On the ground state energy of the Laplacian with a magnetic field created by a rectilinear currentReport as inadecuate




On the ground state energy of the Laplacian with a magnetic field created by a rectilinear current - Download this document for free, or read online. Document in PDF available to download.

1 IMB - Institut de Mathématiques de Bordeaux 2 CPT - E9 Dynamique quantique et analyse spectrale CPT - Centre de Physique Théorique - UMR 7332 3 CPT - Centre de Physique Théorique - UMR 7332 4 Équipe EDP et Physique Mathématique IMB - Institut de Mathématiques de Bordeaux

Abstract : We consider the three-dimensional Laplacian with a magnetic field created by an infinite rectilinear current bearing a constant current. The spectrum of the associated hamiltonian is the positive half-axis as the range of an infinity of band functions all decreasing toward 0. We make a precise asymptotics of the band function near the ground energy and we exhibit a semi-classical behavior. We perturb the hamiltonian by an electric potential. Helped by the analysis of the band functions, we show that for slow decaying potential, an infinite number of negative eigenvalues are created whereas only finite number of eigenvalues appears for fast decaying potential. Our results show different borderline type conditions that in the case where there is no magnetic field.

Mots-clés : Analyse asymptotique Spectral Theory Laplacien magnétique Perturbation électrique





Author: Vincent Bruneau - Nicolas Popoff -

Source: https://hal.archives-ouvertes.fr/



DOWNLOAD PDF




Related documents