Noninertial and spin effects on the 2D Dirac oscillator in the magnetic cosmic string background

Abstract

In this work, we analyze the influence of noninertial and spin effects on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background. To model this background, we consider a uniform magnetic field, the Aharonov-Bohm effect, and a parameter $\eta$ generated by a cosmic string. Posteriorly, we determine the bound-state solutions of the system: the Dirac spinor and the relativistic energy spectrum. We verified that this spinor is written in terms of the generalized Laguerre polynomials and this spectrum depends on the effective quantum number $N_r$, angular velocity $\Omega$ and parameter $s$ associated to the noninertial and spin effects, magnetic flux $\Phi$, cyclotron frequency $\omega_c$, zero-point energy $E_0$, and on the deficit angle $\eta$. In particular, we note that besides this spectrum to be a periodic function and asymmetric, its values infinitely increase when $\eta\to 0$ or $N_r=\omega_c=\Omega\to\infty$. We also note that the energies of the antiparticle with spin down are larger than of the particle with spin up or down. In the nonrelativistic limit, we get the Schr\"{o}dinger-Pauli oscillator with two types of couplings: the spin-orbit coupling and the spin-rotation coupling, and two Hamiltonians: one quantum harmonic oscillator-type and other Zeeman-type. Finally, we compare our results with other works, where we verified that our problem generalizes some particular cases of the literature when $\Omega$, $\omega_c$, $\Phi$, $s$ or $\eta$ are excluded from the system.