Efeitos da rotação e campo magnético em uma partícula quântica confinada a superfície de um toro

Abstract

In this dissertation we study the efect of the magnetic fi eld and the rotation on a confi ned particle on the surface of a torus. The torus has curved symmetry, this curvature of its surface generates a potential known as the geometric potential, or da Costa's potencial. This potential, present in the equation of state, influences the dynamics of the system whose symmetry used is toroidal, characterizing the appearance of bands of energy. In the study of the application of magnetic fi elds there is discursões and experiments on the emergence of potential vector in regions where the fields vanish, studies have reported how this effect is analogous to systems subjected to rotation. The electromagnetic potential vector characterizes the effect Aharonov Bohm, similar to these there are the effect Aharonov Carmi, which refers to the potential vector because of the rotation of a system, so this also influences in the energies of the system. For our study we will solve the Schr odinger's equation based in the hamiltonian for systems subjected to magnetic fi eld and rotation, initially used separate approach and subsequently with combined the effects, so as to obtain the energies for diferentes combinations of magnetic fie elds and rotation, then we discuss how the potential due to the magnetic fi eld and rotation can change the behavior of a particle confi ned to a surface that has a geometric potential. Through our results we observed the formation of the structure of bands of energy, due the metric of toro, whose eigenvalues de ne the edges of the bands, and we can concluded too that The rotation of the system adds a factor to the quantum momentum, in the energy of the particles, similar to the effect of the magnetic fi eld. We also that to observer in a rotating reference frames subjected to a magnetic fi eld it is possible to determine a magnetic flux that canceling the effects of rotation, but it is not possible determined a rotation which cancels the effect of the fi eld, and in our last approach we fi nd that if the magnetic eld is restricted to the interior of the symmetry of the toro (hole of the torus) it is not possible the previous result, that is, there is no field that cancels out the rotation effects.