Groupe de Physique Statistique

In this course we present the Markovian approach for quantum open systems. In this approach we concentrate on the effective dissipative dynamics of a small quantum system in contact with a huge environment which is usually unknown. From this effective dynamics one can construct an environment and an explicit interaction system-environment which give rise to the observed restricted dynamics. This "dilation" of the small system is obtained with the help of quantum noises, by solving an adequate quantum Langevin equation. In this course we shall introduce the notions of quantum noises, quantum Langevin equation and show how this dilation can be explicitely realized. Our approach is based on a very simple physical model: repeated quantum interactions. This is an Hamiltonian model of a simple quantum system interacting repeatedly with some identical pieces of some environment. We shall show that quantum noises are spontaneously emerging from this Hamiltonian model. By the way this will give us a very intuitive and simple approach of what quantum noises are exactly. For example, we will understand why there are exactly 3 quantum noises, no more, no less. The three courses should be more or less divided as follows. 1st course: 1) Open Quantum System (density matrices, completely positive maps) 2) Repeated Quantum Interaction (physical model, mathematical setup, dilation of CP maps)