Abstract We study the fine structure of long‐time quantum noise in correlation functions of AdS/CFT systems. Under standard assumptions of quantum chaos for the dynamics and the observables, we estimate the size of exponentially small oscillations and trace them back to geometrical features of the bulk system. The noise level is highly suppressed by the amount of dynamical chaos and the amount of quantum impurity in the states. This implies that, despite their missing on the details of Poincaré recurrences, ‘virtual’ thermal AdS phases do control the overall noise amplitude even at high temperatures where the thermal ensemble is dominated by large AdS black holes. We also study EPR correlations and find that, in contrast to the behavior of large correlation peaks, their noise level is the same in TFD states and in more general highly entangled states.
Abstract We study the behavior of Rényi entropies for pure states from standard assumptions about chaos in the high-energy spectrum of the Hamiltonian of a many-body quantum system. We compute the exact long-time averages of Rényi entropies and show that the quantum noise around these values is exponentially suppressed in the microcanonical entropy. For delocalized states over the microcanonical band, the long-time average approximately reproduces the equilibration proposal of H. Liu and S. Vardhan, with extra structure arising at the order of non-planar permutations. We analyze the equilibrium approximation for AdS/CFT systems describing black holes in equilibrium in a box. We extend our analysis to the situation of an evaporating black hole, and comment on the possible gravitational description of the new terms in our approximation.
This thesis studies the complexity, thermalization, and entanglement properties of quantum mechanical systems and the implications of their behavior in high energy and condensed matter models. In Chapter 2, we use the geometry of Lie groups to study the circuit complexity of quantum mechanical systems and develop the technology to analytically predict the appearance of the obstruction to the complexity growth of integrable systems. We simulate the spin and fermionic systems, in which the amount of chaos can be controlled, and conjecture the close relation between quantum complexity and thermalization. In Chapter 3, we apply quantum information theory to an evaporating black hole in Jackiw-Teitelboim gravity in the context of AdS/CFT as a quantum error correction protocol. By calculating the entropy measures using gravitational path integrals, we establish the criterion for an error in the Hawking radiation to be correctable and identify the transition in the reversibility of the error channel as the Page transition. In Chapter 4, we study a 1+1 dimensional random circuit with measurement and dissipation. We map this type of quantum system to a classical Ising model analytically and show that the entanglement dynamics can be understood as the thermodynamics of the domain wall formed in the spin model, as one of the spatial dimensions stretches. We then confirm the calculated time scales in the classical theory qualitatively with simulations of realistic qubit circuits. Overall, we present a holistic picture of quantum systems, from those evolving with pure unitary, to those evolving also with influence from the environment. The complexity of the theory and entanglement of the states exhibit universal behavior at early times (∼ O(N)) and distinct long-time behavior, determined by their thermalization properties in spin chains, toy models of black holes in AdS/CFT, and monitored random circuits with dissipation.
Recent work has revealed that entanglement entropy growth in conformal field theories (CFTs) can be suppressed when a local operator quench interacts with a mixed-state excitation, providing a dual interpretation in terms of black hole scattering in AdS. This phenomenon, termed \emph{entanglement suppression}, opens several promising directions for exploration. In this proposal, I outline five distinct yet interconnected research trajectories: generalization to higher dimensions, the role of quantum chaos via out-of-time-order correlators (OTOCs), the absence of suppression in integrable models, the extension to entanglement negativity as a probe of mixedness, and a geometric interpretation based on scattering cross sections in AdS. Each direction offers new insights into the interplay between holography, non-equilibrium dynamics, and quantum information.
We study unitary quantum dynamics in noisy Brownian models with global continuous symmetries, such as
U(1) and
SU(2), focusing on Rényi entanglement entropies and hydrodynamic and non-hydrodynamic correlators. By mapping the averaged late-time dynamics to the low-energy physics of effective replica Hamiltonians, we find that the evolution is controlled by the quantum geometry of their ground-state manifolds, which is directly related to the geometry of
k-commutants---the symmetry algebra of
k replicas of the system. In interacting systems, these
k-commutants are generically determined solely by the symmetries of the system, independent of microscopic details of the noisy evolution. This allows us to use the time-dependent variational principle (TDVP) to provide simple geometric explanations for the sub-ballistic Rényi entanglement growth and the anomalous decay of non-hydrodynamic correlators in interacting systems with continuous symmetries. We find this behavior to be intimately connected to singularities within the
k-commutant manifolds, arising from frozen ``void'' states in the Hilbert space that exist due to continuous on-site symmetries. This also demystifies the important role of voids in the dynamics of these observables, previously identified in
U(1) symmetric systems. We compare these behaviors in interacting systems with Abelian and non-Abelian continuous symmetries and in free-fermion systems, which differ in the geometry of their
k-commutants. Ultimately, this work provides a general geometric framework for systematically studying observables in noisy systems with continuous symmetries, including Haar-random circuits.
Abstract Noise sources are ubiquitous in Nature and give rise to a description of quantum systems in terms of stochastic Hamiltonians. Decoherence dominates the noise-averaged dynamics and leads to dephasing and the decay of coherences in the eigenbasis of the fluctuating operator. For energy-diffusion processes stemming from fluctuations of the system Hamiltonian the characteristic decoherence time is shown to be proportional to the heat capacity. We analyze the decoherence dynamics of entangled CFTs and characterize the dynamics of the purity, and logarithmic negativity, that are shown to decay monotonically as a function of time. The converse is true for the quantum Renyi entropies. From the short-time asymptotics of the purity, the decoherence rate is identified and shown to be proportional to the central charge. The fixed point characterizing long times of evolution depends on the presence degeneracies in the energy spectrum. We show how information loss associated with decoherence can be attributed to its leakage to an auxiliary environment and discuss how gravity duals of decoherence dynamics in holographic CFTs looks like in AdS/CFT. We find that the inner horizon region of eternal AdS black hole is highly squeezed due to decoherence.
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.