We define the magnetic Schrödinger operator on an infinite graph by the data of a magnetic field, some weights on vertices and some weights on edges. We discuss essential self-adjointness of this operator for graphs of bounded degree. The main result is a discrete version of a result of two authors of the present paper.
On définit l’opérateur de Schrödinger avec champ magnétique sur un graphe infini par la donnée d’un champ magnétique, de poids sur les sommets et de poids sur les arêtes. Lorsque le graphe est de degré borné, on étudie le caractère essentiellement auto-adjoint d’un tel opérateur. Le résultat principal est une version discrète d’un résultat de deux des auteurs du présent article.
Yves Colin de Verdière 1; Nabila Torki-Hamza 2; Françoise Truc 1
@article{AFST_2011_6_20_3_599_0,
author = {Yves Colin de Verdi\`ere and Nabila Torki-Hamza and Fran\c{c}oise Truc},
title = {Essential self-adjointness for combinatorial {Schr\"odinger} operators {III-} {Magnetic} fields},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {599--611},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 20},
number = {3},
year = {2011},
doi = {10.5802/afst.1319},
mrnumber = {2894840},
zbl = {1250.47025},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1319/}
}
TY - JOUR AU - Yves Colin de Verdière AU - Nabila Torki-Hamza AU - Françoise Truc TI - Essential self-adjointness for combinatorial Schrödinger operators III- Magnetic fields JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2011 SP - 599 EP - 611 VL - 20 IS - 3 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1319/ DO - 10.5802/afst.1319 LA - en ID - AFST_2011_6_20_3_599_0 ER -
%0 Journal Article %A Yves Colin de Verdière %A Nabila Torki-Hamza %A Françoise Truc %T Essential self-adjointness for combinatorial Schrödinger operators III- Magnetic fields %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2011 %P 599-611 %V 20 %N 3 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1319/ %R 10.5802/afst.1319 %G en %F AFST_2011_6_20_3_599_0
Yves Colin de Verdière; Nabila Torki-Hamza; Françoise Truc. Essential self-adjointness for combinatorial Schrödinger operators III- Magnetic fields. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 3, pp. 599-611. doi : 10.5802/afst.1319. https://afst.centre-mersenne.org/articles/10.5802/afst.1319/
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