Fases geométricas de estados coerentes e deslocados para análogos dos níveis de Landau

Abstract

In this thesis, we review the Landau levels, the coherent and displaced states for the harmonic oscillator, and Berry phase. We obtain the eigenstates for analogous Landau levels of neutral particles through the formalism of operators that become easier the construction of coherent states and displaced the mentioned systems. The analogous Landau levels shown here are the called i) Landau-Aharonov-Casher, neutral particle with permanent magnetic dipole, ii) Landau-He-McKellar-Wilkens, neutral particle with permanent electric dipole and iii) Landau-Wei-Han-Wei, neutral particle wiht induced electric dipole. For such systems was constructed coherent states and it was also made a comparison of such states with the standard states of the systems. And the differences between the coherent states of the analogous Landau levels was discussed. Displaced states for the three analogous systems was also obtained, which yield comparisons and discussions relative the standard displace state. Analyses were also made about the properties of the displaced state of the analogous levels and both their coherent and number states. Finally are calculated Berry phases of the displaced states of the study systems using as control parameters, external fields and others specifications of the systems. No abelian and abelian Berry phases are obtained and discussed too.