Absolutely Continuous Spectrum of a Polyharmonic Operator with a Limit Periodic Potential in Dimension Two

Details Absolutely Continuous Spectrum of a Polyharmonic Operator with a Limit Periodic Potential in Dimension Two Absolutely Continuous Spectrum of a Polyharmonic Operator with a Limit Periodic Potential in Dimension Two

2007-11-28

arxiv.org/abs/0711.4404v1

Physics

Mathematical Physics

33 pages, 8 figures

Scientific paper

We consider a polyharmonic operator $H=(-\Delta)^l+V(x)$ in dimension two
with $l\geq 6$, $l$ being an integer, and a limit-periodic potential $V(x)$. We
prove that the spectrum contains a semiaxis of absolutely continuous spectrum.

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