期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 11, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP11(2017)048
关键词
AdS-CFT Correspondence; Black Holes; Matrix Models; Random Systems
资金
- Fannie and John Hertz Foundation
- Stanford Graduate Fellowship program
- Simons Foundation through the It from Qubit collaboration
- Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NSF) [PHY-1125565]
- Gordon and Betty Moore Foundation [GBMF-2644]
- U.S. Department of Energy, Office of Science, Office of High Energy Physics [DE-SC0011632]
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Research and Innovation
- Direct For Mathematical & Physical Scien
- Division Of Physics [1125565] Funding Source: National Science Foundation
Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians and analytically compute out-of-time-ordered correlation functions (OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and circuit complexity. While our random matrix analysis gives a qualitatively correct prediction of the late-time behavior of chaotic systems, we find unphysical behavior at early times including an O(1) scrambling time and the apparent breakdown of spatial and temporal locality. The salient feature of GUE Hamiltonians which gives us computational traction is the Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics look the same in any basis. Motivated by this property of the GUE, we introduce k-invariance as a precise definition of what it means for the dynamics of a quantum system to be described by random matrix theory. We envision that the dynamical onset of approximate k-invariance will be a useful tool for capturing the transition from early-time chaos, as seen by OTOCs, to late-time chaos, as seen by random matrix theory.
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