A Strategy for Proving the Strong Eigenstate Thermalization Hypothesis : Chaotic Systems and Holography
arXiv:2411.09746 · doi:10.1007/JHEP01(2025)095
Abstract
The strong eigenstate thermalization hypothesis (ETH) provides a sufficient condition for thermalization and equilibration. Although it is expected to be hold in a wide class of highly chaotic theories, there are only a few analytic examples demonstrating the strong ETH in special cases, often through methods related to integrability. In this paper, we explore sufficient conditions for the strong ETH that may apply to a broad range of chaotic theories. These conditions are expressed as inequalities involving the long-time averages of real-time thermal correlators. Specifically, as an illustration, we consider simple toy examples which satisfy these conditions under certain technical assumptions. This toy models have same properties as holographic theories at least in the perturbation in large . We give a few comments for more realistic holographic models.
70 pages, 13 figures
References in corpus (65)
- Gauge Theory Correlators from Non-Critical String Theory
- Probing many-body dynamics on a 51-atom quantum simulator
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- A bound on chaos
- Comments on the Sachdev-Ye-Kitaev model
- Eternal Black Holes in AdS
- Black holes and the butterfly effect
- Black holes as mirrors: quantum information in random subsystems
- Fast Scramblers
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Time Evolution of Entanglement Entropy from Black Hole Interiors
- Holography from Conformal Field Theory
- Canonical Typicality
- Quantum mechanical evolution towards thermal equilibrium
- The approach to thermal equilibrium in quantized chaotic systems
- Thermalization and prethermalization in isolated quantum systems: a theoretical overview
- Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
- Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
- Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma
- Entanglement Tsunami: Universal Scaling in Holographic Thermalization
- Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
- Virasoro Conformal Blocks and Thermality from Classical Background Fields
- Holographic Evolution of Entanglement Entropy
- Holographic Thermalization
- Finite-size scaling of eigenstate thermalization
- Emergent Spacetime and Holographic CFTs
- Quantum equilibration in finite time
- Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
- Weak Field Black Hole Formation in Asymptotically AdS Spacetimes
- Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
- Subsystem ETH
- On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems
- Bulk and Boundary Dynamics in BTZ Black Holes
- Black Hole Collapse in the 1/c Expansion
- Very Long Time Scales and Black Hole Thermal Equilibrium
- A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its Spots
- Eigenstate thermalization in the Sachdev-Ye-Kitaev model
- Fluctuation Theorem for Many-Body Pure Quantum States
- Eigenstate Thermalization Hypothesis and Free Probability
- Typicality of thermal equilibrium and thermalization in isolated macroscopic quantum systems
- The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories
- Evolution of Two-Point Functions from Holography
- A Matrix Model for Black Hole Thermalization
- Modular Invariance, Tauberian Theorems, and Microcanonical Entropy
- Probing thermality beyond the diagonal
- Finite-size scaling of out-of-time-ordered correlators at late times
- ETH and Modular Invariance of 2D CFTs
- On thermality of CFT eigenstates
- Quantum Error Correcting Codes in Eigenstates of Translation-Invariant Spin Chains
- Numerical Large Deviation Analysis of Eigenstate Thermalization Hypothesis
- Gravitational orbits, double-twist mirage, and many-body scars
- Poincare Recurrences and Topological Diversity
- Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
- Macroscopic and Microscopic Thermal Equilibrium
- Atypicality of Most Few-Body Observables
- On the local equivalence between the canonical and the microcanonical distributions for quantum spin systems
- Eigenstate Thermalization in Long-Range Interacting Systems
- Thermalization in Large-N CFTs
- Geometry And Quantum Noise
- Information loss, mixing and emergent type III factors
- How accurately can the microcanonical ensemble describe small isolated quantum systems?
- Bulk renormalization and the AdS/CFT correspondence
- Macrostate equivalence of two general ensembles and specific relative entropies
- Microstate Distinguishability, Quantum Complexity, and the Eigenstate Thermalization Hypothesis