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For manifolds with geodesic flow that is ergodic on the unit tangent bundle, the quantum ergodicity theorem implies that almost all Laplacian eigenfunctions become equidistributed as the eigenvalue goes to infinity. For a locally symmetric…
We study the phenomenon of weak ergodicity breaking for a class of globally correlated random walk dynamics defined over a finite set of states. The persistence in a given state or the transition to another one depends on the whole previous…
In addition to the well known scarring effect of periodic orbits, we show here that homoclinic and heteroclinic orbits, which are cornerstones in the theory of classical chaos, also scar eigenfunctions of classically chaotic systems when…
We experimentally and theoretically demonstrate spinor gases driven by spin-flopping fields are excellent platforms for investigating ergodicity breaking and quantum scarring. We observe that specific initial states remain nonthermal at…
We describe explicitly how entanglement between quantum mechanical subsystems can lead to emergent gauge symmetry in a classical limit. We first provide a precise characterisation of when it is consistent to treat a quantum subsystem…
We study the ergodic properties of quantized ergodic maps of the torus. It is known that these satisfy quantum ergodicity: For almost all eigenstates, the expectation values of quantum observables converge to the classical phase-space…
Quantum ergodicity, which expresses the semiclassical convergence of almost all expectation values of observables in eigenstates of the quantum Hamiltonian to the corresponding classical microcanonical average, is proven for…
Eigenstate thermalization hypothesis (ETH) represents a breakthrough in many-body physics since it allows to link thermalization of physical observables with the applicability of random matrix theory (RMT). Recent years were also extremely…
Non-equilibrium properties of quantum materials present many intriguing properties, among them athermal behavior, which violates the eigenstate thermalization hypothesis. Such behavior has primarily been observed in disordered systems. More…
One of the defining traits of quantum mechanics is the uncertainty principle which was originally expressed in terms of the standard deviation of two observables. Alternatively, it can be formulated using entropic measures, and can also be…
As the name indicates, a periodic orbit is a solution for a dynamical system that repeats itself in time. In the regular regime, periodic orbits are stable, while in the chaotic regime, they become unstable. The presence of unstable…
We study the time evolution after a quantum quench in a family of models whose degrees of freedom are fermions coupled to spins, where quenched disorder appears neither in the Hamiltonian parameters nor in the initial state. Focussing on…
Quantum many-body scars (QMBS) constitute a new quantum dynamical regime in which rare "scarred" eigenstates mediate weak ergodicity breaking. One open question is to understand the most general setting in which these states arise. In this…
Quantum annealers play a major role in the ongoing development of quantum information processing and in the advent of quantum technologies. Their functioning is underpinned by the many-body adiabatic evolution connecting the ground state of…
We test the time evolution of quite general initial states in a model that is exactly solvable, $i.e.$ a semi-infinite $XY$ spin chain with an impurity at the boundary. The dynamics is portrayed through the observation of the site…
Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the…
It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. While the existing theory provides a rather complete picture…
We examine the logical structure of the emergence of classical stochasticity for a quantum system governed by a Pauli-type master equation. It is well-known that while such equations describe the evolution of probabilities, they do not…
The quantum chaos conjecture associates the spectral statistics of a quantum system with abstract notions of quantum ergodicity. Such associations are taken to be of fundamental and sometimes defining importance for quantum chaos, but their…
We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit conjecture: A dynamical system with full classical chaos has a quantum energy spectrum with universal fluctuations on the scale of the mean level spacing.…