O efeito Hall quântico não-comutativo com momento magnético anômalo em três diferentes cenários relativísticos

Abstract

In this doctoral thesis, we investigate the bound-state solutions of the noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios: the Minkowski spacetime (inertial flat case), the spinning cosmic string spacetime (inertial curved case) and the spinning cosmic string spacetime with noninertial effects (noninertial curved case). Therefore, we work in two different relativistic backgrounds, where one is exclusive to the Special Theory of Relativity (first scenario) and the other to the General Theory of Relativity (second and third scenario), both in (2+1)-dimensions. In particular, in the first two scenarios, we have an inertial frame of reference while in the third we have a rotating frame of reference (noninertial frame of reference). With respect to solutions, we focus our attention mainly on the solutions of a given eigenvalue equation, that is, on the eigenfunctions (two-component Dirac spinor and the Schrödinger wave function) and on the energy eigenvalues (energy spectrum or Landau levels). To obtain such solutions, we work with the noncommutative Dirac Equation in polar coordinates with minimal and nonminimal couplings, whose coupling constants are the electric charge and the anomalous magnetic moment of the Dirac fermion. Furthermore, using the normalized Dirac spinor it was also possible to obtain the expression for the radial probability density of the system. So, once the solutions had been obtained, we discussed in detail the influence of all parameters and physical quantities on relativistic energy levels as well as on probability density (via graphs). Finally, we analyzed the nonrelativistic limit (low energy regime) of our three scenarios, where we also compared our problem with other works. Consequently, we verified that our results generalize several particular cases of the literature.