A geometric result links quantum thermalization in almost all accessible pure states to saturation of controllably nonlocal out-of-time-ordered correlators, avoiding statistical averages entirely.
Quantum Ergodicity and Mixing
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This is an expository article for the Encyclopedia of Mathematical Physics on the subject in the title.
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A large-scale analogue of Zelditch's quantum mixing theorem is established for compact hyperbolic surfaces using the wave equation and geodesic flow mixing, valid for arithmetic and Weil-Petersson random surfaces.
Bean- and peanut-shaped billiards show strong correlations between classical chaos indicators and quantum statistical/dynamical measures, including eigenfunction scarring.
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Provable quantum thermalization without statistical averages
A geometric result links quantum thermalization in almost all accessible pure states to saturation of controllably nonlocal out-of-time-ordered correlators, avoiding statistical averages entirely.
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Quantum Mixing and Benjamini-Schramm Convergence of Hyperbolic Surfaces
A large-scale analogue of Zelditch's quantum mixing theorem is established for compact hyperbolic surfaces using the wave equation and geodesic flow mixing, valid for arithmetic and Weil-Petersson random surfaces.
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Classical and quantum chaos in bean- and peanut-shaped billiards
Bean- and peanut-shaped billiards show strong correlations between classical chaos indicators and quantum statistical/dynamical measures, including eigenfunction scarring.