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

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...

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Bibliographic Details
Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 80; no. 4 Pt 2; p. 045201
Main Authors Martínez-Mares, M, Robledo, A
Format Journal Article
LanguageEnglish
Published United States 01.10.2009
Subjects
Algorithms
Computer Simulation
Electron Transport
Manufactured Materials
Models, Chemical
Nonlinear Dynamics
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Summary: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 a function of the 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.
ISSN:1550-2376
DOI:10.1103/PhysRevE.80.045201