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In an isolated quantum many-body system undergoing unitary evolution, we study the thermalization of a subsystem, treating the rest of the system as a bath. In this setting, the eigenstate thermalization hypothesis (ETH) was proposed to…

Statistical Mechanics · Physics 2023-11-30 Aram W. Harrow , Yichen Huang

We investigate steady states of macroscopic quantum systems under dissipation not obeying the detailed balance condition. We argue that the Gibbs state at an effective temperature gives a good description of the steady state provided that…

Statistical Mechanics · Physics 2020-04-17 Tatsuhiko Shirai , Takashi Mori

Under the Eigenstate Thermalization Hypothesis (ETH), quantum-quenched systems equilibrate towards canonical, thermal ensembles. While at first glance the ETH might seem a very strong hypothesis, we show that it is indeed not only…

Quantum Physics · Physics 2016-02-03 Giacomo De Palma , Alessio Serafini , Vittorio Giovannetti , Marcus Cramer

Understanding how an isolated quantum system evolves toward a thermal state from an initial state far from equilibrium such as one prepared by a global quantum quench has attracted significant interest in recent years. This phenomenon can…

High Energy Physics - Theory · Physics 2025-01-23 Mohsen Alishahiha , Mohammad Javad Vasli

There is a dichotomy in the nonequilibrium dynamics of quantum many body systems. In the presence of integrability, expectation values of local operators equilibrate to values described by a generalized Gibbs ensemble, which retains…

Strongly Correlated Electrons · Physics 2019-05-15 Neil J. Robinson , Andrew J. A. James , Robert M. Konik

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…

The eigenstate thermalization hypothesis (ETH) posits how isolated quantum many-body systems thermalize, assuming that individual eigenstates at the same energy density have identical expectation values of local observables in the limit of…

Statistical Mechanics · Physics 2026-01-14 Maksym Serbyn , Alexander Avdoshkin , Oriana K. Diessel , David A. Huse

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…

Statistical Mechanics · Physics 2015-05-29 Peter Reimann

An isolated quantum many-body system in an initial pure state will come to thermal equilibrium if it satisfies the eigenstate thermalization hypothesis (ETH). We consider alternatives to ETH that have been proposed. We first show that von…

Statistical Mechanics · Physics 2012-03-15 Marcos Rigol , Mark Srednicki

The eigenstate thermalization hypothesis (ETH), which asserts that every eigenstate of a many-body quantum system is indistinguishable from a thermal ensemble, plays a pivotal role in understanding thermalization of isolated quantum…

Statistical Mechanics · Physics 2025-05-27 Shoki Sugimoto , Ryusuke Hamazaki , Masahito Ueda

Understanding the evolution towards thermal equilibrium of an isolated quantum system is at the foundation of statistical mechanics and a subject of interest in such diverse areas as cold atom physics or the quantum mechanics of black…

Statistical Mechanics · Physics 2014-03-13 Sergei Khlebnikov , Martin Kruczenski

If and how an isolated quantum system thermalizes despite its unitary time evolution is a long-standing, open problem of many-body physics. The eigenstate thermalization hypothesis (ETH) postulates that thermalization happens at the level…

Quantum Gases · Physics 2018-11-06 Anna Posazhennikova , Mauricio Trujillo-Martinez , Johann Kroha

The Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. However, its connection to the timescale of thermalization for open system dynamics has remained…

Quantum Physics · Physics 2023-03-30 Chi-Fang Chen , Fernando G. S. L. Brandão

The eigenstate thermalization hypothesis (ETH) provides a powerful framework for understanding thermalization in isolated quantum many-body systems, yet a complete and conceptually transparent derivation has remained elusive. In this work,…

Statistical Mechanics · Physics 2025-12-23 Yucheng Wang

The eigenstate thermalization hypothesis (ETH) insists that for nonintegrable systems each energy eigenstate accurately gives microcanonical expectation values for a class of observables. As a mechanism for ETH to hold, we show that the…

Statistical Mechanics · Physics 2018-05-15 Takaaki Monnai

If we prepare an isolated, interacting quantum system in an eigenstate and perturb a local observable at an initial time, its expectation value will relax towards a thermal expectation value, even though the time evolution of the system is…

Quantum Physics · Physics 2024-06-04 Tobias Helbig , Tobias Hofmann , Ronny Thomale , Martin Greiter

We consider the set of all initial states within a microcanonical energy shell of an isolated many-body quantum system, which exhibit the same, arbitrary but fixed non-equilibrium expectation value for some given observable $A$. On…

Statistical Mechanics · Physics 2018-07-04 Peter Reimann

A class of autonomous quantum heat baths satisfying the eigenstate thermalization hypothesis (ETH) criteria is proposed. We show that such systems are expected to cause thermal relaxation of much smaller quantum systems coupled to one of…

Quantum Physics · Physics 2015-08-10 O. Fialko

Eigenstate thermalization hypothesis (ETH) is discussed. We show that one common formulation of ETH does not necessarily imply thermalization of an observable of isolated many body quantum system. To get thermalization one has to postulate…

Statistical Mechanics · Physics 2020-02-06 Oleg Inozemcev , Igor Volovich

The Eigenstate Thermalization Hypothesis (ETH) has played a key role in recent advances in the high energy and condensed matter communities. It explains how an isolated quantum system in a far-from-equilibrium initial state can evolve to a…

Quantum Physics · Physics 2026-04-14 Elena Cáceres , Stefan Eccles , Jason Pollack , Sarah Racz
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