Microcanonical Operator Spectrum, BPS Chaos and Free Probability Theory

arXiv:2609.22422 · hep-th, cond-mat.str-el · Submitted 2026-09-18 · Read on arXiv

hep-th, cond-mat.str-el

Submitted: 2026-09-18

Updated: 2026-10-01

Terminology

• Degeneracy — 11× in this paper · explained in 3 episodes
• Hilbert Space — 10× in this paper · explained in 2 episodes
• Trace — 9× in this paper · explained in 2 episodes
• Eigenstate Thermalization Hypothesis — 5× in this paper
• Generalization — 4× in this paper · explained in 13 episodes
• SYK Model — 2× in this paper · explained in 2 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Eigenstate Thermalization Hypothesis (ETH) — 1× in this paper · explained in 4 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Universality Class — 1× in this paper · explained in 2 episodes
• alpha — 1× in this paper · explained in 1 episode

Sources

• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• The Eigenstate Thermalization Hypothesis and Out of Time Order Correlators
• Eigenstate Correlations, Thermalization and the Butterfly Effect
• Bounds on chaos from the eigenstate thermalization hypothesis
• Non-Gaussianities in the Statistical Distribution of Heavy OPE Coefficients and Wormholes
• OPE statistics from higher-point crossing
• Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies
• Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
• Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems
• Canonical Universality
• Microcanonical Truncations of Observables in Quantum Chaotic Systems
• Matrix models for eigenstate thermalization
• JT gravity with matter, generalized ETH, and Random Matrices
• Holography for people with no time
• Looking at supersymmetric black holes for a very long time
• BPS Chaos
• Mastering the Master Field
• Beyond islands: A free probabilistic approach
• Quantum Signatures of Chaos from Free Probability
• Eigenstate Thermalization Hypothesis and Free Probability

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