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The absence of the absolutely continuous spectrum for \(\delta'\) Wannier-Stark ladders. (English) Zbl 0884.47049

Summary: A modification of the Kronig-Penney model consisting of equidistantly spaced \(\delta'\) interactions is considered. We prove that an absolutely continuous spectrum of such a system disappears under the influence of an external electric field. The result extends to periodic lattices of nonidentical \(\delta'\) interactions and potentials which are lower unbounded and, up to a bounded term, asymptotically decreasing with bounded first two derivatives.

MSC:

47N50 Applications of operator theory in the physical sciences
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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