Résonances près de seuils d'opérateurs magnétiques de Pauli et de Dirac
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | SAMBOU, Diomba | |
| dc.date.accessioned | 2024-04-04T02:24:19Z | |
| dc.date.available | 2024-04-04T02:24:19Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189809 | |
| dc.description.abstractEn | We consider the perturbations $H := H_{0} + V$ and $D := D_{0} + V$ of the free $3$D Hamiltonians $H_{0}$ of Pauli and $D_{0}$ of Dirac with non-constant magnetic field, and $V$ is a electric potential which decays super-exponentially with respect to the variable along the magnetic field. We show that in appropriate Banach spaces, the resolvents of $H$ and $D$ defined on the upper half-plane admit meromorphic extensions. We define the resonances of $H$ and $D$ as the poles of these meromorphic extensions. We study the distribution of resonances of $H$ close to the origin $0$ and that of $D$ close to $\pm m$, where $m$ is the mass of a particle. In both cases, we first obtain an upper bound of the number of resonances in small domains in a vicinity of $0$ and $\pm m$. Moreover, under additional assumptions, we establish asymptotic expansions of the number of resonances which imply their accumulation near the thresholds $0$ and $\pm m$. In particular, for a perturbation $V$ of definite sign, we obtain information on the distribution of eigenvalues of $H$ and $D$ near $0$ and $\pm m$ respectively. | |
| dc.language.iso | fr | |
| dc.subject | Opérateurs magnétiques de Pauli et de Dirac | |
| dc.subject | résonances. | |
| dc.subject | résonances | |
| dc.title | Résonances près de seuils d'opérateurs magnétiques de Pauli et de Dirac | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| dc.identifier.arxiv | 1201.6552 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-00664839 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00664839v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.title=R%C3%A9sonances%20pr%C3%A8s%20de%20seuils%20d'op%C3%A9rateurs%20magn%C3%A9tiques%20de%20Pauli%20et%20de%20Dirac&rft.atitle=R%C3%A9sonances%20pr%C3%A8s%20de%20seuils%20d'op%C3%A9rateurs%20magn%C3%A9tiques%20de%20Pauli%20et%20de%20Dirac&rft.au=SAMBOU,%20Diomba&rft.genre=preprint |
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