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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…

Statistical Mechanics · Physics 2018-11-05 Oleg Inozemcev , Igor Volovich

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…

Statistical Mechanics · Physics 2025-12-01 Elisa Vallini , Laura Foini , Silvia Pappalardi

Thermalization of isolated quantum systems has been studied intensively in recent years and significant progresses have been achieved. Here, we study thermalization of small quantum systems that interact with large chaotic environments…

Statistical Mechanics · Physics 2019-06-05 Jiaozi Wang , Wen-ge Wang , Jiao Wang

This paper is about quantum heat defined as the change in energy of a bath during a process. The presentation takes into account recent developments in classical strong-coupling thermodynamics, and addresses a version of quantum heat which…

Statistical Mechanics · Physics 2018-06-13 Erik Aurell

The eigenstate thermalization hypothesis (ETH) describes the properties of diagonal and off-diagonal matrix elements of local operators in the eigenenergy basis. In this work, we propose a relation between (i) the singular behaviour of the…

Quantum Physics · Physics 2025-03-18 Luca Capizzi , Jiaozi Wang , Xiansong Xu , Leonardo Mazza , Dario Poletti

The phenomenon of quantum many-body scars (QMBS) has been studied both theoretically and experimentally, due to its unusual violation of the eigenstate thermalization hypothesis (ETH). In this paper, we extend the ETH to a new description…

Quantum Physics · Physics 2026-03-09 Jia-wei Wang , Xiang-Fa Zhou , Guang-Can Guo , Zheng-Wei Zhou

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…

Statistical Mechanics · Physics 2018-04-19 Fabio Anza , Christian Gogolin , Marcus Huber

An exact stochastic model for the thermalisation of quantum states is proposed. The model has various physically appealing properties. The dynamics are characterised by an underlying Schrodinger evolution, together with a nonlinear term…

Quantum Physics · Physics 2009-10-30 D. C. Brody , L. P. Hughston

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…

Quantum Physics · Physics 2022-10-14 Yunxiang Liao , Victor Galitski

The Eigenstate Thermalization Hypothesis (ETH) explains emergence of the thermodynamic equilibrium by assuming a particular structure of observable's matrix elements in the energy eigenbasis. Schematically, it postulates that off-diagonal…

Statistical Mechanics · Physics 2022-05-11 Jiaozi Wang , Mats H. Lamann , Jonas Richter , Robin Steinigeweg , Anatoly Dymarsky , Jochen Gemmer

The last decade has witnessed the remarkable progress in our understanding of thermalization in isolated quantum systems. Combining the eigenstate thermalization hypothesis with quantum measurement theory, we extend the framework of quantum…

Statistical Mechanics · Physics 2018-10-31 Yuto Ashida , Keiji Saito , Masahito Ueda

We discuss a qubit weakly coupled to a finite-size heat bath (calorimeter) from the point of view of quantum thermodynamics. The energy deposited to this environment together with the state of the qubit provides a basis to analyze the heat…

Mesoscale and Nanoscale Physics · Physics 2016-05-04 J. P. Pekola , S. Suomela , Y. M. Galperin

The eigenstate thermalization hypothesis (ETH) is foundational to modern discussions of thermalization in closed quantum systems. In this work, we expand on traditional explanations for the prevalence of ETH by emphasizing the role of…

Quantum Physics · Physics 2025-02-10 Stefan Eccles

We study thermalization in many-body quantum systems locally coupled to an external bath. It is shown that quantum chaotic systems do thermalize, that is, they exhibit relaxation to an invariant ergodic state which, in the bulk, is well…

Quantum Physics · Physics 2010-05-31 Marko Znidaric , Tomaz Prosen , Giuliano Benenti , Giulio Casati , Davide Rossini

Recently, there have been significant new insights concerning conditions under which closed systems equilibrate locally. The question if subsystems thermalize---if the equilibrium state is independent of the initial state---is however much…

Quantum Physics · Physics 2012-10-02 M. Cramer

The emergence of statistical mechanics from quantum dynamics is a central problem in quantum many-body physics. Deriving observables aligned with the prediction of the canonical ensemble for a quantum system relies on the presence of a bath…

Statistical Mechanics · Physics 2026-01-05 Nikolay V. Gnezdilov , Andrei I. Pavlov

Thermalization of a closed chaotic quantum system is commonly addressed in terms of the eigenstate thermalization hypothesis (ETH). An alternative approach uses the Bohigas-Giannoni-Schmit (BGS) conjecture. The comparison shows that the two…

Mathematical Physics · Physics 2025-09-29 Hans A. Weidenmüller

Temperature is a deceptively simple concept that still raises deep questions at the forefront of quantum physics research. The observation of thermalisation in completely isolated quantum systems, such as cold-atom quantum simulators,…

Quantum Physics · Physics 2022-03-09 Mark T. Mitchison , Archak Purkayastha , Marlon Brenes , Alessandro Silva , John Goold

Isolated quantum many-body systems which thermalize under their own dynamics are expected to act as their own thermal baths, thereby bringing their local subsystems to thermal equilibrium. Here we show that the infinite-dimensional limit of…

Strongly Correlated Electrons · Physics 2025-03-25 Antonio Picano , Giulio Biroli , Marco Schirò

The quantum thermalization of the Jaynes-Cummings (JC) model in both equilibrium and non-equilibrium open-system cases is sdudied, in which the two subsystems, a two-level system and a single-mode bosonic field, are in contact with either…

Quantum Physics · Physics 2020-08-04 Li-Bao Fan , Yue-Hui Zhou , Fen Zou , Huan Guo , Jin-Feng Huang , Jie-Qiao Liao
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