SELF-ADJOINTNESS OF MAGNETIC LAPLACIANS ON TRIANGULATIONS - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Filomat Année : 2023

SELF-ADJOINTNESS OF MAGNETIC LAPLACIANS ON TRIANGULATIONS

Colette Anné
  • Fonction : Auteur
  • PersonId : 1099271
Nabila Torki-Hamza
  • Fonction : Auteur
  • PersonId : 861603

Résumé

The notions of magnetic difference operator defined on weighted graphs or magnetic exterior derivative 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 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.
Fichier principal
Vignette du fichier
MAG_OP_vf_NOV22.pdf (797.13 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03230953 , version 1 (20-05-2021)
hal-03230953 , version 2 (24-11-2022)

Identifiants

Citer

Colette Anné, Hela Ayadi, Yassin Chebbi, Nabila Torki-Hamza. SELF-ADJOINTNESS OF MAGNETIC LAPLACIANS ON TRIANGULATIONS. Filomat, 2023, 37 (11), pp.3527-3550. ⟨hal-03230953v2⟩

Collections

CNRS INSMI CHL ANR
248 Consultations
113 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More