Non-commutativity and non-inertial effects on the Dirac oscillator in a cosmic string space–time

Cuzinatto, R. R.; Montigny, M. de; Pompeia, P. J.

doi:10.1007/s10714-019-2593-3

Cited by 9 publications

(11 citation statements)

References 94 publications

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“…In particular, in the absence of the rotating frame (ω = 0), we obtain exactly (with s = +1) the nonrelativistic spectrum in the spinning CS spacetime, given by (114). Now, ignoring the last term in (142) and in the absence of the NC phase space (θ = η = 0), AMM (E m = 0), spinning CS (α = 1 and β), with m l ≤ 0 and s = +1, we get the spectrum of the nonrelativistic QHE in a rotating frame for electrons [78]. In addition, we note that the spectrum (142) has some similarities and some differences with the relativistic case (for the particle).…”

Section: Nonrelativistic Limitmentioning

confidence: 88%

“…Now, from a nonrelativistic point of view, the combination of these two effects has already been applied in the study of quantum dots [138], scattering [139], bound states for neutral particles with AMM and electric dipole moment [140], and in the QHE [141]. Recently, the Dirac, Klein-Gordon, and DKP-like oscillators have been studied under the influence of the noncommutativity and noninertial effects in a cosmic string spacetime [142][143][144]. However, in all these works, only the purely static case of the CS was considered, i.e., its intrinsic spin angular momentum or simply its angular momentum was not taken into account.…”

Section: Introductionmentioning

confidence: 99%

“…Be-sides, in Refs. [142][143][144] the NC of the positions was also not taken into account. Therefore, for a more general description, in our work, we consider a CS with an angular momentum non-null and also the NC of the positions, respectively.…”

Section: Introductionmentioning

confidence: 99%

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

Oliveira¹,

Alencar²,

Landim³

2022

Preprint

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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.

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Section: Nonrelativistic Limitmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

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

Oliveira¹,

Alencar²,

Landim³

2022

Preprint

View full text Add to dashboard Cite

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“…The comparison between the Lagrangians L B−osc and L NC−osc and the comparison between the field equations in Eqs. (17) and (20) exhibit the following mapping between the non-commutativity parameters and the components of vector potential:…”

Section: Non-commutativity As a Magnetic Fieldmentioning

confidence: 99%

Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 1: Klein-Gordon oscillator

Cuzinatto,

de Montigny,

Pompeia

2022

Preprint

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We analyse the Klein-Gordon oscillator in a cosmic string space-time and study the effects stemming from the rotating frame and non-commutativity in momentum space. We show that the latter mimics a constant magnetic field, imparting physical interpretation to the setup. The field equation for the scalar field is solved via separations of variables, and we obtain quantization of energy and angular momentum. The space-time metric is non-degenerate as long as the particle is confined within a hard-wall, whose position depends on the rotation frame velocity and the string mass parameter. We investigate the energy quantization both for a finite hard-wall (numerical evaluation) and in the limit of an infinite hard-wall (analytical treatment). We stress the effect of non-commutativity upon the energy quantization in each case.

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“…The equation for the DKP-like oscillator is obtained from the KG equation with the non-minimal coupling [13][14][15][16]:…”

Section: Introductionmentioning

confidence: 99%

Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 2: Spin-zero Duffin-Kemmer-Petiau-like oscillator

Cuzinatto,

de Montigny,

Pompeia

2022

Preprint

Self Cite

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We study the non-inertial effects of a rotating frame on a spin-zero, Duffin-Kemmer-Petiau (DKP)-like oscillator in a cosmic string space-time with non-commutative geometry in the momentum space. The spin-zero DKP-like oscillator is obtained from the Klein-Gordon Lagrangian with a non-standard prescription for the oscillator coupling. We find that the solutions of the time-independent radial equation with the non-zero non-commutativity parameter parallel to the string are related to the confluent hypergeometric function. We find the quantized energy eigenvalues of the non-commutative oscillator.

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Non-commutativity and non-inertial effects on the Dirac oscillator in a cosmic string space–time

Cited by 9 publications

References 94 publications

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

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

Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 1: Klein-Gordon oscillator

Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 2: Spin-zero Duffin-Kemmer-Petiau-like oscillator

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