1111.0953 (W. N. Yessen)

Spectral analysis of tridiagonal Fibonacci Hamiltonians    [PDF]

W. N. Yessen

We consider a family of discrete Jacobi operators on the one-dimensional integer lattice, with the diagonal and the off-diagonal entries given by two sequences generated by the Fibonacci substitution on two letters. We show that the spectrum is a Cantor set of zero Lebesgue measure, and discuss its fractal structure and Hausdorff dimension. We also extend some known results on the diagonal and the off-diagonal Fibonacci Hamiltonians.

View original: http://arxiv.org/abs/1111.0953