Geodesic
Self-adjointness of magnetic Laplacians on triangulations
Filomat, Tome 37 (2023) no. 11, p. 3527

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DOI

The notions of magnetic difference operator or magnetic exterior derivative defined on weighted graphs are discrete analogues of the notion of covariant derivative on sections of a fibre bundle and its extension on differential forms. In this paper, we extend these notions 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 χ−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 caracterize the domain of the self-adjoint extension.
DOI : 10.2298/FIL2311527A
Classification : 39A12, 05C63, 47B25, 05C12, 05C50
Keywords: Graph, 2-Simplicial complex, Discrete magnetic operators, Essential self-adjointness, χ-completeness 
Colette Anné; Hela Ayadi; Yassin Chebbi; Nabila Torki-Hamza. Self-adjointness of magnetic Laplacians on triangulations. Filomat, Tome 37 (2023) no. 11, p. 3527 . doi: 10.2298/FIL2311527A
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     title = {Self-adjointness of magnetic {Laplacians} on triangulations},
     journal = {Filomat},
     pages = {3527 },
     year = {2023},
     volume = {37},
     number = {11},
     doi = {10.2298/FIL2311527A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2311527A/}
}
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