Home > Search Results: keywords:"two-dimensional quantum systems|magnetic field|nonlocal perturbations|translational invariance|spectral properties"
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National Repository of Grey Literature 1 records found  Search took 0.01 seconds. 
Magnetic transport along translationally invariant obstacles
 Grňo, Michal ; Exner, Pavel (advisor) ; Lotoreichik, Vladimir (referee)
We discuss the spectra of magnetic Schrödinger operators of the form (−i∇+ ⃗A(x))2 + V (x) on L2 (Ω), where Ω is either R2 , a half-plane, a strip, or a thin layer in R3 . This class of operators includes the Landau Hamiltonian, as well as the Iwatsuka Hamiltonian and other translationally invariant perturbations of it. We provide a comprehensive list of the known results regarding these operators, and inspect two Hamiltonians that have not yet been studied: the Landau Hamiltonian with a δ-interaction supported on a line and the Landau Hamiltonian in a half-plane with a Robin boundary condition. We prove that the spectra of these two Hamiltonians are purely absolute continuous and that the former has gaps between adjacent Landau levels. 1
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