## 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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### References:

 [1] DOI: 10.1007/BF02099175 · Zbl 0743.35053 [2] DOI: 10.1088/0305-4470/26/7/006 · Zbl 0772.34059 [3] DOI: 10.1103/RevModPhys.63.91 [4] DOI: 10.1016/0034-4877(86)90045-5 · Zbl 0638.70016 [5] DOI: 10.1088/0305-4470/26/2/025 · Zbl 0778.58069 [6] DOI: 10.1006/jfan.1993.1006 · Zbl 0790.47039 [7] DOI: 10.1103/PhysRevLett.72.896 · Zbl 0942.34503 [8] DOI: 10.1007/BF01217772 · Zbl 0684.47010 [9] DOI: 10.1088/0305-4470/28/4/030 · Zbl 0854.47033 [10] Brasche J. F., Ukrainian J. Math. 46 pp 37– (1994) [11] Nenciu G., Func. Anal. Appl. 19 pp 81– (1985) · Zbl 0582.34056 [12] DOI: 10.1007/BF01597402
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