Confining quantum particles with a purely magnetic field

Yves Colin de Verdière (1) , Francoise Truc (1)

1 IF - Institut Fourier

We consider an open domain with a compact boundary in an Euclidean space and a Schroedinger operator with magnetic field on this domain. We give sufficient conditions on the rate of growth of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of view, it means that the quantum particle is confined in the domain by the magnetic field. We construct examples on polytopes and domains with smooth boundaries; these examples of "magnetic bottles" are highly simplified models of what is done for nuclear fusion in tokamacs.

Mots clés: magnetic field; Schrödinger operator; self-adjointness

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Géométrie différentielle [math.DG]; Théorie spectrale [math.SP]

Yves Colin de Verdière, Francoise Truc. Confining quantum particles with a purely magnetic field. 2009. ⟨hal-00365828v2⟩