"Quantum mechanics: basic mathematical structures and their operational interpretation"

Summer Term 2007, Thursday 15:00-16:30, MPI MiS, A2, Inselstr. 22, 04103 Leipzig

In the first part of the course we will follow an axiomatic approach based on experience and physical reasoning in order to fix basic mathematical structures of quantum mechanics. The focus will be on the crucial concepts of state and measurement presented from an operational point of view. In the second part we will consider quantum lattice systems as they arise in the framework of quantum statistical mechanics and which may model a quantum counterpart of classical (discrete) stochastic processes. This is in analogy to Kolmogorov's representation of stochastic processes by means of deterministic dynamics on sample path spaces. We will discuss some special classes of quantum lattice states which are proposed in the literature as quantum generalisation of classical Markov processes.

Keywords: state space, observables, quantum operations, quantum spin-lattice-systems, quantum Markov processes, algebraic states