Geodesic
Absolute continuity of the periodic Schrödinger operator in transversal geometry
Journal of the European Mathematical Society, Tome 19 (2017) no. 2, pp. 531-550

Voir la notice de l'article provenant de la source EMS Press

We show that the spectrum of a Schrödinger operator on Rn,n≥3, with a periodic smooth Riemannian metric, whose conformal multiple has a product structure with one Euclidean direction, and with a periodic electric potential in Llocn=2​(Rn), is purely absolutely continuous. Previous results in the case of a general metric are obtained in [12], see also [9], under the assumption that the metric, as well as the potential, are reflection symmetric.
DOI : 10.4171/jems/673
Classification : 35-XX, 47-XX, 81-XX
Keywords: Periodic Schrödinger operator, spectrum, absolute continuity, Riemannian metric, spectral clusters, resolvent estimates 
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     author = {Katsiaryna Krupchyk and Gunther Uhlmann},
     title = {Absolute continuity of the periodic {Schr\"odinger} operator in transversal geometry},
     journal = {Journal of the European Mathematical Society},
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     doi = {10.4171/jems/673},
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Katsiaryna Krupchyk; Gunther Uhlmann. Absolute continuity of the periodic Schrödinger operator in transversal geometry. Journal of the European Mathematical Society, Tome 19 (2017) no. 2, pp. 531-550. doi: 10.4171/jems/673

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