Magnetic Transport Along Translationally Invariant Obstacles

A thesis by Michal Grňo, supervised by prof. Pavel Exner.

Links

• The thesis in PDF
• Supervisor's review (in Czech)
• Opponent's review

Abstract

We discuss the spectra of magnetic Schrödinger operators of the form ${(-\mathrm i\nabla + \vec{A}(x))^2 + V(x)}$ on ${L^2(\Omega)}$, where $\Omega$ is either $\mathbb R^2$, a half-plane, a strip, or a thin layer in $\mathbb R^3$. 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 $\delta$-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.

Template

The template used for the TeX document was made by:

• Martin Mareš mj@ucw.cz – správce šablony
• Arnošt Komárek komarek@karlin.mff.cuni.cz
• Michal Kulich kulich@karlin.mff.cuni.cz