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 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.
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 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.
This dissertation presents a comprehensive investigation of fermionic quantum matter into the intricate relationship between quantum chaos, thermalization, and their connection to gravitational duals, with particular emphasis on the Sachdev-Ye-Kitaev (SYK) model and its extensions. Through an integrated approach combining analytical solutions in the large-N limit with advanced numerical techniques, we explore fundamental questions in quantum many-body physics, including the interplay of chaos and ergodicity, universal transport in non-Fermi liquids, and the role of gravitational analogs in strongly correlated systems. We first demonstrate that coupled SYK lattices evade instantaneous thermalization despite weak charge fluctuations, governed by a discrete wave equation dependent solely on hopping strength, independent of on-site interactions. Thermodynamically, coupled SYK models exhibit critical exponents universal to van der Waals fluids and AdS black holes, yet diverge from the Hawking-Page transition at ultralow temperatures, revealing a continuum of first-order phase transitions. They simultaneously retain the quantum chaotic properties of both a single-dot SYK model and black holes. In extended SYK chains, we identify a universal DC conductivity bound across interaction regimes, identifying crossovers between insulating, Fermi liquid, strange metal, and bad metal phases with signatures of holographic insulator behavior. Quench dynamics in mixed SYK systems reveal rapid thermalization without prethermal plateaus, enabling direct observation of thermalization in closed quantum systems in the thermodynamic limit. To diagnose ergodicity-breaking, we introduce the Krylov variance, a probe of operator localization in Krylov space, validated through mass-deformed SYK and quantum East models. Finally, we uncover Page curve entanglement dynamics and temporal quantum phase transitions in entanglement Hamiltonians of interacting fermionic chains, where symmetry-sector crossings highlight limitations of perturbative calculations performed around initial times, such as in Hawking’s analysis of black hole evaporation. We provide a condensed matter analog of the holographic “island formula” — a mechanism invoking quantum extremal surfaces to resolve the black hole information paradox. Methodologically, this work integrates large-N-type expansions, Keldysh contour techniques, and numerical methods to bridge condensed matter physics, quantum information, and gravitational duality. The results establish SYK-type systems as a universal framework for studying non-Fermi liquids, quantum criticality, and black hole analogs, while paving the way for exploring bosonic extensions and generalizations to open quantum systems.
Abstract Recent studies of out-of-time ordered thermal correlation functions (OTOC) in holographic systems and in solvable models such as the Sachdev-Ye-Kitaev (SYK) model have yielded new insights into manifestations of many-body chaos. So far the chaotic behavior has been obtained through explicit calculations in specific models. In this paper we propose a unified description of the exponential growth and ballistic butterfly spreading of OTOCs across different systems using a newly formulated “quantum hydrodynamics,” which is valid at finite ℏ and to all orders in derivatives. The scrambling of a generic few-body operator in a chaotic system is described as building up a “hydrodynamic cloud,” and the exponential growth of the cloud arises from a shift symmetry of the hydrodynamic action. The shift symmetry also shields correlation functions of the energy density and flux, and time ordered correlation functions of generic operators from exponential growth, while leads to chaotic behavior in OTOCs. The theory also predicts an interesting phenomenon of the skipping of a pole at special values of complex frequency and momentum in two-point functions of energy density and flux. This pole-skipping phenomenon may be considered as a “smoking gun” for the hydrodynamic origin of the chaotic mode. We also discuss the possibility that such a hydrodynamic description could be a hallmark of maximally chaotic systems.
Chaos in many-body quantum systems is of great importance to both many-body physics as well as black hole physics. In the field of many-body physics, interactions and disorder in the system can lead to various dynamic phenomena, be it thermalisation, many-body localisation, chaotic behavior and scrambling of quantum information. In the field of high energy physics, the holographic principle connects chaos and scrambling in many-body quantum systems with the information-theoretic properties of black holes. Theoretical quantum physics provides the framework for the models, methods, and results in this thesis, while black hole physics partly provides some motivation and inspiration. First, we introduce a new model for a many-body quantum system based on random quantum circuits. These are a popular framework for theoretic study of disordered spin chains. By drawing the random unitaries in the circuit from different ensembles, we can adjust the disorder strength in the interactions, which in turn leads to a thermal/many-body localisation phase transition. Next, we study the Brownian SYK model, a disordered model of Majorana fermions with all-to-all interactions, motivated by its link to the holographic principle. We develop a new numerical method based on an effective permutational symmetry to reduce computational cost from exponential to linear or quadratic in system size N. As a consequence, we can compute scrambling quantifiers in detail, and find a log N scrambling time, as conjectured in the context of fast scrambling for black holes. Finally, we develop a model based on the continuous-time limit of a random quantum circuit. It serves as a microscopic toy model for the evaporation of a black hole. With a similar method as developed for the Brownian SYK model, we can analyse its information theoretic properties. In particular, we follow established protocols for information retrieval from the Hawking radiation. We find a separation of time scales for entanglement growth and information retrieval, related to the intrinsic black hole dynamics (∝log N) and the coupling to the environment (∝N).
Quantum chaos entails an entropic and computational obstruction to describing a system and thus is intrinsically difficult to characterize. An understanding of quantum chaos is fundamentally related to the mechanism of thermalization in many-body systems and the quantum nature of black holes. In this thesis we adopt the view that quantum information theory provides a powerful framework in which to elucidate chaos in strongly-interacting quantum systems. We first push towards a more precise understanding of chaotic dynamics by relating different diagnostics of chaos, studying the time-evolution of random matrix Hamiltonians, and quantifying random matrix behavior in physical systems. We derive relations between out-of-time ordered correlation functions, spectral quantities, and frame potentials to relate the scrambling of quantum information, decay of correlators, and Haar-randomness. We give analytic expressions for these quantities in random matrix theory to explore universal aspects of late-time dynamics. Motivated by our random matrix results, we define k-invariance in order to capture the onset of random matrix behavior in physical systems. We then refine our diagnostics in order to study chaotic systems with symmetry by considering Haar-randomness with respect to quotients of the unitary group, and in doing so we generalize our quantum information machinery. We further consider extended random matrix ensembles in the context of strongly-interacting quantum systems dual to black holes. Lastly, we study operator growth in classes of random quantum circuits.
This thesis investigates important connection between two longstanding problems in theoretical physics: the information loss paradox in quantum gravity and the thermalization phenomena in quantum many-body systems.Although these problems originate from entirely different contexts, the AdS/CFT correspondence which is theoretical duality between chaotic quantum many body systems and gravity reveals that they are, in fact, two manifestations of the same underlying phenomenon.Black holes exhibit thermodynamic behavior, and semiclassical gravity predicts information loss during Hawking evaporation, apparently contradicting unitarity.In the AdS/CFT framework, however, gravitational dynamics including black hole formation is mapped to the unitary time evolution of strongly coupled quantum many-body systems.This correspondence provides a precise reformulation of Maldacena's information loss problem: the late-time behavior of thermal correlation functions predicted by semiclassical gravity fails to match the exact unitary evolution of the dual quantum system.A key ingredient in resolving this discrepancy is the eigenstate thermalization hypothesis (ETH), which characterizes thermalization in chaotic manybody systems.By studying the large-deviation technique for thermal correlation functions, we give a possible way of probing ETH for single non-integrable Hamiltonian with some non-trivial assumptions.In holographic systems, ETH captures the non-perturbative physics responsible for wormhole contributions in the gravitational path integral, thereby providing a quantitative and conceptual resolution of Maldacena's version of the information loss paradox.Moreover the thesis further develops a holographic framework for open quantum systems, motivated by Hawking's original information loss problem in asymptotically flat spacetime.We are introducing non-Hermitian deformations such as imaginary Janus interfaces and brane-based constructions.We identify geometric counterparts of dissipative dynamics and measurementinduced like processes.
Quantum chaos remains a challenging concept because classical signatures of chaos do not directly transfer to quantum systems. This thesis investigates which indicators of chaos are shared between classical and quantum mechanics and how they can be used to characterise non-integrable many-body systems. We examine ergodicity and thermalisation by means of the Eigenstate Thermalisation Hypothesis (ETH) as signatures of non-integrability, and study the Out-of-Time-Ordered Correlator (OTOC) as a probe of information scrambling and as a measure of sensitivity to initial conditions. We briefly discuss the appearance of chaotic wavefunctions and observations such as quantum scars and quantum ergodicity in individual eigenmodes of the Bunimovich stadium potential. Using the OTOC, we discuss extensions of the Lyapunov exponent to quantum systems and apply these ideas to the Sachdev–Ye–Kitaev (SYK) model. In the large-N limit, and using the AdS/CFT correspondence, we find that the model might potentially be the dual of a black hole and that it is maximally chaotic. We conclude by discussing additional proposed signatures of quantum chaos and prospects for experimental realisations of the SYK model.