Relativistic Landau levels in the rotating cosmic string spacetime

Abstract

In the spacetime induced by a rotating cosmic string we compute the energy levels of a massive spinless particle coupled covariantly to a homogeneous magnetic field parallel to the string. Afterwards, we consider the addition of a scalar potential with a Coulomb-type and a linear confining term and completely solve the Klein-Gordon equations for each configuration. Finally, assuming rigid-wall boundary conditions, we find the Landau levels when the linear defect is itself magnetized. Remarkably, our analysis reveals that the Landau quantization occurs even in the absence of gauge fields provided the string is endowed with spin.

Landau levels in the presence of a cosmic string in rainbow gravity

“…These energy levels have already been considered previously by the authors in Refs. [25][26][27][28][29], which shows the consistency of our results.…”

“…The study of the Landau levels in the presence of a standard cosmic string (or a disclination in condensed matter systems) was already performed in [25][26][27][28][29], and we will follow the same line of investigation. In this case, the Hamiltonian corresponding to a charged particle in the presence of a gauge field in a curved background given generically by a metric g ij is written asĤ…”

“…An additional motivation to consider cosmic string is the possibility to investigate some of its properties in laboratory through the condensed matter counterpart known as disclination and that is mostly found liquid crystals condensed matter systems [22][23][24]. Studies of Landau levels in the spacetime of a cosmic string (disclination) has been conducted in Refs [25][26][27][28][29]. 2 The Landau levels have previously been considered in the context of modified theories of gravity, basically those ones involving the Generalized Uncertainty Principle, and can be 2 The effect of rainbow functions on energy levels has also been analyzed in the context of the Casimir effect in the Einstein universe [30] and for the Dirac oscillator in [31].…”

Landau levels in a gravitational field: the Levi-Civita and Kerr spacetimes case

“…The last point we would like to comment on here is that it would be natural now to attempt to apply the same techniques used above to the case of a rotating cylinder. Unfortunately, however, to deal with such a case one has to use the so-called Lewis spacetime [35], which is even more complicated than the metric (II.2). Given that the Lewis spacetime reduces in the limit of zero radius of the cylinder to that of a rotating cosmic string (see, e.g., Ref.…”

Scalar bosons with Coulomb potentials in a cosmic string background: scattering and bound states

“…In Ref. [23], relativistic Landau levels in the rotating cosmic string space-time with the Cornell potential, is considered. It was shown that the Landau levels of the spinning cosmic string remain the same even when the internal magnetic flux vanishes.…”