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arXiv · 2105.10171

Self-adjointness of magnetic laplacians on triangulations

Colette Anné·Hela Ayadi·Yassin Chebbi·Nabila Torki-Hamza
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Abstract

The notions of magnetic difference operator defined on weighted graphs or magnetic exterior derivative are discrete analogues of the notionof covariant derivative on sections of a fibre bundle and its extension on differential forms. In this paper, we extend this notion to certain 2-simplicial complexes called triangulations, in a manner compatible with changes of gauge. Then we study the magnetic Gauss-Bonnet operator naturally defined in this context and introduce the geometric hypothesis of $\chi-$completeness which ensures the essential self-adjointness of this operator. This gives also the essential self-adjointness of the magnetic Laplacian on triangulations. Finally we introduce an hypothesis of bounded curvature for the magnetic potential which permits to characterize the domain of the self-adjoint extension.

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Colette Anné, Hela Ayadi, Yassin Chebbi, Nabila Torki-Hamza. 2021-05-21. Self-adjointness of magnetic laplacians on triangulations. https://arxiv.org/abs/2105.10171

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