Quantum to classical transition in the theory of open systems

Classicality is an emergent property of open quantum systems, since both main features of this process - quantum decoherence (QD) and classical correlations (CC) - strongly depend on the interaction between the system and its environment. In the framework of the Lindblad theory for open quantum systems, based on quantum dynamical semigroups, we determine the degree of QD and the degree of CC and analyze the possibility of simultaneous realization of QD and CC for a system consisting of a harmonic oscillator in a thermal bath. To this end, we find the evolution of the density matrix and Wigner function of the considered system and then apply the criterion of QD and CC. We find that the system manifests a QD which is more and more significant in time, whereas CC are less and less strong as the system evolves in time, and we describe the transition of the system from quantum to classical behavior. (author)