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arXiv · 0905.4686

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

M. Martinez-Mares·A. Robledo
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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.

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M. Martinez-Mares, A. Robledo. 2009-05-28. Equivalence between the mobility edge of electronic transport on disorderless networks and the onset of chaos via intermittency in deterministic maps. https://doi.org/10.1103/physreve.80.045201

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