Dinâmica de Partículas em Estruturas Periódicas - Vieira, Marcelo da Silva (2010)
One of the foundations of the actual technology is the Quantum Mechanics. Through Quantum Mechanics, with the development of semiconductors physics, we are able to build devices which, manipulate particles for certain purposes. As an example of these devices, we have the diode and transistor. In this thesis we seek physical systems, to obtain some quantum effects, theorically. The quantum effects which we want to obtain, are a band structure for photons and charged particles, the Aharonov-Bohm effect for photons and geometric phases for relativistic particles described by non-Hermitian Hamiltonian. For this purpose, the issues addressed here are: the study of photons in photonic crystals formed by topological insulators, the description of systems of charged particles of varying mass, the study of dynamics of the charged particles with periodic mass, the study of the Aharonov- Bohm for the photon through a viscous uid, and the appearance of geometric phases for relativistic particles described by non hermitian Hamiltonian. The main contributions of our work was the proposal for a Hamiltonian which describes particles with variable mass, obtaining a structure of energy bands for a charged particle with periodic mass, obtaining a structure of frequency bands for photons in a photonic crystal formed by topological insulators , showing the Aharonov-Bohm effect for the photon, where the vorticity of a viscous uid is the role of magnetic fields confined, and show that relativistic particles subject to non-Hermitian Hamiltonian which varies slowly, has complex geometric phases.