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Spectral Determinants, RG Flow, and GUE Universality (Physics Version) | Synapse

April 25, 2026Open Access

Spectral Determinants, RG Flow, and GUE Universality (Physics Version)

Key Points

This research aims to explore the emergence of Gaussian Unitary Ensemble (GUE) statistics from quantum-inspired Hamiltonians and their relation to spectral stability.
Utilized trace formulas to analyze spectral correlations
Applied renormalization group (RG) techniques to study fixed points
Reformulated the Riemann Hypothesis using spectral stability conditions
Demonstrated that GUE statistics are a unique stable fixed point of spectral correlation functions
Showed a connection between spectral stability and the Riemann Hypothesis through Fredholm determinants

Abstract

AbstractWe study a quantum-inspired logarithmic prime Hamiltonian with trace-class perturbations.Using trace formulas and renormalization group (RG) arguments, we show that Gaussian UnitaryEnsemble (GUE) statistics emerge as the unique stable fixed point of spectral correlationfunctions. The Riemann Hypothesis is reformulated as a spectral stability condition of the corresponding Fredholm determinant.

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Cite This Study

Oleg Glushkov (Thu,) studied this question.

synapsesocial.com/papers/69ec5b3d88ba6daa22dacda4 https://doi.org/https://doi.org/10.5281/zenodo.19707908

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