Dahlem Center for Complex Quantum Systems, Freie Universitat Berlin, 14195 Berlin, Germany. ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany.
Rep Prog Phys. 2016 May;79(5):056001. doi: 10.1088/0034-4885/79/5/056001. Epub 2016 Apr 18.
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.
我们回顾了在复杂量子多体系统的理论理解方面的一些进展，这些进展涉及到新兴的量子统计力学概念。我们涵盖了纯态统计力学中的平衡和热化、本征态热化假设、系综等价性、全局和局部淬火以及斜坡后的非平衡动力学等主题。我们还讨论了初始状态独立性、热化缺失和多体局域化。我们阐明了这些现象的关键概念所扮演的角色，例如 Lieb-Robinson 边界、纠缠增长、典型性论证、量子最大熵原理和广义 Gibbs 系综以及量子（非）可积性。我们强调了严格的方法，并以统一的语言呈现了最重要的结果。
