Essential self-adjointness for combinatorial Schrödinger operators III- Magnetic fields

Yves Colin de Verdière (1) , Nabila Torki-Hamza (1, 2) , Francoise Truc (1)

1 IF - Institut Fourier
2 05/UR/15-02 - Mathématiques et Applications

We define the magnetic Schrödinger 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.

Mots clés: essential self-adjointness; Magnetic field; magnetic Schrödinger operator; weighted graph Laplacian; essential self-adjointness.

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Yves Colin de Verdière, Nabila Torki-Hamza, Francoise Truc. Essential self-adjointness for combinatorial Schrödinger operators III- Magnetic fields. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2011, 20 (3), pp.597-609. ⟨hal-00541062⟩