Entanglement and decoherence in many-body physics

The thesis deals with several features of quantum many-body systems. They are described both in terms of reversible unitary transformations and as an environment interacting with other systems. An introductory part introduces the main ideas of quantum noise and dissipative dynamics. A chapter is also dedicated to some useful aspects of entanglement. The second part of the thesis concerns the orginal results. A chapter describes the dynamics of two qubits interacting with a common environment. This chapter is focused on the derivation of a new Markovian approximation, finer than the standard weak coupling limit, and its application on the dynamical generation of the entanglement. The second topic concerns the developping of some procedures to reconstruct the parameters governing a large class of Markovian and non-Markovian dissipative dynamics of a quantum particle. These procedures are based on the symplectic tomography of the evolved state. The third topic concerns the physics of many identical bosons, with a special focus on Bose-Einstein condensates. The relevance of entanglement and spin squeezing for quantum metrology with high accuracy is discussed in connection with the quantum Fisher information and collective and squeezing inequalities. A third part summerizes the results. Some useful tools are described in the appendices.