Topological and noninertial effects in an Aharonov-Bohm ring

Abstract

In this paper, we study the influence of topological and noninertial effects on a Dirac particle confined in an Aharonov-Bohm (AB) ring. Next, we explicitly determine the Dirac spinor and the energy spectrum for the relativistic bound states. We observe that this spectrum depends on the quantum number $n$, magnetic flux $\Phi$ of the ring, angular velocity $\omega$ associated to the noninertial effects of a rotating frame, and on the deficit angle $\eta$ associated to the topological effects of a cosmic string. We verified that this spectrum is a periodic function and grows in values as a function of $n$, $\Phi$, $\omega$, and $\eta$. In the nonrelativistic limit, we obtain the equation of motion for the particle, where now the topological effects are generated by a conic space. However, unlike relativistic case, the spectrum of this equation depends linearly on the velocity $\omega$ and decreases in values as a function of $\omega$. Comparing our results with other works, we note that our problem generalizes some particular cases of the literature. For instance, in the absence of the topological and noninertial effects ($\eta=1$ and $\omega=0$) we recover the usual spectrum of a particle confined in an AB ring ($\Phi\neq{0}$) or in an 1D quantum ring ($\Phi=0$).