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.

arXiv comment28 pages, 3 figures, v2: minor clarification added, v3: typos corrected

References in corpus (34)

• A bound on chaos
• Comments on the Sachdev-Ye-Kitaev model
• Black holes and the butterfly effect
• Operator Spreading in Random Unitary Circuits
• Chaos in AdS${}_2$ holography
• Localized shocks
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Analyticity in Spin in Conformal Theories
• Two-dimensional conformal field theory and the butterfly effect
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Universal Charge Diffusion and the Butterfly Effect
• Slow scrambling in disordered quantum systems
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Operator growth in the SYK model
• A quantum hydrodynamical description for scrambling and many-body chaos
• Black hole scrambling from hydrodynamics
• Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
• Many-body chaos and energy dynamics in holography
• Quantum chaos on a critical Fermi surface
• Onset of many-body chaos in the $O(N)$ model
• Thermal diffusivity and chaos in metals without quasiparticles
• Universal Diffusion in Incoherent Black Holes
• Effective field theory for dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current
• Effective Field Theory for Chaotic CFTs
• Diffusion and Chaos from near AdS${}_2$ horizons
• On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections
• On the relation between the magnitude and exponent of OTOCs
• On CFT and Quantum Chaos
• Scrambling in Hyperbolic Black Holes: shock waves and pole-skipping
• Chaos in the butterfly cone
• Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs
• Pole-skipping of scalar and vector fields in hyperbolic space: conformal blocks and holography

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• Planckian Dissipation in Metals
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• Chaos bound and its violation in charged Kiselev black hole
• Chaos in a many-string scattering amplitude
• Chaos and pole-skipping in a simply spinning plasma
• Pole-skipping of gravitational waves in the backgrounds of four-dimensional massive black holes
• Angular momentum and chaos bound of charged particles around Einstein-Euler-Heisenberg AdS black holes
• Seeing behind black hole horizons in SYK
• Pole skipping in holographic theories with gauge and fermionic fields
• Subleading Bounds on Chaos
• Pole-Skipping in Rotating BTZ Black Holes
• T-linear resistivity, optical conductivity and Planckian transport for a holographic local quantum critical metal in a periodic potential
• Construction of bulk solutions for towers of pole-skipping points
• Fast Scrambling due to Rotating Shockwaves in BTZ
• Extremal Chaos
• Effective description of sub-maximal chaos: stringy effects for SYK scrambling
• Fast Scrambling of Mutual Information in Kerr-AdS${}_4$
• On pole-skipping with gauge-invariant variables in holographic axion theories
• Holographic Schwinger-Keldysh field theory of SU(2) diffusion
• Fast Scrambling of mutual information in Kerr-AdS${}_{\text{5}}$
• Long-time tails in the SYK chain from the effective field theory with a large number of derivatives
• Spatial regions, chaos bound and its violation
• JT gravity and near-extremal thermodynamics for Kerr black holes in $Ad{S}_{4,5}$ for rotating perturbations
• Growth of a renormalized operator as a probe of chaos
• Wilsonian renormalisation group and thermal field theory in the Schwinger-Keldysh closed-time-path formalism
• Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models
• Probing Stringy Horizons with Pole-Skipping in Non-Maximal Chaotic Systems
• Beyond the ensemble paradigm in low dimensional quantum gravity: Schwarzian density, quantum chaos and wormhole contributions