Neste trabalho introduzimos brevemente o formalismo matemático da Mecânica Quântica e analisamos em detalhe a classe dos operadores completamente positivos (e sua conhecida representação de Kraus). Seguindo [10], definimos que chamamos de semigrupos dinâmicos quânticos (QDS) e semigrupos markovianos quânticos (QMS), em analogia aos semigrupos clássicos da teoria de processos estocásticos com t real e t ≥ 0. Explorando a relação entre o semigrupo e seu gerador infinitesimal, encontramos condições necessárias e suficientes para que um operador seja o gerador infinitesimal de um destes semigrupos quânticos com t real e t ≥ 0. Um operador que satisfaz esta condição é chamado de operador condicionalmente completamente positivo. O tópico mais importante nesta dissertação é o seguinte: seguindo [10] descrevemos uma representação destes geradores originalmente devida à Lindblad [23]. / In this work we briey introduce the mathematical formalism of the theory of Quantum Mechanics and we we analyze in great details the class of completely positive operators (and also their well-known Kraus representation). Following [10], we define what we call quantum dynamical semigroups (QDS) and quantum markov semigroups (QMS), in analogy with classical semigroups arrising from stochastic processes theory where t is real and t ≥ 0. Exploring the relation between a semigroup and his infinitesimal generator, we find necessary and suficient conditions to an operator become an infinitesimalgenerator of one of those quantum semigroups where t is real and t ≥ 0. An operator which satisfies this condition is called conditionally completely positive. We present (following [10]) a representation for those generators originally due to Lindblad [23].

The paper is an analysis of a special class of the master equations such that the Dissipation superoperator is L(ρ) = [M, [M, ρ]], where M is an hermitian andunitary operator and ρ a density matrix. It mainly investigates the dynamics ofρ and its properties such as boundness of the operators of the master equation,the eigenvalues of these operators, the purity of the states, the steady states. In the study of the temporal evolution of ρ it has been done an analysis of Decoherence free subspaces(DFS). A special attention is given to von Neumannentropy. For what it regards this last topic there are also specific referencesto the camel-like behaviour, a phenomenon regarding the entropy that happenswhen certain conditions of the dissipation superaoperator are not satisfied.There are Python simulations of the expectation values of some operators, andof the von Neumann entropy, and Linear Entropy.