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R. R. S. Oliveira

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

26 records · Page 2Linked to original sources
arXiv2022

The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios

In the present paper, we investigate the bound-state solutions of the noncommutative quantum Hall effect (NCQHE) with anomalous magnetic moment (AMM) in three different relativistic scenarios, namely: the Minkowski spacetime (inertial flat case), the spinning cosmic string (CS) spacetime (inertial curved case), and the spinning CS spacetime with noninertial effects (noninertial curved case). In particular, in the first two scenarios, we have an inertial frame, while in the third, we have a rotating frame. With respect to bound-state solutions, we focus primarily on eigenfunctions (Dirac spinor and wave function) and on energy eigenvalues (Landau levels), where we use the flat and curved Dirac equation in polar coordinates to reach such solutions. However, unlike the literature, here we consider a CS with an angular momentum non-null and also the NC of the positions, and therefore, we seek a more general description for the QHE. Once the solutions are obtained, we discuss the influence of all parameters and physical quantities on relativistic energy levels. Finally, we analyze the nonrelativistic limit, and we also compared our problem with other works, where we verified that our results generalize some particular cases of the literature.

hep-th↗
arXiv2020

Noninertial and spin effects on the 2D Dirac oscillator in the magnetic cosmic string background

In this work, we analyze the influence of noninertial and spin effects on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background. To model this background, we consider a uniform magnetic field, the Aharonov-Bohm effect, and a parameter $η$ generated by a cosmic string. Posteriorly, we determine the bound-state solutions of the system: the Dirac spinor and the relativistic energy spectrum. We verified that this spinor is written in terms of the generalized Laguerre polynomials and this spectrum depends on the effective quantum number $N_r$, angular velocity $Ω$ and parameter $s$ associated to the noninertial and spin effects, magnetic flux $Φ$, cyclotron frequency $ω_c$, zero-point energy $E_0$, and on the deficit angle $η$. In particular, we note that besides this spectrum to be a periodic function and asymmetric, its values infinitely increase when $η\to 0$ or $N_r=ω_c=Ω\to\infty$. We also note that the energies of the antiparticle with spin down are larger than of the particle with spin up or down. In the nonrelativistic limit, we get the Schrödinger-Pauli oscillator with two types of couplings: the spin-orbit coupling and the spin-rotation coupling, and two Hamiltonians: one quantum harmonic oscillator-type and other Zeeman-type. Finally, we compare our results with other works, where we verified that our problem generalizes some particular cases of the literature when $Ω$, $ω_c$, $Φ$, $s$ or $η$ are excluded from the system.

hep-th↗
arXiv2019

Topological and noninertial effects in an Aharonov-Bohm ring

In this paper, we study the influence of topological and noninertial effects on a Dirac particle confined in an Aharonov-Bohm (AB) ring. Next, we explicitly determine the Dirac spinor and the energy spectrum for the relativistic bound states. We observe that this spectrum depends on the quantum number $n$, magnetic flux $Φ$ of the ring, angular velocity $ω$ associated to the noninertial effects of a rotating frame, and on the deficit angle $η$ associated to the topological effects of a cosmic string. We verified that this spectrum is a periodic function and grows in values as a function of $n$, $Φ$, $ω$, and $η$. In the nonrelativistic limit, we obtain the equation of motion for the particle, where now the topological effects are generated by a conic space. However, unlike relativistic case, the spectrum of this equation depends linearly on the velocity $ω$ and decreases in values as a function of $ω$. Comparing our results with other works, we note that our problem generalizes some particular cases of the literature. For instance, in the absence of the topological and noninertial effects ($η=1$ and $ω=0$) we recover the usual spectrum of a particle confined in an AB ring ($Φ\neq{0}$) or in an 1D quantum ring ($Φ=0$).

hep-th↗
arXiv2019

Thermodynamic properties of neutral Dirac particles in the presence of an electromagnetic field

In this paper, we investigate the thermodynamic properties of a set of neutral Dirac particles in the presence of an electromagnetic field in contact with a heat bath for the relativistic and non-relativistic cases. In order to perform the calculations, the high-temperature limit is considered and the Euler-MacLaurin formula is taking into account. Next, we explicitly determine the behavior of the main thermodynamic functions of the canonical ensemble: the Helmholtz free energy, the mean energy, the entropy, and the heat capacity. As a result, we verified that the mean energy and the heat capacity for the relativistic case are two times the values of the non-relativistic case, thus, satisfying the so-called Dulong-Petit law. In addition, we also verified that the Helmholtz free energy and the entropy in both cases increase as a function of the electric field. Finally, we note that there exists no influence on the thermodynamic functions due to the magnetic field.

quant-ph↗
arXiv2018

The relativistic Aharonov-Bohm-Coulomb system with position-dependent mass

In this work, we study the Aharonov-Bohm-Coulomb (ABC) system for a relativistic Dirac particle with position-dependent mass (PDM). To solve our system, we use the left-handed and right-handed projection operators. Next, we explicitly obtain the eigenfunctions and the energy spectrum of the particle. We verify that these eigenfunctions are written in terms of the generalized Laguerre polynomials and the energy spectrum depends on the parameters Z, $Φ_{AB}$ and $κ$. We notice that the parameter $κ$ has the function of increasing the values of the energy levels of the system. In addition, the usual ABC system is recovered when one considers the limit of constant mass ($κ\to{0}$). Moreover, also we note that even in the absence of ABC system ($Z=Φ_{AB}=0$), the particle with PDM still has a discrete energy spectrum.

quant-ph↗
arXiv2018

Exact solutions of the Dirac oscillator under the influence of the Aharonov-Casher effect in the cosmic string background

In this work, we study the Aharonov-Casher effect in the $(2+1)$-dimensional Dirac oscillator coupled to an external electromagnetic field. We set up our system in two different scenarios: in the Minkowski spacetime and the cosmic string spacetime. In both cases, we solve exactly the Dirac oscillator and we determine the energy spectrum and the eigenfunctions for the bound states. We verify that in the Minkowski spacetime, the Dirac oscillator spectrum depends linearly on the strength of the magnetic field $B$, and on the Aharonov-Casher phase. In addition, we explicitly obtain the corrections on the Dirac spinors and the energy levels due to the curvature effects in the cosmic string background. Finally, we investigate the nonrelativistic limit and compare our results with those found in the literature.

quant-ph↗
arXiv2018

Bound state solutions of the Dirac oscillator in an Aharonov-Bohm-Coulomb system

In this work, we study of the (2+1)-dimensional Dirac oscillator in the presence of a homogeneous magnetic field in an Aharonov-Bohm-Coulomb system. To solve our system, we apply the $left$-$handed$ and $right$-$handed$ projection operators in the Dirac oscillator to obtain a biconfluent Heun equation. Next, we explicitly determine the energy spectrum for the bound states of the system and their exact dependence on the cyclotron frequency $ω_c$ and on the parameters $Z$ and $Φ_{AB}$ that characterize the Aharonov-Bohm-Coulomb system. As a result, we observe that by adjusting the frequency of the Dirac oscillator to resonate with the cyclotron half-frequency the energy spectrum reduces to the rest energy of the particle. Also, we determine the exact eigenfunctions, angular frequencies, and energy levels of the Dirac oscillator for the ground state ($n=1$) and the first excited state ($n=2$). In this case, the energy levels do not depend on the homogeneous magnetic field, and the angular frequencies are real and positive quantities, increase quadratically with the energy and linearly with $ω_{c}$.

quant-ph↗