Lieb-Thirring inequalities for radial magnetic bottles in the disk

Francoise Truc (1)

1 IF - Institut Fourier

We consider a Schrodinger operator H with a magnetic field and Dirichlet boundary conditions on the unit disk. We assume growth conditions on the magnetic field near the boundary which guarantee compactness of the resolvent of this operator. Under some assumptions on an additional potential V the operator H+ V has a discrete negative spectrum and we prove a Lieb-Thirring inequality on these negative eigenvalues if moreover the magnetic field and the potential are assumed to be radially symmetric.

Mots clés: magnetic bottles; Lieb-Thirring inequalities; Schrödinger operator

Domaines: Physique mathématique [math-ph]

Francoise Truc. Lieb-Thirring inequalities for radial magnetic bottles in the disk. 2012. ⟨hal-00588164v1⟩