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

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

2009-05-28

arxiv.org/abs/0905.4686v2

Physical Review E 80, 045201(R) (2009)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

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

Scientific paper

10.1103/PhysRevE.80.045201

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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