Topological, noninertial and spin effects on the 2D Dirac oscillator in the presence of the Aharonov–Casher effect

Oliveira, R. R. S.

doi:10.1140/epjc/s10052-019-7237-y

Cited by 18 publications

(20 citation statements)

References 87 publications

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“…The DO has been also studied in the context of minimal length uncertainty [33,34]. The DO is an exactly solvable system and this important fact makes the DO is a useful system to determine the influence of spacetime topology on the dynamics of the corresponding systems [5,[35][36][37][38][39][40]. However, in many areas of the modern physics, a quantum oscillator is used to determine the dynamics of the interacting particles [6].…”

Section: Introductionmentioning

confidence: 99%

Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction

Guvendi¹

2021

Eur. Phys. J. C

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We introduce a unique model for a fermion-antifermion pair interacting via Dirac oscillator coupling in the presence of an external uniform magnetic field. This model is based on an exact solution of the corresponding form of a fully-covariant two-body Dirac equation (one-time). The dynamic symmetry of the system allows to study in $$2+1$$ 2 + 1 dimensions and we choose the interaction of the particles with the external uniform magnetic field in the symmetric gauge. The corresponding equation leads $$4\times 4$$ 4 × 4 dimensional matrix equation for such a static composite system. For spin antisymmetric state of the fermion-antifermion pair, we perform an exact solution of the matrix equation and obtain relativistic Landau levels of a fermion-antifermion pair interacting via Dirac oscillator coupling. The results show that such a composite system behaves like a single relativistic quantum oscillator carrying total rest mass of the particles. We discuss several interesting features of this system and show that the obtained energy spectrum agrees well with the previously announced results for one-body systems. We think that the introduced model in this manuscript has a great potential for many theoretical and experimental applications.

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Section: Introductionmentioning

confidence: 99%

Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction

Guvendi¹

2021

Eur. Phys. J. C

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“…We have shown that the energy levels of the particle and antiparticle depend on the values of the physical parameters involved. In the case of energy (71), its validity is conditioned to Equation (72). Depending on the choice we make for the parameters, we can obtain forbidden energies.…”

Section: Discussionmentioning

confidence: 99%

“…However, there is no need to solve them here because they have both energy and wave functions similar to those obtained above. Let us study the energies ( 70) and (71). First, we see that the energy E ð>Þ n depends only on the quantum number n and the magnetic field B.…”

Section: Solution Of the Equation Of Motion To E ≠ ±Mmentioning

confidence: 99%

“…Because of this, we analyze in detail only the energy (71). One of the objectives in our analysis is to show that the combined effect of the external magnetic field, the Aharonov-Bohm flux, the rotation, and the curvature modifies the energy spectrum of the particle.…”

Section: Solution Of the Equation Of Motion To E ≠ ±Mmentioning

confidence: 99%

“…[70]. The presence of noninertial effects also was considered in this context [71]. Reference [72] treats the problem of a charged half-spin particle depicted by the Dirac equation in the presence of a uniform magnetic field in the rotating cosmic string spacetime.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Relativistic Quantum Motion of an Electron in Spinning Cosmic String Spacetime in the Presence of Uniform Magnetic Field and Aharonov-Bohm Potential

Cunha

Silva

2021

Advances in High Energy Physics

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In this manuscript, we study the relativistic quantum mechanics of an electron in external fields in the spinning cosmic string spacetime. We obtain the Dirac equation and write the first- and second-order equations from it, and then, we solve these equations for bound states. We show that there are bound state solutions for the first-order equation Dirac. For the second-order equation, we obtain the corresponding wave functions, which depend on the Kummer functions. Then, we determine the energies of the particle. We examine the behavior of the energies as a function of the physical parameters of the model, such as rotation, curvature, magnetic field, Aharonov-Bohm flux, and quantum numbers. We find that, depending on the values of these parameters, there are energy nonpermissible levels.

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

2023

Self Cite

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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.

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Topological, noninertial and spin effects on the 2D Dirac oscillator in the presence of the Aharonov–Casher effect

Cited by 18 publications

References 87 publications

Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction

Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction

Relativistic Quantum Motion of an Electron in Spinning Cosmic String Spacetime in the Presence of Uniform Magnetic Field and Aharonov-Bohm Potential

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

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