相关论文: Complete Hilbert-Space Ergodicity in Quantum Dynam…
Ergodicity has been one of the fundamental concepts underpinning our understanding of thermalization in isolated systems since the first developments in classical statistical mechanics. Recently, a similar notion has been introduced for…
Ergodicity, the property that all allowed configurations are explored over time, plays a pivotal role in explaining the equilibrium behavior of classical dynamical systems. Yet, such a property is typically precluded in quantum systems…
The maximum entropy principle is foundational for statistical analyses of complex dynamics. This principle has been challenged by the findings of a previous work [arXiv:1701.07596], where it was argued that a quantum system driven in time…
Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum…
We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by i) the temporal trajectory of…
Systems reaching thermal equilibrium are ubiquitous. For classical systems, this phenomenon is typically understood statistically through ergodicity in phase space, but translating this to quantum systems is a long-standing problem of…
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,…
Using the ergodicity principle for the expectation values of several types of observables, we investigate the thermalization process in isolated fermionic systems. These are described by the two-body random ensemble, which is a paradigmatic…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
Explaining quantum many-body dynamics is a long-held goal of physics. A rigorous operator algebraic theory of dynamics in locally interacting systems in any dimension is provided here in terms of time-dependent equilibrium (Gibbs)…
The eigenstate thermalization hypothesis (ETH) is the leading interpretation in our current understanding of quantum thermalization. Recent results uncovered strong connections between quantum correlations in thermalizing systems and the…
Disorder in quantum many-body systems can drive transitions between ergodic and non-ergodic phases, yet the nature--and even the existence--of these transitions remains intensely debated. Using a two-dimensional array of superconducting…
By means of a Floquet analysis, we study the quantum dynamics of a fully connected Lipkin-Ising ferromagnet in a periodically driven transverse field showing that thermalization in the steady state is intimately connected to properties of…
If we prepare an isolated, interacting quantum system in an eigenstate and perturb a local observable at an initial time, its expectation value will relax towards a thermal expectation value, even though the time evolution of the system is…
One of the fundamental problems of quantum statistical physics is how an ideally isolated quantum system can ever reach thermal equilibrium behavior despite the unitary time evolution of quantum-mechanical systems. Here, we study, via…
The concept of ergodicity---the convergence of the temporal averages of observables to their ensemble averages---is the cornerstone of thermodynamics. The transition from a predictable, integrable behavior to ergodicity is one of the most…
The emergence of statistical mechanics for isolated classical systems comes about through chaotic dynamics and ergodicity. Here we review how similar questions can be answered in quantum systems. The crucial point is that individual energy…
The validity of the ergodic hypothesis in quantum systems can be rephrased in the form of the eigenstate thermalisation hypothesis (ETH), a set of statistical properties for the matrix elements of local observables in energy eigenstates,…
Let us imagine that there is an overall quantum theory (not necessarily recognized yet) of matter and energy ({\it i.e.}, of elementary fermions and bosons) interacting with the physical spacetime (treated on a quantum level). Since states…
Ergodic theory provides a rigorous mathematical description of chaos in classical dynamical systems, including a formal definition of the ergodic hierarchy. How ergodic dynamics is reflected in the energy levels and eigenstates of a quantum…