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Title: Butterflies from information metric
Authors: Miyaji, Masamichi
Keywords: 1/N Expansion
AdS-CFT Correspondence
Black Holes
Conformal Field Theory
Issue Date: 1-Sep-2016
Publisher: Springer Nature
Journal title: Journal of High Energy Physics
Volume: 2016
Thesis number: 2
Abstract: We study time evolution of distance between thermal states excited by local operators, with different external couplings. We find that growth of the distance implies growth of commutators of operators, signifying the local excitations are scrambled. We confirm this growth of distance by holographic computation, by evaluating volume of codimension 1 extremal volume surface. We find that the distance increases exponentially as e_2πt/β. Our result implies that, in chaotic system, trajectories of excited thermal states exhibit high sensitivity to perturbation to the Hamiltonian, and the distance between them will be significant at the scrambling time. We also confirm the decay of two point function of holographic Wilson loops on thermofield double state.
Rights: © 2016, The Author(s). JHEP is an open-access journal funded by SCOAP3 and licensed under CC BY 4.0
DOI(Published Version): 10.1007/JHEP09(2016)002
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