A fase geométrica e a dinâmica de dipolos elétricos e magnéticos

Abstract

In this work, we study the geometric phase and the dynamics of electric and magnetic dipoles. We present your origins, some relevant works in this area as well as your results. The appearance of a geometric phase is explained when a study of quantum dynamics of the particle is made, during a complete cycle and that is subject to cyclic adiabatic processes. The present study begins with an introduction about the geometric phase, where we present examples used to illustrate it. Next, the adiabatic theorem was presented in both classical and quantum systems and a discourse on adiabatic invariants. After this, we present its final mathematical formulation and also its obtaining for a spin 1/2 particle. Soon after, we obtained the Lagrangian and its Hamiltonian, we find the quantum phase that the particle acquired in the efect Aharonov- Bohm and Aharonov - Casher. We have also seen the quantum dynamics of both electric and magnetic dipoles, where we start from the Lagrangian and study its field configurations, we reach the Ananda phase, where in the next step we obtain phases for some of the Field configurations in the Ananda phase from phase of Aharonov - Casher where we made the electric dipole moment equal to zero, as well as the He - Mckellar - Welkens phase with magnetic dipole moment equal to zero, and the Casella efect thus obtaining a particle case of the Ananda phase.