The fractal dimension of the spectrum of quasiperiodical schrodinger operators
arXiv:1006.4095
Abstract
We study the fractal dimension of the spectrum of a quasiperiodical Schrodinger operator associated to a sturmian potential. We consider potential defined with irrationnal number verifying a generic diophantine condition. We recall how shape and box dimension of the spectrum is linked to the irrational number properties. In the first place, we give general lower bound of the box dimension of the spectrum, true for all irrational numbers. In the second place, we improve this lower bound for almost all irrational numbers. We finally recall dynamical implication of the first bound.
This paper has been fused with the next one to give: "On and Off-diagonal Sturmian operator: dynamic and spectral dimension"