Métodos semi-clássicos para abordagem de sistemas dinâmicos quânticos.

Abstract

This work studies the semiclassical behaviour of quantum models according to their dynamics. On the first part, we analyse quantum models with well defined classical limit and define a corresponding classical dynamics. We are intend to investigate here how those systems behave at this classical limit and how the quantum dynamics can be approximated. For that we make use of a semiclassical approximation as a systematic way of finding quantum corrections to the classical mean values of observables. We also make use of exact results for testing the semiclassical approximation for calculating typical quantum effects and the fidelity of the approximate state with the exact one. In the second part we deal with the classical limit of quantum mechanics through intercation with environment. The evolution of quantum and classical probability distributions are compared using the Wigner representation. We find then conditions under which the coupling of the system with the environment preserves two initially identical particles as identical and the we analyze the process of decoherence in that system.