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Understanding the emergence of chaos in many-body quantum systems away from semi-classical limits, particularly in spatially local interacting spin Hamiltonians, has been a long-standing problem. In these intrinsically quantum regimes,…
The eigenstate thermalization hypothesis (ETH), which dictates that all diagonal matrix elements within a small energy shell be almost equal, is a major candidate to explain thermalization in isolated quantum systems. According to the…
The Eigenstate-Thermalization-Hypothesis (ETH) has been established as the general framework to understand quantum statistical mechanics. Only recently has the attention been paid to so-called full ETH, which accounts for higher-order…
Ergodic isolated quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH), i.e., the expectation values of local observables in the system's eigenstates approach the predictions of the microcanonical ensemble.…
We study the statistical distribution of components in the non-perturbative parts of energy eigenfunctions (EFs), in which main bodies of the EFs lie. Our numerical simulations in five models show that deviation of the distribution from the…
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 eigenstate thermalization hypothesis (ETH) explains why chaotic quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity ("charge"), the ETH implies thermalization…
Given a quantum many-body system and the expectation-value dynamics of some operator, we study how this reference dynamics is altered due to a perturbation of the system's Hamiltonian. Based on projection operator techniques, we unveil that…
This review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is introduced as a natural extension of…
We consider a minimal model for quantum thermalization of coupled chaotic subsystems. The route towards ergodicity is explored as a function of the coupling strength. The results are contrasted with the predictions of standard Random Matrix…
In this work we revisit the problem of equilibration in isolated many-body interacting quantum systems. We pay particular attention to quantum chaotic Hamiltonians, and rather than focusing on the properties of the asymptotic states and how…
Having analytical instances of the Eigenstate Thermalization Hypothesis (ETH) is of obvious interest, both for fundamental and applied reasons. This is generically a hard task, due to the belief that non-linear interactions are basic…
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 eigenstate thermalization hypothesis (ETH) provides a fundamental mechanism for emergent statistical mechanics in isolated chaotic quantum systems, asserting that individual energy eigenstates behave as pseudorandom vectors within an…
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 verify that the eigenstate thermalization hypothesis (ETH) holds universally for locally interacting quantum many-body systems. Introducing random-matrix ensembles with interactions, we numerically obtain a distribution of maximum…
We study the relative entropy of highly excited quantum states. First, we sample states from the Wishart ensemble and develop a large-N diagrammatic technique for the relative entropy. The solution is exactly expressed in terms of…
Under unitary time evolution, expectation values of physically reasonable observables often evolve towards the predictions of equilibrium statistical mechanics. The eigenstate thermalization hypothesis (ETH) states that this is also true…
Even though foundations of the eigenstate thermalization hypothesis (ETH) are based on random matrix theory, physical Hamiltonians and observables substantially differ from random operators. One of the major challenges is to embed local…
We investigate the chaotic phase of the Bose-Hubbard model [L. Pausch et al, Phys. Rev. Lett. 126, 150601 (2021)] in relation to the bosonic embedded random matrix ensemble, which mirrors the dominant few-body nature of many-particle…