Equivalence between the mobility edge of electronic transport on disorderless networks and the onset of chaos via intermittency in deterministic maps.
We exhibit a remarkable equivalence between the dynamics of an intermittent nonlinear map and the electronic transport properties (obtained via the scattering matrix) of a crystal defined on a double Cayley tree. This strict analogy reveals in detail the nature of the mobility edge normally studied near (not at) the metal-insulator transition in electronic systems. We provide an analytical expression for the conductance as a function of the system size that at the transition obeys a q-exponential form. This manifests as power-law decay or few and far between large spike oscillations according to different kinds of boundary conditions.
Martínez-Mares
M
M
Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, México, Distrito Federal, Mexico.
Robledo
A
A
D000465:Algorithms; D003198:Computer Simulation; D004579:Electron Transport; D008420:Manufactured Materials; D008956:Models, Chemical; D017711:Nonlinear Dynamics