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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2504.10537 |
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| _version_ | 1866917208610832384 |
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| author | Guvendi, Abdullah Mustafa, Omar Jafari, Nosratollah |
| author_facet | Guvendi, Abdullah Mustafa, Omar Jafari, Nosratollah |
| contents | This work explores the two-dimensional Dirac oscillator (DO) within the framework of Amelino-Camelia doubly special relativity (DSR), employing a modified Dirac equation that preserves the first-order nature of the relativistic wave equation. By introducing non-minimal couplings, the system provides an exact analytical solution in terms of confluent hypergeometric functions, along with closed-form expressions for the energy spectrum (indulging a Landau-like signature along with accidental spin-degeneracies)-. In the low-energy limit, the results reproduce the well-known two-dimensional Dirac oscillator spectrum, and in the nonrelativistic regime, the results reduce the Schrödinger oscillator spectrum. First-order corrections in this DSR model introduce a mass-splitting term proportional to $\pm \mathcal{E}_{\circ}/\mathcal{E}_p$, where $\mathcal{E}_{\circ} = mc^2$ is the rest energy and $\mathcal{E}_p$ is the Planck energy. These corrections preserve the symmetry between the energies of particles and antiparticles around zero energy, but induce a shift in the energy levels that becomes more significant for higher excited states ($n > 0$). By mapping the system to a DSR-deformed charged Dirac oscillator in the presence of an out-of-plane uniform magnetic field, we show that the leading-order Planck-scale corrections vanish at a critical magnetic field $\mathcal{B}^{c}_{0}$, and as the magnetic field approaches this critical value, the relativistic energy levels approach $\mathcal{E}_{n,\pm} = \pm \mathcal{E}_{\circ}$. Finally, we identify a previously undetermined feature in two-dimensional charged Dirac oscillator systems in a magnetic field, revealing that the corresponding modes manifest as spinning magnetic vortices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Amelino-Camelia DSR effects on charged Dirac oscillators: Modulated spinning magnetic vortices Guvendi, Abdullah Mustafa, Omar Jafari, Nosratollah General Physics This work explores the two-dimensional Dirac oscillator (DO) within the framework of Amelino-Camelia doubly special relativity (DSR), employing a modified Dirac equation that preserves the first-order nature of the relativistic wave equation. By introducing non-minimal couplings, the system provides an exact analytical solution in terms of confluent hypergeometric functions, along with closed-form expressions for the energy spectrum (indulging a Landau-like signature along with accidental spin-degeneracies)-. In the low-energy limit, the results reproduce the well-known two-dimensional Dirac oscillator spectrum, and in the nonrelativistic regime, the results reduce the Schrödinger oscillator spectrum. First-order corrections in this DSR model introduce a mass-splitting term proportional to $\pm \mathcal{E}_{\circ}/\mathcal{E}_p$, where $\mathcal{E}_{\circ} = mc^2$ is the rest energy and $\mathcal{E}_p$ is the Planck energy. These corrections preserve the symmetry between the energies of particles and antiparticles around zero energy, but induce a shift in the energy levels that becomes more significant for higher excited states ($n > 0$). By mapping the system to a DSR-deformed charged Dirac oscillator in the presence of an out-of-plane uniform magnetic field, we show that the leading-order Planck-scale corrections vanish at a critical magnetic field $\mathcal{B}^{c}_{0}$, and as the magnetic field approaches this critical value, the relativistic energy levels approach $\mathcal{E}_{n,\pm} = \pm \mathcal{E}_{\circ}$. Finally, we identify a previously undetermined feature in two-dimensional charged Dirac oscillator systems in a magnetic field, revealing that the corresponding modes manifest as spinning magnetic vortices. |
| title | Amelino-Camelia DSR effects on charged Dirac oscillators: Modulated spinning magnetic vortices |
| topic | General Physics |
| url | https://arxiv.org/abs/2504.10537 |