On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field
| hal.structure.identifier | Laboratoire de Mathématiques de Reims [LMR] | |
| dc.contributor.author | AMOUR, Laurent | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | FAUPIN, Jérémy | |
| hal.structure.identifier | Laboratoire de Mathématiques Jean Leray [LMJL] | |
| dc.contributor.author | GREBERT, Benoit | |
| hal.structure.identifier | Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP] | |
| dc.contributor.author | GUILLOT, Jean-Claude | |
| dc.date.accessioned | 2024-04-04T02:43:22Z | |
| dc.date.available | 2024-04-04T02:43:22Z | |
| dc.date.issued | 2009 | |
| dc.date.conference | 2008-07 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191328 | |
| dc.description.abstractEn | We consider a non-relativistic electron interacting with a classical magnetic field pointing along the $x_3$-axis and with a quantized electromagnetic field. The system is translation invariant in the $x_3$-direction and we consider the reduced Hamiltonian $H(P_3)$ associated with the total momentum $P_3$ along the $x_3$-axis. For a fixed momentum $P_3$ sufficiently small, we prove that $H(P_3)$ has a ground state in the Fock representation if and only if $E'(P_3)=0$, where $P_3 \mapsto E'(P_3)$ is the derivative of the map $P_3 \mapsto E(P_3) = \inf \sigma (H(P_3))$. If $E'(P_3) \neq 0$, we obtain the existence of a ground state in a non-Fock representation. This result holds for sufficiently small values of the coupling constant. | |
| dc.language.iso | en | |
| dc.source.title | Spectral and Scattering Theory for Quantum Magnetic Systems | |
| dc.title.en | On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field | |
| dc.type | Communication dans un congrès | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| dc.subject.hal | Physique [physics]/Physique mathématique [math-ph] | |
| dc.subject.hal | Mathématiques [math]/Théorie spectrale [math.SP] | |
| dc.identifier.arxiv | 0812.3562 | |
| bordeaux.page | 1-24 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.conference.title | Spectral and Scattering Theory for Quantum Magnetic Systems | |
| bordeaux.country | FR | |
| bordeaux.title.proceeding | Spectral and Scattering Theory for Quantum Magnetic Systems | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00348375 | |
| hal.version | 1 | |
| hal.invited | non | |
| hal.proceedings | oui | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00348375v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=Spectral%20and%20Scattering%20Theory%20for%20Quantum%20Magnetic%20Systems&rft.date=2009&rft.spage=1-24&rft.epage=1-24&rft.au=AMOUR,%20Laurent&FAUPIN,%20J%C3%A9r%C3%A9my&GREBERT,%20Benoit&GUILLOT,%20Jean-Claude&rft.genre=unknown |
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