ON THE SEMI-CLASSICAL ANALYSIS OF THE GROUNDSTATE ENERGY OF THE DIRICHLET PAULI OPERATOR III: MAGNETIC FIELDS THAT CHANGE SIGN

Bernard Helffer (1, 2) , Hynek Kovařík (3) , Mikael Persson Sundqvist (4)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LMO - Laboratoire de Mathématiques d'Orsay
3 UniBs - Università degli Studi di Brescia = University of Brescia
4 Skane University Hospital [Lund]

We consider the semi-classical Dirichlet Pauli operator in bounded connected domains in the plane, and focus on the case when the magnetic field changes sign. We show, in particular, that the ground state energy of this Pauli operator will be exponentially small as the semi-classical parameter tends to zero and estimate this decay rate, extending previous results by Ekholm–Kovařík–Portmann and Helffer–Sundqvist.

Domaines: Physique mathématique [math-ph]

Bernard Helffer, Hynek Kovařík, Mikael Persson Sundqvist. ON THE SEMI-CLASSICAL ANALYSIS OF THE GROUNDSTATE ENERGY OF THE DIRICHLET PAULI OPERATOR III: MAGNETIC FIELDS THAT CHANGE SIGN. 2017. ⟨hal-01622813⟩