Typical length scales in conducting disorderless networks

TL;DR

This paper explores the scattering properties and localization length in disorderless conducting networks using a novel equivalence with nonlinear maps, providing new insights into electronic transport at the mobility edge.

Contribution

It introduces a new approach linking nonlinear map dynamics to scattering matrix properties in disorderless networks, enhancing understanding of localization and transport.

Findings

Derived general expressions for electronic transport.

Provided a physical interpretation of the generalized localization length.

Expanded knowledge of scattering properties at the mobility edge.

Abstract

We take advantage of a recently established equivalence, between the intermittent dynamics of a deterministic nonlinear map and the scattering matrix properties of a disorderless double Cayley tree lattice of connectivity $K$, to obtain general electronic transport expressions and expand our knowledge of the scattering properties at the mobility edge. From this we provide a physical interpretation of the generalized localization length.