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.


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


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.