Quantum and Classical Connections and Topological Phases:  A Study of a Perturbed Rotator

In this paper are discussed the quantum mechanical connection and its classical counterpart, as well as the quantum and classical topological angles. The two were calculated for a model system to see whether they show any resemblance. The most interesting result we found is that the quantum and the classical topological phases are each formed due to a single discontinuous jump that occurs at some time during the external cycle. However, whereas the quantum mechanical topological phase is formed in the usual adiabatic limit, we had to establish a new parameter which, by allowing it to approach its limiting value, forms the classical topological phase.