Absolute continuity conjecture for periodic second-order elliptic operators

Let $L$ be a periodic second-order elliptic operator with sufficiently nice coefficients. Absolute continuity conjecture. The spectrum of $L$ is absolutely continuous, and hence $L$ has no bound states. This is presented as the expected general absence of point spectrum for periodic second-order elliptic operators; higher-order elliptic operators and operators lacking sufficient unique continuation can have bound states, so the precise coefficient assumptions remain important.