Quantum rings in a space with topological defects

Topological defects generally they occur in a system when phase transitions take place. We have examples of arrangements with these defects both in Gravitation and Condensed Matter. Depending on how they are generated, this kind of defects make the space present curvature or torsion. There is a wide literature about this matter, much from a gauge field point of view [1, 2, 3], and probing different aspects [6] as the existence of Landau levels [4, 5] or quantum phases [7], for example. However, there is not an unique fundamental theory for describing defects in solids. In our work we follow the Geometric Thery of Defects (TGD) which has the work by Katanaev [8] as a good way of describing continuum media with topological defects. This last theoretical framework is our compass. Besides, we are interested in mesoscopic systems, an important subject right before the role played by nanodevices. In our work we study quantum rings in a space with a screw dislocation. This kind of space presents torsion. The confinement is modelled by a potential that describes different kinds of mesoscopic systems (quantum dots, antidots and quantum wires). We found some results showing the changes in the behaviour of properties as energy eigenvalues and magnetization.