Extended States for the Schroedinger Operator with Quasi-Periodic Potential in Dimension Two (eBook)

Yulia E Karpeshina (Autor)

eBook Download: PDF

2019
139 Seiten
American Mathematical Society (Verlag)
978-1-4704-5069-4 (ISBN)

Infos

The authors consider a Schroedinger operator $H=-/Delta +V(/vec x)$ in dimension two with a quasi-periodic potential $V(/vec x)$. They prove that the absolutely continuous spectrum of $H$ 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 $e^i/langle /vec /varkappa ,/vec x/rangle $ in the high energy region. Second, the isoenergetic curves in the space of momenta $/vec /varkappa $ corresponding to these eigenfunctions have the form of slightly distorted circles with holes (Cantor type structure). A new method of multiscale analysis in the momentum space is developed to prove these results. The result is based on a previous paper on the quasiperiodic polyharmonic operator $(-/Delta )^l+V(/vec x)$, $l>1$. Here the authors address technical complications arising in the case $l=1$. However, this text is self-contained and can be read without familiarity with the previous paper.

Produkt-Details

• Erscheint lt. Verlag: 4.10.2019
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• ISBN-10: 1-4704-5069-0 / 1470450690
• ISBN-13: 978-1-4704-5069-4 / 9781470450694