Theory of Quantum Open Systems

The course introduces a formulation of quantum mechanics based on positive operator-valued measures and statistical operators, stressing that quantum mechanics has to be understood as a probability theory different from the classical one. Within this probabilistic viewpoint, the course addresses the mathematical formulation of quantum measurement theory and of open quantum system theory. Open quantum system theory deals with the dynamics of quantum systems affected by other quantum degrees of freedom. The ensuing dynamics are not unitary and call for the introduction of more general evolution equations with respect to the Schroedinger equation. Emphasis is put on the conceptual aspects and on the mathematical formulation of the theory. Key notions introduced are complete positivity, quantum dynamical semigroups, projection operator techniques, master equation, map representation, Naimark's dilation theorem. The new phenomena of dissipation and decoherence appearing in this context are discussed by means of examples, together with a brief introduction to non-Markovian dynamics.