Análise de sistemas quânticos com massa variando com a posição numa topologia não plana.

Abstract

The study of quantum systems in the space with several topologies has been investigated in different areas of the physics as, for example, in the gravitation and in the condensed matter physics. The change in the topology in an elastic medium introduced by a linear defect as a disclination, dislocation or dispiration produces some effects in the physical properties of the system. The influence of those defects in the physical quantities can be understood through a geometric approach that is based on the correspondence, of the mathematical point of view, between the theory of defects in solids and the theory of the gravitation. In this work we will study the behavior of a particle in a quantum system with variable mass \m(p) = M (1 + //A2/?2)] in the presence of a dispiration in an uniform magnetic field in the scenery of the theory of defects in solids of Katanaev-Volovich. We analyze the influence of the topology and of the mass distribution in the Landau levels, as well as, i t influences in the quantum non-relativistic quantum scattering.