The European Physical Journal Special Topics

, Volume 226, Issue 3, pp 417–425 | Cite as

Typical length scales in conducting disorderless networks

  • M. Martínez-MaresEmail author
  • V. Domínguez-RochaEmail author
  • A. RobledoEmail author
Regular Article
Part of the following topical collections:
  1. Nonlinearity, Nonequilibrium and Complexity: Questions and Perspectives in Statistical Physics


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Martínez-Mares, A. Robledo, Phys. Rev. E 80, 045201(R) (2009)ADSCrossRefGoogle Scholar
  2. 2.
    Y. Jiang, M. Martínez-Mares, E. Castaño, A. Robledo, Phys. Rev. E 85, 057202 (2012)ADSCrossRefGoogle Scholar
  3. 3.
    V. Domínguez-Rocha, M. Martínez-Mares, J. Phys. A: Math. Theor. 46, 235101 (2013)ADSCrossRefGoogle Scholar
  4. 4.
    H.G. Schuster, Deterministic Chaos. An Introduction (VCH Publishers, Weinheim, 1988)Google Scholar
  5. 5.
    A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16, 285 (1985)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    F. Baldovin, A. Robledo, Europhys. Lett. 60, 518 (2002)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    M. Büttiker, IBM J. Res. Dev. 32, 317 (1988)CrossRefGoogle Scholar
  8. 8.
    P.A. Lee, T.V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985)ADSCrossRefGoogle Scholar
  9. 9.
    C.W.J. Beenakker, Rev. Mod. Phys. 69, 731 (1997)ADSCrossRefGoogle Scholar
  10. 10.
    P.A. Mello, N. Kumar, in Quantum Transport in Mesoscopic Systems. Complexity and Statistical Fluctuations (Oxford University Press, New York, 2004), p. 289Google Scholar

Copyright information

© EDP Sciences and Springer 2017

Authors and Affiliations

  1. 1.Departamento de Física, Universidad Autónoma Metropolitana-IztapalapaCiudad de MéxicoMexico
  2. 2.Instituto de Ciencias Físicas, Universidad Nacional Autónoma de MéxicoCuernavaca Mor.Mexico
  3. 3.Instituto de Física y Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de MéxicoCiudad de MéxicoMexico

Personalised recommendations