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GUE Random Matrix Theory

The Gaussian Unitary Ensemble — Hermitian matrices whose eigenvalue statistics govern chaotic quantum systems.

The Gaussian Unitary Ensemble is the space of N×N Hermitian matrices with independent Gaussian entries, invariant under unitary conjugation. Its eigenvalue distribution obeys the Wigner semicircle law, and its spacings follow the Wigner surmise.

Heavy-nucleus resonance spectra, quantum-chaotic billiards, and Riemann zeros all exhibit the same local statistics. That universality is why a single spectral toolkit generalizes across all three domains.

Our neutronic solver projects the transport operator onto a GUE-anchored basis so that eigenvalue statistics are inherited rather than sampled.

// related concepts

Montgomery Pair Correlation

The conjecture that normalized spacings of Riemann zeta zeros match GUE eigenvalue statistics.

Spectral Neutronics

Closed-form eigenexpansion of the neutron transport operator over a Riemann-anchored basis.

Monte Carlo vs Analytical Closure

Why stochastic sampling is not the only path — and why analytical closure changes the deployment economics of advanced reactors.