University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Spectral Properties of Schroedinger Operator with a Quasi-periodic Potential in Dimension Two

Spectral Properties of Schroedinger Operator with a Quasi-periodic Potential in Dimension Two

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Mustapha Amrani.

Periodic and Ergodic Spectral Problems

Co-author: Roman Shterenberg (UAB)

We consider $H=-Delta+V(x)$ in dimension two, $V(x)$ being a quasi-periodic potential. We prove that the spectrum of $H$ contains a semiaxis (Bethe-Sommerfeld conjecture) and that 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 $e^{ilangle ec k, ec x angle }$ at the high energy region. Second, the isoenergetic curves in the space of momenta $ ec k$ corresponding to these eigenfunctions have a form of slightly distorted circles with holes (Cantor type structure). It is shown that the spectrum corresponding to these eigenfunctions is absolutely continuous. A method of multiscale analysis in the momentum space is developed to prove the results.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2024 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity