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The Eigenstate Thermalization Hypothesis (ETH) has played a key role in recent advances in the high energy and condensed matter communities. It explains how an isolated quantum system in a far-from-equilibrium initial state can evolve to a…
This work aims at understanding the interplay between the Eigenstate Thermalization Hypothesis (ETH), initial state independent equilibration and quantum chaos in systems that do not have a direct classical counterpart. It is based on…
The Eigenstate Thermalization Hypothesis (ETH) was developed as a framework for understanding how the principles of statistical mechanics emerge in the long-time limit of isolated quantum many-body systems. Since then, ETH has shifted the…
In this thesis, we present a comprehensive study of chaos and thermalization of the one-dimensional Bose-Hubbard Model (BHM) within the classical field approximation. Two quantitative measures are compared: the ensemble-averaged Finite-time…
In this work we study a scenario where dynamics is restricted to a single excitation manifold, for particular physical observables with support in the manifold, which we label a `correlated quench'. We ask how such dynamics may in general…
The eigenstate thermalization hypothesis as well as the quantum ergodic theorem are studied in the light of quantum Fisher information. We show how global bounds on quantum Fisher information set the ETH and ergodicity conditions.…
In this paper, we study the Feingold-Peres model as an example, which is a well-known paradigm of quantum chaos. Using semiclassical analysis and numerical simulations, we study the statistical properties of observables in few-body systems…
Eigenstate thermalization hypothesis is a detailed statement of the matrix elements of few-body operators in energy eigenbasis of a chaotic Hamiltonian. Part of the statement is that the off-diagonal elements fall exponential for large…
The thermalization phenomenon and many-body quantum statistical properties are studied on the example of several observables in isolated spin-chain systems, both integrable and generic non-integrable ones. While diagonal matrix elements for…
Ergodic isolated quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH), i.e., the expectation values of local observables in the system's eigenstates approach the predictions of the microcanonical ensemble.…
Using a Krylov-subspace time evolution algorithm, we simulate the real-time dynamics of translation invariant non-integrable finite spin rings to quite long times with high accuracy. We systematically study the finite-size deviation between…
Experiments with trapped atomic gases have opened novel possibilities for studying the evolution of nonequilibrium finite quantum systems, which revived the necessity of reconsidering and developing the theory of such processes. This review…
We discuss eigenstate correlations for ergodic, spatially extended many-body quantum systems, in terms of the statistical properties of matrix elements of local observables. While the eigenstate thermalization hypothesis (ETH) is known to…
We study a generic model of quantum computer, composed of many qubits coupled by short-range interaction. Above a critical interqubit coupling strength, quantum chaos sets in, leading to quantum ergodicity of the computer eigenstates. In…
Out-of-time-order correlators (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation in interacting quantum many-body systems. It was recently argued that the expected exponential growth of…
The Eigenstate Thermalization Hypothesis explains thermalization in isolated quantum systems through the statistical properties of observables in the energy eigenbasis. We investigate the crossover from integrability to chaos in the…
The main topic of this thesis is the proof of two fundamental entropic inequalities for quantum Gaussian channels. Quantum Gaussian channels model the propagation of electromagnetic waves through optical fibers and free space in the quantum…
Quantum many-body scars (QMBS) are exceptional eigenstates that defy thermalization, enabling long-lived coherent dynamics in strongly interacting systems. However, their stability under perturbations remains inadequately understood. In…
We study the relaxation of a quantum system towards the thermal equilibrium using tools developed within the context of quantum information theory. We consider a model in which the system is a qubit, and reaches equilibrium after several…
Time dynamics of isolated many-body quantum systems has long been an elusive subject. Very recently, however, meaningful experimental studies of the problem have finally become possible, stimulating theoretical interest as well. Progress in…