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Title: A quantum hydrodynamical description for scrambling and many-body chaos

Abstract

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. Here, we alsomore » discuss the possibility that such a hydrodynamic description could be a hallmark of maximally chaotic systems.« less

Authors:
 [1];  [1];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1483400
Grant/Contract Number:  
SC0012567
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Volume: 2018; Journal Issue: 10; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Effective Field Theories; Gauge-gravity correspondence; Quantum Dissipative Systems

Citation Formats

Blake, Mike, Lee, Hyunseok, and Liu, Hong. A quantum hydrodynamical description for scrambling and many-body chaos. United States: N. p., 2018. Web. doi:10.1007/JHEP10(2018)127.
Blake, Mike, Lee, Hyunseok, & Liu, Hong. A quantum hydrodynamical description for scrambling and many-body chaos. United States. doi:10.1007/JHEP10(2018)127.
Blake, Mike, Lee, Hyunseok, and Liu, Hong. Fri . "A quantum hydrodynamical description for scrambling and many-body chaos". United States. doi:10.1007/JHEP10(2018)127. https://www.osti.gov/servlets/purl/1483400.
@article{osti_1483400,
title = {A quantum hydrodynamical description for scrambling and many-body chaos},
author = {Blake, Mike and Lee, Hyunseok and Liu, Hong},
abstractNote = {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. Here, we also discuss the possibility that such a hydrodynamic description could be a hallmark of maximally chaotic systems.},
doi = {10.1007/JHEP10(2018)127},
journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 10,
volume = 2018,
place = {United States},
year = {2018},
month = {10}
}

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