Periodic Schrödinger operators with large gaps and Wannier-Stark ladders

J. E. Avron*, P. Exner, Y. Last

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

96 Scopus citations


We describe periodic, one dimensional Schrödinger operators, with the property that the widths of the forbidden gaps increase at large energies and the gap to band ratio is not small. Such systems can be realized by periodic arrays of geometric scatterers, e.g., a necklace of rings. Small, multichannel scatterers lead (for low energies) to the same band spectrum as that of a periodic array of (singular) point interactions known as δ'. We consider the Wannier-Stark ladder of δ' and show that the corresponding Schrödinger operator has no absolutely continuous spectrum.

Original languageAmerican English
Pages (from-to)896-899
Number of pages4
JournalPhysical Review Letters
Issue number6
StatePublished - 1994
Externally publishedYes


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