Spectral properties of a limit-periodic Schrödinger operator in dimension two

Autor: Yulia Karpeshina, Young-Ran Lee
Rok vydání: 2013
Předmět:
Zdroj: Journal d'Analyse Mathématique. 120:1-84
ISSN: 1565-8538
0021-7670
DOI: 10.1007/s11854-013-0014-1
Popis: We study the Schrodinger operator H = −Δ + V(x) in dimension two, V(x) being a limit-periodic potential. We prove that the 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 exp( $$i\left\langle {\overrightarrow k ,\overrightarrow x } \right\rangle $$ ) at the high energy region. Second, the isoenergetic curves in the space of momenta $$\overrightarrow k $$ corresponding to these eigenfunctions have the form of slightly distorted circles with holes (Cantor type structure). Third, the spectrum corresponding to the eigenfunctions (the semiaxis) is absolutely continuous.
Databáze: OpenAIRE
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