GUE sine-kernel: R_2(s) = 1 - (sin(pi s)/(pi s))^2; level repulsion at s=0 and Poisson at s->inf

Layer 1 — Physicsin the quantum-chaos subtree

GUE random-matrix sine-kernel framework (Dyson 1962). Setup: for chaotic quantum systems with time-reversal symmetry broken (e.g. Aharonov-Bohm billiards), Berry-Tabor semiclassics predicts the local level statistics match those of…

Related concepts

Fredholm operator
Theorem: GUE R_2(s) limits R_2(0) = 0 (strong repulsion), R_2(s->inf) = 1 (decorrelation)

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