2015/03/31 by C. Gogolin, J. Eisert · 1 citation
Physics and Astronomy · Mathematics · #quant-ph #cond-mat.dis-nn #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1088/0034-4885/79/5/056001
published as Rep. Prog. Phys. 79, 056001 (2016) · 114 pages, 6 figures, 429 references, version as published with minor typos corrected, updated funding sources in acknowledgements to those of the published version to fulfill requirements of Marie Sklodowska-Curie grant
arxiv created 2018/06/13 · arxiv updated 2018/06/14
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.