Why do black holes emit thermal radiation? And how does a closed quantum system thermalize? These apparently unrelated questions might be both connected to an essential feature of quantum... Show moreWhy do black holes emit thermal radiation? And how does a closed quantum system thermalize? These apparently unrelated questions might be both connected to an essential feature of quantum techanics: the dynamics of quantum information and its chaotic properties. Indeed, regardless of the unitary time evolution, quantum information seems to be dissipated. The solution to these contradictions may heavily affect the near future technologies, in light of the recent progresses towards building a quantum computer.In this thesis we investigate the fascinating idea that such chaotic properties leave traces on the late time hydrodynamic excitations. We do this from two opposite directions, both from weakly coupled field theories, using a combination of field theory techniques, and from strongly-coupled field theories, using the AdS/CFT correspondence. Moreover, we studied a fermionic and bosonic quantum critical point, which are 'exotic' states of matter where quantum information plays an important role. The main results of this thesis consist of the formulation of a Boltzmann-like equation for many-body chaos, the discovery of a new property of thermal correlation functions (pole-skipping), and the analysis of which is the correct and meaningful observable to measure experimentally in order to probe quantum chaos. Show less
