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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…

There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…

Recent advances in quantum simulators allow direct experimental access to ensembles of pure states generated by measuring part of an isolated quantum many-body system. These projected ensembles encode fine-grained information beyond thermal…

We develop a rigorous system-agnostic method to predict quantum thermalization in an overwhelming fraction of accessible pure states in a many-body system, entirely in terms of certain out-of-time-ordered correlators of few-body…

Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems,…

Quantum state designs, by enabling an efficient sampling of random quantum states, play a quintessential role in devising and benchmarking various quantum protocols with broad applications ranging from circuit designs to black hole physics.…

Random many-body states are both a useful tool to model certain physical systems and an important asset for quantum computation. Realising them, however, generally requires an exponential (in system size) amount of resources. Recent…

Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the…

We extend the formalism of pure state thermodynamics to matrix product states. In pure state thermodynamics finite temperature properties of quantum systems are derived without the need of statistical mechanics ensembles, but instead using…

Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…

We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to…

This paper is concerned with the ergodic subspaces of the state spaces of isolated quantum systems. We prove a new ergodic theorem for closed quantum systems which shows that the equilibrium state of the system takes the form of a grand…

We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In…

We study the internal dynamics of an elementary quantum system placed close to a body held at a temperature different from that of the surrounding radiation. We derive general expressions for lifetime and density matrix valid for bodies of…

We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full…

Why is thermalisation a universal phenomenon? How does a quantum system reach thermodynamical equilibrium? These questions are not new, dating even from the very birth of quantum theory and have been the subject of a renewed interest over…

The apparent randomness of chaotic eigenstates in interacting quantum systems hides subtle correlations dynamically imposed by their finite energy per particle. These correlations are revealed when Berrys approach for chaotic eigenfunctions…

The thermal or equilibrium ensemble is one of the most ubiquitous states of matter. For models comprised of many locally interacting quantum particles, it describes a wide range of physical situations, relevant to condensed matter physics,…

The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…

Quantum many-body scar (QMBS) in kinetically constrained quantum systems challenges the conventional eigenstate thermalization hypothesis (ETH). We develop an effective open-system description for constrained dynamics and introduce the…