The study of the dynamics of a small quantum system, with a finite number of degrees of freedom, interacting with extended thermal reservoirs has important applications in many areas of physics. Such open quantum systems are also of theoretical interest as simple models for nonequilibrium statistical mechanics.
I will review some results obtained during the last decade in a joint program with Vojkan Jaksic (McGill University, Montreal):
- Nonequilibrium Steady States (NESS): construction and structural properties;
- entropy production in NESS;
- linear response theory of NESS;
- Ruelle's scattering approach and the Landauer-Buettiker formalism;
- Fluctuations: central limit theorem and more ?

Some of these results were obtained in collaboration with Walter Aschbacher (TU-München), Yoshiko Ogata (Tokyo University) and Yan Pautrat (Universite d'Orsay).