Topological and noninertial effects in an Aharonov-Bohm ring
GENERAL RELATIVITY AND GRAVITATION, (2019)DOI: 10.1007/s10714-019-2606-2
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 not equal 0) or in an 1D quantum ring (Phi=0).