Superluminal chaos after a quantum quench
Abstract 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 comput...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-12-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2019)132 |
| _version_ | 1818844681240313856 |
|---|---|
| author | Vijay Balasubramanian Ben Craps Marine De Clerck Kévin Nguyen |
| author_facet | Vijay Balasubramanian Ben Craps Marine De Clerck Kévin Nguyen |
| author_sort | Vijay Balasubramanian |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-12-19T05:17:38Z |
| format | Article |
| id | doaj.art-2b884ba3150642039b4661b47c904455 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-19T05:17:38Z |
| publishDate | 2019-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-2b884ba3150642039b4661b47c9044552022-12-21T20:34:37ZengSpringerOpenJournal of High Energy Physics1029-84792019-12-0120191214110.1007/JHEP12(2019)132Superluminal chaos after a quantum quenchVijay Balasubramanian0Ben Craps1Marine De Clerck2Kévin Nguyen3David Rittenhouse Laboratory, University of PennsylvaniaTheoretische Natuurkunde, Vrije Universiteit Brussel (VUB) and The International Solvay InstitutesTheoretische Natuurkunde, Vrije Universiteit Brussel (VUB) and The International Solvay InstitutesTheoretische Natuurkunde, Vrije Universiteit Brussel (VUB) and The International Solvay InstitutesAbstract 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.https://doi.org/10.1007/JHEP12(2019)132AdS-CFT CorrespondenceGauge-gravity correspondence |
| spellingShingle | Vijay Balasubramanian Ben Craps Marine De Clerck Kévin Nguyen Superluminal chaos after a quantum quench Journal of High Energy Physics AdS-CFT Correspondence Gauge-gravity correspondence |
| title | Superluminal chaos after a quantum quench |
| title_full | Superluminal chaos after a quantum quench |
| title_fullStr | Superluminal chaos after a quantum quench |
| title_full_unstemmed | Superluminal chaos after a quantum quench |
| title_short | Superluminal chaos after a quantum quench |
| title_sort | superluminal chaos after a quantum quench |
| topic | AdS-CFT Correspondence Gauge-gravity correspondence |
| url | https://doi.org/10.1007/JHEP12(2019)132 |
| work_keys_str_mv | AT vijaybalasubramanian superluminalchaosafteraquantumquench AT bencraps superluminalchaosafteraquantumquench AT marinedeclerck superluminalchaosafteraquantumquench AT kevinnguyen superluminalchaosafteraquantumquench |