Journal of High Energy Physics

, 2019:264 | Cite as

On the evolution of operator complexity beyond scrambling

  • J.L.F. BarbónEmail author
  • E. Rabinovici
  • R. Shir
  • R. Sinha
Open Access
Regular Article - Theoretical Physics


We study operator complexity on various time scales with emphasis on those much larger than the scrambling period. We use, for systems with a large but finite number of degrees of freedom, the notion of K-complexity employed in [1] for infinite systems. We present evidence that K-complexity of ETH operators has indeed the character associated with the bulk time evolution of extremal volumes and actions. Namely, after a period of exponential growth during the scrambling period the K-complexity increases only linearly with time for exponentially long times in terms of the entropy, and it eventually saturates at a constant value also exponential in terms of the entropy. This constant value depends on the Hamiltonian and the operator but not on any extrinsic tolerance parameter. Thus K-complexity deserves to be an entry in the AdS/CFT dictionary. Invoking a concept of K-entropy and some numerical examples we also discuss the extent to which the long period of linear complexity growth entails an efficient randomization of operators.


AdS-CFT Correspondence Random Systems 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • J.L.F. Barbón
    • 1
    Email author
  • E. Rabinovici
    • 2
    • 3
  • R. Shir
    • 2
  • R. Sinha
    • 1
  1. 1.Instituto de Fisica Teorica IFT-UAM/CSICMadridSpain
  2. 2.Racah InstituteThe Hebrew UniversityJerusalemIsrael
  3. 3.Institut des Hautes Etudes ScientifiquesBures-sur-YvetteFrance

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