Math Seminars
David Damanik
(Rice)
The Fractal Dimension of the Spectrum of the Fibonacci Operator
The Fibonacci operator is the most prominent model of a
one-dimensional quasicrystal and it has been studied since the early
1980's by both physicists and mathematicians. It is known that its
spectrum is a Cantor set of zero Lebesgue measure. In this talk we
discuss the dimension of this set. We present upper and lower bounds
that give a precise answer in the large coupling limit. We also present
consequences of these bounds for the spreading in space of a solution to
the time-dependent Schr"odinger equation with Fibonacci potential. This
is joint work with Mark Embree, Anton Gorodetski, and Serguei
Tcheremchantsev.