The quantum dynamical semigroups are the natural extensions of Markovian approach in the open quantum systems. These semigroups give the more general structure that guarantees the von Neumann conditions of the density matrix ρ at all time of the evolution : preservation of hermiticity, positivity and the Tr[ρ] . We are concerned to show the equivalence, up to second order in the Kubo number, between two formalisms that arrive to these semigroups. One way is to consider the microscopic dynamics that starts from a total Hamiltonian with three terms: the free dynamic of the system under study, the free dynamic of the bath and a term wich consider the interaction between them. The other formalism, asigns a wave function to the open quantum system, that evolves with the Schrödinger-Langevin (S-L) equation. This stochastic linear dynamic, takes in account the interaction between the system and the bath introducing a pure dissipative operator and an stochastic operator in the Schröedinger equation.
In the semigroup that we have written starting from S-L, there are two contribution terms: a positive operator that produces relaxation in the density matrix and another fluctuating superoperator that comes from the stochastic operator in the S-L equation.
From the equivalence between the semigroups obtained from both formalisms, it is posible to analize the quantum expresions of the dissipation and fluctuation in the dynamic of the system.
On the other hand, we provide an stochastic non Markovian evolution that represents, in mean value, the dynamic of the open quantum system.
TRABAJO PRESENTADO COMO POSTER POR AK CHATTAH
