Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems

By Christian Gogolin, Jens Eisert. Reports on progress in physics. Physical Society, 2015

959 citations recorded by the source corpus.

We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb–Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/959a461883601a615434148f9b98b0f599f20626

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In Artificial Intelligence

1. A. Nahum
2. Matthew Fisher
3. V. Khemani
4. S. Vijay
5. Thierry Lahaye
6. Frank Pollmann
7. Tibor Rakovszky
8. Antoine Browaeys

In Atomic and Molecular Physics, and Optics

1. V. Khemani
2. A. Nahum
3. Matthew Fisher
4. S. Vijay
5. Frank Pollmann
6. Tibor Rakovszky
7. R. Verresen
8. V. Ros

In Statistical and Nonlinear Physics

1. A. Nahum
2. V. Khemani
3. S. Vijay
4. Matthew Fisher
5. John Goold
6. J. de Boer
7. Mehul Malik
8. Pablo Sala

Citations in the corpus

• Random Quantum Circuits (2022, background): “The possibility of highly coherent and controllable Hamiltonian dynamics has led to important questions about universality in the approach to thermal equilibrium (34, 1), and situations in which quenched disorder can arrest thermalization entirely via the phenomenon of many-body localization (MBL) (”
• Quantum computing with neutral atoms (2020, background): “It can be used to introduce controllable disorder, which is known to dramatically influence the behaviour of many-body systems [42, 43, 44, 45].”
• Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics (2017, background): “lly constrained models, Refs. [8, 9]; for large deviations, Refs. [10, 11, 12]. In the case of quantum systems, comprehensive recent reviews on thermalisation and many-body localisation include Refs. [13, 14, 15]; and on open quantum systems, Refs. [16, 17, 18, 19]. The selection of topics, many of ”
• Entanglement certification from theory to experiment (2018, methodology): “[190] Christian Gogolin and Jens Eisert, “Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems,” Rep.”
• Statistical localization: From strong fragmentation to strong edge modes (2019, background): “[8] Christian Gogolin and Jens Eisert, “Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems,” Reports on Progress in Physics”
• The role of quantum information in thermodynamics—a topical review (2015, background): “To complete the picture presented here we recommend the article [28] where an extensive review of the literature on foundations of statistical mechanics is provided.”
• Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians (2019, background): “[8] Christian Gogolin and Jens Eisert, “Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems,” Reports on Progress in Physics 79, 056001 (2016).”