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:
-
- Univ. of Bristol (United Kingdom). School of Mathematics
- 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.
Blake, Mike, & Liu, Hong. On systems of maximal quantum chaos. United States. https://doi.org/10.1007/jhep05(2021)229
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.
@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}
}
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