Related papers: Eigenstate thermalization hypothesis and integrals…
A plausible mechanism of thermalization in isolated quantum systems is based on the strong version of the eigenstate thermalization hypothesis (ETH), which states that all the energy eigenstates in the microcanonical energy shell have…
Many properties of a quantum system can be obtained from just a single eigenstate of its Hamiltonian. For example, a single eigenstate can be used to determine whether a system is integrable or chaotic and, in the latter case, to establish…
The eigenstate thermalization hypothesis (ETH) is a successful theory that provides sufficient criteria for ergodicity in quantum many-body systems. Most studies were carried out for Hamiltonians relevant for ultracold quantum gases and…
The Eigenstate Thermalization Hypothesis (ETH) provides a sufficient condition for thermalization of isolated quantum systems. While the standard ETH is formulated in the absence of degeneracy, physical systems often possess symmetries that…
The eigenstate thermalization hypothesis (ETH) postulates that the energy eigenstates of an isolated many-body system are thermal, i.e., each of them already yields practically the same expectation values as the microcanonical ensemble at…
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…
In a recent Letter [PhysRevLett.119.030601 (2017), arXiv:1702.08227], Shiraishi and Mori claim to provide a general method for constructing local Hamiltonians that do not exhibit eigenstate thermalization. We argue that the claim is based…
It is commonly believed that quantum isolated systems satisfying the eigenstate thermalization hypothesis (ETH) are diffusive. We show that this assumption is too restrictive, since there are systems that are asymptotically in a thermal…
We use field-theoretic methods to explore the statistics of eigenfunctions of the Floquet operator for a large family of Floquet random quantum circuits. The correlation function of the quasienergy eigenstates is calculated and shown to…
We derive semiclassical analytical solutions for both the diagonal and off-diagonal functions in the eigenstate thermalization hypothesis (ETH) in a quarter-stadium quantum billiard. For a representative observable, we obtain an explicit…
The eigenstate thermalization hypothesis (ETH) underpins much of our modern understanding of the thermalization of closed quantum many-body systems. Here, we investigate the statistical properties of observables in the eigenbasis of the…
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…
We derive an upper bound on the difference between the long-time average and the microcanonical ensemble average of observables in isolated quantum systems. We propose, numerically verify, and analytically support a new hypothesis,…
In this paper, we study the Feingold-Peres model as an example, which is a well-known paradigm of quantum chaos. Using semiclassical analysis and numerical simulations, we study the statistical properties of observables in few-body systems…
We consider a quantum system A U B made up of degrees of freedom that can be partitioned into spatially disjoint regions A and B. When the full system is in a pure state in which regions A and B are entangled, the quantum mechanics of…
We study the matrix elements of local and nonlocal operators in the single-particle eigenstates of two paradigmatic quantum-chaotic quadratic Hamiltonians; the quadratic Sachdev-Ye-Kitaev (SYK2) model and the three-dimensional Anderson…
In this work, we use quantum complexity theory to quantify the difficulty of distinguishing eigenstates obeying the Eigenstate Thermalization Hypothesis (ETH). After identifying simple operators with an algebra of low-energy observables and…
We consider a realistic nonequilibrium protocol, where a quantum system in thermal equilibrium is suddenly subjected to an external force. Due to this force, the system is driven out of equilibrium and the expectation values of certain…
We study the characteristics of thermalizing and non-thermalizing operators in integrable theories as we turn on a non-integrable deformation. Specifically, we show that $\sigma^z$, an operator that thermalizes in the integrable transverse…
We study the long-time average of the reduced density matrix (RDM) of an $m$-level central system, which is locally coupled to a large environment, under an overall Schr\"{o}dinger evolution of the total system. We consider a class of…