Spectral properties of three-dimensional Anderson model

The three-dimensional Anderson model represents a paradigmatic to understand the localization transition. In this work we first review some key results obtained for in past 50 years, and then study its properties from perspective of modern numerical approaches. Our main focus is on quantitative comparison between level sensitivity statistics statistics. While former studies Hamiltonian eigenlevels upon inserting magnetic flux, latter unperturbed eigenlevels. We define two versions dimensionless conductance, corresponding width curvature distribution relative mean spacing, second ratio Heisenberg Thouless time spectral form factor. show that both conductances look remarkably similar around transition, particular, they predict nearly identical critical point consistent with other measures further those quantities: curvatures, discuss particular similarities differences characteristic energy studied by Edwards their pioneering [J. Phys. C. 5, 807 (1972)]. context factor, at it enters broad time-independent regime, which value compressibility variance. Finally, test scaling solution average spacing crossover regime using cost function minimization approach introduced [Phys. Rev. B. 102, 064207 (2020)]. find extracted transition coefficient agree literature high accuracy.