Magnetic bottles on the Poincaré half-plane: spectral asymptotics.

Abderemane Morame (1) , Francoise Truc (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 IF - Institut Fourier

We consider a magnetic laplacian P(A) on the Poincaré half-plane, when the magnetic field dA is infinite at infinity such that P(A) has pure discret spectrum. We give the asymptotic behavior of the counting function of the eigenvalues.

Mots clés: magnetic bottles; hyperbolic plane; minimax principle; spectral asymptotics

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Abderemane Morame, Francoise Truc. Magnetic bottles on the Poincaré half-plane: spectral asymptotics.. Journal of Mathematics of Kyoto University, 2008, 48 (3), p 597-616. ⟨10.1215/kjm/1250271385⟩. ⟨hal-00195370⟩