On the ground state energy of the Laplacian with a magnetic field created by a rectilinear current
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BRUNEAU, Vincent | |
| hal.structure.identifier | CPT - E8 Dynamique quantique et analyse spectrale | |
| hal.structure.identifier | Centre de Physique Théorique - UMR 7332 [CPT] | |
| hal.structure.identifier | Équipe EDP et Physique Mathématique | |
| dc.contributor.author | POPOFF, Nicolas | |
| dc.date.accessioned | 2024-04-04T02:19:25Z | |
| dc.date.available | 2024-04-04T02:19:25Z | |
| dc.date.created | 2013 | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0022-1236 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189400 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | INITIATIVE D'EXCELLENCE AIX MARSEILLE UNIVERSITE - ANR-11-IDEX-0001 | |
| dc.description.sponsorship | ARCHIMEDE / Mathématiques - ANR-11-LABX-0033 | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject | Perturbation électrique | |
| dc.subject | Laplacien magnétique | |
| dc.subject | Spectral Theory | |
| dc.subject | Analyse asymptotique | |
| dc.title.en | On the ground state energy of the Laplacian with a magnetic field created by a rectilinear current | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.jfa.2014.11.015 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Théorie spectrale [math.SP] | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| dc.identifier.arxiv | 1402.4693 | |
| bordeaux.journal | Journal of Functional Analysis | |
| bordeaux.page | 1277-1307 | |
| bordeaux.volume | 268 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 5 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00911208 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00911208v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Functional%20Analysis&rft.date=2015&rft.volume=268&rft.issue=5&rft.spage=1277-1307&rft.epage=1277-1307&rft.eissn=0022-1236&rft.issn=0022-1236&rft.au=BRUNEAU,%20Vincent&POPOFF,%20Nicolas&rft.genre=article |
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