ON THE SEMI-CLASSICAL ANALYSIS OF THE GROUNDSTATE ENERGY OF THE DIRICHLET PAULI OPERATOR

Bernard Helffer (1, 2) , Mikael Persson Sundqvist (3)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 Skane University Hospital [Lund]

We complete and improve the results of a recent paper by Ekholm, Kovarik and Portmann in connection with a question of C. Guillarmou about the semiclassical expansion of the lowest eigenvalue of the Pauli operator with Dirichlet conditions. We exhibit connections with the properties of the torsion function in mechanics, the exit time of a Brownian motion and the analysis of the low eigenvalues of some Witten Laplacian.

Mots clés: Pauli operator; eigenvalue; Witten Laplacian

Domaines: Mathématiques [math]

Bernard Helffer, Mikael Persson Sundqvist. ON THE SEMI-CLASSICAL ANALYSIS OF THE GROUNDSTATE ENERGY OF THE DIRICHLET PAULI OPERATOR. Journal of Mathematical Analysis and Applications, 2017, 449 (1), pp.138--153. ⟨hal-01435168⟩