work with the curved DO in spherical coordinates, where we use the tetrad formalism. So, by defining a stationary ansatz for the spinor, we obtain two coupled first-order differential equations, and by substituting one equation into the other, we obtain a second-order differential equation. To analytically and exactly solve this differential equation, we use a change of function and of variable. From this, we obtain the well-known Whittaker equation, whose solution is the Whittaker function. Consequently, we obtain the energy spectrum, which is quantized in terms of the radial quantum number $n$ and the angular quantum number $κ$, and explicitly depends on the angular frequency $ω$ (describes the DO), curvature parameter $a$ (describes the cloud of strings), and on the effective rest mass $m_{\text{eff}}$ (describes the rest mass modified by the curvature of spacetime). Besides, we graphically analyze the behavior of the spectrum as a function of $ω$ and $a$ for three different values of $n$ and $κ$, as well as the behavior of the radial probability density for four different values of $κ$, $ω$, and $a$ (with $n=0$).

hep-th↗

arXiv2026

Comment on "Quantum phase transitions of Dirac particles in a magnetized rotating curved background: Interplay of geometry, magnetization, and thermodynamics"

In this comment, we obtain the complete energy spectra for the paper by Sahan et al. [1], that is, the energy spectra dependent on two quantum numbers, namely, the radial quantum number (given by $n\geq 0$) and the angular quantum number (given by $m\neq 0$). In particular, what motivated us to carry out such a study was the fact that the quantized energy spectra for Dirac particles in a curved or flat spacetime in polar coordinates explicitly depend on two quantum numbers. From this, the following question arose: Why do the energy spectra in the paper by Sahan et al. [1] depends on only one quantum number and not two, given that they worked with the Dirac equation in polar coordinates? So, using several important papers in the literature on the Dirac equation in curved spacetimes, as well as the most commonly used definition for Dirac gamma matrices in (2+1)-dimensions, we corrected some minor errors in the paper by Sahan et al. [1]. Consequently, we obtain the true second-order differential equation for their problem, as well as the complete energy spectra, which explicitly depend on both $n$ and $m$. Finally, we note that for $m<0$ (negative angular momentum) with $s=-1$ (lower component of the Dirac spinor), we obtain (except for one term with the incorrect sign) the particular energy spectra of Sahan et al. [1].

gr-qc↗

arXiv2025

Charged Dirac fermions with anomalous magnetic moment in the presence of the chiral magnetic effect and of a noncommutative phase space

In this paper, we analyze the relativistic energy spectrum (or relativistic Landau levels) for charged Dirac fermions with anomalous magnetic moment (AMM) in the presence of the chiral magnetic effect (CME) and of a noncommutative (NC) phase space, where we work with the $(3+1)$-dimensional Dirac equation in cylindrical coordinates. Using a similarity transformation, we obtain four coupled first-order differential equations. Subsequently, obtain four non-homogeneous second-order differential equations. To solve these equations exactly and analytically, we use a change of variable, the asymptotic behavior, and the Frobenius method. Consequently, we obtain the relativistic spectrum for the electron/positron, where we note that this spectrum is quantized in terms of the radial quantum number $n$ and the angular quantum number $m_j$, and explicitly depends on the position and momentum NC parameters $θ$ and $η$ (describes the NC phase space), cyclotron frequency $ω_c$ (an angular frequency that depends on the electric charge $e$, mass $m$, and external magnetic field $B$, i.e., $ω_c=eB/m$), anomalous magnetic energy $E_m$ (an energy generated through the interaction of the AMM with the external magnetic field), $z$-momentum $k_z$ (linear momentum along the $z$-axis), and on the fermion and chiral chemical potential $μ$ and $μ_5$ (describes the CME). However, through $θ$, $η$, and $m$, we define two types of ''NC angular frequencies'', given by $ω_θ=4/mθ$ and $ω_η=η/m$ (our spectrum depends on three angular frequencies). Comparing our spectrum with other papers, we verified that it generalizes several particular cases found in the literature. Besides, we also graphically analyze the behavior of the spectrum as a function of $B$, $μ$, $μ_5$, $k_z$, $θ$, and $η$ for three different values of $n$ and $m_j$.

hep-th↗

arXiv2025

Comment on "Unruh effect for neutrinos interacting with accelerated matter"

In the present comment, we show that the fundamental equation worked by Dvornikov in his paper, which is the Dirac equation for a massive neutrino interacting with linearly accelerated matter, is incorrect. In particular, Dvornikov incorrectly wrote/defined the effective external current in a curved space-time. In other words, Dvornikov wrote/defined such an effective current in a flat space-time, which is a mistake. Consequently, the second-order differential equation (generated through the quadratic Dirac equation) in your paper is incorrect, where such an equation is given by the Whittaker equation. So, since the solutions of such a differential equation (whose solutions are the Whittaker functions) are the basis for its results, it implies that such results are also incorrect. In this way, starting from the true/correct Dirac equation with an effective external current in a curved space-time, we obtain in detail the second-order differential equation (also a Whittaker equation) and its solutions for a neutrino interacting with linearly accelerated matter.

hep-ph↗

arXiv2025

Comment on "Galvano-rotational effect induced by electroweak interactions in pulsars"

In this comment, we show that the fundamental equation worked by Dvornikov in his paper is incorrect, which is given by the Dirac equation for a neutrino interacting with matter in a rotating frame (or curved space-time). In particular, Dvornikov incorrectly wrote/defined the interaction term (effective potentials or background matter) in a curved space-time. Consequently, one of his main results (if not the main one), namely the relativistic energy spectrum, is also incorrect (actually partially incorrect). So, starting from the correct Dirac equation with effective potentials in a curved space-time, we obtain the correct energy spectrum for a neutrino interacting with matter in a rotating frame. We observe that the square root of this spectrum is very different from that obtained by Dvornikov. In fact, in our case, the spectrum was obtained from a Bessel equation subject to a hard-wall confining potential, while the Dvornikov spectrum was obtained from an associated Laguerre equation. However, we note that the only correct thing in the Dvornikov spectrum are the terms outside the square root, which agree with those of the correct spectrum.

hep-ph↗

arXiv2025

Bound-state solutions for the charged Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime

In this paper, we determine the relativistic bound-state solutions for the charged (DO) Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime in $(2+1)$-dimensions, where such solutions are given by the two-component normalizable Dirac spinor and by the relativistic energy spectrum. To analytically solve our problem, we consider two approximations, where the first is that the cosmological constant is very small (conical approximation), and the second is that the linear velocity of the rotating frame is much less than the speed of light (slow rotation regime). After solving a second-order differential equation, we obtain a generalized Laguerre equation, whose solutions are the generalized Laguerre polynomials. Consequently, we obtain the energy spectrum, which is quantized in terms of the radial and total magnetic quantum numbers $n$ and $m_j$, and depends on the angular frequency $ω$ (describes the DO), cyclotron frequency $ω_c$ (describes the external magnetic field), angular velocity $Ω$ (describes the rotating frame), spin parameter $s$ (describes the ``spin''), spinorial parameter $u$ (describes the components of the spinor), effective rest mass $m_{eff}$ (describes the rest mass modified by the spin-rotation coupling), and on a real parameter $σ$ and cosmological constant $Λ$ (describes the Bonnor-Melvin-Lambda spacetime). In particular, we note that this spectrum is asymmetrical (due to $Ω$) and has its degeneracy broken (due to $σ$ and $Λ$). Besides, we also graphically analyze the behavior of the spectrum and of the probability density as a function of the parameters of the system for different values of $n$ and $m_j$.

gr-qc↗

arXiv2025

Comment on "Exact massless spinor quasibound states of Schwarzschild black hole"

In this comment, we point out a series of errors made by Senjaya in your paper (2024) \cite{Senjaya}. In particular, these errors involved the Dirac equation in the 3+1 dimensional Schwarzschild spacetime, tetrad field, curved gamma matrices, and the time-independent Dirac equation written in terms of the inner/scalar product between the gamma matrices and the orbital angular momentum (i.e., $\vecγ\cdot\vec{L}$). Besides, the strange/peculiar thing about all this is that even Senjaya \cite{Senjaya} citing Collas and Klein \cite{Collas}, where the (mathematical) formalism is correct, everything indicates that he ``ignored'' or ``forgot'' to use such formalism in your paper. Therefore, using Ref. \cite{Collas}, we show here the correct form of the errors made by Senjaya \cite{Senjaya}.

gr-qc↗

arXiv2025

Dirac fermions with electric dipole moment and position-dependent mass in the presence of a magnetic field generated by magnetic monopoles

In this paper, we determine the bound-state solutions for Dirac fermions with electric dipole moment (EDM) and position-dependent mass (PDM) in the presence of a radial magnetic field generated by magnetic monopoles. To achieve this, we work with the $(2+1)$-dimensional (DE) Dirac equation with nonminimal coupling in polar coordinates. Posteriorly, we obtain a second-order differential equation via quadratic DE. Solving this differential equation through a change of variable and the asymptotic behavior, we obtain a generalized Laguerre equation. From this, we obtain the bound-state solutions of the system, given by the two-component Dirac spinor and by the relativistic energy spectrum. So, we note that such spinor is written in terms of the generalized Laguerre polynomials, and such spectrum (for a fermion and an antifermion) is quantized in terms of the radial and total magnetic quantum numbers $n$ and $m_j$, and explicitly depends on the EDM $d$, PDM parameter $κ$, magnetic charge density $λ_m$, and on the spinorial parameter $s$. In particular, the quantization is a direct result of the existence of $κ$ (i.e., $κ$ acts as a kind of ``external field or potential''). Besides, we also analyze the nonrelativistic limit of our results, that is, we also obtain the nonrelativistic bound-state solutions. In both cases (relativistic and nonrelativistic), we discuss in detail the characteristics of the spectrum as well as graphically analyze its behavior as a function of $κ$ and $λ_m$ for three different values of $n$ (ground state and the first two excited states).

quant-ph↗

arXiv2025

Comment on "Neutrino interaction with matter in a noninertial frame"

In this comment, we obtain the complete energy levels for Dvornikov's paper, that is, the energy levels dependent on two quantum numbers, namely, the radial quantum number (given by $N$) and the angular quantum number (given by $J_z$). In particular, what motivated us to do this was the fact that the quantized energy levels for particles (fermions or bosons) in polar, cylindrical, or spherical coordinates depend on two quantum numbers: a radial quantum number and an angular quantum number. From this, the following question/doubt arose: Why do the energy levels in Dvornikov's paper only depend on one quantum number? That is, Where did the angular quantum number given by $J_z$ go? So, using Studenikin's paper as a starting point (as well as others in the literature), we write one of the equations from Dvornikov's paper in matrix form. Next, we use the four-component Dirac spinor and obtain a set/system of four coupled first-order differential equations. From the first two equations with $m\to 0$ (massless neutrino or ultrarelativistic regime), we obtain a (compact) second-order differential equation for the last two spinor components. So, solving this equation, we obtain the neutrino energy levels, which explicitly depend on both $N$ and $J_z$. Finally, we note that for $J_z>0$ (positive angular momentum) with $u=+1$ (component $ψ_3$), we obtain exactly the particular energy levels of Dvornikov's paper.

physics.gen-ph↗

arXiv2024

Dirac fermions in a spinning conical Gödel-type spacetime

In this paper, we determine the relativistic and nonrelativistic energy levels for Dirac fermions in a spinning conical Gödel-type spacetime in $(2+1)$-dimensions, where we work with the curved Dirac equation in polar coordinates and we use the tetrads formalism. Solving a second-order differential equation for the two components of the Dirac spinor, we obtain a generalized Laguerre equation, and the relativistic energy levels of the fermion and antifermion, where such levels are quantized in terms of the radial and total magnetic quantum numbers $n$ and $m_j$, and explicitly depends on the spin parameter $s$ (describes the ``spin''), spinorial parameter $u$ (describes the two components of the spinor), curvature and rotation parameters $α$ and $β$ (describes the conical curvature and the angular momentum of the spinning cosmic string), and on the vorticity parameter $Ω$ (describes the Gödel-type spacetime). In particular, the quantization is a direct result of the existence of $Ω$ (i.e. $Ω$ acts as a kind of ``external field or potential''). We see that for $m_j>0$, the energy levels do not depend on $s$ and $u$; however, depend on $n$, $m_j$, $α$, and $β$. In this case, $α$ breaks the degeneracy of the energy levels and such levels can increase infinitely in the limit $\frac{4Ωβ}α\to 1$. Already for $m_j<0$, we see that the energy levels depends on $s$, $u$ and $n$; however, it no longer depends on $m_j$, $α$ and $β$. In this case, it is as if the fermion ``lives only in a flat Gödel-type spacetime''. Besides, we also study the low-energy or nonrelativistic limit of the system. In both cases (relativistic and nonrelativistic), we graphically analyze the behavior of energy levels as a function of $Ω$, $α$, and $β$ for three different values of $n$ (ground state and the first two excited states).

gr-qc↗

arXiv2024

Comment on "Light deflection with torsion effects caused by a spinning cosmic string"

In this comment, we showed that the line element ("metric'') worked by Jusufi (Eur. Phys. J. C 76: 332, 2016) is incorrect since he worked with a spinning cosmic string with torsion in $(2+1)$-dimensions (and in polar coordinates), which cannot happen. Indeed, as in $(2+1)$-dimensions there are no screw dislocations or screw torsion (a consequence of the absence of the third spatial dimension, i.e., of the $z$-axis), and being a cosmic string with torsion a type of screw dislocation, but of cosmic origin (i.e., are cosmic dislocations), implies that a $(2+1)$-dimensional cosmic string does not have/carry torsion (since $dz=0$). Therefore, the line element worked by Jusufi is physically incoherent/unacceptable and inappropriate for the research/study.

gr-qc↗

arXiv2024

Dirac fermions under rainbow gravity effects in the Bonnor-Melvin-Lambda spacetime

In this paper, we study the relativistic energy spectrum for Dirac fermions under rainbow gravity effects in the $(3+1)$-dimensional Bonnor-Melvin-Lambda spacetime, where we work with the curved Dirac equation in cylindrical coordinates. Using the tetrads formalism of General Relativity and considering a first-order approximation for the trigonometric functions, we obtain a Bessel equation. To solve this differential equation, we also consider a region where a hard-wall confining potential is present (i.e., some finite distance where the radial wave function is null). In other words, we define a second boundary condition (Dirichlet boundary condition) to achieve the quantization of the energy. Consequently, we obtain the spectrum for a fermion/antifermion, which is quantized in terms of quantum numbers $n$, $m_j$ and $m_s$, where $n$ is the radial quantum number, $m_j$ is the total magnetic quantum number, $m_s$ is the spin magnetic quantum number, and explicitly depends on the rainbow functions $F(ξ)$ and $G(ξ)$, curvature parameter $α$, cosmological constant $Λ$, fixed radius $r_0$, and on the rest energy $m_0$, and $z$-momentum $p_z$. So, analyzing this spectrum according to the values of $m_j$ and $m_s$, we see that for $m_j>0$ with $m_s=-1/2$ (positive angular momentum and spin down), and for $m_j<0$ with $m_s=+1/2$ (negative angular momentum and spin up), the spectrum is the same. Besides, we graphically analyze in detail the behavior of the spectrum for the three scenarios of rainbow gravity as a function of $Λ$, $r_0$, and $α$ for three different values of $n$ (ground state and the first two excited states).

gr-qc↗

arXiv2024

Relativistic and nonrelativistic Landau levels for Dirac fermions in the cosmic string spacetime in the context of rainbow gravity

In this paper, we study the relativistic and nonrelativistic Landau levels for Dirac fermions in the cosmic string spacetime in the context of rainbow gravity in $(3+1)$-dimensions, where we work with the curved Dirac equation with minimal coupling in cylindrical coordinates. Using the tetrads formalism of General Relativity, we obtain a second-order differential equation. Solving this differential equation, we obtain a generalized Laguerre equation as well as the relativistic Landau levels for the fermion and antifermion, where such energy levels are quantized in terms of the quantum numbers $n$, $m_j$ and $m_s$, and explicitly depends on the rainbow functions $f(\varepsilon)$ and $g(\varepsilon)$, charge parameter $σ$, cyclotron frequency $ω_c$, curvature parameter $α$, and on the square rest energy $m^2_0$ and square $z$-momentum $k^2_z$, respectively. Posteriorly, we study the nonrelativistic limit of the system, where we obtain the nonrelativistic Landau levels. In both cases (relativistic and nonrelativistic), we graphically analyze the behavior of Landau levels for the three rainbow gravity scenarios as a function of the magnetic field $B$ and of the curvature parameter $α$. In addition, we also compared our problem with other works, where we verified that our results generalize several particular cases in the literature.

gr-qc↗

arXiv2024

Relativistic and nonrelativistic Landau levels for the noncommutative quantum Hall effect with anomalous magnetic moment in a conical Gödel-type spacetime

In this paper, we analyze the relativistic and nonrelativistic energy spectra (fermionic Landau levels) for the noncommutative quantum Hall effect with anomalous magnetic moment in the conical Gödel-type spacetime in (2+1)-dimensions, where such spacetime is the combination of the flat Gödel-type spacetime with a cosmic string (conical gravitational topological defect). To analyze these energy spectra, we start from the noncommutative Dirac equation with minimal and nonminimal couplings in polar coordinates. Using the tetrads formalism, we obtain a second-order differential equation. Next, we solve exactly this differential equation, where we obtain a generalized Laguerre equation, and also a quadratic polynomial equation for the total relativistic energy. By solving this polynomial equation, we obtain the relativistic energy spectrum of the fermion and antifermion. Besides, we also analyze the nonrelativistic limit of the system, where we obtain the nonrelativistic energy spectrum. In both cases (relativistic and nonrelativistic), we discuss in detail the characteristics of each spectrum as well as the influence of all parameters and physical quantities in such spectra. Comparing our problem with other works, we verified that our results generalize several particular cases in the literature.

hep-th↗

arXiv2024

Comment on "Deformations of the spin currents by topological screw dislocation and cosmic dispiration''

In this comment, we showed that the Dirac equation in the screw dislocation space-time also carries a term that represents the torsion of such topological defect, given by $K_μ$. Therefore, the Dirac equation worked by Wang et al. is incomplete since such a term was ignored in your equation (what cannot happen). In other words, it is only possible to work with the Dirac equation in the form presented by Wang et al. if the space-time is torsion-free, which is obviously not the case.

cond-mat.mes-hall↗

arXiv2023

Thermodynamic properties of the noncommutative quantum Hall effect with anomalous magnetic moment

In this paper, we study the thermodynamic properties of the noncommutative quantum Hall effect (NCQHE) with anomalous magnetic moment (AMM) for both relativistic and nonrelativistic cases in the high temperatures regime. Thus, we use the canonical ensemble for a set of $N$-particles in contact with a thermal bath. Next, we explicitly determine the thermodynamic properties of our interest, namely: the Helmholtz free energy, the entropy, the mean energy, and the heat capacity. In order to perform the calculations, we work with the Euler-MacLaurin formula to construct the partition function of the system. In that way, we plotted the graphs of thermodynamic properties as a function of temperature for six different values of the magnetic field and of the NC parameters. As a result, we note that the Helmholtz free energy decreases with the temperature, increases with the NC parameters, and can decrease or increase for certain values of the magnetic field, white that the entropy increases with the temperature, decreases with the NC parameters, and can decrease or increase for certain values of the magnetic field. Besides, the mean energy increases linearly with the temperature and its values for the relativistic case are twice of the nonrelativistic case, consequently, the heat capacity for the relativistic case is twice of the nonrelativistic case, where both are constants, and therefore, satisfying the so-called Dulong-Petit law. Finally, we also verify that there is no influence of the AMM on the thermodynamic properties of the system.

hep-th↗

arXiv2022

Thermodynamic properties of the noncommutative Dirac oscillator with a permanent electric dipole moment

In this paper, we investigate the thermodynamic properties of the noncommutative Dirac oscillator with a permanent electric dipole moment in the presence of an electromagnetic field in contact with a heat bath. Using the canonical ensemble, we determine the properties for both relativistic and nonrelativistic cases through the \textit{Euler-MacLaurin} formula in the high temperatures regime. In particular, the main properties are: the Helmholtz free energy, the entropy, the mean energy, and the heat capacity. Next, we analyze via 2D graphs the behavior of the properties as a function of temperature. As a result, we note that the Helmholtz free energy decreases with the temperature and $ω_θ$, and increases with $ω$, $\Tildeω$, $ω_η$, where $ω$ is the frequency of the oscillator, $\Tildeω$ is a type of cyclotron frequency, and $ω_θ$ and $ω_η$ are the noncommutative frequencies of position and momentum. With respect to entropy, we note an increase with the temperature and $ω_θ$, and a decrease with $ω$, $\Tildeω$, $ω_η$. Now, with respect to mean energy, we note that such property increases linearly with the temperature, and their values for the relativistic case are twice that of the nonrelativistic case. As a direct consequence of this, the value of the heat capacity for the relativistic case is also twice that of the nonrelativistic case, and both are constants, thus satisfying the \textit{Dulong-Petit} law. Lastly, we also note that the electric field does not influence the properties in any way.

hep-th↗

arXiv2022

The noncommutative Dirac oscillator with a permanent electric dipole moment in the presence of an electromagnetic field

In this paper, we investigate the bound-state solutions of the noncommutative Dirac oscillator with a permanent electric dipole moment in the presence of an electromagnetic field in (2+1)-dimensions. We consider a radial magnetic field generated by anti-Helmholtz coils, and the uniform electric field of the Stark effect. Next, we determine the bound-state solutions of the system, given by the two-component Dirac spinor and the relativistic energy spectrum. We note that this spinor is written in terms of the generalized Laguerre polynomials, and this spectrum is a linear function on the potential energy $U$, and depends explicitly on the quantum numbers $n$ and $m$, spin parameter $s$, and of four angular frequencies: $ω$, $\tildeω$, $ω_θ$, and $ω_η$, where $ω$ is the frequency of the oscillator, $\tildeω$ is a type of ``cyclotron frequency'', and $ω_θ$ and $ω_η$ are the noncommutative frequencies of position and momentum. Besides, we discussed some interesting features of such a spectrum, for example, its degeneracy, and then we graphically analyze the behavior of the spectrum as a function of the four frequencies for three different values of $n$, with and without the influence of $U$. Finally, we also analyze in detail the nonrelativistic limit of our results, and comparing our problem with other works, where we verified that our results generalize several particular cases of the literature.

hep-th↗