10-130 Yulia Karpeshina, Young-Ran Lee

Spectral properties of a limit-periodic Schr\"{o}dinger operator in dimension two (549K, LaTeX 2e with 5 EPS Figures) Aug 24, 10

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We study Schr\"{o}dinger operator $H=-\Delta+V(x)$ 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 $e^{i\langle ec k,ec x angle }$ 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). Third, the spectrum corresponding to the eigenfunctions (the semiaxis) is absolutely continuous.

Files: 10-130.src( 10-130.keywords , Schrodinger14.tex , D_1.eps , D_2.eps , Phi_2-1.eps , Phi_3-3.eps , fig1.eps.mm )