Abstract
In the present paper, we investigate the influence of topological, noninertial and spin effects on the 2D Dirac oscillator in the presence of the Aharonov–Casher effect. Next, we determine the two-component Dirac spinor and the relativistic energy spectrum for the bound states. We observe that this spinor is written in terms of the confluent hypergeometric functions and this spectrum explicitly depends on the quantum numbers n and m_l, parameters s and eta associated to the topological and spin effects, quantum phase varPhi _{AC}, and of the angular velocity varOmega associated to the noninertial effects of a rotating frame. In the nonrelativistic limit, we obtain the quantum harmonic oscillator with two types of couplings: the spin-orbit coupling and the spin-rotation coupling. We note that the relativistic and nonrelativistic spectra grow in absolute values as functions of eta , varOmega , and varPhi _{AC} and its periodicities are broken due to the rotating frame. Finally, we compared our problem with other works, where we verified that our results generalizes some particular planar cases of the literature.
Highlights
On the other hand, the study of noninertial effects due to rotating frames have been widely investigated in the literature since to 1910 decade [27], where the best-known effects are the Sagnac [28], Barnett [29], Einstein-de Hass [30] and Mashhoon [31] effects
We see that the spectrum (39) generalizes some relativistic particular planar cases of the literature when Ω, ΦAC, s, or η are excluded of the system
We study the influence of topological, spin and noninertial effects on the relativistic and nonrelativistic quantum dynamics of the 2D Dirac oscillator (DO) in the presence of the AC effect
Summary
The study of noninertial effects due to rotating frames have been widely investigated in the literature since to 1910 decade [27], where the best-known effects are the Sagnac [28], Barnett [29], Einstein-de Hass [30] and Mashhoon [31] effects. The first formal approach on nonrelativistic neutral quantum particles with magnetic dipole moment (MDM) interacting with external electric fields was made by Y. Casher [57], where was verified theoretically that the wave function of the neutral particle acquires a topological quantum phase due to interaction with the field, even the force of Lorentz being null. This peculiar quantum effect is known currently as Aharonov–Casher (AC) effect [58,59]. The present paper has as its goal to study the influence of topological, noninertial and spin effects on the relativistic and nonrelativistic quantum dynamics of the 2D DO in the presence of the AC effect.
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