Amelino-Camelia DSR effects on charged Dirac oscillators: Modulated spinning magnetic vortices
Guvendi A. Mustafa O. Jafari N.
July 2025Elsevier B.V.
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
2025#866
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 ±E∘/Ep, where E∘=mc2 is the rest energy and Ep 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 B0c, and as the magnetic field approaches this critical value, the relativistic energy levels approach En,±=±E∘. 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.
Dirac oscillator , Doubly special relativity , Landau levels , Magnetic vortices , Special functions
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Department of Basic Sciences, Erzurum Technical University, Erzurum, 25050, Turkey
Department of Physics, Eastern Mediterranean University, G. Magusa, north Cyprus, Mersin 10, 99628, Turkey
Fesenkov Astrophysical Institute, Almaty, 050020, Kazakhstan
Al-Farabi Kazakh National University, Al-Farabi av. 71, Almaty, 050040, Kazakhstan
Center for Theoretical Physics, Khazar University, 41 Mehseti Street, Baku, AZ1096, Azerbaijan
Department of Basic Sciences
Department of Physics
Fesenkov Astrophysical Institute
Al-Farabi Kazakh National University
Center for Theoretical Physics
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