Summing non-perturbative contributions in the gravitational path integral, extended via matrix integral saddles including one- and two-eigenvalue instantons, resolves negativity of bulk entropies in two-sided black holes.
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Chaos and Quantum Thermalization
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We show that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey {\it Berry's conjecture}. Berry's conjecture is expected to hold only if the corresponding classical system is chaotic, and essentially states that the energy eigenfunctions behave as if they were gaussian random variables. We review the existing evidence, and show that previously neglected effects substantially strengthen the case for Berry's conjecture. We study a rarefied hard-sphere gas as an explicit example of a many-body system which is known to be classically chaotic, and show that an energy eigenstate which obeys Berry's conjecture predicts a Maxwell--Boltzmann, Bose--Einstein, or Fermi--Dirac distribution for the momentum of each constituent particle, depending on whether the wave functions are taken to be nonsymmetric, completely symmetric, or completely antisymmetric functions of the positions of the particles. We call this phenomenon {\it eigenstate thermalization}. We show that a generic initial state will approach thermal equilibrium at least as fast as $O(\hbar/\Delta)t^{-1}$, where $\Delta$ is the uncertainty in the total energy of the gas. This result holds for an individual initial state; in contrast to the classical theory, no averaging over an ensemble of initial states is needed. We argue that these results constitute a new foundation for quantum statistical mechanics.
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Typical entanglement entropy with fixed global charge is given by the local thermal entropy at fixed charge density for both U(1) and SU(2) symmetries in the thermodynamic limit.
In open quantum systems, environmental coupling turns deterministic Krylov phase-space trajectories into stochastic ones by adding diffusion, destroying the hyperbolic mechanism for exponential complexity growth beyond a controlled scale.
An on-shell framework derives local detailed balance and the black hole thermal spectrum from spin universality and unitarity.
Establishes correspondence between flat, thermal, and defect conformal partial waves via shadow formalism, obtaining thermal blocks from flat four-point and defect two-point functions and reducing the Casimir equation diagonally.
A form-factor-based framework is introduced for expectation values after an integrable boundary quantum quench in the Lee-Yang model and validated numerically via adapted truncated conformal space approach.
Quantum systems reach a Maximal Entanglement Limit where entanglement geometry produces thermal reduced density matrices and probabilistic behavior in statistical and high-energy physics.
A gapped parent Hamiltonian built from two copies of a target Hamiltonian plus ultra-local inter-copy couplings allows adiabatic preparation of high-fidelity thermofield double states for ETH-obeying systems.
Energy-energy correlators in heavy-ion collisions exhibit classical hydrodynamic scaling from collective flow at large angles within the small-angle regime, collective modes at smaller angles, and light-ray OPE at even smaller angles.
An emergent gauge symmetry valid only in a subset of sectors of the fragmented S=1 dipole-conserving spin chain enables exact quantum simulation of gauge theories using a non-gauge-invariant Hamiltonian.
The study demonstrates that long-range couplings and heterogeneous degree distributions in Ising spin networks on path, Erdős–Rényi, and Watts–Strogatz topologies accelerate quantum information scrambling and chaos, diagnosed via OTOCs, tripartite information, Krylov complexity, and spectral form fa
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 integrability breaking and multifractality.
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 matrix completion of enlarged type III algebras.
Arnoldi coefficients approach unity exponentially in heating phases of driven CFTs but oscillate in non-heating phases; lattice realizations show distinct spectral and graph signatures despite similar CFT Krylov growth.
Finite cutoff in JT gravity causes faster ERB-length saturation, deformation-dependent baby-universe emission only under Lorentzian evolution, and possible one-cut universality corrections in the matrix dual.
Numerical study of a qutrit lattice with conserved charge shows thermalization signatures in states outside microcanonical windows of energy and charge, supporting a generalized form of ETH called generic ETH.
Melnikov analysis shows charge is essential for chaos under temporal perturbations in Hayward black holes with string fluids while spatial perturbations always produce chaos, with Lyapunov exponents modulated by string density and regularization.
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.
citing papers explorer
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Living on the edge: a non-perturbative resolution to the negativity of bulk entropies
Summing non-perturbative contributions in the gravitational path integral, extended via matrix integral saddles including one- and two-eigenvalue instantons, resolves negativity of bulk entropies in two-sided black holes.
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Typical entanglement entropy with charge conservation
Typical entanglement entropy with fixed global charge is given by the local thermal entropy at fixed charge density for both U(1) and SU(2) symmetries in the thermodynamic limit.
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Stochastic Krylov Dynamics: Revisiting Operator Growth in Open Quantum Systems
In open quantum systems, environmental coupling turns deterministic Krylov phase-space trajectories into stochastic ones by adding diffusion, destroying the hyperbolic mechanism for exponential complexity growth beyond a controlled scale.
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Black Hole Thermodynamics Meets On-Shell Amplitudes: Local Detailed Balance and Thermal Spectrum from Spin Universality and Unitarity
An on-shell framework derives local detailed balance and the black hole thermal spectrum from spin universality and unitarity.
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Thermal conformal partial waves from flat-space and defect CFT
Establishes correspondence between flat, thermal, and defect conformal partial waves via shadow formalism, obtaining thermal blocks from flat four-point and defect two-point functions and reducing the Casimir equation diagonally.
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Expectation values after an integrable boundary quantum quench
A form-factor-based framework is introduced for expectation values after an integrable boundary quantum quench in the Lee-Yang model and validated numerically via adapted truncated conformal space approach.
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The Maximal Entanglement Limit in Statistical and High Energy Physics
Quantum systems reach a Maximal Entanglement Limit where entanglement geometry produces thermal reduced density matrices and probabilistic behavior in statistical and high-energy physics.
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Preparing High-Fidelity Thermofield Double States
A gapped parent Hamiltonian built from two copies of a target Hamiltonian plus ultra-local inter-copy couplings allows adiabatic preparation of high-fidelity thermofield double states for ETH-obeying systems.
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Hydrodynamics and Energy Correlators
Energy-energy correlators in heavy-ion collisions exhibit classical hydrodynamic scaling from collective flow at large angles within the small-angle regime, collective modes at smaller angles, and light-ray OPE at even smaller angles.
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Hilbert Space Fragmentation and Gauge Symmetry
An emergent gauge symmetry valid only in a subset of sectors of the fragmented S=1 dipole-conserving spin chain enables exact quantum simulation of gauge theories using a non-gauge-invariant Hamiltonian.
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Topological Control of Quantum Chaos Diagnostics: OTOCs, Spectral Statistics, and Information Scrambling in Ising Model
The study demonstrates that long-range couplings and heterogeneous degree distributions in Ising spin networks on path, Erdős–Rényi, and Watts–Strogatz topologies accelerate quantum information scrambling and chaos, diagnosed via OTOCs, tripartite information, Krylov complexity, and spectral form fa
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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 integrability breaking and multifractality.
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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 matrix completion of enlarged type III algebras.
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Krylov Complexity in Periodically Driven CFTs and Critical Fermions
Arnoldi coefficients approach unity exponentially in heating phases of driven CFTs but oscillate in non-heating phases; lattice realizations show distinct spectral and graph signatures despite similar CFT Krylov growth.
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Finite cutoff JT gravity: Baby universes, Matrix dual, and (Krylov) Complexity
Finite cutoff in JT gravity causes faster ERB-length saturation, deformation-dependent baby-universe emission only under Lorentzian evolution, and possible one-cut universality corrections in the matrix dual.
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Generic ETH: Eigenstate Thermalization beyond the Microcanonical
Numerical study of a qutrit lattice with conserved charge shows thermalization signatures in states outside microcanonical windows of energy and charge, supporting a generalized form of ETH called generic ETH.
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A Note on Chaos in Hayward Black Holes with String Fluids
Melnikov analysis shows charge is essential for chaos under temporal perturbations in Hayward black holes with string fluids while spatial perturbations always produce chaos, with Lyapunov exponents modulated by string density and regularization.
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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.