Geodesic
Magnetic Bloch theory and noncommutative geometry
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 193-205

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An interpretation of the magnetic Bloch theory in terms of noncommutative geometry is given. As an application we obtain a mathematical interpretation of the quantum Hall effect. 
@article{TM_2012_279_a11,
     author = {A. G. Sergeev},
     title = {Magnetic {Bloch} theory and noncommutative geometry},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {193--205},
     publisher = {mathdoc},
     volume = {279},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_279_a11/}
}
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A. G. Sergeev. Magnetic Bloch theory and noncommutative geometry. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 193-205. http://geodesic.mathdoc.fr/item/TM_2012_279_a11/