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Eigenstate Randomization Hypothesis: Why Does the Long-Time Average Equal the Microcanonical Average?

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arxiv 1012.3237 v4 pith:6W4AMFHS submitted 2010-12-15 cond-mat.stat-mech

Eigenstate Randomization Hypothesis: Why Does the Long-Time Average Equal the Microcanonical Average?

Tatsuhiko N. Ikeda , Yu Watanabe , Masahito Ueda This is my paper
classification cond-mat.stat-mech
keywords averagehypothesiseigenstatemicrocanonicalboundlong-timeobservablesrandomization
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We derive an upper bound on the difference between the long-time average and the microcanonical ensemble average of observables in isolated quantum systems. We propose, numerically verify, and analytically support a new hypothesis, eigenstate randomization hypothesis (ERH), which implies that in the energy eigenbasis the diagonal elements of observables fluctuate randomly. We show that ERH includes eigenstate thermalization hypothesis (ETH) and makes the aforementioned bound vanishingly small. Moreover, ERH is applicable to integrable systems for which ETH breaks down. We argue that the range of the validity of ERH determines that of the microcanonical description.

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  1. Eigenstate Thermalization Hypothesis with projective representation

    hep-th 2025-09 conditional novelty 6.0

    For systems with projective symmetry representations, the paper proposes a modified ETH and shows that charged operators with symmetry-supplied charges thermalize to a generalized Gibbs ensemble, not the ordinary Gibb...