Related papers: Eigenstate Thermalization Hypothesis for Wigner Ma…
The eigenstate thermalization hypothesis (ETH) explains how generic quantum many-body systems thermalize internally. It implies that local operators' time-averaged expectation values approximately equal their thermal expectation values,…
The eigenstate thermalization hypothesis (ETH) is one of the cornerstones in our understanding of quantum statistical mechanics. The extent to which ETH holds for nonlocal operators is an open question that we partially address in this…
Eigenstate thermalization hypothesis (ETH) is discussed. We point out that the common formulation of the ETH suffers from the mixing of random and deterministic variables. We suggest a modified formulation of the ETH which includes only…
A profound quest of statistical mechanics is the origin of irreversibility - the arrow of time. New stimulants have been provided, thanks to unprecedented degree of control reached in experiments with isolated quantum systems and rapid…
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…
We study the eigenvalues and the eigenvectors of $N\times N$ structured random matrices of the form $H = W\tilde{H}W+D$ with diagonal matrices $D$ and $W$ and $\tilde{H}$ from the Gaussian Unitary Ensemble. Using the supersymmetry technique…
We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite…
The Eigenstate Thermalization Hypothesis(ETH) is a standard tool to understand the thermalization properties of an isolated quantum system. Its generalization to higher order correlations of matrix elements of local operators, dubbed the…
We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size $N$ converge to the Tracy--Widom laws at a rate $O(N^{-1/3+\omega})$, as $N$ tends to infinity. For Wigner matrices this…
We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables in a typical translation invariant system of quantum spins with mean field interaction. This mathematically verifies the observation made in [L.Santos and…
We prove that the local eigenvalue statistics of real symmetric Wigner-type matrices near the cusp points of the eigenvalue density are universal. Together with the companion paper [arXiv:1809.03971], which proves the same result for the…
Currently there are two main approaches to describe how quantum statistical physics emerges from an isolated quantum many-body system in a pure state: Canonical Typicality (CT) and Eigenstate Thermalization Hypothesis (ETH). These two…
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…
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…
We prove that any finite collection of quadratic forms (overlaps) of general deterministic matrices and eigenvectors of an $N\times N$ Wigner matrix has joint Gaussian fluctuations. This can be viewed as the random matrix analogue of the…
A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind…
In this paper we consider Wigner random matrices -- symmetric n by n random matrices whose entries are independent identically distributed real random variables. We prove that the probability distribution of one or several eigenvalues close…
Eugene Wigner's revolutionary vision predicted that the energy levels of large complex quantum systems exhibit a universal behavior: the statistics of energy gaps depend only on the basic symmetry type of the model. Simplified models of…
We develop a class of matrix models which implement and formalize the `eigenstate thermalization hypothesis' (ETH) and point out that in general these models must contain non-Gaussian corrections, already in order to correctly capture…
The recent discovery that for large Hilbert spaces, almost all (that is, typical) Hamiltonians have eigenstates that place small subsystems in thermal equilibrium, has shed much light on the origins of irreversibility and thermalization.…