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The noncommutative geometry of wire networks from triply periodic surfaces

By Ralph M. Kaufmann, Sergei Khlebnikov and Birgit Wehefritz-Kaufmann

Abstract

We study wire networks that are the complements of triply periodic minimal surfaces. Here we consider the P, D, G surfaces which are exactly the cases in which the corresponding graphs are symmetric and self-dual. Our approach is using the Harper Hamiltonian in a constant magnetic field. We treat this system with the methods of noncommutative geometry and obtain a classification for all the $C^*$ geometries that appear.Comment: 15 pages, 5 figure

Topics: Mathematical Physics
Year: 2012
DOI identifier: 10.1088/1742-6596
OAI identifier: oai:arXiv.org:1208.5462

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