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

TL;DR

This paper demonstrates a detailed analogy between the onset of chaos in deterministic maps and the mobility edge in electronic transport on networks, providing analytical insights into conductance behavior at the transition.

Contribution

It establishes a novel equivalence between nonlinear map dynamics and electronic transport properties on complex networks, with analytical expressions for conductance at the transition.

Findings

Conductance at the transition follows a q-exponential form.

System size influences conductance decay and oscillations.

The analogy clarifies the nature of the mobility edge in electronic systems.

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.