On systems of maximal quantum chaos

Blake, Mike; Liu, Hong

doi:10.1007/jhep05(2021)229

On systems of maximal quantum chaos

Journal Article · Tue May 25 00:00:00 EDT 2021 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep05(2021)229· OSTI ID:1851674

Blake, Mike ^[1]; Liu, Hong ^[2]

Univ. of Bristol (United Kingdom). School of Mathematics; Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics

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.

View Accepted Manuscript (DOE)

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0012567

OSTI ID:: 1851674

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 5 Vol. 2021; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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