Georgia Institute of Technology College of Sciences

The motivation is to compute the spectral properties of the Schrodinger operator describing an electron in a quasicrystal. The talk will focus on the case of the Fibonacci sequence (one dimension), to illustrate the method. Then the Wannier transform will be defined. It will be shown that the Hamiltonian can be seen as a direct integral over operators with discrete spectra, in a way similar to the construction of band spectra for crystal. A discussion of the differences with crystal will conclude this talk.This is joint work with Giuseppe De Nittis and Vida Milani