On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field - Archive ouverte HAL
Communication Dans Un Congrès Année : 2009

On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field

Résumé

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.
Fichier principal
Vignette du fichier
exitfock.pdf (325.03 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00348375 , version 1 (18-12-2008)

Identifiants

Citer

Laurent Amour, Jérémy Faupin, Benoit Grebert, Jean-Claude Guillot. On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field. Spectral and Scattering Theory for Quantum Magnetic Systems, Jul 2008, France. pp.1-24. ⟨hal-00348375⟩
258 Consultations
117 Téléchargements

Altmetric

Partager

More