Absolute continuity of the spectrum of the magnetic Schrödinger operator with a metric in a two-dimensional periodic waveguide. (English. Russian original) Zbl 1057.35024
St. Petersbg. Math. J. 14, No. 2, 305-343 (2003); translation from Algebra Anal. 14, No. 2, 159-206 (2002).
Schrödinger operators in periodic wave guides with periodic magnetic and electric field on a periodically curved background are considered. The authors give a thorough review of the existing literature. The main result is a rather general sufficient criterion for such operators to have absolutely continuous spectrum.
Reviewer: Heinz Siedentop (München)
MSC:
| 35P25 | Scattering theory for PDEs |
| 35J10 | Schrödinger operator, Schrödinger equation |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
