Related papers: Graph-theory measures capture weak ergodicity brea…

Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs.…

Symmetry breaking plays a central role in classifying the phases of quantum many-body systems. Recent developments have highlighted a novel symmetry-breaking pattern, in which the strong symmetry of a density matrix spontaneously breaks to…

The recent observations of persistent revivals in the Rydberg atom chain have revealed a weak ergodicity breaking mechanism known as quantum many-body scars, which is typically a collection of states with low entanglement embedded in…

Quantum measurement is physically realized through a finite dynamical interaction between a system and a measuring apparatus, giving rise to a continuous transition from weak to strong regimes. While this crossover is well understood under…

Consider a sequence of finite regular graphs (GN) converging, in the sense of Benjamini-Schramm, to the infinite regular tree. We study the induced quantum graphs with equilateral edge lengths, Kirchhoff conditions (possibly with a non-zero…

We consider the dynamics of continuously measured many-body chaotic quantum systems. Focusing on the observable of state purification, we analytically describe the limits of strong and weak measurement rate, where in the latter case…

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials,…

We study the semiclassical behaviour of eigenfunctions of quantum systems with ergodic classical limit. By the quantum ergodicity theorem almost all of these eigenfunctions become equidistributed in a weak sense. We give a simple derivation…

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…

A quantum many-body system can undergo transitions in the presence of continuous measurement. In this work, we find that a generic class of critical dynamical scaling behavior can emerge at these measurement-induced transitions. Remarkably,…

We consider a class of weakly interacting particle systems of mean-field type. The interactions between the particles are encoded in a graph sequence, i.e., two particles are interacting if and only if they are connected in the underlying…

A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…

Motivated by dynamical experiments on cold atomic gases, we develop a quantum kinetic approach to weakly perturbed integrable models out of equilibrium. Using the exact matrix elements of the underlying integrable model we establish an…

Inspired by "quantum graphity" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very…

Eigenstate Thermalization Hypothesis(ETH) has played a pivotal role in understanding ergodicity and its breaking in isolated quantum many-body systems. Recent experiment on 51-atom Rydberg quantum simulator and subsequent theoretical…

Thermodynamic irreversibility is a fundamental concept in statistical physics, yet its experimental measurement remains challenging, especially for complex systems. We introduce a novel random coarse-graining framework to identify…

Developing measures of quantum ergodicity and chaos stands as a foundational task in the study of quantum many-body systems. In this work, we propose metrics for these effects based on Hamiltonian learning that unify multiple advantages of…

Strong nonlinearity at the single photon level represents a crucial enabling tool for optical quantum technologies. Here we report on experimental implementation of a strong Kerr nonlinearity by measurement-induced quantum operations on…

We outline some recent proofs of quantum ergodicity on large graphs and give new applications in the context of irregular graphs. We also discuss some remaining questions.

Matrix-based centrality measures have enjoyed significant popularity in network analysis, in no small part due to our ability to rigorously analyze their behavior as parameters vary. Recent work has considered the relationship between…