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arxiv: 0904.2891 · v1 · submitted 2009-04-19 · 🧮 math-ph · math.MP

Absolute continuity of the spectrum of a Landau Hamiltonian perturbed by a generic periodic potential

classification 🧮 math-ph math.MP
keywords gammaperiodicpotentialfieldgenerichamiltonianlandaumagnetic
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Consider $\Gamma$, a non-degenerate lattice in $\R^2$ and a constant magnetic field $B$ with a flux though a cell of $\Gamma$ that is a rational multiple of $2\pi$. We prove that for a generic $\Gamma$-periodic potential $V$, the spectrum of the Landau Hamiltonian with magnetic field $B$ and periodic potential $V$ is purely absolutely continuous.

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