Quantum chaos · level statistics · ETH · thermalization in closed systems
The Eigenstate Thermalization Hypothesis (Deutsch 1991, Srednicki 1994): for a chaotic quantum system, each energy eigenstate |n⟩ gives expectation values ⟨n|A|n⟩ = A(E_n) + e^{-S/2}f(E)R_{nm}, where S is entropy and R is a random matrix. ETH implies thermalization: any initial state with well-defined energy thermalizes as off-diagonal dephasing kills quantum coherences. The signature: level statistics follow Wigner-Dyson (GUE/GOE) for chaotic systems vs Poisson for integrable ones.