Equivalence between the mobility edge of electronic transport on disorderless networks and the onset of chaos via intermittency in deterministic maps

Möbius transformations and electronic transport properties of large disorderless networks

We show that the key transport states, insulating and conducting, of large regular networks of scatterers can be described generically by negative and zero Lyapunov exponents, respectively, of Möbius maps that relate the scattering matrix of systems with successive sizes. The conductive phase is represented by weakly chaotic attractors that have been linked with anomalous transport and ergodicity breaking. Our conclusions, verified for serial as well as parallel stub and ring structures, reveal that mesoscopic behavior results from a drastic reduction of degrees of freedom.