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Fast Scramblers
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We consider the problem of how fast a quantum system can scramble (thermalize) information, given that the interactions are between bounded clusters of degrees of freedom; pairwise interactions would be an example. Based on previous work, we conjecture: 1) The most rapid scramblers take a time logarithmic in the number of degrees of freedom. 2) Matrix quantum mechanics (systems whose degrees of freedom are n by n matrices) saturate the bound. 3) Black holes are the fastest scramblers in nature. The conjectures are based on two sources, one from quantum information theory, and the other from the study of black holes in String Theory.
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Cited by 54 Pith papers
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Strong unitary designs in optimal depth and space
For every fixed k and error tolerance, strong approximate unitary k-designs are constructed in optimal Theta(log n) depth on the n system qubits using random perfect-matching layers.
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Overcrowding and the Finite-$N$ Hilbert Space
For d Hermitian N x N matrices, any all-single-trace choice of primary coordinates must miss a trace direction by degree 2 log_d N + log_d log_d N + O(1), parametrically below the first trace identity.
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Microscopic Side Information Controls Ordered Hayden--Preskill Recovery
Without microscopic position labels, Hayden–Preskill recovery of a fixed diary requires Θ(n^{2/3}) output qubits; coarse block labels reduce this to n^{2/3}B^{-1/3} or n/B.
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A de Sitter Anti-Scrambling Algebra
In a toy model of de Sitter quantum gravity, shockwave time advances break the KMS condition and prevent the Hartle-Hawking state from being a trace on the observer's crossed-product algebra.
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Smooth horizons from topology change in canonical quantum gravity
Topology change in canonical JT gravity resolves the firewall paradox by making the connected two-interior branch dominate after Page time, with gravitational constraints annihilating the firewall branch and identifyi...
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Probabilistic Causality from Graviton Fluctuations
In a thermal state of gravitons at temperature T, metric fluctuations induce a Gaussian spread in the causal structure of a scalar field with Var(x²) = 16 G_N T t³ / 3 after vacuum subtraction.
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Evaporating Black Hole Interior and Complexity Evolution
In JT gravity with an end-of-the-world brane, the renormalized interior length — read as subsystem complexity — grows linearly, peaks around the Page time, and then decays exponentially, with growing relative fluctuat...
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Entanglement Revivals and Scrambling for Evaporating Black Holes
Increasing black hole scrambling time in JT and RST evaporating geometries suppresses and eliminates late-time entanglement revivals in 2d CFT mutual information for disjoint intervals, interpolating between quasipart...
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Towards a Refinement of Krylov Complexity: Scrambling, Classical Operator Growth and Replicas
LogK complexity via replicas distinguishes genuine scrambling from saddle effects in quantum and classical systems and refines the measure for integrable cases.
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Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography
In the continuum limit the discrete Krylov chain becomes a Klein-Gordon field in AdS2, with Lanczos growth rate α identified as πT, recovering the maximal chaos bound and requiring the Breitenlohner-Freedman bound for...
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Quantum Ising Model on $(2+1)-$Dimensional Anti$-$de Sitter Space using Tensor Networks
Tensor network simulations of the Ising model on hyperbolic lattices with coordination number 7 reveal power-law boundary spin correlations in the disordered phase and logarithmic boundary entanglement entropy at crit...
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Cosmological pole-skipping, shock waves and quantum chaotic dynamics of de Sitter horizons
Pole-skipping in Schwarzschild-de Sitter predicts superluminal and imaginary butterfly velocities, confirmed by shock wave analysis, hinting at nonlocal and non-Hermitian dual dynamics.
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Symmetric Product Orbifold Universality and the Mirage of an Emergent Spacetime
Symmetric product orbifolds have large-N thermal correlators identical to BTZ, undercutting the claim that a type III1 von Neumann algebra implies a sharp emergent horizon.
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Superluminal chaos after a quantum quench
In BTZ-Vaidya holographic quenches, out-of-time-order correlators imply a transient superluminal butterfly velocity v_B = r_+/r_- > 1 while Lyapunov growth saturates the chaos bounds set by the local temperatures.
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Black hole evaporation and semiclassicality at large D
At large spacetime dimension D, semiclassical black holes require entropy S_BH > (D/4π)^(D+3) log D, a bound stronger than the usual curvature and backreaction conditions.
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The Speed of Quantum Information Spreading in Chaotic Systems
For chaotic systems with initial entanglement fraction f, quantum information spreads at speed v_E(f)/(1-f), interpolating between the entanglement speed at f=0 and the butterfly speed at f=1.
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Matrix Multiverses Meet Multiple Mythologies
The authors construct a model where asymptotically de Sitter universes are finite-entropy subsystems inside black holes in a maximal-entropy p=ρ universe, decaying on timescales far shorter than recurrence times.
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Page transition for the complexity of an evaporating black hole
The complexity of radiation from an evaporating black hole is argued to undergo a sharp Page-like transition, dominated after the Page time by the volume of an island in the entanglement wedge.
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Berry Picking: Random Wave Chaos Hierarchy for BPS Microstate Geometries
Wave chaos in BPS microstate geometries strengthens toward black-hole-like throats while geodesic chaos weakens, and weak-coupling CFT Renyi entropies do not share that bulk hierarchy.
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Black Holes and Random Variables
High-energy CFT and black-hole interval counts are conjectured to obey the FHK extreme-value law; the resulting O(1) erratic fluctuations limit semiclassical AdS precision to e^{-S0}.
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Macroscopic Black-Hole Remnants in a Nonlocal Field Theory: Towards Hawking Radiation in SFT
In a smeared massless scalar on dynamical black hole, outgoing particle number drops to zero after scrambling time due to SFT nonlocality, implying macroscopic remnant.
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Black Hole Photon Rings Saturate the Quantum Chaos Bound
Photon rings around black holes saturate the quantum chaos bound via Lyapunov exponents of null geodesics and OTOCs in the near-ring region.
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Pseudorandom Dynamics in the SYK Model and Cryptographic Censorship in JT Gravity
SYK disorder is shown to be an approximate unitary k-design for poly(N) k; under the planted-SYK hardness conjecture this yields gravitationally pseudorandom unitaries, implying cryptographic censorship in JT gravity ...
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Chaos-Integrability Transition in the BPS Subspace of the $\mathcal{N}=2$ SYK Model
Numerical analysis shows that spectral statistics of a BPS-projected operator in an interpolating N=2 SYK model transition from random-matrix to Poisson behavior as the model moves from chaotic to integrable.
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Butterflies in $\textrm{T}\overline{\textrm{T}}$ deformed anomalous CFT$_2$
In TTbar-deformed anomalous CFT2 the chaos bound stays saturated while butterfly velocity depends nontrivially on deformation strength and anomaly, with a Hagedorn regime where the chaotic response turns complex.
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Black Hole Mergers as the Fastest Photon Ring Scramblers
Merger remnant mass and spin are claimed to maximize the average Lyapunov exponent of the photon shell of an effective Kerr black hole, matching numerical relativity fits within a few percent for q ≲ 20.
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Attention in Krylov Space: Transformer-Based Extrapolation of Lanczos Coefficients
A transformer trained on short Lanczos-coefficient prefixes extrapolates coefficients and reconstructed observables more accurately than asymptotic fits, and transfers across system sizes in the two tested chaotic models.
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Searching for emergent spacetime in spin glasses
Spectral functions of SYK, p-spin, and SU(M) Heisenberg models show exponential tails in spin-glass phases and quasiparticle families in spin-liquid phases, with a proof that exponential decay blocks detection of bulk...
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From Confinement to Chaos in AdS/CFT Correspondence via Non-equilibrium Local States
In holographic confining backgrounds, temporal peak statistics of boundary correlators after local quenches approach the Gaussian Symplectic Ensemble for heavy operators and, in capped BTZ, even for massless ones.
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Random matrix theory signatures in free field theory
In finite-volume massive free scalar field theory after local quench, spacing ratios of two-point function extrema follow GOE statistics and an extrema-based form factor shows RMT dip-ramp-plateau.
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Butterfly effect and $\textrm{T}\overline{\textrm{T}}$-deformation
For T\bar{T}-deformed BTZ black holes, the butterfly velocity is v_B = sqrt(1 - 8π² μ/β²), exceeding the Mezei-Stanford bound for μ<0 while the Lyapunov exponent stays at the maximal value 2π/β.
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Genuine multi-entropy and holography
A new 'genuine multi-entropy' separates true q-party entanglement from lower-party pieces, and holographic systems are shown to carry O(1/G_N) genuine multipartite entanglement for connected regions.
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Scrambling Enabled Entropy Accumulation in Open Quantum Systems
A weak probe coupled to an open quantum system accumulates a finite Rényi entropy increase only when the system is in the scrambling phase, vanishing in the dissipative phase as the probe coupling goes to zero.
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Hot wormholes and chaos dynamics in a two-coupled SYK model
First numerical Lyapunov exponents for the unstable hot wormhole phase of the two-coupled SYK model, obtained via cooling and periodic-driving protocols.
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Quasinormal Modes and the Switchback Effect in Schwarzschild-de Sitter
The paper derives eikonal quasinormal mode frequencies and shock-wave switchback delays in Schwarzschild-de Sitter for arbitrary mass, using static-sphere observers and reflecting boundary conditions.
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Spectral form factors for curved spacetimes with horizon
The spectral form factor of brick-wall normal modes shows a random-matrix-like dip-ramp-plateau for both BTZ and de Sitter horizons, while the generalized three-level form factor distinguishes these integrable systems...
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ISCOs and the weak gravity conjecture bound in higher derivative theories of gravity
Derives WGC bound on probe charge-to-mass ratio from positivity of anomalous dimensions in dual CFT for charged particles in higher-derivative AdS black holes, with bound increasing with couplings and ISCOs existing u...
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Von Neumann Algebras in Double-Scaled SYK
Double-scaled SYK chord algebra is a Type II₁ factor whose empty state is tracial, cyclic, and separating.
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Black Hole Interiors via Spin Models
Numerical simulations show that a mean-field Hamiltonian reproduces exact time evolution of a four-spin quantum system up to the scrambling time, and that the system fast-scrambles with a scrambling time growing logar...
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Global Symmetry and Maximal Chaos
For arbitrary-high-charge operators in a system with a global symmetry and chemical potential, the chaos bound weakens to 2πT/(1-|μ/μ_c|), where μ_c is the critical chemical potential.
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Probing weak chaos in $\mathcal N=4$ super Yang-Mills and long-range spin chains
Finite-loop truncations of the planar dilatation operator in N=4 SYM exhibit GOE-like level statistics at large coupling for two- and four-loops (but not three), with eigenvector and Krylov diagnostics indicating weak...
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Spacetime from Operator Algebras
Reconstructs spacetime metric, curvature, and Einstein equations from matter field operator algebras in the G to 0 limit without using Bekenstein-Hawking area law, then models finite-N discrete spectra via random matr...
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Finite N Black Holes through the Brick Wall
Reinterprets the brick-wall model as an effective description of finite-N departures from the semiclassical near-horizon continuum in AdS/CFT, producing residual reflections and model-dependent echoes.
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Emergence of Krylov complexity through quantum walks: An exploration of the quantum origins of complexity
Reducing a graph walk to distance-layers reproduces Krylov/spread complexity, yielding analytic finite-q SYK Lanczos coefficients and hypercube complexity D sin²(t/D), with faster saturation than classical-walk circuits.
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Black Hole Multi-Entropy Curves
For a Haar-random model of an evaporating black hole, the q-partite Renyi multi-entropy of the black hole plus q-1 radiation subsystems peaks at a multi-entropy time later than the Page time and does not vanish at com...
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UV Effects and Short-Lived Hawking Radiation: Alternative Resolution of Information Paradox
Hawking radiation terminates around the scrambling time due to trans-Planckian stringy effects in GUP and string-field-theory-inspired toy models, yielding negligible evaporation and a mostly classical black hole.
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Spacetime and Universal Soft Modes --- Black Holes and Beyond
The paper argues that black hole interiors, Rindler horizons, and de Sitter horizons all emerge from coarse-graining soft modes of low-energy fields, selected by the Born rule.
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Post-Selection Probability and Fidelity of Bidirectional Teleportation
Post-selection probability and fidelity of bidirectional teleportation are expressed via the Loschmidt echo, revealing initial-state dependence of fidelity and stability of probability in integrable models.
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A Dynamical Systems Framework for Reinforcement Learning Safety and Robustness Verification
The claimed RL safety verification framework is absent from the manuscript; the body text is an unrelated high-energy physics paper about de Sitter horizon chaos.
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Comparative study of the butterfly velocity in holographic QCD models at finite temperature and chemical potential
Using three independent holographic methods, the authors obtain matching butterfly velocities for four QCD-like models and find a universal increase with temperature and decrease with chemical potential.
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Turbulent aspects of BMN membrane dynamics
The authors derive leading-order radial and angular stability spectra for two spherical BMN membrane configurations and demonstrate that next-to-leading-order couplings transfer dipole and quadrupole instabilities to ...
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Krylov Complexity
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
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The Case For Black Hole Remnants: A Review
A review arguing that black hole remnants remain viable and that the species and entropy objections to them are not decisive, so remnants could resolve the information paradox.
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Introduction to Black Hole Thermodynamics
A pedagogical review by Edward Witten that derives and explains the standard results of black hole thermodynamics: black hole entropy and temperature, the Unruh effect, the Euclidean approach, and the Ryu-Takayanagi formula.
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