Numerical analysis shows spectral convergence to the critical line in high-dimensional pseudo-Hermitian operators, suggesting implications for quantum chaos.
We investigate spectral properties of a family of finite-dimensional pseudo-Hermitian operators constructed on hierarchical fractal graphs. Numerical analysis reveals systematic convergence of the spectrum to the critical line ℜ(s) = 1/2 as the system dimension increases, with machine-precision agreement observed for systems of order 10^4 vertices. The limiting spectral statistics agree with predictions of random matrix theory for the Gaussian Symplectic Ensemble. Connections to the Hilbert-Polya conjecture and quantum chaos are discussed.
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Roman V. Savenkov (2026) studied this question.
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