A quantum hydrodynamical description for scrambling and many-body chaos
Recent studies of out-of-time ordered thermal correlation functions (OTOC) in holographic systems and in solvable models such as the Sachdev-Ye-Kitaev (SYK) model have yielded new insights into manifestations of many-body chaos. So far the chaotic behavior has been obtained through explicit calculat...
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2018
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| Online Access: | http://hdl.handle.net/1721.1/118909 https://orcid.org/0000-0002-4911-3183 |
| _version_ | 1826206279584972800 |
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| author | Blake, Michael Andrew Lee, Hyunseok Liu, Hong |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Blake, Michael Andrew Lee, Hyunseok Liu, Hong |
| author_sort | Blake, Michael Andrew |
| collection | MIT |
| description | Recent studies of out-of-time ordered thermal correlation functions (OTOC) in holographic systems and in solvable models such as the Sachdev-Ye-Kitaev (SYK) model have yielded new insights into manifestations of many-body chaos. So far the chaotic behavior has been obtained through explicit calculations in specific models. In this paper we propose a unified description of the exponential growth and ballistic butterfly spreading of OTOCs across different systems using a newly formulated “quantum hydrodynamics,” which is valid at finite ℏ and to all orders in derivatives. The scrambling of a generic few-body operator in a chaotic system is described as building up a “hydrodynamic cloud,” and the exponential growth of the cloud arises from a shift symmetry of the hydrodynamic action. The shift symmetry also shields correlation functions of the energy density and flux, and time ordered correlation functions of generic operators from exponential growth, while leads to chaotic behavior in OTOCs. The theory also predicts an interesting phenomenon of the skipping of a pole at special values of complex frequency and momentum in two-point functions of energy density and flux. This pole-skipping phenomenon may be considered as a “smoking gun” for the hydrodynamic origin of the chaotic mode. We also discuss the possibility that such a hydrodynamic description could be a hallmark of maximally chaotic systems. Keywords: Effective Field Theories, Gauge-gravity correspondence, Quantum Dissipative Systems |
| first_indexed | 2024-09-23T13:26:57Z |
| format | Article |
| id | mit-1721.1/118909 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:26:57Z |
| publishDate | 2018 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1189092022-09-28T14:20:05Z A quantum hydrodynamical description for scrambling and many-body chaos Blake, Michael Andrew Lee, Hyunseok Liu, Hong Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Laboratory for Nuclear Science Blake, Michael Andrew Lee, Hyunseok Liu, Hong Recent studies of out-of-time ordered thermal correlation functions (OTOC) in holographic systems and in solvable models such as the Sachdev-Ye-Kitaev (SYK) model have yielded new insights into manifestations of many-body chaos. So far the chaotic behavior has been obtained through explicit calculations in specific models. In this paper we propose a unified description of the exponential growth and ballistic butterfly spreading of OTOCs across different systems using a newly formulated “quantum hydrodynamics,” which is valid at finite ℏ and to all orders in derivatives. The scrambling of a generic few-body operator in a chaotic system is described as building up a “hydrodynamic cloud,” and the exponential growth of the cloud arises from a shift symmetry of the hydrodynamic action. The shift symmetry also shields correlation functions of the energy density and flux, and time ordered correlation functions of generic operators from exponential growth, while leads to chaotic behavior in OTOCs. The theory also predicts an interesting phenomenon of the skipping of a pole at special values of complex frequency and momentum in two-point functions of energy density and flux. This pole-skipping phenomenon may be considered as a “smoking gun” for the hydrodynamic origin of the chaotic mode. We also discuss the possibility that such a hydrodynamic description could be a hallmark of maximally chaotic systems. Keywords: Effective Field Theories, Gauge-gravity correspondence, Quantum Dissipative Systems United States. Department of Energy. Office of High Energy and Nuclear Physics (DE-SC0012567) 2018-11-06T14:45:58Z 2018-11-06T14:45:58Z 2018-10 2018-10 2018-10-24T04:08:36Z Article http://purl.org/eprint/type/JournalArticle 1029-8479 http://hdl.handle.net/1721.1/118909 Blake, Mike, et al. “A Quantum Hydrodynamical Description for Scrambling and Many-Body Chaos.” Journal of High Energy Physics, vol. 2018, no. 10, Oct. 2018. © 2018 The Authors https://orcid.org/0000-0002-4911-3183 en https://doi.org/10.1007/JHEP10(2018)127 Journal of High Energy Physics Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Blake, Michael Andrew Lee, Hyunseok Liu, Hong A quantum hydrodynamical description for scrambling and many-body chaos |
| title | A quantum hydrodynamical description for scrambling and many-body chaos |
| title_full | A quantum hydrodynamical description for scrambling and many-body chaos |
| title_fullStr | A quantum hydrodynamical description for scrambling and many-body chaos |
| title_full_unstemmed | A quantum hydrodynamical description for scrambling and many-body chaos |
| title_short | A quantum hydrodynamical description for scrambling and many-body chaos |
| title_sort | quantum hydrodynamical description for scrambling and many body chaos |
| url | http://hdl.handle.net/1721.1/118909 https://orcid.org/0000-0002-4911-3183 |
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