Eur. Phys. J. Special Topics 227, 1897–1910 (2019)
https://doi.org/10.1140/epjst/e2019-800057-8

Review

Signatures of chaos and thermalization in the dynamics of many-body quantum systems

¹ Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apt. Postal J-48, Puebla, Puebla 72570, Mexico
² Department of Physics, Yeshiva University, New York, NY 10016, USA

^a e-mail: lsantos2@yu.edu

Received: 14 April 2018
Received in final form: 21 June 2018
Published online: 13 February 2019

Abstract

We extend the results of two of our papers [Phys. Rev. A 94, 041603R (2016) and Phys. Rev. B 97, 060303R (2018)] that touch upon the intimately connected topics of quantum chaos and thermalization. In the first, we argued that when the initial state of isolated lattice many-body quantum systems is chaotic, the power-law decay of the survival probability is caused by the bounds in the spectrum, which thus anticipates thermalization. In the current work, we provide stronger numerical support for the onset of these algebraic behaviors. In the second paper, we demonstrated that the correlation hole, which is a direct signature of quantum chaos revealed by the evolution of the survival probability at times beyond the power-law decay, appears also for other observables. In the present work, we investigate the correlation hole in the chaotic regime and in the vicinity to a many-body localized phase for the spin density imbalance, which is an observable studied experimentally.