Amelino-Camelia DSR effects on charged Dirac oscillators: Modulated spinning magnetic vortices

Abstract

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 ${\mathcal{E}}_{\circ }=m{c}^2$ 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 ${\mathcal{B}}_0^c$, 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.

4 pages; 2 figures

References in corpus (12)

• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal
• First experimental realization of the Dirac oscillator
• On the interaction of the Dirac oscillator with the Aharonov-Casher system in topological defect backgrounds
• Exact solution of the two-dimensional Dirac oscillator
• Dirac oscillator in an external magnetic field
• Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction
• On the $\kappa$-Dirac Oscillator revisited
• Revivals of Zitterbewegung of a bound localized Dirac particle
• Fermion-antifermion pairs in Bonnor-Melvin magnetic space-time with non-zero cosmological constant
• An innovative model for coupled fermion-antifermion pairs

Cited by in corpus (2)

• Thermal properties of Klein-Gordon Oscillator in the Context of Amelino-Camelia and Magueijo-Smolin Doubly Special Relativity (DSR) frameworks
• A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics