Spectral properties of a limit-periodic Schrödinger operator

Math Physics Seminar
Wednesday, March 30, 2011 - 4:30pm for 1 hour (actually 50 minutes)
Skiles 006
Yulia Karpeshina – Dept. of Mathematics, University of Alabama, Birmingham
Michael Loss
We study a two dimensional Schrödinger operator for a limit-periodic potential. We prove that the spectrum contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves in the high energy region. Second, the isoenergetic curves in the space of momenta corresponding to these eigenfunctions have a form of slightly distorted circles with holes (Cantor type structure). Third, the spectrum corresponding to these eigenfunctions (the semiaxis) is absolutely continuous.