Black holes and the butterfly effect

Abstract

We use holography to study sensitive dependence on initial conditions in strongly coupled field theories. Specifically, we mildly perturb a thermofield double state by adding a small number of quanta on one side. If these quanta are released a scrambling time in the past, they destroy the local two-sided correlations present in the unperturbed state. The corresponding bulk geometry is a two-sided AdS black hole, and the key effect is the blueshift of the early infalling quanta relative to the $t=0$ slice, creating a shock wave. We comment on string- and Planck-scale corrections to this setup, and discuss points that may be relevant to the firewall controversy.

29 pages, 4 figures. v2: references added/clarified, typos corrected. v3: reference added, referencing clarified

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• Spectral form factor for free large $N$ gauge theory and strings
• Permutation Orbifolds and Chaos
• Modified "complexity equals action" conjecture
• Extending the scope of holographic mutual information and chaotic behavior
• Proof of absence of local conserved quantities in the mixed-field Ising chain
• From ETH to algebraic relaxation of OTOCs in systems with conserved quantities
• Exploring the Membrane Theory of Entanglement Dynamics
• New Concepts for Old Black Holes
• Probing typical black hole microstates
• Quantum Scrambling and State Dependence of the Butterfly Velocity
• The tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model
• Direct photons emission rate and electric conductivity in twice anisotropic QGP holographic model with first-order phase transition
• Spatio-temporal spread of perturbations in a driven dissipative Duffing chain: an OTOC approach
• Synthetic Fuzzballs: A Linear Ramp from Black Hole Normal Modes
• Weyl corrections to diffusion and chaos in holography
• Spectral Representation of Thermal OTO Correlators
• Controlling local thermalization dynamics in a Floquet-engineered dipolar ensemble
• Angular momentum and chaos bound of charged particles around Einstein-Euler-Heisenberg AdS black holes
• Arresting classical many-body chaos by kinetic constraints
• The bound on chaos for closed strings in Anti-de Sitter black hole backgrounds
• Magic Resources of the Heisenberg Picture
• Traversable wormholes in AdS and bounds on information transfer
• Smooth Causal Patches for AdS Black Holes
• Diagnosis of information scrambling from Hamiltonian evolution under decoherence
• The inside outs of AdS(3)/CFT(2): Exact AdS wormholes with entangled CFT duals
• Computational Complexity and Black Hole Horizons
• Chaos in the Quantum Field Theory $S$-matrix
• Energy and Information Near Black Hole Horizons
• Chaos in a $Q\bar{Q}$ system at finite temperature and baryon density
• Scrambling time from local perturbations of the rotating BTZ black hole
• Comments on Microcausality, Chaos, and Gravitational Observables
• Collective diffusion and quantum chaos in holography
• From black holes to baby universes in CGHS gravity
• Quantum Nature of Black Holes: Fast Scrambling versus Echoes
• Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models
• Butterfly Velocity Bound and Reverse Isoperimetric Inequality
• Quantifying non-stabilizerness via information scrambling
• Black holes as clouded mirrors: the Hayden-Preskill protocol with symmetry
• Dynamical Scaling Laws of Out-of-Time-Ordered Correlators
• Going beyond ER=EPR in the SYK model
• Slow scrambling in extremal BTZ and microstate geometries
• Out-of-time-ordered correlators and the Loschmidt echo in the quantum kicked top: How low can we go?
• Exact Embeddings of JT Gravity in Strings and M-theory
• Non-perturbative dynamics of the operator size distribution in the Sachdev-Ye-Kitaev model
• Quantum critical scaling and holographic bound for transport coefficients near Lifshitz points
• Cluster State Generation with Spin-Orbit Coupled Fermionic Atoms in Optical Lattices
• Eigenstate entanglement between quantum chaotic subsystems: universal transitions and power laws in the entanglement spectrum
• Abelian Tensor Models on the Lattice
• Operator front broadening in chaotic and integrable quantum chains
• Soft graviton exchange and the information paradox
• Holographic Probes of Inner Horizons
• Chaos, Diffusivity, and Spreading of Entanglement in Magnetic Branes, and the Strengthening of the Internal Interaction
• Quantum chaos without false positives
• Maximal Chaos from Strings, Branes and Schwarzian Action
• Refined quantum Lyapunov exponents from replica out-of-time-order correlators
• Holographic Butterfly Effect and Diffusion in Quantum Critical Region
• Complexity growth and shock wave geometry in AdS-Maxwell-power-Yang-Mills theory
• A class of non-equilibrium states and the black hole interior
• Fast scrambling in holographic Einstein-Podolsky-Rosen pair
• Entanglement formation in continuous-variable random quantum networks
• Symmetries and spectral statistics in chaotic conformal field theories
• Out-of-Time-Order Correlation as a Witness for Topological Phase Transitions
• Unitary Networks from the Exact Renormalization of Wave Functionals
• Chaos and Complexity from Quantum Neural Network: A study with Diffusion Metric in Machine Learning
• Holographic study of entanglement and complexity for mixed states
• Generalized conformal structure, dilaton gravity and SYK
• Superluminal chaos after a quantum quench
• Anisotropic and frame dependent chaos of suspended strings from a dynamical holographic QCD model with magnetic field
• Strongly coupled quantum phonon fluid in a solvable model
• Operational Metric for Quantum Chaos and the Corresponding Spatiotemporal Entanglement Structure
• A Survey of Black Hole Thermodynamics
• Pole skipping in holographic theories with gauge and fermionic fields
• From Shockwaves to the Gravitational Memory Effect
• Seeing behind black hole horizons in SYK
• Entanglement and Confinement in Coupled Quantum Systems
• Hayden-Preskill decoding from noisy Hawking radiation
• Out-of-time-order correlator in the quantum Rabi model
• Information Scrambling with Conservation Laws
• Spectral Form Factor in Non-Gaussian Random Matrix Theories
• Broken bridges: A counter-example of the ER=EPR conjecture
• Interferometric-Spectroscopy With Quantum-Light; Revealing Out-of-Time-Ordering Correlators
• Butterflies from Information Metric
• Overcounting of interior excitations: A resolution to the bags of gold paradox in AdS
• Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model
• $2\to 2N$ scattering: Eikonalisation and the Page curve
• Ultrafast Entanglement Dynamics in Monitored Quantum Circuits
• Operator growth in random quantum circuits with symmetry
• Quantifying information scrambling via Classical Shadow Tomography on Programmable Quantum Simulators
• Firewalls and flat mirrors: An alternative to the AMPS experiment which evades the Harlow-Hayden obstacle
• Subleading Bounds on Chaos
• Pole-Skipping in Rotating BTZ Black Holes
• On the Butterfly Effect in 3D Gravity
• Observer-dependent black hole interior from operator collision
• Operator Growth from Global Out-of-time-order Correlators
• The Most Irrational Rational Theories
• Bands and gaps in Nekrasov partition function
• Emergent Symmetry in Brownian SYK Models and Charge Dependent Scrambling
• Horndeski Gravity and the Violation of Reverse Isoperimetric Inequality
• Timelike BKL singularities and chaos in AdS/CFT
• Diffusion for Holographic Lattices
• Shear transport far from equilibrium via holography
• Emergence of correlations in the process of thermalization of interacting bosons
• The Timescales of Quantum Breaking
• Thermalisation in a Bose-Hubbard dimer with modulated tunneling
• Dynamical route to ergodicity and quantum scarring in kicked coupled top
• The entanglement membrane in exactly solvable lattice models
• Krylov Complexity in Mixed Phase Space
• A holographic study of the characteristics of chaos and correlation in the presence of backreaction
• Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries
• Tracking the quantized information transfer at the edge of a chiral Floquet phase
• Quantum many-body dynamics on the star graph
• Mixed State Entanglement and Thermal Phase Transitions
• Black Hole and de Sitter Microstructures from a Semiclassical Perspective
• Transient chaos analysis of string scattering
• Holographic Non-equilibrium Heating
• State estimation with quantum extreme learning machines beyond the scrambling time
• Thermalization and its Breakdown for a Large Nonlinear Spin
• Weyl transformation and regular solutions in a deformed Jackiw-Teitelboim model
• Highly Excited Strings I: Generating Function
• Constraints on hydrodynamics from many-body quantum chaos
• The smallest matrix black hole model in the classical limit
• Fast Scrambling due to Rotating Shockwaves in BTZ
• Out-of-time-order correlators and Lyapunov exponents in sparse SYK
• Bound on Lyapunov exponent in Einstein-Maxwell-Dilaton-Axion black holes
• Variational Preparation of the Sachdev-Ye-Kitaev Thermofield Double
• Holographic complexity for black branes with momentum relaxation
• Size of bulk fermions in the SYK model
• Chaos in Celestial CFT
• Out-of-time-ordered correlators of the Hubbard model: SYK strange metal in the spin freezing crossover region
• Bound on Lyapunov exponent in Kerr-Newman-de Sitter black holes by a charged particle
• Eigenstate correlations, the eigenstate thermalization hypothesis, and quantum information dynamics in chaotic many-body quantum systems
• Holographic measurement in CFT thermofield doubles
• Boundary signature of singularity in the presence of a shock wave
• Barren plateaus from learning scramblers with local cost functions
• The shared universality of charged black holes and the many many-body SYK model
• Criticality in Third Order Lovelock Gravity and the Butterfly effect
• Computational pseudorandomness, the wormhole growth paradox, and constraints on the AdS/CFT duality
• Schwinger-Keldysh path integral for the quantum harmonic oscillator
• Quantifying scrambling in quantum neural networks
• Chaos and fast scrambling delays of dyonic Kerr-Sen-AdS${}_4$ black hole and its ultra-spinning version
• The chaotic emergence of thermalization in highly excited string decays
• Constraining Weil-Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity
• Probing quantum chaos in multipartite systems
• Speeding up the spread of quantum information in chaotic systems
• Extremal Chaos
• Sachdev-Ye-Kitaev circuits for braiding and charging Majorana zero modes
• Jackiw-Teitelboim quantum gravity with defects and the Aharonov-Bohm effect
• Chaos exponents of SYK traversable wormholes
• Seeing the Entanglement Wedge
• Unveiling operator growth in SYK quench dynamics
• Similar early growth of out-of-time-ordered correlators in quantum chaotic and integrable Ising chains
• Quantum Causal Influence
• Locality Bound for Dissipative Quantum Transport
• Scrambling via Braiding of Nonabelions
• Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation
• Revisiting noninteracting string partition functions in Rindler space
• Loschmidt echo in many-spin systems: contrasting time-scales of local and global measurements
• Local quenches and quantum chaos from higher spin perturbations
• Entanglement Wedge Minimum Cross-section in Holographic Massive Gravity Theory
• Quantum chaos associated with emergent ergosurface in transition layer between type-I and type-II Weyl semimetals
• Measuring operator size growth in quantum quench experiments
• Scrambling in quantum cellular automata
• Chiral Algebras of Two-Dimensional SYK Models
• Information Transfer and Black Hole Evaporation via Traversable BTZ Wormholes
• Entwinement as a possible alternative to complexity
• Operator growth bounds in a cartoon matrix model
• AdS Black Holes with a Bouncing Interior
• A universal bound on Quantum Chaos from Random Matrix Theory
• Entanglement and chaos near critical point in strongly coupled gauge theory
• Quantum simulation of operator spreading in the chaotic Ising model
• $T\bar{T}$ deformation on multiquantum mechanics and regenesis
• Shockwaves in black hole microstate geometries
• Nonuniqueness of scattering amplitudes at special points
• Probing emergent geometry through phase transitions in free vector and matrix models
• Entanglement wedge cross-section in shock wave geometries
• Holographic QCD and magnetic fields
• Quasinormal modes of a semi-holographic black brane and thermalization
• Quantum steering as a witness of quantum scrambling
• Shock waves, black hole interiors and holographic RG flows
• Speed limits to the growth of Krylov complexity in open quantum systems
• Measuring the distance between quantum many-body wave functions
• Sampling and scrambling on a chain of superconducting qubits
• Witnessing quantum chaos using observational entropy
• A quantum circuit interpretation of evaporating black hole geometry
• Diffusivities bounds in the presence of Weyl corrections
• Integrable Field Theories and Their CCFT Duals
• Loschmidt echo in many-spin systems: a quest for intrinsic decoherence and emergent irreversibility
• Entanglement asymmetry dynamics in random quantum circuits
• Out of Time Order Correlations in the Quasi-Periodic Aubry-André model
• Supersymmetric Many-Body Systems from Partial Symmetries: Integrability, Localization and Scrambling
• Black holes often saturate entanglement entropy the fastest
• A Tale of Two Butterflies: An Exact Equivalence in Higher-Derivative Gravity
• Chaos in Three-dimensional Higher Spin Gravity
• Scrambling with conservation law
• Effective description of sub-maximal chaos: stringy effects for SYK scrambling
• Dynamic Properties of Two-Dimensional Latticed Holographic System
• Fingerprint of chaos and quantum scars in kicked Dicke model: An out-of-time-order correlator study
• Regge conformal blocks from the Rindler-AdS black hole and the pole-skipping phenomena
• Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states
• Exactly solvable many-body dynamics from space-time duality
• Scattering strings off quantum extremal surfaces
• Using Disorder to Identify Bogoliubov Fermi-Surface States
• Primordial Gravitational Wave Circuit Complexity
• Coarse-grained Entanglement and Operator Growth in Anomalous Dynamics
• Slow relaxation of out-of-time-ordered correlators in interacting integrable and nonintegrable spin-1/2 XYZ chains
• M2-brane Dynamics in the Classical Limit of the BMN Matrix Model
• Collision in the interior of wormhole
• Local operator quench induced by two-dimensional inhomogeneous and homogeneous CFT Hamiltonians
• Quantum information scrambling and quantum chaos in little string theory
• Operator Size Distribution in Large $N$ Quantum Mechanics of Majorana Fermions
• The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations
• Transport properties in non-Fermi liquid phases of nodal-point semimetals
• Chaotic dynamics of a suspended string in a gravitational background with magnetic field
• Slow scrambling in sonic black holes
• Holography Abhors Visible Trapped Surfaces
• Hydrodynamic theory of scrambling in chaotic long-range interacting systems
• Quantum information probes of charge fractionalization in large-$N$ gauge theories
• Spatio-temporal spread of perturbations in power-law models at low temperatures: Exact results for OTOC
• Fast Scrambling of Mutual Information in Kerr-AdS${}_4$
• Reparametrization modes in 2d CFT and the effective theory of stress tensor exchanges
• Generalized black hole entropy in two dimensions
• Causality bounds chaos in geodesic motions
• Soft modes in $\mathcal{N}=2$ SYK model
• Chaos Bound and its violation in Black p-brane
• Strongly coupled phonon fluid and Goldstone modes in an anharmonic quantum solid: transport and chaos
• Generalized Free Cumulants for Quantum Chaotic Systems
• Out-of-time-ordered correlators and quantum walks
• Phase diagram of QCD chaos in linear sigma models and holography
• Schwarzian correction to quantum correlation in SYK model
• Note on global symmetry and SYK model
• Quantum Information Scrambling in Molecules
• Purification and scrambling in a chaotic Hamiltonian dynamics with measurements
• The black hole information puzzle and the quantum de Finetti theorem
• Weak chaos and mixed dynamics in the string S-matrix
• The quantum cat map on the modular discretization of extremal black hole horizons
• Out-of-Time-Order Correlators in One-Dimensional XY model
• An Inelastic Bound on Chaos
• Quantum information spreading in random spin chains with topological order
• Long-Range Bell States from Local Measurements and Many-Body Teleportation without Time-Reversal
• Classical simulation of quantum circuits by dynamical localization: analytic results for Pauli-observable scrambling in time-dependent disorder
• Krylov Complexity as a Probe for Chaos
• Rescuing Complementarity With Little Drama
• Holographic Butterfly Velocities in Brane Geometry and Einstein-Gauss-Bonnet Gravity with Matters
• Charge transport, information scrambling and quantum operator-coherence in a many-body system with U(1) symmetry
• Notes on Scrambling in Conformal Field Theory
• Minkowski Conformal Blocks and the Regge Limit for SYK-like Models
• Quantum Information Scrambling Through a High-Complexity Operator Mapping
• Local Operator Entanglement in Spin Chains
• Effects of quintessence dark energy on the action growth and butterfly velocity
• Classical and quantum butterfly effect in nonlinear vector mechanics
• Uncomputably Complex Renormalisation Group Flows
• Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator
• Stringy Effects and the Role of the Singularity in Holographic Complexity
• Entanglement dynamics of thermofield double states in integrable models
• Quartic Horndeski, planar black holes, holographic aspects and universal bounds
• Scrambling in Yang-Mills
• Complexity Growth Following Multiple Shocks
• Measuring out-of-time-ordered correlation functions with a single impurity qubit in a bosonic Josephson junction
• Quantum and Classical Dynamics with Random Permutation Circuits
• Universal properties of many-body quantum chaos at Gross-Neveu criticality
• Gravitational Corner Conditions in Holography
• Classical approach to equilibrium of out-of-time ordered correlators in mixed systems
• Quantum Correction to Chaos in Schwarzian Theory
• Violation of the viscosity/entropy bound in translationally invariant non-Fermi liquids
• Holographic scalar and vector exchange in OTOCs and pole-skipping phenomena
• Gravitational shockwaves on rotating black holes
• Interactions resolve state-dependence in a toy-model of AdS black holes
• On 1D, N = 4 Supersymmetric SYK-Type Models (I)
• Chaos in the Fishnet
• Large-$d$ phase transitions in holographic mutual information
• Correlations vs connectivity in R-charge
• Collisions of localized shocks and quantum circuits
• Asymmetric butterfly velocities in Hamiltonian and circuit models
• Asymmetric butterfly velocities in 2-local Hamiltonians
• Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model: Dynamical Aspects
• Quantum chaos and thermalization in the two-mode Dicke model
• Geometric encoding of renormalization group $\beta -$functions in an emergent holographic dual description
• Fast Scrambling of mutual information in Kerr-AdS${}_{\text{5}}$
• Chaos-induced depletion of a Bose-Einstein condensate
• Probing Dynamical Sensitivity of a Non-KAM System Through Out-of-Time-Order Correlators
• Solvable entanglement dynamics in quantum circuits with generalized space-time duality
• The Cosmological Switchback Effect II
• Scrambling in Two-Dimensional Conformal Field Theories with Light and Smeared Operators
• Exponential speedup in measuring out-of-time-ordered correlators with a single bit of quantum information
• Quantum Lyapunov exponent in dissipative systems
• Complexity is not Enough for Randomness
• Time dependence of entanglement for steady state formation in AdS${}_3$/CFT${}_2$
• Black Holes and Marchenko-Pastur Distribution
• Classical route to ergodicity and scarring in collective quantum systems
• Localized chaos due to rotating shock waves in Kerr-AdS black holes and their ultraspinning version
• Chaos and relative entropy
• On the universality of late-time correlators in semi-classical 2d CFTs
• Space-Time Duality between Quantum Chaos and Non-Hermitian Boundary Effect
• Entanglement Wedge Minimum Cross-Section for Holographic Aether Gravity
• Bouncing inside the horizon and scrambling delays
• Experimental tests of Lieb-Robinson bounds
• Conformal Blocks Beyond the Semi-Classical Limit
• Exact solutions and critical chaos in dilaton gravity with a boundary
• Symmetry classes, many-body zero modes, and supersymmetry in the complex Sachdev-Ye-Kitaev model
• Quantum chaos in the Dicke model and its variants
• Butterfly velocity and bulk causal structure
• Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits
• Butterfly Effect and Holographic Mutual Information under External Field and Spatial Noncommutativity
• Out-of-Time-Ordered Correlation in Anisotropic Dicke Model
• Diving inside holographic metals
• Long-Range Nonlocality in Six-Point String Scattering: simulation of black hole infallers
• Scaling at the OTOC Wavefront: free versus chaotic models
• Odd entanglement entropy in $\text{T}\bar{\text{T}}$ deformed CFT${}_2$s and holography
• Quantum computation toolbox for decoherence-free qubits using multi-band alkali atoms
• Information Scrambling and the Correspondence of Entanglement- and Operator Dynamics in Systems with Nonlocal Interactions
• A Solvable Model of Quantum Darwinism-Encoding Transitions
• The Limits of Quantum Information Scrambling
• Concentration of OTOC and Lieb-Robinson velocity in random Hamiltonians
• Perturbing a quantum black hole
• Probing Pole Skipping through Scalar-Gauss-Bonnet coupling
• Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d
• Operator Space Entangling Power of Quantum Dynamics and Local Operator Entanglement Growth in Dual-Unitary Circuits
• Long-time dynamics in quantum spin lattices: ergodicity and hydrodynamic projections at all frequencies and wavelengths
• Quantum Chaos and Circuit Parameter Optimization
• SYK/AdS duality with Yang-Baxter deformations
• $SL(2,R)$ lattices as information processors
• Mixed-state Entanglement for AdS Born-Infeld Theory
• Information spreading and scrambling in disorder-free multiple-spin interacting models
• A toy model for time evolving QFT on a lattice with controllable chaos
• Linear Cross Entropy Benchmarking with Clifford Circuits
• Realizing the Hayden-Preskill Protocol with Coupled Dicke Models
• Operator size growth in Lindbladian SYK
• Entanglement wedge method, out-of-time-ordered correlators, and pole skipping
• Hayden-Preskill protocol and decoding Hawking radiation at finite temperature
• Worldsheet traversable wormholes
• Parisi's hypercube, Fock-space frustration and near-AdS${}_2$/near-CFT${}_1$ holography
• Quantum Chaos for the Unitary Fermi Gas from the Generalized Boltzmann Equations
• Fermionic Open EFT from Holography
• Butterfly Velocity in Quadratic Gravity
• Floquet engineered inhomogeneous quantum chaos in critical systems
• Operator Spreading in the Memory Matrix Formalism
• Slow scrambling and hidden integrability in a random rotor model
• Complexity Growth, Butterfly Velocity and Black hole Thermodynamics
• Fidelity-dissipation relations in quantum gates
• How to Recover a Qubit That Has Fallen Into a Black Hole
• Global Symmetry and Maximal Chaos
• Holographic Naturalness
• Holographic Complexity and Phase Transition for AdS Black Holes
• Quantum algorithm for evaluating operator size with Bell measurements
• Multi-trace Correlators in the SYK Model and Non-geometric Wormholes
• Scalar field as a null dust
• Holographic thermal correlators: A tale of Fuchsian ODEs and integration contours
• Relevant OTOC operators: footprints of the classical dynamics
• Wormholes and the Thermodynamic Arrow of Time
• Chaos in $SU(2)$ Yang-Mills Chern-Simons Matrix Model
• Non-Fermi liquid behavior in the Sachdev-Ye-Kitaev model for a one dimensional incoherent semimetal
• Quantum Chaos of the Bose-Fermi Kondo model at the intermediate temperature
• Conformal Bootstrap in dS/CFT and Topological Quantum Gravity
• Phase-transition-like behavior in information retrieval of a quantum scrambled random circuit system
• Holographic complexity under a global quantum quench
• Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain
• Signatures of the interplay between chaos and local criticality on the dynamics of scrambling in many-body systems
• Hayden-Preskill Recovery in Hamiltonian Systems
• Codification Volume of an operator algebra and its irreversible growth through thermal processes
• Temporal fluctuations of correlators in integrable and chaotic quantum systems
• Quantifying operator spreading and chaos in Krylov subspaces with quantum state reconstruction
• Information Scrambling in Free Fermion Systems with a Sole Interaction
• Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics
• Chaotic and Thermal Aspects in the Highly Excited String S-Matrix
• Quantum chaos in the presence of non-conformality
• Stochastic Sampling of Operator Growth Dynamics
• 3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator
• D-commuting SYK model: building quantum chaos from integrable blocks
• The Ergodicity Landscape of Quantum Theories
• Krylov operator complexity in holographic CFTs: Smeared boundary reconstruction and the dual proper radial momentum
• Stationary equilibrium of test particles near charged black branes with the hyperscaling violating factor
• Maximally Chaotic Dynamical Systems and Fundamental Interactions
• Four-point function in the IOP matrix model
• Electric fields and quantum wormholes
• Operator Size for Holographic Field Theories
• Recovering Infalling Information via String Spreading
• Horizons Protect Church-Turing
• Effective Thermal Physics in Holography: A Brief Review
• Quantum Mechanics in the Infrared
• Quantum circuits with classically simulable operator scrambling
• Berry Curvature and Riemann Curvature in Kinematic Space with Spherical Entangling Surface
• Asymmetric interiors for small black holes
• A Quantum Correction To Chaos
• Chaos from Equivariant Fields on Fuzzy $S^4$
• Conformal quantum mechanics of causal diamonds: Time evolution, thermality, and instability via path integral functionals
• Universal distributions of overlaps from generic dynamics in quantum many-body systems
• Universal Early-Time Growth in Quantum Circuit Complexity
• Holographic study of shear viscosity and butterfly velocity for magnetic field-driven quantum criticality
• Pole-skipping and chaos in D3-D7 brane systems
• Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics
• Simulating Floquet scrambling circuits on trapped-ion quantum computers
• Quantum reservoir probing: an inverse paradigm of quantum reservoir computing for exploring quantum many-body physics
• Correlation functions for open strings and chaos
• Black Holes at Exp-time
• Dynamical phase transitions of information flow in random quantum circuits
• Out-of-Time Ordered Correlators in Kicked Coupled Tops: Information Scrambling in Mixed Phase Space and the Role of Conserved Quantities
• Scheme to Detect the Strong-to-weak Symmetry Breaking via Randomized Measurements
• Chaotic Information Processing by Extremal Black Holes
• Scrambling in charged hairy black holes and the Kasner interior
• Soft thermodynamics of gravitational shock wave
• Many-body chaos in the antiferromagnetic quantum critical metal
• Error-resilient Reversal of Quantum Chaotic Dynamics Enabled by Scramblons
• Holographic Micro Thermofield Geometries of BTZ Black Holes
• Control of spatiotemporal chaos by stochastic resetting
• Fast scrambling dynamics and many-body localization transition in an all-to-all disordered quantum spin model
• Bulk Reconstruction from Generalized Free Fields
• Holographic Van der Waals phase transition of the higher dimensional electrically charged hairy black hole
• Scrambling in the Quantum Lifshitz Model
• Optimally scrambling chiral spin-chain with effective black hole geometry
• Long-time Quantum Scrambling and Generalized Tensor Product Structures
• Universality in the OPE Coefficients of Holographic 2d CFTs
• Motions of spinning particles and chaos bound in Reissner-Nordström spacetime
• Breakdown of quantum-classical correspondence and dynamical generation of entanglement
• Quantum Chaos, Thermodynamics and Black Hole Microstates in the mass deformed SYK model
• The Ultraviolet Structure of Quantum Field Theories. Part 1: Quantum Mechanics
• Relaxation exponents of OTOCs and overlap with local Hamiltonians
• Mimicking black hole event horizons in atomic and solid-state systems
• Scrambling under quench
• Virasoro blocks and the reparametrization formalism
• JT gravity and near-extremal thermodynamics for Kerr black holes in $Ad{S}_{4,5}$ for rotating perturbations
• Generalized quantum master equations can improve the accuracy of semiclassical predictions of multitime correlation functions
• Fast pseudorandom quantum state generators via inflationary quantum gates
• Chaotic Correlation Functions with Complex Fermions
• Holographic Aspects of Quasi-topological Gravity
• Jackiw-Teitelboim gravity and near-extremal BTZ thermodynamics
• Quantum chaos in PT symmetric quantum systems
• On the Nonequilibrium Dynamics of Gravitational Algebras
• A Strategy for Proving the Strong Eigenstate Thermalization Hypothesis : Chaotic Systems and Holography
• Circuit Complexity From Supersymmetric Quantum Field Theory With Morse Function
• Quasinormal Modes and the Switchback Effect in Schwarzschild-de Sitter
• Out-of-time-ordered correlator in the one-dimensional Kuramoto-Sivashinsky and Kardar-Parisi-Zhang equations
• Shadows and Observational Images of a Schwarzschild-like Black Hole Surrounded by a Dehnen-type Dark Matter Halo
• Stationary Solution to Charged Hairy Black Hole in AdS4: Kasner Interior, Rotating Shock Waves, and Fast Scrambling
• Spinning Particle Geometries in AdS${}_3$/CFT${}_2$
• Key Observable for Linear Thermalization
• Quantum purification spectroscopy
• Puzzles and pitfalls involving Haar-typicality in holography
• Wormholes, geons, and the illusion of the tensor product
• Unambiguous measurement of information scrambling in a hierarchical star-topology system
• Complexity in One- and Two-Qubit Systems
• Scrambling Transition in Free Fermion Systems Induced by a Single Impurity
• Size Winding Mechanism beyond Maximal Chaos
• Quantum many-body physics from a gravitational lens
• Super-maximal chaos and instability
• Quantum Annealing with chaotic driver Hamiltonians
• Holographic Kolmogorov-Sinai entropy and the quantum Lyapunov spectrum
• Disordered $\mathcal{N}=(2,2)$ Supersymmetric Field Theories
• Random Circuits in the Black Hole Interior
• Complexity growth rate, grand potential and partition function
• Disorder-free Sachdev-Ye-Kitaev models: Integrability and a precursor of chaos
• Out of Time Order Correlation of the Hubbard Model with Random Local Disorder
• Quantum chaos in a weakly-coupled field theory with nonlocality
• Chaotic Dynamics of the Mass Deformed ABJM Model
• Saturation of Chaos Bound in a Phenomenological Rotating Black Hole--Effective Matter System at Low-Temperature Limit
• $\mathcal{N}=2$ SYK models with dynamical bosons and fermions
• Instabilities of microstate geometries with antibranes
• Anomalous Quantum Information Scrambling for ${\mathbb{Z}}_3$ Parafermion Chains
• Typical Event Horizons in AdS/CFT
• Chaos from Massive Deformations of Yang-Mills Matrix Models
• Schwarzian for colored Jackiw-Teitelboim gravity
• Void formation in operator growth, entanglement, and unitarity
• Transient and steady-state chaos in dissipative quantum systems
• Quantum instability and Ehrenfest time for an inverted harmonic oscillator
• Bipartite OTOC in open quantum systems: information scrambling and irreversibility
• Butterfly Velocities for Holographic Theories of General Spacetimes
• Traveling discontinuity at the quantum butterfly front
• Complexity Near Horizons
• Tensor Field Theories: Renormalization and Random Geometry
• What's inside a hairy black hole in massive gravity?
• Kinetics of information scrambling in correlated electrons: disorder-driven transition from shock-wave to FKPP dynamics
• Loschmidt echo and scrambling of systematic errors in tomography -- a quantum signature of chaos
• Reparametrization mode Ward Identities and chaos in higher-pt. correlators in CFT${}_2$
• Quantum Chaos in Non-Markovian Open Quantum Systems: Interferometric OTOC, Loschmidt Echo and Commutator Operator Norm
• Global Out of Time Order Correlators as a Signature of Scrambling Dynamics of Local Observables
• Scrambling in Ising spin systems with periodic transverse magnetic fields
• Inverse Hamiltonian design of highly-entangled quantum systems
• ER for typical EPR
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling
• Hidden Non-Locality and Self-Superrenormalization of Quantum Gravity
• Field theory in Rindler frame and more on the correspondence with thermal field theory formalisms
• Quantum chaos and Hénon-Heiles model: Dirac's variational approach with Jackiw-Kerman function
• Quantum signatures of chaos in a cavity-QED-based stimulated Raman adiabatic passage
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos
• Benchmarking quantum chaos from geometric complexity
• Periodicity of dynamical signatures of chaos in quantum kicked top
• Pseudochaotic Many-Body Dynamics as a Pseudorandom State Generator
• Recovery of damaged information via scrambling in indefinite casual order
• Fast Scrambling under an RG-flow
• Random Permutation Circuits Beyond Qubits are Quantum Chaotic
• Ruelle-Pollicott Decay of Out-of-Time-Order Correlators in Many-Body Systems
• Out-of-time-ordered correlators of mean-field bosons via Bogoliubov theory
• Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• Directional scrambling of quantum information in helical multiferroics
• Fast Pre-scramblers
• Quantum speed limit for the OTOC from an open systems perspective
• Entanglement wedge cross section inequalities in AdS/BCFT
• SYK model based $\beta$ regime dependent two-qubit dynamical wormhole-inspired teleportation protocol simulation
• Quantum Darwinism-encoding transitions on expanding trees
• Detecting quantum chaos via pseudo-entropy
• Covariant odd entanglement entropy in AdS${}_3$/CFT${}_2$
• Quantum Chaos of Unitary Fermi Gases in Strong Pairing Fluctuation Region
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• Black Hole Entropy and the Pseudo Goldstone Bosons of Conformal Symmetry
• Spacetime topology from holographic entanglement
• Information scrambling of the dilute Bose gas at low temperature
• Grothendieck's point of view and complexity in the black hole paradox
• Learning out-of-time-ordered correlators with classical kernel methods
• Rate of cluster decomposition via Fermat-Steiner point
• Probabilistic deconstruction of a theory of gravity, Part II: curved space
• Arnol'd cat map lattices
• Tensor Product Structure Geometry under Unitary Channels
• Information scrambling and entanglement dynamics in Floquet Time Crystals
• Caustics bounding entanglement wedges
• Out-of-time-order correlator computation based on discrete truncated Wigner approximation
• Hot wormholes and chaos dynamics in a two-coupled SYK model
• Black Hole Complementarity and ER/EPR
• Markov Gap and Bound Entanglement in Haar Random State
• Chaos in the holographic matrix models for meson and baryon
• From Confinement to Chaos in AdS/CFT Correspondence via Non-equilibrium Local States
• Simulating sparse SYK model with a randomized algorithm on a trapped-ion quantum computer
• Localization of information driven by stochastic resetting
• Coherence-induced deep thermalization transition in random permutation quantum dynamics
• Holographic Black Hole Formation and Scrambling in Time-Ordered Correlators
• Position and momentum operators for a moving particle in bulk
• Nonuniqueness of Green's functions at special points
• Chaos-protected locality
• Experimental Measurement of Out-of-Time-Ordered Correlators at Finite Temperature
• Rotating particles in AdS: Holography at weak gauge coupling and without conformal symmetry
• Bound on the Lyapunov exponent in Kerr-Newman black holes via a charged particle
• Haar averaged moments of correlation functions and OTOCs in Floquet systems
• Why is AI hard and Physics simple?
• Fast Scramblers, Democratic Walks and Information Fields
• Quantum Entanglement and Spectral Form Factor
• A polynomial time algorithm for studying physical observables in chaotic eigenstates
• Cosmic Censorship of Trans-Planckian Field Ranges in Gravitational Collapse
• Chaos and anomalous transport in a semiclassical Bose-Hubbard chain
• Mechanisms of scrambling and unscrambling of quantum information in the ground state in spin chains: domain-walls, spin-flips and scattering phase shifts
• Holographic Entanglement and Causal Shadow in Time-Dependent Janus Black Hole
• Local Geometric Bounds on Generalized Entropy Evolution along Null Horizons
• The trans-Planckian problem and gravitational interactions
• A Reverse Black Hole Information Problem
• Out-of-time-order correlators of nonlocal block-spin and random observables in integrable and nonintegrable spin chains
• Quantum three-rotor problem in the identity representation
• Long-Range Pairing in the Kitaev Model: Krylov Subspace Signatures
• Schwinger-Keldysh path integral formalism for a Quenched Quantum Inverted Oscillator
• Operator delocalization in disordered spin chains via exact MPO marginals
• Probing Stringy Horizons with Pole-Skipping in Non-Maximal Chaotic Systems
• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal
• Hybrid Brownian SYK-Hubbard Model: from Spectral Function to Quantum Chaos
• Searching for emergent spacetime in spin glasses
• High Energy Reflection Coefficients of Black Holes and Branes
• Wormholes and out-of-time ordered correlators in gauge/gravity duality
• Scrambling dynamics across a thermalization-localization quantum phase transition
• Krylov Winding and Emergent Coherence in Operator Growth Dynamics
• Interferometric and Bipartite OTOC for Non-Markovian Open Quantum Spin-Chains and Lipkin-Meshkov-Glick Model
• Yang-Mills Classical and Quantum Mechanics and Maximally Chaotic Dynamical Systems
• Comparative Study of Indicators of Chaos in the Closed and Open Dicke Model
• Out-of-time-order correlation and detection of phase structure in Floquet transverse Ising spin system
• Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models
• Chaos in Matrix Gauge Theories with Massive Deformations
• Quantum entanglement in the t-J chain: From charge-spin separation to recombination
• Waveguide QED toolboxes for universal quantum matter
• Diagnosing chaos with projected ensembles of process tensors
• A graph-theoretic approach to chaos and complexity in quantum systems
• Spinning constraints on chaotic large $c$ CFTs
• Quantum Information for Particle Theorists
• Turbulent aspects of BMN membrane dynamics
• Fast Scrambling in Classically Simulable Quantum Circuits
• Information acquisition, scrambling, and sensitivity to errors in quantum chaos
• Higher-spin localized shocks
• AdS black holes in two-dimensional dilaton gravity and holography
• Black Hole Time Scales: Thermalization, Infall and Complexity
• Recent developments in the holographic description of quantum chaos
• Odd Entanglement Entropy and Logarithmic Negativity for Thermofield Double States
• On a Matrix Ensemble for Arbitrary Complex Quantum Systems
• Butterflies dragging the jets: on the chaotic nature of holographic QCD
• Scrambling and the black hole atmosphere
• Maximally Chaotic Dynamical System of Infinite Dimensionality
• Scrambling time for analogue black holes embedded in AdS space
• Maximally chaotic dynamical systems of Anosov-Kolmogorov
• Quantum transitions, ergodicity, and quantum scars in the coupled top model
• If you want to cross singularity, wrap it!