The Dirac-Oscillator Green's Function

Alhaidari, A. D.

doi:10.1023/b:ijtp.0000048591.51927.e9

Cited by 7 publications

(3 citation statements)

References 9 publications

(23 reference statements)

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“…. .. We can observe the energy spectrum (13) has the same form that the energy for the case of free fermion (10), but now the wave length takes discrete values as is shown in (14). Thus, we can observe that the main effect of the linear potential that appears in Eq.…”

Section: Regime Of Critical External Magnetic Fieldsupporting

confidence: 52%

Quantum phase transition in the chirality of the (2+1)-dimensional Dirac oscillator

Quimbay,

Strange

2013

Preprint

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We study the (2+1)-dimensional Dirac oscillator in the presence of an external uniform magnetic field (B). We show how the change of the strength of B leads to the existence of a quantum phase transition in the chirality of the system. A critical value of the strength of the external magnetic field (B c ) can be naturally defined in terms of physical parameters of the system.While for B = B c the fermion can be considered as a free particle without defined chirality, for B < B c (B > B c ) the chirality is left (right) and there exist a net potential acting on the fermion.For the three regimes defined in the quantum phase transition of chirality, we observe that the energy spectra for each regime is drastically different. Then, we consider the z-component of the orbital angular momentum as an order parameter that characterizes the quantum phase transition.

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Section: Regime Of Critical External Magnetic Fieldsupporting

confidence: 52%

Quantum phase transition in the chirality of the (2+1)-dimensional Dirac oscillator

Quimbay,

Strange

2013

Preprint

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“…The completeness of these eigenfunctions (11) has been proved in [7] as a straightforward exercise. See the figure 1 for an explanation of the two possibilities of the spectrum according to the parity of the orbital angular momentum l. Here it is worth to mention that these solutions constitute a way to write a propagator in spectral form, and that the wavefunctions themselves can be computed through the exact expression of the Dirac oscillator Green's function, obtained in [8,17].…”

Section: Stationary Solutionsmentioning

confidence: 99%

The Dirac-Moshinsky oscillator: theory and applications

Sadurní

2011

AIP Conference Proceedings

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This work summarizes the most important developments in the construction and application of the Dirac-Moshinsky oscillator (DMO) with which the author has come in contact. The literature on the subject is voluminous, mostly because of the avenues that exact solvability opens towards our understanding of relativistic quantum mechanics. Here we make an effort to present the subject in chronological order and also in increasing degree of complexity of its parts. We start our discussion with the seminal paper by Moshinsky and Szczepaniak and the immediate implications stemming from it. Then we analyze the extensions of this model to many particles. The one-particle DMO is revisited in the light of the Jaynes-Cummings model in quantum optics and exactly solvable extensions are presented. Applications and implementations in hexagonal lattices are given, with a particular emphasis in the emulation of graphene in electromagnetic billiards.

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“…Specifically, for the Dirac oscillator have been studied several properties as its covariance [6], its energy spectrum, its corresponding eigenfunctions and the form of the electromagnetic potential associated with its interaction in (3+1) dimensions [7], its Lie Algebra symmetries [8], the conditions for the existence of bound states [9], its connection with supersymmetric (non-relativistic) quantum mechanics [10], the absence of the Klein paradox in this system [11], its conformal invariance [12], its complete energy spectrum and its corresponding eigenfunctions in (2+1) dimensions [13], the existence of a physical picture for its interaction [14]. For this system, other aspects have been also studied as the completeness of its eigenfunctions in (1+1) and (3+1) dimensions [15], its thermodynamic properties in (1+1) dimensions [16], the characteristics of its two-point Green functions [17], its energy spectrum in the presence of the Aharonov-Bohm effect [18], the momenta representation of its exact solutions [19],…”

Section: Introductionmentioning

confidence: 99%

Canonical quantization of the Dirac oscillator field in (1+1) and (3+1) dimensions

Quimbay¹,

Pérez²,

Hernandez³

2012

Preprint

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The main goal of this work is to study the Dirac oscillator as a quantum field using the canonical formalism of quantum field theory and to develop the canonical quantization procedure for this system in (1 + 1) and (3 + 1) dimensions. This is possible because the Dirac oscillator is characterized by the absence of the Klein paradox and by the completeness of its eigenfunctions.We show that the Dirac oscillator field can be seen as constituted by infinite degrees of freedom which are identified as decoupled quantum linear harmonic oscillators. We observe that while for the free Dirac field the energy quanta of the infinite harmonic oscillators are the relativistic energies of free particles, for the Dirac oscillator field the quanta are the energies of relativistic linear harmonic oscillators.

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The Dirac-Oscillator Green's Function

Cited by 7 publications

References 9 publications

Quantum phase transition in the chirality of the (2+1)-dimensional Dirac oscillator

Quantum phase transition in the chirality of the (2+1)-dimensional Dirac oscillator

The Dirac-Moshinsky oscillator: theory and applications

Canonical quantization of the Dirac oscillator field in (1+1) and (3+1) dimensions

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