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Möbius transformations and electronic transport properties of large disorderless networks

Yu Jiang1, M. Martínez-Mares1, E. Castaño1, and A. Robledo2

  • 1Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, A. P. 55-534, 09340 México Distrito Federal, Mexico
  • 2Instituto de Física, Universidad Nacional Autónoma de México, A. P. 20-364, 01000 México Distrito Federal, Mexico

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Phys. Rev. E 85, 057202 – Published 17 May, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.057202

Abstract

We show that the key transport states, insulating and conducting, of large regular networks of scatterers can be described generically by negative and zero Lyapunov exponents, respectively, of Möbius maps that relate the scattering matrix of systems with successive sizes. The conductive phase is represented by weakly chaotic attractors that have been linked with anomalous transport and ergodicity breaking. Our conclusions, verified for serial as well as parallel stub and ring structures, reveal that mesoscopic behavior results from a drastic reduction of degrees of freedom.

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Outline

Information

Phys. Rev. E 85, 057202– Published 17 May, 2012
  • Received 5 April 2011

©2012 American Physical Society

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