We show that the set of limit-periodic Schroedinger operators with
purely absolutely continuous spectrum is dense in the space of
limit-periodic
Schroedinger operators in arbitrary dimensions. This result was previously
known only in dimension one.
The proof proceeds through the non-perturbative construction of
limit-periodic
extended states. The proof relies on a new estimate of the probability (in
quasi-momentum) that the Floquet Bloch operators have only simple
eigenvalues.