Eigenstate Thermalization Hypothesis
⟨n|Â|n⟩ = A(Ē) + e^{-S(Ē)/2} f_A(Ē,ω) R_{nm} — ETH Ansatz
Hamiltonian
Matrix size N:
40
Integrability (0=chaotic):
0.0
Observable type:
σᶻ
Generate New H
Diagonal variance:
—
Off-diag RMS:
—
ETH satisfied:
—
Level spacing:
—
ETH
(Srednicki 1994, Deutsch 1991): matrix elements of physical observables in energy eigenstates are smooth functions of energy.
Integrable
→ conserved quantities → no thermalization.
Chaotic
→ ETH holds → eigenstate → thermal state.
Left: diagonal ⟨n|A|n⟩ vs energy. Right: off-diagonal |⟨n|A|m⟩|² distribution.