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, it 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 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, together with a brief introduction to non-Markovian dynamics.
Prerequisites for admission
Basic knowledge of quantum mechanics.
Lectures and exercises
H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press, 2002 T. Heinosaari and M. Ziman, The Mathematical Language of Quantum Theory Cambridge, 2012 Lectute notes on the Ariel platform http://www0.mi.infn.it/~vacchini/oqs/
Assessment methods and Criteria
The final examination consists of an oral exam.
In the oral exam, the student will be required to illustrate results presented during the course and will be required to solve problems regarding open quantum system in order to evaluate her/his knowledge and comprehension of the arguments covered as well as the capacity to apply them.
Final marks are given using the numerical range 0-30, and will be communicated immediately after the oral examination.