Spectral properties of a tight binding Hamiltonian with period doubling potential

• DOI: 10.1007/bf02098048
• Publication Date: 2005-09-12T14:44:49Z
• Authors: Jean Bellissard; Anton Bovier; Jean-Michel Ghez
• Keywords: Hamiltonian (control theory); Lebesgue measure; Absolute continuity; Tight binding; Sequence (biology)

We study a one dimensional tight binding hamiltonian with a potential given by the period doubling sequence. We prove that its spectrum is purely singular continuous and supported on a Cantor set of zero Lebesgue measure, for all nonzero values of the potential strength. Moreover, we obtain the exact labelling of all spectral gaps and compute their widths asymptotically for small potential strength.