TY - JOUR
T1 - Periodic Schrödinger operators with large gaps and Wannier-Stark ladders
AU - Avron, J. E.
AU - Exner, P.
AU - Last, Y.
PY - 1994
Y1 - 1994
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=12044260159&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.72.896
DO - 10.1103/PhysRevLett.72.896
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AN - SCOPUS:12044260159
SN - 0031-9007
VL - 72
SP - 896
EP - 899
JO - Physical Review Letters
JF - Physical Review Letters
IS - 6
ER -