TY - JOUR
T1 - On the evolution of operator complexity beyond scrambling
AU - Barbón, J. L.F.
AU - Rabinovici, E.
AU - Shir, R.
AU - Sinha, R.
N1 - Publisher Copyright:
© 2019, The Author(s).
PY - 2019/10/1
Y1 - 2019/10/1
N2 - 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.
AB - 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.
KW - AdS-CFT Correspondence
KW - Random Systems
UR - http://www.scopus.com/inward/record.url?scp=85074299618&partnerID=8YFLogxK
U2 - 10.1007/JHEP10(2019)264
DO - 10.1007/JHEP10(2019)264
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AN - SCOPUS:85074299618
SN - 1126-6708
VL - 2019
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 10
M1 - 264
ER -