Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: On systems of maximal quantum chaos

Abstract

A remarkable feature of chaos in many-body quantum systems is the existence of a bound on the quantum Lyapunov exponent. An important question is to understand what is special about maximally chaotic systems which saturate this bound. Here we provide further evidence for the ‘hydrodynamic’ origin of chaos in such systems, and discuss hallmarks of maximally chaotic systems. We first provide evidence that a hydrodynamic effective field theory of chaos we previously proposed should be understood as a theory of maximally chaotic systems. We then emphasize and make explicit a signature of maximal chaos which was only implicit in prior literature, namely the suppression of exponential growth in commutator squares of generic few-body operators. We provide a general argument for this suppression within our chaos effective field theory, and illustrate it using SYK models and holographic systems. We speculate that this suppression indicates that the nature of operator scrambling in maximally chaotic systems is fundamentally different to scrambling in non-maximally chaotic systems. We also discuss a simplest scenario for the existence of a maximally chaotic regime at sufficiently large distances even for non-maximally chaotic systems.

Authors:
 [1];  [2]
+ Show Author Affiliations
  1. Univ. of Bristol (United Kingdom). School of Mathematics
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1851674
Grant/Contract Number:  
SC0012567
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2021; Journal Issue: 5; Journal ID: ISSN 1029-8479
Publisher:
Springer Nature
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; physics; AdS-CFT correspondence; effective field theories; gauge-gravity correspondence

Citation Formats

Blake, Mike, and Liu, Hong. On systems of maximal quantum chaos. United States: N. p., 2021. Web. doi:10.1007/jhep05(2021)229.
Copy to clipboard
Blake, Mike, & Liu, Hong. On systems of maximal quantum chaos. United States. https://doi.org/10.1007/jhep05(2021)229
Copy to clipboard
Blake, Mike, and Liu, Hong. Tue . "On systems of maximal quantum chaos". United States. https://doi.org/10.1007/jhep05(2021)229. https://www.osti.gov/servlets/purl/1851674.
Copy to clipboard
@article{osti_1851674,
title = {On systems of maximal quantum chaos},
author = {Blake, Mike and Liu, Hong},
abstractNote = {A remarkable feature of chaos in many-body quantum systems is the existence of a bound on the quantum Lyapunov exponent. An important question is to understand what is special about maximally chaotic systems which saturate this bound. Here we provide further evidence for the ‘hydrodynamic’ origin of chaos in such systems, and discuss hallmarks of maximally chaotic systems. We first provide evidence that a hydrodynamic effective field theory of chaos we previously proposed should be understood as a theory of maximally chaotic systems. We then emphasize and make explicit a signature of maximal chaos which was only implicit in prior literature, namely the suppression of exponential growth in commutator squares of generic few-body operators. We provide a general argument for this suppression within our chaos effective field theory, and illustrate it using SYK models and holographic systems. We speculate that this suppression indicates that the nature of operator scrambling in maximally chaotic systems is fundamentally different to scrambling in non-maximally chaotic systems. We also discuss a simplest scenario for the existence of a maximally chaotic regime at sufficiently large distances even for non-maximally chaotic systems.},
doi = {10.1007/jhep05(2021)229},
journal = {Journal of High Energy Physics (Online)},
number = 5,
volume = 2021,
place = {United States},
year = {Tue May 25 00:00:00 EDT 2021},
month = {Tue May 25 00:00:00 EDT 2021}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1007/jhep05(2021)229
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Diffusion and chaos from near AdS2 horizons
journal, February 2017

Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos
journal, October 2018

Slow scrambling in disordered quantum systems
journal, February 2017

Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory
journal, September 2015

A quantum hydrodynamical description for scrambling and many-body chaos
journal, October 2018

  • Blake, Mike; Lee, Hyunseok; Liu, Hong
  • Journal of High Energy Physics, Vol. 2018, Issue 10
  • DOI: 10.1007/JHEP10(2018)127

A bound on chaos
journal, August 2016

  • Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)106

Chaos in the butterfly cone
journal, January 2020

Effective field theory of dissipative fluids
journal, September 2017

  • Crossley, Michael; Glorioso, Paolo; Liu, Hong
  • Journal of High Energy Physics, Vol. 2017, Issue 9
  • DOI: 10.1007/JHEP09(2017)095

Effective field theory of dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current
journal, September 2017

  • Glorioso, Paolo; Crossley, Michael; Liu, Hong
  • Journal of High Energy Physics, Vol. 2017, Issue 9
  • DOI: 10.1007/JHEP09(2017)096

The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
journal, May 2018

  • Kitaev, Alexei; Suh, S. Josephine
  • Journal of High Energy Physics, Vol. 2018, Issue 5
  • DOI: 10.1007/JHEP05(2018)183

On CFT and quantum chaos
journal, December 2016

  • Turiaci, Gustavo J.; Verlinde, Herman
  • Journal of High Energy Physics, Vol. 2016, Issue 12
  • DOI: 10.1007/JHEP12(2016)110

Black holes and the butterfly effect
journal, March 2014

  • Shenker, Stephen H.; Stanford, Douglas
  • Journal of High Energy Physics, Vol. 2014, Issue 3
  • DOI: 10.1007/JHEP03(2014)067

Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
journal, May 2017

  • Gu, Yingfei; Qi, Xiao-Liang; Stanford, Douglas
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)125

On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections
journal, January 2019

On the relation between the magnitude and exponent of OTOCs
journal, February 2019

Thermal diffusivity and chaos in metals without quasiparticles
journal, November 2017

Stringy effects in scrambling
journal, May 2015

  • Shenker, Stephen H.; Stanford, Douglas
  • Journal of High Energy Physics, Vol. 2015, Issue 5
  • DOI: 10.1007/JHEP05(2015)132

Universal diffusion in incoherent black holes
journal, October 2016

Analyticity in spin in conformal theories
journal, September 2017

Pole-skipping of scalar and vector fields in hyperbolic space: conformal blocks and holography
journal, September 2020

  • Ahn, Yongjun; Jahnke, Viktor; Jeong, Hyun-Sik
  • Journal of High Energy Physics, Vol. 2020, Issue 9
  • DOI: 10.1007/JHEP09(2020)111

Many-body chaos and energy dynamics in holography
journal, October 2018

  • Blake, Mike; Davison, Richard A.; Grozdanov, Sašo
  • Journal of High Energy Physics, Vol. 2018, Issue 10
  • DOI: 10.1007/JHEP10(2018)035

Microscopic model of quantum butterfly effect: Out-of-time-order correlators and traveling combustion waves
journal, December 2016

Black Hole Scrambling from Hydrodynamics
journal, June 2018

Operator growth in the SYK model
journal, June 2018

  • Roberts, Daniel A.; Stanford, Douglas; Streicher, Alexandre
  • Journal of High Energy Physics, Vol. 2018, Issue 6
  • DOI: 10.1007/JHEP06(2018)122

Localized shocks
journal, March 2015

  • Roberts, Daniel A.; Stanford, Douglas; Susskind, Leonard
  • Journal of High Energy Physics, Vol. 2015, Issue 3
  • DOI: 10.1007/JHEP03(2015)051

Effective field theory for chaotic CFTs
journal, October 2018

Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs
journal, November 2019

  • Haehl, Felix M.; Reeves, Wyatt; Rozali, Moshe
  • Journal of High Energy Physics, Vol. 2019, Issue 11
  • DOI: 10.1007/JHEP11(2019)102

Onset of many-body chaos in the O ( N ) model
journal, September 2017

Scrambling in hyperbolic black holes: shock waves and pole-skipping
journal, October 2019

  • Ahn, Yongjun; Jahnke, Viktor; Jeong, Hyun-Sik
  • Journal of High Energy Physics, Vol. 2019, Issue 10
  • DOI: 10.1007/JHEP10(2019)257

Quantum chaos on a critical Fermi surface
journal, February 2017

  • Patel, Aavishkar A.; Sachdev, Subir
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 8
  • DOI: 10.1073/pnas.1618185114

Universal Charge Diffusion and the Butterfly Effect in Holographic Theories
journal, August 2016

    Sort by:
    [ × clear filter / sort ]

    Similar Records in DOE PAGES and OSTI.GOV collections: