Quantum chaos and entanglement in ergodic and nonergodic systems

Angelo Piga, Maciej Lewenstein, and James Q. Quach
Phys. Rev. E 99, 032213 – Published 15 March 2019

Abstract

We study entanglement entropy (EE) as a signature of quantum chaos in ergodic and nonergodic systems. In particular we look at the quantum kicked top and kicked rotor as multispin systems and investigate the single-spin EE which characterizes bipartite entanglement of this spin with the rest of the system. We study the correspondence of the Kolmogorov-Sinai entropy of the classical kicked systems with the EE of their quantum counterparts. We find that EE is a signature of global chaos in ergodic systems and local chaos in nonergodic systems. In particular, we show that EE can be maximized even when systems are highly nonergodic, when the corresponding classical system is locally chaotic. In contrast, we find evidence that the quantum analog of Kolmogorov-Arnol'd-Moser (KAM) tori are tori of low entanglement entropy. We conjecture that entanglement should play an important role in any quantum KAM theory.

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  • Received 9 May 2018

DOI:https://doi.org/10.1103/PhysRevE.99.032213

©2019 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsQuantum Information, Science & Technology

Authors & Affiliations

Angelo Piga1, Maciej Lewenstein1,2, and James Q. Quach1,3,*

  • 1ICFO–Institut de Ciències Fotòniques, Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain
  • 2ICREA, Pg. Lluis Companys 23, ES-08010 Barcelona, Spain
  • 3Institute for Photonics and Advanced Sensing and School of Chemistry and Physics, University of Adelaide, South Australia 5005, Australia

  • *quach.james@gmail.com

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Vol. 99, Iss. 3 — March 2019

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