Geodesic
Absolute continuity of the spectrum of two-dimensional periodic Schr\"odinger operators with strongly subordinate magnetic potential
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 279-320

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A two-dimensional periodic magnetic Schrödinger operator with variable metric is considered. It is shown that under the condition of strong subordination of the magnetic potential the spectrum of the operator is absolutely continuous. A similar result concerning the Schrödinger operator in a simply connected periodic waveguide is also formulated. 
@article{ZNSL_2003_303_a14,
     author = {R. G. Shterenberg},
     title = {Absolute continuity of the spectrum of two-dimensional periodic {Schr\"odinger} operators with strongly subordinate magnetic potential},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {279--320},
     publisher = {mathdoc},
     volume = {303},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a14/}
}
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R. G. Shterenberg. Absolute continuity of the spectrum of two-dimensional periodic Schr\"odinger operators with strongly subordinate magnetic potential. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 279-320. http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a14/