1006.4095 (Laurent Marin)

The fractal dimension of the spectrum of quasiperiodical schrodinger
operators    [PDF]

Laurent Marin

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.

View original: http://arxiv.org/abs/1006.4095