Relativistic Quantum Dynamics of a Neutral Dirac Fermion in the Presence of an Electromagnetic Field

Oliveira, R. R. S.; Sousa, M. F.

doi:10.1007/s13538-019-00660-x

Cited by 10 publications

(13 citation statements)

References 41 publications

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“…In this sense, our discussion begins initially with the discrete energy spectrum for relativistic Dirac particles with MDM µ in the presence of an external electromagnetic field, given by Ref. [45], namely…”

Section: Thermodynamic Properties Of Dirac Fermionsmentioning

confidence: 99%

“…In particular, for δm j > 0, the spectra ( 1) and ( 2) present finite degeneracy, while for δm j < 0, presents an infinite degeneracy [45]. In addition, since it has a significant influence in the thermodynamic properties of a physical system [20,27,46], we will work on the spectra that represent only finite degeneracy.…”

Section: Thermodynamic Properties Of Dirac Fermionsmentioning

confidence: 99%

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

Oliveira

Filho

2020

Eur. Phys. J. Plus

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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 nonrelativistic 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.

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Section: Thermodynamic Properties Of Dirac Fermionsmentioning

confidence: 99%

Section: Thermodynamic Properties Of Dirac Fermionsmentioning

confidence: 99%

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

Oliveira

Filho

2020

Eur. Phys. J. Plus

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“…Since we are working planar spacetime, it is convenient to write the matrices γ = (γ 1 , γ 2 , 0) = (−γ 1 , −γ 2 , 0) and γ 0 and S = 0, 0, 1 2 Σ 3 in terms of the Pauli matrices, i.e., γ 1 = σ 3 σ 1 = iσ 2 , γ 2 = sσ 3 σ 2 = −isσ 1 and γ 0 = Σ 3 = σ 3 [71,78,79,87]. By using this information and setting the following ansatz for the two-component Dirac spinor [71,88] (t, ρ, ϕ) = e i(m l ϕ−Et)…”

Section: Relativistic Quantum Dynamics Of the Dirac Oscillator In Thementioning

confidence: 99%

“…Next, some researchers formulated the relativistic AC effect via DE [60][61][62]. Moreover, the DE for spin-1/2 particles in the presence of external electric fields is study in connection with the graphene [63,64], fermions pair production [65,66], noncommutative quantum electrodynamics [67], vacuum instability [68], magnetic fields in conical and flat spacetimes [69][70][71], electric dipole moment [72,73], and so on. It is important to mention that the DO was originated through of neutral Dirac particles with MDM interacting with external electric fields [74].…”

Section: Introductionmentioning

confidence: 99%

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

Oliveira

2019

Eur. Phys. J. C

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In the present paper, we investigate the influence of topological, noninertial and spin effects on the 2D Dirac oscillator in the presence of the Aharonov-Casher effect. Next, we determine the two-component Dirac spinor and the relativistic energy spectrum for the bound states. We observe that this spinor is written in terms of the confluent hypergeometric functions and this spectrum explicitly depends on the quantum numbers n and m l , parameters s and η associated to the topological and spin effects, quantum phase Φ AC , and of the angular velocity Ω associated to the noninertial effects of a rotating frame. In the nonrelativistic limit, we obtain the quantum harmonic oscillator with two types of couplings: the spin-orbit coupling and the spin-rotation coupling. We note that the relativistic and nonrelativistic spectra grow in absolute values as functions of η, Ω, and Φ AC and its periodicities are broken due to the rotating frame. Finally, we compared our problem with other works, where we verified that our results generalizes some particular planar cases of the literature.

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“…Since we are working planar spacetime, it is convenient to write the gamma matrices [60,68,[71][72][73]. In particular, the parameter s (spin parameter) characterizes the two spin states, with s = +1 for spin "up" and s = −1 for spin "down", respectively.…”

Section: Relativistic Quantum Dynamics Of the Dirac Oscillator In The...mentioning

confidence: 99%

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

Oliveira¹

2019

Preprint

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We investigate the influence of noninertial and spin effects on the 2D Dirac oscillator (DO) interacting with a uniform magnetic field and with the Aharonov-Bohm (AB) effect in the cosmic string spacetime. As results, we verify that the Dirac spinor is written in terms of the confluent hypergeometric functions and the energy spectrum depends of the quantum numbers n and m l , parameters s and η associated to the spin effects and to topology of the cosmic string, magnetic flux Φ of the AB effect, cyclotron frequency ω c generated by magnetic field, and of the angular velocity Ω of the rotating frame. In the nonrelativistic limit, we obtain the equation of motion of the quantum harmonic oscillator with two types of couplings: the spin-orbit coupling and the spin-rotation coupling. In particular, the relativistic and nonrelativistic energy spectra are periodic functions and increase in function of η and Ω. Finally, we comparing our results with other works, where verified that our problem generalizes some particular planar cases of the literature.

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Relativistic Quantum Dynamics of a Neutral Dirac Fermion in the Presence of an Electromagnetic Field

Cited by 10 publications

References 41 publications

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

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

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

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

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