Problem dossier · Dynamics & Analysis
Berry–Tabor conjecture
The energy-level spacings of a generic quantized integrable system follow Poisson statistics — in contrast to random-matrix statistics for chaotic systems.
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Status
Open as a general theorem; proved in special arithmetic cases (e.g. certain flat tori via Sarnak, Eskin–Margulis–Mozes). Overwhelming numerical support.
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The Angle of Attack
Simulate spectra of integrable billiards, flat tori, and quantum maps; test spacing statistics at scale and probe the exceptional (non-generic) parameter sets where Poisson fails.
Tags: quantum chaos · level spacing · spectra · random matrices
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The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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