Advanced Quantum Tight-Binding Simulation Suite: Empirical Results on Metallic Mean Vogel Arrays

This report details the empirical findings from a comprehensive numerical simulation suite analyzing the topological, spectral, and transport dynamics of metallic mean Vogel arrays. Utilizing a tight-binding Hamiltonian framework, we conduct four distinct quantum laboratory experiments. The results explicitly verify sub-diffusive quantum transport, sharp spatial localization transitions (mobility edges), macroscopic spectral robustness against broken time-reversal symmetry, and universal density of states scaling across varying aperiodic sequences.