TY - JOUR T1 - Quantum Lyapunov Spectrum JF - JHEP04 Y1 - 2019 A1 - Hrant Gharibyan A1 - Masanori Hanada A1 - Brian Swingle A1 - Masaki Tezuka AB -

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. 

VL - 082 UR - https://arxiv.org/abs/1809.01671 U5 - https://doi.org/10.1007/JHEP04(2019)082 ER -