Journal of Statistical Physics

, Volume 65, Issue 3, pp 715–723

Power law growth for the resistance in the Fibonacci model

  • B. Iochum
  • D. Testard

DOI: 10.1007/BF01053750

Cite this article as:
Iochum, B. & Testard, D. J Stat Phys (1991) 65: 715. doi:10.1007/BF01053750


Many one-dimensional quasiperiodic systems based on the Fibonacci rule, such as the tight-binding HamiltonianHψ(n)=ψ(n+1)+ψ(n−1)+λv(n)ψ(n),nεℤ,ψεl2(ℤ),λεℝ, wherev(n)=[(n+1)α]−[],[x] denoting the integer part ofx and α the golden mean\((\sqrt 5 --1)/2\), give rise to the same recursion relation for the transfer matrices. It is proved that the wave functions and the norm of transfer matrices are polynomially bounded (critical regime) if and only if the energy is in the spectrum of the Hamiltonian. This solves a conjecture of Kohmoto and Sutherland on the power-law growth of the resistance in a one-dimensional quasicrystal.

Key words

Periodic Hamiltonian Fibonacci chain transfer matrix 

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • B. Iochum
    • 1
    • 2
  • D. Testard
    • 1
    • 3
  1. 1.Centre de Physique Théorique (Unité Propre de Recherche 7061)CNRS Luminy, Case 907Marseille Cedex 9France
  2. 2.Université de ProvenceMarseilleFrance
  3. 3.Université d'Aix-Marseille IILuminyFrance

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