GUP corrections to the Dirac oscillator in the external magnetic field

Tyagi, Vishakha; Kumar, Sumit; Mandal, Bhabani Prasad

doi:10.1209/0295-5075/128/30004

Cited by 14 publications

(2 citation statements)

References 104 publications

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“…Particularly, in [39] the authors have shown that the (2+1)dimensional Dirac oscillator with frequency ω in an external magnetic field taken along the z-direction and represented by the vector potential A = B 2 (−y, x), can be mapped onto the Dirac oscillator without magnetic field but with reduced angular frequency given by ω − ω, where ω = eB 2mc and e and m are the charge and the mass of the electron. This result has been used, for example, to study atomic transitions in a radiation field [39] as well as for its corrections through the generalized uncertainty principle [40]. Following the same approach, the (2+1)dimensional DKP oscillator (DKPO) has been studied under an external magnetic field [31,33,34,38], where the authors have calculated the eigensolutions of massive spin-0 and spin-1 particles both in commutative and non-commutative phase-space.…”

Section: Introductionmentioning

confidence: 99%

Splitting frequency of the (2+1)-dimensional Duffin-Kemmer-Petiau oscillator in an external magnetic field

Gomez,

Santos,

Abla

2020

Preprint

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We revisit the (2+1)-dimensional DKP oscillator in an external magnetic field by means of 4×4 and 6×6 representations of the DKP field, thus obtaining several cases studied in the literature. We found an splitting in the frequency of the DKP oscillator according to the spin projection that arises as an interplay between the oscillator, the external field and the spin, from which the energies and the eigenfunctions are expressed in a unified way. For certain critical values of the magnetic field the oscillation in the components of spin projections -1 and 1 is cancelled. We study the thermodynamics of the canonical ensemble of the vectorial sector, where a phase transition is reported when the cancellation of the oscillation occurs. Thermodynamic potentials converge rapidly to their asymptotical expressions in the high temperature limit with the partition function symmetric under the reversion of the magnetic field.

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Section: Introductionmentioning

confidence: 99%

Splitting frequency of the (2+1)-dimensional Duffin-Kemmer-Petiau oscillator in an external magnetic field

Gomez,

Santos,

Abla

2020

Preprint

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“…[3,4,5,6] an harmonic potential has been incorporated by adding to the linear momentum (non-minimum coupling) a linear function, thus obtaining the so called Dirac and Klein-Gordon oscillators, that in the non-relativistic limit gives the quantum harmonic oscillator for spinless and strong spin-orbit coupling fermionic particles. These type of linear interactions were employed in quarks mass spectra [7], on a coulomb-like potential [8,9], in 2D massless fermions [10] and propagators [11], in curved space-time [12], in systems with extended and generalized uncertainty principle [13,14]. These studies emerge from the importance of the relativistic symmetries, that were explored for spin and pseudospin [15,16,17], which have a fruitful background on the quantum field theory [18].…”

Section: Introductionmentioning

confidence: 99%

Morse potential in relativistic contexts from generalized momentum operator, Pekeris approximation revisited and mapping

Gomez,

Santos,

Abla

2020

Preprint

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In this work we explore a generalization of the Dirac and Klein-Gordon oscillators, where the linear momentum is replaced by a deformed version inspired in nonextensive statistics, that gives place to the Morse potential in both relativistic contexts by first principles. We employ a canonical transformation that maps the harmonic oscillator with a generalized momentum operator into the Morse potential. We study the 1D and the 3D cases, using the Pekeris approximation in the later case. In the non-relativistic limit we reproduce the S-wave states of the H 2 molecule while in the null deformation limit we recover spinless (KG) and spin-orbit (Dirac) oscillators.

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Examples of PT Phase Transition : QM to QFT

Mandal

2021

J. Phys.: Conf. Ser.

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Parity Time Reversal (PT) phase transition is a typical characteristic of most of the PT symmetric non-Hermitian (NH) systems. Depending on the theory, a particular system and spacetime dimensionality PT phase transition has various interesting features. In this article we review some of our works on PT phase transitions in quantum mechanics (QM) as well as in Quantum Field theory (QFT). We demonstrate typical characteristics of PT phase transition with the help of several analytically solved examples. In one dimensional QM, we consider examples with exactly as well as quasi exactly solvable (QES) models to capture essential features of PT phase transition. The discrete symmetries have rich structures in higher dimensions which are used to explore the PT phase transition in higher dimensional systems. We consider anisotropic SHOs in two and three dimensions to realize some connection between the symmetry of original hermitian Hamiltonian and the unbroken phase of the NH system. We consider the 2+1 dimensional massless Dirac particle in the external magnetic field with PT symmetric non-Hermitian spin-orbit interaction in the background of the Dirac oscillator potential to show the PT phase transition in a relativistic system. A small mass gap, consistent with the other approaches and experimental observations is generated only in the unbroken phase of the system. Finally we develop the NH formulation in an SU(N) gauge field theoretic model by using the natural but unconventional Hermiticity properties of the ghost fields. Deconfinement to confinement phase transition has been realized as PT phase transition in such a non-hermitian model.

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GUP corrections to the Dirac oscillator in the external magnetic field

Cited by 14 publications

References 104 publications

Splitting frequency of the (2+1)-dimensional Duffin-Kemmer-Petiau oscillator in an external magnetic field

Splitting frequency of the (2+1)-dimensional Duffin-Kemmer-Petiau oscillator in an external magnetic field

Morse potential in relativistic contexts from generalized momentum operator, Pekeris approximation revisited and mapping

Examples of PT Phase Transition : QM to QFT

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