On the ground state energy of the Laplacian with a magnetic field created by a rectilinear current
POPOFF, Nicolas
CPT - E8 Dynamique quantique et analyse spectrale
Centre de Physique Théorique - UMR 7332 [CPT]
Équipe EDP et Physique Mathématique
CPT - E8 Dynamique quantique et analyse spectrale
Centre de Physique Théorique - UMR 7332 [CPT]
Équipe EDP et Physique Mathématique
POPOFF, Nicolas
CPT - E8 Dynamique quantique et analyse spectrale
Centre de Physique Théorique - UMR 7332 [CPT]
Équipe EDP et Physique Mathématique
< Reduce
CPT - E8 Dynamique quantique et analyse spectrale
Centre de Physique Théorique - UMR 7332 [CPT]
Équipe EDP et Physique Mathématique
Language
en
Article de revue
This item was published in
Journal of Functional Analysis. 2015, vol. 268, n° 5, p. 1277-1307
Elsevier
English 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 ...Read more >
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.Read less <
Keywords
Perturbation électrique
Laplacien magnétique
Spectral Theory
Analyse asymptotique
ANR Project
INITIATIVE D'EXCELLENCE AIX MARSEILLE UNIVERSITE - ANR-11-IDEX-0001
ARCHIMEDE / Mathématiques - ANR-11-LABX-0033
ARCHIMEDE / Mathématiques - ANR-11-LABX-0033
Origin
Hal imported