Efeitos topológicos devido a uma deslocação em espiral em sistemas quânticos relativísticos e não-relativísticos - Maia, Anderson Vinícius Dantas Marques (2022)
In this work, we analyse the influence of the topological defects, like a spiral dislocation in two different scenarios, firstly a non-relativistic system using the Schrödinger equation for a charged particle subject to a confining potential. Furthermore, two systems with spiral dislocation in the presence of a nonuniform radial electric field, one of them with a topology-induced cut-off point yields eigenvalues of energy which are infinitely degenerated. Besides, we study Landau levels with and without rotation effects for a point charge. Thus, in this first non-relativistic part we show that there are cases where an analog of the Ahanorov-Bohm effect exists for bound states and quantum revivals. Next, we analyse the interaction of a relativistic electron with a uniform magnetic field in spiral dislocation. As well, the behaviour of the Dirac field subject to a hard-wall potential. We also show that both rotation and the topology of the spacetime impose a restriction on the values of the radial coordinate. As results, we demonstrate through the Foldy-Wouthuysen approximation that the non-relativistic limits of these situations are consistent with the solutions obtained in the first part of the thesis.