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
Romero-Bermúdez, A.; Schalm, K.E.; Scopelliti, V. 2019
We study the contour dependence of the out-of-time-ordered correlation function (OTOC) both in weakly coupled field theory and in the Sachdev-Ye-Kitaev (SYK) model. We show that its value,... Show moreWe study the contour dependence of the out-of-time-ordered correlation function (OTOC) both in weakly coupled field theory and in the Sachdev-Ye-Kitaev (SYK) model. We show that its value, including its Lyapunov spectrum, depends sensitively on the shape of the complex time contour in generic weakly coupled field theories. For gapless theories with no thermal mass, such as SYK, the Lyapunov spectrum turns out to be an exception; their Lyapunov spectra do not exhibit contour dependence, though the full OTOCs do. Our result puts into question which of the Lyapunov exponents computed from the exponential growth of the OTOC reflects the actual physical dynamics of the system. We argue that, in a weakly coupled Phi(4) theory, a kinetic theory argument indicates that the symmetric configuration of the time contour, namely the one for which the bound on chaos has been proven, has a proper interpretation in terms of dynamical chaos. Finally, we point out that a relation between these OTOCs and a quantity which may be measured experimentally - the Loschmidt echo - also suggests a symmetric contour configuration, with the subtlety that the inverse periodicity in Euclidean time is half the physical temperature. In this interpretation the chaos bound reads lambda <= 2 pi/beta=pi T-physical. Show less
Romero-Bermúdez, A.; Schalm, K.E.; Scopelliti, V. 2019
We study the contour dependence of the out-of-time-ordered correlation function (OTOC) both in weakly coupled field theory and in the Sachdev-Ye-Kitaev (SYK) model. We show that its value,... Show moreWe study the contour dependence of the out-of-time-ordered correlation function (OTOC) both in weakly coupled field theory and in the Sachdev-Ye-Kitaev (SYK) model. We show that its value, including its Lyapunov spectrum, depends sensitively on the shape of the complex time contour in generic weakly coupled field theories. For gapless theories with no thermal mass, such as SYK, the Lyapunov spectrum turns out to be an exception; their Lyapunov spectra do not exhibit contour dependence, though the full OTOCs do. Our result puts into question which of the Lyapunov exponents computed from the exponential growth of the OTOC reflects the actual physical dynamics of the system. We argue that, in a weakly coupled Phi(4) theory, a kinetic theory argument indicates that the symmetric configuration of the time contour, namely the one for which the bound on chaos has been proven, has a proper interpretation in terms of dynamical chaos. Finally, we point out that a relation between these OTOCs and a quantity which may be measured experimentally - the Loschmidt echo - also suggests a symmetric contour configuration, with the subtlety that the inverse periodicity in Euclidean time is half the physical temperature. In this interpretation the chaos bound reads lambda <= 2 pi/beta=pi T-physical. Show less
