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

Abstract

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 function of 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.

4 pages, 3 figures, minor changes in content, changed references, changed figure

References in corpus (2)

• q-Deformed Statistical-Mechanical Property in the Dynamics of Trajectories en route to the Feigenbaum Attractor
• Dynamical approach to chains of scatterers

Cited by in corpus (6)

• Generalized Statistical Mechanics at the Onset of Chaos
• Evolution with size in a locally periodic system: Scattering and deterministic maps
• Möbius transformations and electronic transport properties of large disorderless networks
• Typical length scales in conducting disorderless networks
• Manifestations of the onset of chaos in condensed matter and complex systems
• Experimental validation of the theoretical prediction for the optical $S$ matrix