Journal of Statistical Physics

, Volume 56, Issue 3, pp 525–531

Singular continuous spectrum on a cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian

  • András Sütő
Short Communications

DOI: 10.1007/BF01044450

Cite this article as:
Sütő, A. J Stat Phys (1989) 56: 525. doi:10.1007/BF01044450

Abstract

It is rigorously proven that the spectrum of the tight-binding Fibonacci Hamiltonian,Hmnm, n+1m, n−1m, nμ[(n+1)α]−[nα]) where α=(√5−1)/2 and [·] means integer part, is a Cantor set of zero Lebesgue measure for all real nonzeroμ, and the spectral measures are purely singular continuous. This follows from a recent result by Kotani, coupled with the vanishing of the Lyapunov exponent in the spectrum.

Key words

Schrödinger equationCantor spectrumsingular continuityLyapunov exponent

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • András Sütő
    • 1
  1. 1.Institut de Physique ThéoriqueUniversité de LausanneLausanneSwitzerland