Related papers: Ubiquitous quantum scarring does not prevent ergod…
We study the quantum dynamics of Josephson junction arrays. We find isolated groups of low-entanglement eigenstates, that persist even when the Josephson interaction is strong enough to destroy the organization of the spectrum in…
Quantum ergordic theorem for a large class of quantum systems was proved by von Neumann [Z. Phys. {\bf 57}, 30 (1929)] and again by Reimann [Phys. Rev. Lett. {\bf 101}, 190403 (2008)] in a more practical and well-defined form. However, it…
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…
Interacting many-body quantum systems and their dynamics, while fundamental to modern science and technology, are formidable to simulate and understand. However, by discovering their symmetries, conservation laws, and integrability one can…
In simple -- but selected -- quantum systems, the probability distribution determined by the ground state wave function is infinitely divisible. Like all simple quantum systems, the Euclidean temporal extension leads to a system that…
Quantum many-body scars in Rydberg atom arrays have thus far only been observed on bipartite lattices, leaving open the question of whether and how they survive frustration, and what the appropriate initial states are that lead to…
We study the eigenstate properties of a nonintegrable spin chain that was recently realized experimentally in a Rydberg-atom quantum simulator. In the experiment, long-lived coherent many-body oscillations were observed only when the system…
The concept of weak ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak ergodicity breaking describes a weakly chaotic dynamical system: a nonlinear map which generates subdiffusion…
We exhibit scarring for certain nonlinear ergodic toral automorphisms. There are perturbed quantized hyperbolic toral automorphisms preserving certain co-isotropic submanifolds. The classical dynamics is ergodic, hence in the semiclassical…
We show that the transition from regular to chaotic spectral statistics in interacting many-body quantum systems has an unambiguous signature in the distribution of Schmidt coefficients dynamically generated from a generic initial state,…
A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). For single particle systems with fully chaotic classical…
We describe the statistics of chaotic wavefunctions near periodic orbits using a basis of states which optimise the effect of scarring. These states reflect the underlying structure of stable and unstable manifolds in phase space and…
Quantum dynamics in certain kinetically-constrained systems can display a strong sensitivity to the initial condition, wherein some initial states give rise to persistent quantum revivals -- a type of weak ergodicity breaking known as…
Highly frustrated magnets, with their macroscopically-degenerate classical ground states and massively-entangled quantum spin liquid phases, have been pivotal to the development of modern condensed matter concepts such as emergent…
Recent advances in quantum simulations have opened access to the real-time dynamics of lattice gauge theories, providing a new setting to explore how quantum criticality influences thermalization and ergodicity far from equilibrium. Using…
It is shown, by means of a simple specific example, that for integrable systems it is possible to build up approximate eigenfunctions, called {\it asymptotic eigenfunctions}, which are concentrated as much as one wants to a classical…
We review the main ideas and results in the stationary problems of quantum chaos in generic (mixed) systems, whose classical dynamics has regular (invariant tori) and chaotic regions coexisting in the phase space. First we discuss the…
Recent studies of interacting systems of quantum spins, ultracold atoms and correlated fermions have shed a new light on how isolated many-body systems can avoid rapid equilibration to their thermal state. It has been shown that many such…
We generalize Page's result on the entanglement entropy of random pure states to the many-body eigenstates of realistic disordered many-body systems subject to long range interactions. This extension leads to two principal conclusions:…
A generic closed quantum many-body system will inevitably tend to thermalization, whose local information encoded in the initial state eventually scrambles into the full space, known as quantum ergodicity. A paradigmatic exception in closed…