Superluminal chaos after a quantum quench

Balasubramanian, Vijay; Craps, Ben; De Clerck, Marine; Nguyen, Kévin

doi:10.1007/jhep12(2019)132

Title: Superluminal chaos after a quantum quench

Journal Article · 16 December 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep12(2019)132 · OSTI ID:1800261

Balasubramanian, Vijay ^[1];

^[2]; De Clerck, Marine ^[2];

^[2]

Univ. of Pennsylvania, Philadelphia, PA (United States). David Rittenhouse Lab.; Vrije Universiteit Brussel (VUB) and The International Solvay Institutes, Brussels (Belgium). Theoretische Natuurkunde; OSTI
Vrije Universiteit Brussel (VUB) and The International Solvay Institutes, Brussels (Belgium). Theoretische Natuurkunde

Thermal states holographically dual to black holes in Einstein gravity display maximal Lyapunov growth as well as “butterfly effect cones”. We study these effects in highly non-equilibrium states, obtained from an initial thermal state by the sudden injection of energy. We do this by computing out-of-time-order correlators (OTOCs) in BTZ-Vaidya spacetimes, which describe transitions between black holes at different temperatures. If both pairs of boundary operators appearing in the OTOC are inserted before the energy injection, we recover standard results, with butterfly effect cones displaying a light-cone structure. But when one pair of operators is inserted before and the other pair after the energy injection, the Lyapunov growth saturates the chaos bounds set by the local temperatures and the butterfly effect cones can “open up”, becoming superluminal, albeit in a way that does not violate causality. In the limiting case, in which the initial state is the vacuum, Lyapunov growth only starts after the energy injection. Our computations of the OTOCs are phrased in terms of gravitationally interacting particles, where fields are treated in a geodesic approximation and the eikonal phase shift is expressed in terms of stress tensors and shock waves associated to geodesics.

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Research Organization:: Duke Univ., Durham, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-05ER41367

OSTI ID:: 1800261

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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