Computational modeling demonstrates Wigner-Dyson statistics in deterministic Jacobi Hamiltonians, indicating an arithmetic origin of quantum chaos without disorder.
A deterministic, zero-free-parameter, fully reproducible 50x50 Jacobi Hamiltonian derived from moments of completed L-functions (Riemann xi, Dirichlet beta, Ramanujan delta) exhibits Wigner-Dyson level statistics, quantum-chaotic wave-packet dynamics, and L-function-specific interference fingerprints — without disorder or classical chaos. Supplementary online resources (interactive visualization, Chinese popular-science version, reviewer-response page, latest typeset PDF) are linked under Related identifiers.
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Zhuo Chen (2026) studied this question.
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