Related papers: Necessity of eigenstate thermalization for equilib…
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…
We consider many-body quantum systems that exhibit quantum chaos, in the sense that the observables of interest act on energy eigenstates like banded random matrices. We study the time-dependent expectation values of these observables,…
The eigenstate thermalisation hypothesis (ETH) is a statistical characterisation of eigen-energies, eigenstates and matrix elements of local operators in thermalising quantum systems. We develop an ETH-like ansatz of a partially…
This chapter discusses the conditions and timescales under which isolated many-body quantum systems, initially far from equilibrium, ultimately reach thermal equilibrium. We also examine quantities that, during the relaxation process,…
One explanation of the thermalization of an isolated quantum system is the eigenstate thermalization hypothesis, which posits that all energy eigenstates are thermal. Based on this idea, we use dynamical typicality to predict the thermal…
The observable long-time behavior of an isolated many-body system after a quantum quench is considered, i.e., an eigenstate (or an equilibrium ensemble) of some pre-quench Hamiltonian $H$ serves as initial condition which then evolves in…
We show that eigen-energies and energy eigenstates play different roles in the equilibration process of an isolated quantum system. Their roles are revealed numerically by exchanging the eigen-energies between an integrable model and a…
It is usually expected and observed that non-integrable isolated quantum systems thermalize. However, for some non-integrable spin chain models, in a numerical study, initial states with oscillations that persisted for some time were found…
Thermalization play a central role in out-of-equilibrium physics of ultracold atoms or electronic transport phenomena. On the other hand, entanglement concepts have proven to be extremely useful to investigate quantum phases of matter.…
The Eigenstate Thermalization Hypothesis (ETH) was developed as a framework for understanding how the principles of statistical mechanics emerge in the long-time limit of isolated quantum many-body systems. Since then, ETH has shifted the…
Thermalization is the process through which a physical system evolves toward a state of thermal equilibrium. Determining whether or not a physical system will thermalize from an initial state has been a key question in condensed matter…
We derive the Eigenstate Thermalization Hypothesis (ETH) from a random matrix Hamiltonian by extending the model introduced by J. M. Deutsch [Phys. Rev. A 43, 2046 (1991)]. We approximate the coupling between a subsystem and a many-body…
Ability of dynamical systems to relax to equilibrium has been investigated since the invention of statistical mechanics, which establishes the connection between dynamics of many-body Hamiltonian systems and phenomenological thermodynamics.…
Generic rotationally invariant random matrix models satisfy a simple relation: the probability distribution of off-diagonal elements and the one of half the difference between any two diagonal elements coincide. In the spirit of the…
According to the eigenstate thermalization hypothesis (ETH), even isolated quantum systems can thermalize because the eigenstate-to-eigenstate fluctuations of typical observables vanish in the limit of large systems. Of course, isolated…
Prethermalization of the equation of state and the kinetic temperature to their equilibrium values occurs on time scales dramatically shorter than the thermal equilibration time. This is a crucial ingredient for the understanding of…
We ask whether the Eigenstate Thermalization Hypothesis (ETH) is valid in a strong sense: in the limit of an infinite system, {\it every} eigenstate is thermal. We examine expectation values of few-body operators in highly-excited many-body…
Despite being ubiquitous, out-of-equilibrium quantum systems are much less understood than systems at equilibrium. Progress in the field has benefited from a symbiotic relationship between theoretical studies and new experiments on coherent…
Many theoretical and experimental results show that even isolated quantum systems evolving unitarily may equilibrate, since the evolution of some observables may be around an equilibrium value with negligible fluctuations most of the time.…
Understanding how isolated quantum systems thermalize has recently gathered renewed interest almost 100 years after the first work by von Neumann, thanks to the experimental realizations of such systems. Experimental and numerical pieces of…