Abstract:
We define a class of periodic electric potentials for which the spectrum of
the two-dimensional Schrödinger operator is absolutely continuous in the case of a homogeneous magnetic field $B$ with a rational flux $\eta=
(2\pi)^{-1}Bv(K)$, where $v(K)$ is the area of an elementary cell $K$ in the lattice of potential periods. Using properties of functions in this class,
we prove that in the space of periodic electric potentials in $L^2_{\mathrm{loc}}(\mathbb R^2)$ with a given period lattice and identified with $L^2(K)$, there
exists a second-category set (in the sense of Baire) such that for any
electric potential in this set and any homogeneous magnetic field with a rational flow $\eta$, the spectrum of the two-dimensional Schrödinger
operator is absolutely continuous.
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