Quantum Lyapunov spectrum

Gharibyan, Hrant (0000000419368956, Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA, 94305, U.S.A.) ; Hanada, Masanori (0000000096214564, Department of Physics, University of Colorado, Boulder, Colorado, 80309, U.S.A.) ; Swingle, Brian (0000 0001 0941 7177, Condensed Matter Theory Center, Maryland Center for Fundamental Physics, Joint Center for Quantum Information and Computer Science, and Department of Physics, University of Maryland, College Park, MD, 20742, U.S.A.) ; Tezuka, Masaki (0000 0004 0372 2033, Department of Physics, Kyoto University, Kyoto, 606-8502, Japan)

12 April 2019

Abstract: 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.

Published in: JHEP 1904 (2019) 082
Published by: Springer/SISSA
DOI: 10.1007/JHEP04(2019)082
arXiv: 1809.01671
License: CC-BY-4.0

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