Eigenstate thermalization hypothesis

Abstract

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 eigenstates behave in many ways like a statistical ensemble. A more detailed statement of this is named the eigenstate thermalization hypothesis (ETH). The reasons for why it works in so many cases are rooted in the early work of Wigner on random matrix theory and our understanding of quantum chaos. The ETH has now been studied extensively by both analytic and numerical means, and applied to a number of physical situations ranging from black hole physics to condensed matter systems. It has recently become the focus of a number of experiments in highly isolated systems. Current theoretical work also focuses on where the ETH breaks down leading to new interesting phenomena. This review of the ETH takes a somewhat intuitive approach as to why it works and how this informs our understanding of many body quantum states.

Microscopic foundation of the second law of thermodynamics within nonunitary Newtonian gravity

“…This choice allows us to perform a first step towards the simulation of macroscopic systems where the Second Law of thermodynamics is more relevant. A numerical simulation is carried out by starting from an initial pure physical state with mean energy E, drawn uniformly at random by superposing a huge number of energy eigenstates within the energy interval ∆E around E, according to the prescriptions of the Eigenstate Thermalization Hypothesis (ETH) [24,25]. In this way the behavior of the von Neumann entropy as a function of time is obtained, which is consistent with the one for a thermalizing system.…”

“…In this work the ability of the NNG model to produce gravity induced thermalization in a closed quantum many-body system has been investigated by studying a specific three-dimensional harmonic nanocrystal model. A numerical simulation compatible with the ETH prescriptions for the choice of the initial state [24,25] has been carried out, and the time evolution of the system has been calculated. The result shows a monotonic increase of the von Neumann entropy, followed by a stabilization at late times.…”

“…While, of course, the general model need to be tested against properly designed future experiments, anyway we can say that it is the first self-consistent low-energy gravity model implying in a natural way the emergence of Thermodynamics even in a closed system. Incidentally, within the framework of ETH [24,25], a physical entropy can only be introduced by previously applying an ad-hoc de-phasing map to the state of the system.…”

Fock-space correlations and the origins of many-body localization

“…In addition to the important question of the fate of single-particle Anderson localisation [9] upon the introduction of interactions, many-body localised systems are of fundamental interest due to their violation of the eigenstate thermalisation hypothesis (ETH). In generic ergodic systems, ETH explains the emergence of equilibrium thermodynamics and statistical mechanics, since eigenstate expectation values of local observables depend only on a few macroscopic state variables such as eigenenergies [10][11][12].…”

Hierarchy of Relaxation Timescales in Local Random Liouvillians

“…For unitary quantum many-body dynamics, the characterization of generic features common to the vast majority of systems is well developed, in the form of an effective random matrix theory [1-6]. It is for example a crucial ingredient to our understanding of thermalization in unitary quantum systems, manifest in the eigenstate thermalization hypothesis (ETH) [7][8][9][10][11][12][13].For open quantum many-body systems analogous organizing principles are yet missing. Only very recently the first developments in this direction appeared with the investigation of spectral features of a purely random Liouvillian [14-18], describing generic properties of trace preserving positive quantum maps.…”