Quantum Lyapunov spectrum

  • Hrant Gharibyan
  • Masanori Hanada
  • Brian Swingle
  • Masaki TezukaEmail author
Open Access
Regular Article - Theoretical Physics


We introduce a simple quantum generalization of the spectrum of classical Lyapunov exponents. We apply it to the SYK and XXZ models, and study the Lyapunov growth and entropy production. Our numerical results suggest that a black hole is not just the fastest scrambler, but also the fastest entropy generator. We also study the statistical features of the quantum Lyapunov spectrum and find universal random matrix behavior, which resembles the recently-found universality in classical chaos. The random matrix behavior is lost when the system is deformed away from chaos, towards integrability or a many-body localized phase. We propose that quantum systems holographically dual to gravity satisfy this universality in a strong form. We further argue that the quantum Lyapunov spectrum contains important additional information beyond the largest Lyapunov exponent and hence provides us with a better characterization of chaos in quantum systems.


AdS-CFT Correspondence Field Theories in Lower Dimensions Random Systems 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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© The Author(s) 2019

Authors and Affiliations

  1. 1.Stanford Institute for Theoretical PhysicsStanford UniversityStanfordU.S.A.
  2. 2.Department of PhysicsUniversity of ColoradoBoulderU.S.A.
  3. 3.Condensed Matter Theory Center, Maryland Center for Fundamental Physics, Joint Center for Quantum Information and Computer Science, and Department of PhysicsUniversity of MarylandCollege ParkU.S.A.
  4. 4.Department of PhysicsKyoto UniversityKyotoJapan

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