On absolute continuity of the spectrum of a periodic magnetic Schrödinger operator

Details On absolute continuity of the spectrum of a periodic magnetic Schrödinger operator On absolute continuity of the spectrum of a periodic magnetic Schrödinger operator

2009-02-19

arxiv.org/abs/0902.3371v2

J. Phys. A: Math. Theor. 42 (2009) 275204

Physics

Mathematical Physics

25 pages

Scientific paper

10.1088/1751-8113/42/27/275204

We consider the Schr\"odinger operator in ${\mathbb R}^n$, $n\geq 3$, with the electric potential $V$ and the magnetic potential $A$ being periodic functions (with a common period lattice) and prove absolute continuity of the spectrum of the operator in question under some conditions which, in particular, are satisfied if $V\in L^{n/2}_{{\mathrm {loc}}}({\mathbb R}^n)$ and $A\in H^q_{{\mathrm {loc}}}({\mathbb R}^n;{\mathbb R}^n)$, $q>(n-1)/2$.

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